Handbook of Radiotherapy

E.B. Podgorsak Technical Editor
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Radiation Oncology Physics: A Handbook for Teachers and Students E.B. Podgorsak Technical Editor Sponsored by the IAEA and endorsed by the COMP/CCPM, EFOMP, ESTRO, IOMP, PAHO and WHO

Cover photograph courtesy of E. Izewski

RADIATION ONCOLOGY PHYSICS: A HANDBOOK FOR TEACHERS AND STUDENTS

The following States are Members of the International Atomic Energy Agency: AFGHANISTAN GREECE PAKISTAN ALBANIA GUATEMALA PANAMA ALGERIA HAITI PARAGUAY ANGOLA HOLY SEE PERU ARGENTINA HONDURAS PHILIPPINES ARMENIA HUNGARY POLAND AUSTRALIA ICELAND PORTUGAL AUSTRIA INDIA QATAR AZERBAIJAN INDONESIA REPUBLIC OF MOLDOVA BANGLADESH IRAN, ISLAMIC REPUBLIC OF ROMANIA BELARUS IRAQ RUSSIAN FEDERATION BELGIUM IRELAND SAUDI ARABIA BENIN ISRAEL SENEGAL BOLIVIA ITALY SERBIA AND MONTENEGRO BOSNIA AND HERZEGOVINA JAMAICA SEYCHELLES BOTSWANA JAPAN SIERRA LEONE BRAZIL JORDAN SINGAPORE BULGARIA KAZAKHSTAN SLOVAKIA BURKINA FASO KENYA SLOVENIA CAMEROON KOREA, REPUBLIC OF SOUTH AFRICA CANADA KUWAIT SPAIN CENTRAL AFRICAN KYRGYZSTAN SRI LANKA REPUBLIC LATVIA SUDAN CHILE LEBANON SWEDEN CHINA LIBERIA SWITZERLAND COLOMBIA LIBYAN ARAB JAMAHIRIYA SYRIAN ARAB REPUBLIC COSTA RICA LIECHTENSTEIN TAJIKISTAN CÔTE D’IVOIRE LITHUANIA THAILAND CROATIA LUXEMBOURG THE FORMER YUGOSLAV CUBA MADAGASCAR REPUBLIC OF MACEDONIA CYPRUS MALAYSIA TUNISIA CZECH REPUBLIC MALI TURKEY DEMOCRATIC REPUBLIC MALTA UGANDA OF THE CONGO MARSHALL ISLANDS UKRAINE DENMARK MAURITANIA UNITED ARAB EMIRATES DOMINICAN REPUBLIC MAURITIUS UNITED KINGDOM OF ECUADOR MEXICO GREAT BRITAIN AND EGYPT MONACO NORTHERN IRELAND EL SALVADOR MONGOLIA UNITED REPUBLIC ERITREA MOROCCO OF TANZANIA ESTONIA MYANMAR UNITED STATES OF AMERICA ETHIOPIA NAMIBIA URUGUAY FINLAND NETHERLANDS UZBEKISTAN FRANCE NEW ZEALAND VENEZUELA GABON NICARAGUA VIETNAM GEORGIA NIGER YEMEN GERMANY NIGERIA ZAMBIA GHANA NORWAY ZIMBABWE The Agency’s Statute was approved on 23 October 1956 by the Conference on the Statute of the IAEA held at United Nations Headquarters, New York; it entered into force on 29 July 1957. The Headquarters of the Agency are situated in Vienna. Its principal objective is “to accelerate and enlarge the contribution of atomic energy to peace, health and prosperity throughout the world’’.

RADIATION ONCOLOGY PHYSICS: A HANDBOOK FOR TEACHERS AND STUDENTS INTERNATIONAL ATOMIC ENERGY AGENCY VIENNA, 2005

COPYRIGHT NOTICE All IAEA scientific and technical publications are protected by the terms of the Universal Copyright Convention as adopted in 1952 (Berne) and as revised in 1972 (Paris). The copyright has since been extended by the World Intellectual Property Organization (Geneva) to include electronic and virtual intellectual property. Permission to use whole or parts of texts contained in IAEA publications in printed or electronic form must be obtained and is usually subject to royalty agreements. Proposals for non-commercial reproductions and translations are welcomed and will be considered on a case by case basis. Enquiries should be addressed by email to the Publishing Section, IAEA, at sales.publications@iaea.org or by post to: Sales and Promotion Unit, Publishing Section International Atomic Energy Agency Wagramer Strasse 5 P.O. Box 100 A-1400 Vienna Austria fax: +43 1 2600 29302 tel.: +43 1 2600 22417 http://www.iaea.org/books © IAEA, 2005 Printed by the IAEA in Austria July 2005 STI/PUB/1196 IAEA Library Cataloguing in Publication Data Radiation oncology physics : a handbook for teachers and students / editor E. B. Podgorsak ; sponsored by IAEA … [et al.]. — Vienna : International Atomic Energy Agency, 2005. p.; 24 cm. STI/PUB/1196 ISBN 92–0–107304–6 Includes bibliographical references. 1. Radiation dosimetry — Handbooks, manuals, etc. 2. Dosimeters — Handbooks, manuals, etc. 3. Radiation — Measurement — Handbooks, manuals, etc. 4. Radiation — Dosage — Handbooks, manuals, etc. 5. Radiotherapy — Handbooks, manuals, etc. 6. Photon beams. 7. Electron beams. 8. Radioisotope scanning. I. Podgorsak, E. B., ed. II. International Atomic Energy Agency. IAEAL 05–00402

FOREWORD In the late 1990s the IAEA initiated for its Member States a systematic and comprehensive plan to support the development of teaching programmes in medical radiation physics. Multiple projects were initiated at various levels that, together with the well known short term training courses and specialization fellowships funded by the IAEA Technical Cooperation programme, aimed at supporting countries to develop their own university based master of science programmes in medical radiation physics. One of the early activities of the IAEA in this period was the development of a syllabus in radiotherapy physics, which had the goal of harmonizing the various levels of training that the IAEA provided. This was carried out during 1997–1998, and the result of this work was released as a report used for designing IAEA training courses. In 1999–2000 a more detailed teachers’ guide was developed, in which the various topics in the syllabus were expanded to form a detailed ‘bullet list’ containing the basic guidelines of the material to be included in each topic so that lectures to students could be prepared accordingly. During the period 2001–2002 E.B. Podgorsak (Canada) was appointed editor of the project and redesigned the contents so that the book became a comprehensive handbook for teachers and students, with coverage deeper than a simple teachers’ guide. The initial list of topics was expanded considerably by engaging an enhanced list of international contributors. The handbook was published as working material in 2003 and placed on the Internet in order to seek comments, corrections and feedback. This handbook aims at providing the basis for the education of medical physicists initiating their university studies in the field. It includes the recent advances in radiotherapy techniques; however, it is not designed to replace the large number of textbooks available on radiotherapy physics, which will still be necessary to deepen knowledge in the specific topics reviewed here. It is expected that this handbook will successfully fill a gap in the teaching material for medical radiation physics, providing in a single manageable volume the largest possible coverage available today. Its wide dissemination by the IAEA will contribute to the harmonization of education in the field and will be of value to newcomers as well as to those preparing for their certification as medical physicists, radiation oncologists, medical dosimetrists and radiotherapy technologists. Endorsement of this handbook has been granted by the following international organizations and professional bodies: the International Organization for Medical Physics (IOMP), the European Society for Therapeutic Radiology and Oncology (ESTRO), the European Federation of Organisations for Medical Physics (EFOMP), the World Health Organization

(WHO), the Pan American Health Organization (PAHO), the Canadian Organization of Medical Physicists (COMP) and the Canadian College of Physicists in Medicine (CCPM). The following international experts are gratefully acknowledged for making major contributions to the development of an early version of the syllabus: B. Nilsson (Sweden), B. Planskoy (United Kingdom) and J.C. Rosenwald (France). The following made major contributions to this handbook: R. Alfonso (Cuba), G. Rajan (India), W. Strydom (South Africa) and N. Suntharalingam (United States of America). The IAEA scientific officers responsible for the project were (in chronological order) P. Andreo, J. Izewska and K.R. Shortt. EDITORIAL NOTE Although great care has been taken to maintain the accuracy of information contained in this publication, neither the IAEA nor its Member States assume any responsibility for consequences which may arise from its use. The use of particular designations of countries or territories does not imply any judgement by the publisher, the IAEA, as to the legal status of such countries or territories, of their authorities and institutions or of the delimitation of their boundaries. The mention of names of specific companies or products (whether or not indicated as registered) does not imply any intention to infringe proprietary rights, nor should it be construed as an endorsement or recommendation on the part of the IAEA. The authors are responsible for having obtained the necessary permission for the IAEA to reproduce, translate or use material from sources already protected by copyrights.

PREFACE Radiotherapy, also referred to as radiation therapy, radiation oncology or therapeutic radiology, is one of the three principal modalities used in the treatment of malignant disease (cancer), the other two being surgery and chemotherapy. In contrast to other medical specialties that rely mainly on the clinical knowledge and experience of medical specialists, radiotherapy, with its use of ionizing radiation in the treatment of cancer, relies heavily on modern technology and the collaborative efforts of several professionals whose coordinated team approach greatly influences the outcome of the treatment. The radiotherapy team consists of radiation oncologists, medical physicists, dosimetrists and radiation therapy technologists: all professionals characterized by widely differing educational backgrounds and one common link — the need to understand the basic elements of radiation physics, and the interaction of ionizing radiation with human tissue in particular. This specialized area of physics is referred to as radiation oncology physics, and proficiency in this branch of physics is an absolute necessity for anyone who aspires to achieve excellence in any of the four professions constituting the radiotherapy team. Current advances in radiation oncology are driven mainly by technological development of equipment for radiotherapy procedures and imaging; however, as in the past, these advances rely heavily on the underlying physics. This book is dedicated to students and teachers involved in programmes that train professionals for work in radiation oncology. It provides a compilation of facts on the physics as applied to radiation oncology and as such will be useful to graduate students and residents in medical physics programmes, to residents in radiation oncology, and to students in dosimetry and radiotherapy technology programmes. The level of understanding of the material covered will, of course, be different for the various student groups; however, the basic language and knowledge for all student groups will be the same. The text will also be of use to candidates preparing for professional certification examinations, whether in radiation oncology, medical physics, dosimetry or radiotherapy technology. The intent of the text is to serve as a factual supplement to the various textbooks on medical physics and to provide basic radiation oncology physics knowledge in the form of a syllabus covering all modern aspects of radiation oncology physics. While the text is mainly aimed at radiation oncology professionals, certain parts of it may also be of interest in other branches of medicine that use ionizing radiation not for the treatment of disease but for the diagnosis of disease (diagnostic radiology and nuclear medicine). The contents

may also be useful for physicists who are involved in studies of radiation hazards and radiation protection (health physics). This book represents a collaborative effort by professionals from many different countries who share a common goal of disseminating their radiation oncology physics knowledge and experience to a broad international audience of teachers and students. Special thanks are due to J. Denton-MacLennan for critically reading and editing the text and improving its syntax. E.B. Podgorsak

CONTRIBUTORS Andreo, P. University of Stockholm, Karolinska Institute, Sweden Evans, M.D.C. McGill University Health Centre, Canada Hendry, J.H. International Atomic Energy Agency Horton, J.L. University of Texas MD Anderson Cancer Center, United States of America Izewska, J. International Atomic Energy Agency Mijnheer, B.J. Netherlands Cancer Institute, Netherlands Mills, J.A. Walsgrave Hospital, United Kingdom Olivares, M. McGill University Health Centre, Canada Ortiz López, P. International Atomic Energy Agency Parker, W. McGill University Health Centre, Canada Patrocinio, H. McGill University Health Centre, Canada Podgorsak, E.B. McGill University Health Centre, Canada Podgorsak, M.B. Roswell Park Cancer Institute, United States of America Rajan, G. Bhabha Atomic Research Centre, India Seuntjens, J.P. McGill University Health Centre, Canada Shortt, K.R. International Atomic Energy Agency Strydom, W. Medical University of Southern Africa, South Africa Suntharalingam, N. Thomas Jefferson University Hospital, United States of America Thwaites, D.I. University of Edinburgh, United Kingdom Tolli, H. International Atomic Energy Agency

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CONTENTS CHAPTER 1. BASIC RADIATION PHYSICS . . . . . . . . . . . . . . . . . . . 1 1.1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1. Fundamental physical constants (rounded off to four significant figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.2. Important derived physical constants and relationships . . 1 1.1.3. Physical quantities and units . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.4. Classification of forces in nature . . . . . . . . . . . . . . . . . . . . . 4 1.1.5. Classification of fundamental particles . . . . . . . . . . . . . . . . 4 1.1.6. Classification of radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.7. Classification of ionizing photon radiation . . . . . . . . . . . . . 6 1.1.8. Einstein’s relativistic mass, energy and momentum relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.9. Radiation quantities and units . . . . . . . . . . . . . . . . . . . . . . . 7 1.2. ATOMIC AND NUCLEAR STRUCTURE . . . . . . . . . . . . . . . . . . 7 1.2.1. Basic definitions for atomic structure . . . . . . . . . . . . . . . . 7 1.2.2. Rutherford’s model of the atom . . . . . . . . . . . . . . . . . . . . . 9 1.2.3. Bohr’s model of the hydrogen atom . . . . . . . . . . . . . . . . . . 10 1.2.4. Multielectron atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.5. Nuclear structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.2.6. Nuclear reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.2.7. Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.2.8. Activation of nuclides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.2.9. Modes of radioactive decay . . . . . . . . . . . . . . . . . . . . . . . . 20 1.3. ELECTRON INTERACTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.3.1. Electron–orbital electron interactions . . . . . . . . . . . . . . . . 23 1.3.2. Electron–nucleus interactions . . . . . . . . . . . . . . . . . . . . . . . 23 1.3.3. Stopping power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.3.4. Mass scattering power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.4. PHOTON INTERACTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.4.1. Types of indirectly ionizing photon radiation . . . . . . . . . . . 26 1.4.2. Photon beam attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.4.3. Types of photon interaction . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.4.4. Photoelectric effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.4.5. Coherent (Rayleigh) scattering . . . . . . . . . . . . . . . . . . . . . . 29

1.4.6. Compton effect (incoherent scattering) . . . . . . . . . . . . . . . 30 1.4.7. Pair production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 1.4.8. Photonuclear reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 1.4.9. Contributions to attenuation coefficients . . . . . . . . . . . . . . 34 1.4.10. Relative predominance of individual effects . . . . . . . . . . . 36 1.4.11. Effects following photon interactions . . . . . . . . . . . . . . . . . 37 1.4.12. Summary of photon interactions . . . . . . . . . . . . . . . . . . . . . 38 1.4.13. Example of photon attenuation . . . . . . . . . . . . . . . . . . . . . 40 1.4.14. Production of vacancies in atomic shells . . . . . . . . . . . . . . . 41 BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 CHAPTER 2. DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS . . . . . . . . . . . . . . . . . . . . . . 45 2.1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.2. PHOTON FLUENCE AND ENERGY FLUENCE . . . . . . . . . . . . 45 2.3. KERMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.4. CEMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.5. ABSORBED DOSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.6. STOPPING POWER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.7. RELATIONSHIPS BETWEEN VARIOUS DOSIMETRIC QUANTITIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.7.1. Energy fluence and kerma (photons) . . . . . . . . . . . . . . . . . 54 2.7.2. Fluence and dose (electrons) . . . . . . . . . . . . . . . . . . . . . . . . 56 2.7.3. Kerma and dose (charged particle equilibrium) . . . . . . . . 57 2.7.4. Collision kerma and exposure . . . . . . . . . . . . . . . . . . . . . . . 60 2.8. CAVITY THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 2.8.1. Bragg–Gray cavity theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 2.8.2. Spencer–Attix cavity theory . . . . . . . . . . . . . . . . . . . . . . . . . 62 2.8.3. Considerations in the application of cavity theory to ionization chamber calibration and dosimetry protocols . 64 2.8.4. Large cavities in photon beams . . . . . . . . . . . . . . . . . . . . . . 66 2.8.5. Burlin cavity theory for photon beams . . . . . . . . . . . . . . . . 66 2.8.6. Stopping power ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

CHAPTER 3. RADIATION DOSIMETERS . . . . . . . . . . . . . . . . . . . . . 71 3.1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.2. PROPERTIES OF DOSIMETERS . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.2.1. Accuracy and precision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.2.1.1. Type A standard uncertainties . . . . . . . . . . . . . . 72 3.2.1.2. Type B standard uncertainties . . . . . . . . . . . . . . 73 3.2.1.3. Combined and expanded uncertainties . . . . . . . 73 3.2.2. Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.2.3. Dose rate dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.2.4. Energy dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.2.5. Directional dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.2.6. Spatial resolution and physical size . . . . . . . . . . . . . . . . . . . 76 3.2.7. Readout convenience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.2.8. Convenience of use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.3. IONIZATION CHAMBER DOSIMETRY SYSTEMS . . . . . . . . . 77 3.3.1. Chambers and electrometers . . . . . . . . . . . . . . . . . . . . . . . . 77 3.3.2. Cylindrical (thimble type) ionization chambers . . . . . . . . 78 3.3.3. Parallel-plate (plane-parallel) ionization chambers . . . . . 79 3.3.4. Brachytherapy chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.3.5. Extrapolation chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.4. FILM DOSIMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.4.1. Radiographic film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.4.2. Radiochromic film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.5. LUMINESCENCE DOSIMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.5.1. Thermoluminescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 3.5.2. Thermoluminescent dosimeter systems . . . . . . . . . . . . . . . 86 3.5.3. Optically stimulated luminescence systems . . . . . . . . . . . . 88 3.6. SEMICONDUCTOR DOSIMETRY . . . . . . . . . . . . . . . . . . . . . . . . 89 3.6.1. Silicon diode dosimetry systems . . . . . . . . . . . . . . . . . . . . . 89 3.6.2. MOSFET dosimetry systems . . . . . . . . . . . . . . . . . . . . . . . . 90 3.7. OTHER DOSIMETRY SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . 91 3.7.1. Alanine/electron paramagnetic resonance dosimetry system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 3.7.2. Plastic scintillator dosimetry system . . . . . . . . . . . . . . . . . . 92 3.7.3. Diamond dosimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

3.7.4. Gel dosimetry systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 3.8. PRIMARY STANDARDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.8.1. Primary standard for air kerma in air . . . . . . . . . . . . . . . . . 95 3.8.2. Primary standards for absorbed dose to water . . . . . . . . . 95 3.8.3. Ionometric standard for absorbed dose to water . . . . . . . . 96 3.8.4. Chemical dosimetry standard for absorbed dose to water 96 3.8.5. Calorimetric standard for absorbed dose to water . . . . . . 97 3.9. SUMMARY OF SOME COMMONLY USED DOSIMETRIC SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 CHAPTER 4. RADIATION MONITORING INSTRUMENTS . . . . 101 4.1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4.2. OPERATIONAL QUANTITIES FOR RADIATION MONITORING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 4.3. AREA SURVEY METERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 4.3.1. Ionization chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 4.3.2. Proportional counters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 4.3.3. Neutron area survey meters . . . . . . . . . . . . . . . . . . . . . . . . . 105 4.3.4. Geiger–Müller counters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 4.3.5. Scintillator detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 4.3.6. Semiconductor detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 4.3.7. Commonly available features of area survey meters . . . . 108 4.3.8. Calibration of survey meters . . . . . . . . . . . . . . . . . . . . . . . . 108 4.3.9. Properties of survey meters . . . . . . . . . . . . . . . . . . . . . . . . . 110 4.3.9.1. Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 4.3.9.2. Energy dependence . . . . . . . . . . . . . . . . . . . . . . . 110 4.3.9.3. Directional dependence . . . . . . . . . . . . . . . . . . . . 111 4.3.9.4. Dose equivalent range . . . . . . . . . . . . . . . . . . . . 111 4.3.9.5. Response time . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.3.9.6. Overload characteristics . . . . . . . . . . . . . . . . . . . 111 4.3.9.7. Long term stability . . . . . . . . . . . . . . . . . . . . . . . 112 4.3.9.8. Discrimination between different types of radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 4.3.9.9. Uncertainties in area survey measurements . . . 112 4.4. INDIVIDUAL MONITORING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 4.4.1. Film badge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

4.4.2. Thermoluminescence dosimetry badge . . . . . . . . . . . . . . . . 115 4.4.3. Radiophotoluminescent glass dosimetry systems . . . . . . . 116 4.4.4. Optically stimulated luminescence systems . . . . . . . . . . . . 116 4.4.5. Direct reading personal monitors . . . . . . . . . . . . . . . . . . . . 117 4.4.6. Calibration of personal dosimeters . . . . . . . . . . . . . . . . . . . 118 4.4.7. Properties of personal monitors . . . . . . . . . . . . . . . . . . . . . . 118 4.4.7.1. Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 4.4.7.2. Energy dependence . . . . . . . . . . . . . . . . . . . . . . . 119 4.4.7.3. Uncertainties in personal monitoring measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 4.4.7.4. Equivalent dose range . . . . . . . . . . . . . . . . . . . . . 119 4.4.7.5. Directional dependence . . . . . . . . . . . . . . . . . . . 120 4.4.7.6. Discrimination between different types of radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 CHAPTER 5. TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY . . . . . . . . . . . . . . . . . . . . . . . 123 5.1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.2. X RAY BEAMS AND X RAY UNITS . . . . . . . . . . . . . . . . . . . . . . . 124 5.2.1. Characteristic X rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 5.2.2. Bremsstrahlung (continuous) X rays . . . . . . . . . . . . . . . . . 124 5.2.3. X ray targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5.2.4. Clinical X ray beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 5.2.5. X ray beam quality specifiers . . . . . . . . . . . . . . . . . . . . . . . 127 5.2.6. X ray machines for radiotherapy . . . . . . . . . . . . . . . . . . . . . 127 5.3. GAMMA RAY BEAMS AND GAMMA RAY UNITS . . . . . . . . 129 5.3.1. Basic properties of gamma rays . . . . . . . . . . . . . . . . . . . . . . 129 5.3.2. Teletherapy machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 5.3.3. Teletherapy sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 5.3.4. Teletherapy source housing . . . . . . . . . . . . . . . . . . . . . . . . . 131 5.3.5. Dose delivery with teletherapy machines . . . . . . . . . . . . . . 132 5.3.6. Collimator and penumbra . . . . . . . . . . . . . . . . . . . . . . . . . 132 5.4. PARTICLE ACCELERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 5.4.1. Betatron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 5.4.2. Cyclotron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 5.4.3. Microtron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

5.5. LINACS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 5.5.1. Linac generations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 5.5.2. Safety of linac installations . . . . . . . . . . . . . . . . . . . . . . . . . . 137 5.5.3. Components of modern linacs . . . . . . . . . . . . . . . . . . . . . . . 138 5.5.4. Configuration of modern linacs . . . . . . . . . . . . . . . . . . . . . . 138 5.5.5. Injection system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 5.5.6. Radiofrequency power generation system . . . . . . . . . . . . . 143 5.5.7. Accelerating waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 5.5.8. Microwave power transmission . . . . . . . . . . . . . . . . . . . . . . 144 5.5.9. Auxiliary system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 5.5.10. Electron beam transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 5.5.11. Linac treatment head . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 5.5.12. Production of clinical photon beams in a linac . . . . . . . . . 147 5.5.13. Beam collimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 5.5.14. Production of clinical electron beams in a linac . . . . . . . . . 149 5.5.15. Dose monitoring system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 5.6. RADIOTHERAPY WITH PROTONS, NEUTRONS AND HEAVY IONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 5.7. SHIELDING CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . 152 5.8. COBALT-60 TELETHERAPY UNITS VERSUS LINACS . . . . . 153 5.9. SIMULATORS AND COMPUTED TOMOGRAPHY SIMULATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 5.9.1. Radiotherapy simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 5.9.2. Computed tomography simulator . . . . . . . . . . . . . . . . . . . . 158 5.10. TRAINING REQUIREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 CHAPTER 6. EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 6.1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 6.2. QUANTITIES USED IN DESCRIBING A PHOTON BEAM . . 161 6.2.1. Photon fluence and photon fluence rate . . . . . . . . . . . . . . 162 6.2.2. Energy fluence and energy fluence rate . . . . . . . . . . . . . . . 162 6.2.3. Air kerma in air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 6.2.4. Exposure in air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 6.2.5. Dose to small mass of medium in air . . . . . . . . . . . . . . . . . . 164 6.3. PHOTON BEAM SOURCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

6.4. INVERSE SQUARE LAW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 6.5. PENETRATION OF PHOTON BEAMS INTO A PHANTOM OR PATIENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 6.5.1. Surface dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 6.5.2. Buildup region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 6.5.3. Depth of dose maximum zmax . . . . . . . . . . . . . . . . . . . . . . . . 172 6.5.4. Exit dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 6.6. RADIATION TREATMENT PARAMETERS . . . . . . . . . . . . . . . 172 6.6.1. Radiation beam field size . . . . . . . . . . . . . . . . . . . . . . . . . . 173 6.6.2. Collimator factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 6.6.3. Peak scatter factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 6.6.4. Relative dose factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 6.7. CENTRAL AXIS DEPTH DOSES IN WATER: SOURCE TO SURFACE DISTANCE SET-UP . . . . . . . . . . . . . . . 179 6.7.1. Percentage depth dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 6.7.2. Scatter function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 6.8. CENTRAL AXIS DEPTH DOSES IN WATER: SOURCE TO AXIS DISTANCE SET-UP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 6.8.1. Tissue–air ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 6.8.2. Relationship between TAR(d, AQ, hn) and PDD(d, A, f, hn) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 6.8.3. Scatter–air ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 6.8.4. Relationship between SAR(d, AQ, hn) and S(z, A, f, hn) . 190 6.8.5. Tissue–phantom ratio and tissue–maximum ratio . . . . . . 190 6.8.6. Relationship between TMR(z, AQ, hn) and PDD(z, A, f, hn) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 6.8.7. Scatter–maximum ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 6.9. OFF-AXIS RATIOS AND BEAM PROFILES . . . . . . . . . . . . . . 194 6.9.1. Beam flatness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 6.9.2. Beam symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 6.10. ISODOSE DISTRIBUTIONS IN WATER PHANTOMS . . . . . . . 197 6.11. SINGLE FIELD ISODOSE DISTRIBUTIONS IN PATIENTS . . 199 6.11.1. Corrections for irregular contours and oblique beam incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 6.11.1.1. Effective source to surface distance method . . . 201 6.11.1.2. Tissue–air ratio or tissue–maximum ratio method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

6.11.1.3. Isodose shift method . . . . . . . . . . . . . . . . . . . . . . 202 6.11.2. Missing tissue compensation . . . . . . . . . . . . . . . . . . . . . . . . 202 6.11.2.1. Wedge filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 6.11.2.2. Bolus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 6.11.2.3. Compensators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 6.11.3. Corrections for tissue inhomogeneities . . . . . . . . . . . . . . . . 204 6.11.4. Model based algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 6.12. CLARKSON SEGMENTAL INTEGRATION . . . . . . . . . . . . . . . . 206 6.13. RELATIVE DOSE MEASUREMENTS WITH IONIZATION CHAMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 6.14. DELIVERY OF DOSE WITH A SINGLE EXTERNAL BEAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 6.15. EXAMPLE OF DOSE CALCULATION . . . . . . . . . . . . . . . . . . . . 213 6.16. SHUTTER CORRECTION TIME . . . . . . . . . . . . . . . . . . . . . . . . . . 215 BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 CHAPTER 7. CLINICAL TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 7.1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 7.2. VOLUME DEFINITION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 7.2.1. Gross tumour volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 7.2.2. Clinical target volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 7.2.3. Internal target volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 7.2.4. Planning target volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 7.2.5. Organ at risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 7.3. DOSE SPECIFICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 7.4. PATIENT DATA ACQUISITION AND SIMULATION . . . . . . 223 7.4.1. Need for patient data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 7.4.2. Nature of patient data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 7.4.2.1. Two dimensional treatment planning . . . . . . . . 223 7.4.2.2. Three dimensional treatment planning . . . . . . . 224 7.4.3. Treatment simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 7.4.4. Patient treatment position and immobilization devices . . 226 7.4.5. Patient data requirements . . . . . . . . . . . . . . . . . . . . . . . . . . 228 7.4.6. Conventional treatment simulation . . . . . . . . . . . . . . . . . . . 229 7.4.6.1. Simulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

7.4.6.2. Localization of the target volume and organs at risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 7.4.6.3. Determination of the treatment beam geometry 230 7.4.6.4. Acquisition of patient data . . . . . . . . . . . . . . . . . 230 7.4.7. Computed tomography based conventional treatment simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 7.4.7.1. Computed tomography based patient data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 7.4.7.2. Determination of the treatment beam geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 7.4.8. Computed tomography based virtual simulation . . . . . . . 233 7.4.8.1. Computed tomography simulator . . . . . . . . . . . . 233 7.4.8.2. Virtual simulation . . . . . . . . . . . . . . . . . . . . . . . . . 233 7.4.8.3. Digitally reconstructed radiographs . . . . . . . . . . 234 7.4.8.4. Beam’s eye view . . . . . . . . . . . . . . . . . . . . . . . . . . 234 7.4.8.5. Virtual simulation procedure . . . . . . . . . . . . . . . 235 7.4.9. Conventional simulator versus computed tomography simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 7.4.10. Magnetic resonance imaging for treatment planning . . . . 238 7.4.11. Summary of simulation procedures . . . . . . . . . . . . . . . . . . . 240 7.5. CLINICAL CONSIDERATIONS FOR PHOTON BEAMS . . . . 241 7.5.1. Isodose curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 7.5.2. Wedge filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 7.5.3. Bolus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 7.5.4. Compensating filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 7.5.5. Corrections for contour irregularities . . . . . . . . . . . . . . . . . 246 7.5.5.1. Isodose shift method . . . . . . . . . . . . . . . . . . . . . . 246 7.5.5.2. Effective attenuation coefficient method . . . . . 248 7.5.5.3. Tissue–air ratio method . . . . . . . . . . . . . . . . . . . . 248 7.5.6. Corrections for tissue inhomogeneities . . . . . . . . . . . . . . . . 248 7.5.6.1. Tissue–air ratio method . . . . . . . . . . . . . . . . . . . . 249 7.5.6.2. Batho power law method . . . . . . . . . . . . . . . . . . . 250 7.5.6.3. Equivalent tissue–air ratio method . . . . . . . . . . 250 7.5.6.4. Isodose shift method . . . . . . . . . . . . . . . . . . . . . . 250 7.5.7. Beam combinations and clinical application . . . . . . . . . . . 251 7.5.7.1. Weighting and normalization . . . . . . . . . . . . . . . 251 7.5.7.2. Fixed source to surface distance versus isocentric techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 7.5.7.3. Parallel opposed beams . . . . . . . . . . . . . . . . . . . . 252 7.5.7.4. Multiple coplanar beams . . . . . . . . . . . . . . . . . . . 253

7.5.7.5. Rotational techniques . . . . . . . . . . . . . . . . . . . . . 254 7.5.7.6. Multiple non-coplanar beams . . . . . . . . . . . . . . . 255 7.5.7.7. Field matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 7.6. TREATMENT PLAN EVALUATION . . . . . . . . . . . . . . . . . . . . . . . 256 7.6.1. Isodose curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 7.6.2. Orthogonal planes and isodose surfaces . . . . . . . . . . . . . . . 257 7.6.3. Dose statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 7.6.4. Dose–volume histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 7.6.4.1. Direct dose–volume histogram . . . . . . . . . . . . . . 259 7.6.4.2. Cumulative dose–volume histogram . . . . . . . . . 259 7.6.5. Treatment evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 7.6.5.1. Port films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 7.6.5.2. On-line portal imaging . . . . . . . . . . . . . . . . . . . . . 262 7.7. TREATMENT TIME AND MONITOR UNIT CALCULATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 7.7.1. Treatment time and monitor unit calculations for a fixed source to surface distance set-up . . . . . . . . . . . . . . . . . . . . . 265 7.7.2. Monitor unit and treatment time calculations for isocentric set-ups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 7.7.3. Normalization of dose distributions . . . . . . . . . . . . . . . . . . 270 7.7.4. Inclusion of output parameters in the dose distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 7.7.5. Treatment time calculation for orthovoltage and cobalt-60 units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 CHAPTER 8. ELECTRON BEAMS: PHYSICAL AND CLINICAL ASPECTS . . . . . . . . . . . 273 8.1. CENTRAL AXIS DEPTH DOSE DISTRIBUTIONS IN WATER 273 8.1.1. General shape of the depth dose curve . . . . . . . . . . . . . . . . 273 8.1.2. Electron interactions with an absorbing medium . . . . . . . 274 8.1.3. Inverse square law (virtual source position) . . . . . . . . . . . 276 8.1.4. Range concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 8.1.5. Buildup region (depths between the surface and z max (i.e. 0 £ z £ zmax )) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 8.1.6. Dose distribution beyond zmax (z > zmax) . . . . . . . . . . . . . . 279

8.2. DOSIMETRIC PARAMETERS OF ELECTRON BEAMS . . . . 281 8.2.1. Electron beam energy specification . . . . . . . . . . . . . . . . . . 281 8.2.2. Typical depth dose parameters as a function of energy . . 281 8.2.3. Percentage depth dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 8.2.3.1. Percentage depth doses for small electron field sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 8.2.3.2. Percentage depth doses for oblique beam incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 8.2.4. Output factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 8.2.5. Therapeutic range R90 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 8.2.6. Profiles and off-axis ratios . . . . . . . . . . . . . . . . . . . . . . . . . . 285 8.2.7. Flatness and symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 8.3. CLINICAL CONSIDERATIONS IN ELECTRON BEAM THERAPY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 8.3.1. Dose specification and reporting . . . . . . . . . . . . . . . . . . . . . 286 8.3.2. Small field sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 8.3.3. Isodose curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 8.3.4. Field shaping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 8.3.4.1. Electron applicators . . . . . . . . . . . . . . . . . . . . . . . 289 8.3.4.2. Shielding and cut-outs . . . . . . . . . . . . . . . . . . . . . 289 8.3.4.3. Internal shielding . . . . . . . . . . . . . . . . . . . . . . . . . 290 8.3.4.4. Extended source to surface distance treatments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 8.3.5. Irregular surface correction . . . . . . . . . . . . . . . . . . . . . . . . . 291 8.3.6. Bolus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 8.3.7. Inhomogeneity corrections . . . . . . . . . . . . . . . . . . . . . . . . . . 292 8.3.7.1. Coefficient of equivalent thickness . . . . . . . . . . 292 8.3.7.2. Scatter perturbation (edge) effects . . . . . . . . . . . 293 8.3.8. Electron beam combinations . . . . . . . . . . . . . . . . . . . . . . . . 295 8.3.8.1. Matched (abutted) electron fields . . . . . . . . . . . 295 8.3.8.2. Matched photon and electron fields . . . . . . . . . . 295 8.3.9. Electron arc therapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 8.3.10. Electron therapy treatment planning . . . . . . . . . . . . . . . . . 298 BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 CHAPTER 9. CALIBRATION OF PHOTON AND ELECTRON BEAMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 9.1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

9.1.1. Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 9.1.2. Fricke dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 9.1.3. Ionization chamber dosimetry . . . . . . . . . . . . . . . . . . . . . . . 304 9.1.4. Mean energy expended in air per ion pair formed . . . . . . 304 9.1.5. Reference dosimetry with ionization chambers . . . . . . . . . 305 9.1.5.1. Standard free air ionization chambers . . . . . . . 305 9.1.5.2. Cavity ionization chambers . . . . . . . . . . . . . . . . 306 9.1.5.3. Phantom embedded extrapolation chambers . . 306 9.1.6. Clinical beam calibration and measurement chain . . . . . . 307 9.1.7. Dosimetry protocols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 9.2. IONIZATION CHAMBER BASED DOSIMETRY SYSTEMS . 308 9.2.1. Ionization chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 9.2.2. Electrometer and power supply . . . . . . . . . . . . . . . . . . . . . . 309 9.2.3. Phantoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 9.3. CHAMBER SIGNAL CORRECTION FOR INFLUENCE QUANTITIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 9.3.1. Air temperature, pressure and humidity effects: kT,P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 9.3.2. Chamber polarity effects: polarity correction factor kpol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 9.3.3. Chamber voltage effects: recombination correction factor ksat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 9.3.4. Chamber leakage currents . . . . . . . . . . . . . . . . . . . . . . . . . . 318 9.3.5. Chamber stem effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 9.4. DETERMINATION OF ABSORBED DOSE USING CALIBRATED IONIZATION CHAMBERS . . . . . . . . . . . . . . . . . 319 9.4.1. Air kerma based protocols . . . . . . . . . . . . . . . . . . . . . . . . . . 320 9.4.2. Absorbed dose to water based protocols . . . . . . . . . . . . . . 323 9.5. STOPPING POWER RATIOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 9.5.1. Stopping power ratios for electron beams . . . . . . . . . . . . . 326 9.5.2. Stopping power ratios for photon beams . . . . . . . . . . . . . . 327 9.6. MASS–ENERGY ABSORPTION COEFFICIENT RATIOS . . . 328 9.7. PERTURBATION CORRECTION FACTORS . . . . . . . . . . . . . . . 329 9.7.1. Displacement perturbation factor pdis and effective point of measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 9.7.2. Chamber wall perturbation factor pwall . . . . . . . . . . . . . . . . 331

9.7.3. Central electrode perturbation pcel . . . . . . . . . . . . . . . . . . . 333 9.7.4. Cavity or fluence perturbation correction pcav . . . . . . . . . . 334 9.8. BEAM QUALITY SPECIFICATION . . . . . . . . . . . . . . . . . . . . . . . 335 9.8.1. Beam quality specification for kilovoltage photon beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 9.8.2. Beam quality specification for megavoltage photon beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 9.8.3. Beam quality specification for megavoltage electron beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 9.9. CALIBRATION OF MEGAVOLTAGE PHOTON AND ELECTRON BEAMS: PRACTICAL ASPECTS . . . . . . . . . 342 9.9.1. Calibration of megavoltage photon beams based on the air kerma in air calibration coefficient NK,Co . . . . . . . . . . . . . 342 9.9.2. Calibration of megavoltage photon beams based on the dose to water calibration coefficient ND,w,Co . . . . . . . . 343 9.9.3. Calibration of megavoltage electron beams based on the air kerma in air calibration coefficient NK,Co . . . . . . . . . . . 345 9.9.4. Calibration of high energy electron beams based on the dose to water calibration coefficient ND,w,Co . . . . . . . . . . . . 346 9.10. KILOVOLTAGE DOSIMETRY . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 9.10.1. Specific features of kilovoltage beams . . . . . . . . . . . . . . . . 347 9.10.2. Air kerma based in-phantom calibration method (medium energies) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 9.10.3. Air kerma based backscatter method (low and medium photon energies) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 9.10.4. Air kerma in air based calibration method for very low energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 9.10.5. Absorbed dose to water based calibration method . . . . . . 351 9.11. ERROR AND UNCERTAINTY ANALYSIS FOR IONIZATION CHAMBER MEASUREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 9.11.1. Errors and uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 9.11.2. Classification of uncertainties . . . . . . . . . . . . . . . . . . . . . . . 352 9.11.3. Uncertainties in the calibration chain . . . . . . . . . . . . . . . . . 352 BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

CHAPTER 10. ACCEPTANCE TESTS AND COMMISSIONING MEASUREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 10.1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 10.2. MEASUREMENT EQUIPMENT . . . . . . . . . . . . . . . . . . . . . . . . . . 355 10.2.1. Radiation survey equipment . . . . . . . . . . . . . . . . . . . . . . . . 355 10.2.2. Ionometric dosimetry equipment . . . . . . . . . . . . . . . . . . . . 356 10.2.3. Film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 10.2.4. Diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 10.2.5. Phantoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 10.2.5.1. Radiation field analyser and water phantom . . 357 10.2.5.2. Plastic phantoms . . . . . . . . . . . . . . . . . . . . . . . . . . 357 10.3. ACCEPTANCE TESTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 10.3.1. Safety checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 10.3.1.1. Interlocks, warning lights and patient monitoring equipment . . . . . . . . . . . . . . . . . . . . . 359 10.3.1.2. Radiation survey . . . . . . . . . . . . . . . . . . . . . . . . . . 359 10.3.1.3. Collimator and head leakage . . . . . . . . . . . . . . . 360 10.3.2. Mechanical checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 10.3.2.1. Collimator axis of rotation . . . . . . . . . . . . . . . . . 361 10.3.2.2. Photon collimator jaw motion . . . . . . . . . . . . . . . 361 10.3.2.3. Congruence of light and radiation field . . . . . . . 362 10.3.2.4. Gantry axis of rotation . . . . . . . . . . . . . . . . . . . . . 363 10.3.2.5. Patient treatment table axis of rotation . . . . . . . 363 10.3.2.6. Radiation isocentre . . . . . . . . . . . . . . . . . . . . . . . 364 10.3.2.7. Optical distance indicator . . . . . . . . . . . . . . . . . . 364 10.3.2.8. Gantry angle indicators . . . . . . . . . . . . . . . . . . . . 365 10.3.2.9. Collimator field size indicators . . . . . . . . . . . . . . 365 10.3.2.10. Patient treatment table motions . . . . . . . . . . . . . 365 10.3.3. Dosimetry measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 10.3.3.1. Photon energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366 10.3.3.2. Photon beam uniformity . . . . . . . . . . . . . . . . . . . 366 10.3.3.3. Photon penumbra . . . . . . . . . . . . . . . . . . . . . . . . . 366 10.3.3.4. Electron energy . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 10.3.3.5. Electron beam bremsstrahlung contamination . 367 10.3.3.6. Electron beam uniformity . . . . . . . . . . . . . . . . . . 368 10.3.3.7. Electron penumbra . . . . . . . . . . . . . . . . . . . . . . . . 368 10.3.3.8. Monitor characteristics . . . . . . . . . . . . . . . . . . . . 368 10.3.3.9. Arc therapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370

10.4. COMMISSIONING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 10.4.1. Photon beam measurements . . . . . . . . . . . . . . . . . . . . . . . . 370 10.4.1.1. Central axis percentage depth doses . . . . . . . . . 370 10.4.1.2. Output factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 10.4.1.3. Blocking tray factors . . . . . . . . . . . . . . . . . . . . . . 373 10.4.1.4. Multileaf collimators . . . . . . . . . . . . . . . . . . . . . . 373 10.4.1.5. Central axis wedge transmission factors . . . . . . 374 10.4.1.6. Dynamic wedge . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 10.4.1.7. Transverse beam profiles/off-axis energy changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 10.4.1.8. Entrance dose and interface dosimetry . . . . . . . 376 10.4.1.9. Virtual source position . . . . . . . . . . . . . . . . . . . . . 377 10.4.2. Electron beam measurements . . . . . . . . . . . . . . . . . . . . . . . 378 10.4.2.1. Central axis percentage depth dose . . . . . . . . . . 378 10.4.2.2. Output factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 10.4.2.3. Transverse beam profiles . . . . . . . . . . . . . . . . . . . 383 10.4.2.4. Virtual source position . . . . . . . . . . . . . . . . . . . . . 383 10.5. TIME REQUIRED FOR COMMISSIONING . . . . . . . . . . . . . . . . 384 BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 CHAPTER 11. COMPUTERIZED TREATMENT PLANNING SYSTEMS FOR EXTERNAL PHOTON BEAM RADIOTHERAPY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 11.1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 11.2. SYSTEM HARDWARE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388 11.2.1. Treatment planning system hardware . . . . . . . . . . . . . . . . . 388 11.2.2. Treatment planning system configurations . . . . . . . . . . . . . 389 11.3. SYSTEM SOFTWARE AND CALCULATION ALGORITHMS 390 11.3.1. Calculation algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 11.3.2. Beam modifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 11.3.2.1. Photon beam modifiers . . . . . . . . . . . . . . . . . . . . 393 11.3.2.2. Electron beam modifiers . . . . . . . . . . . . . . . . . . 394 11.3.3. Heterogeneity corrections . . . . . . . . . . . . . . . . . . . . . . . . . . 395 11.3.4. Image display and dose–volume histograms . . . . . . . . . . . 395 11.3.5. Optimization and monitor unit calculations . . . . . . . . . . . . 396 11.3.6. Record and verify systems . . . . . . . . . . . . . . . . . . . . . . . . . . 396 11.3.7. Biological modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397

11.4. DATA ACQUISITION AND ENTRY . . . . . . . . . . . . . . . . . . . . . . . 397 11.4.1. Machine data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 11.4.2. Beam data acquisition and entry . . . . . . . . . . . . . . . . . . . . . 398 11.4.3. Patient data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 11.5. COMMISSIONING AND QUALITY ASSURANCE . . . . . . . . . . 400 11.5.1. Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 11.5.2. Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401 11.5.3. Spot checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402 11.5.4. Normalization and beam weighting . . . . . . . . . . . . . . . . . . . 402 11.5.5. Dose–volume histograms and optimization . . . . . . . . . . . . 403 11.5.6. Training and documentation . . . . . . . . . . . . . . . . . . . . . . . . 403 11.5.7. Scheduled quality assurance . . . . . . . . . . . . . . . . . . . . . . . . . 403 11.6. SPECIAL CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 CHAPTER 12. QUALITY ASSURANCE OF EXTERNAL BEAM RADIOTHERAPY . . . . . . . . . . . . . . . . . . . . . . . 407 12.1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 12.1.1. Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 12.1.1.1. Quality assurance . . . . . . . . . . . . . . . . . . . . . . . . . 407 12.1.1.2. Quality assurance in radiotherapy . . . . . . . . . . . 407 12.1.1.3. Quality control . . . . . . . . . . . . . . . . . . . . . . . . . . . 408 12.1.1.4. Quality standards . . . . . . . . . . . . . . . . . . . . . . . . . 408 12.1.2. Need for quality assurance in radiotherapy . . . . . . . . . . . . 408 12.1.3. Requirements on accuracy in radiotherapy . . . . . . . . . . . . 409 12.1.4. Accidents in radiotherapy . . . . . . . . . . . . . . . . . . . . . . . . . . 411 12.2. MANAGING A QUALITY ASSURANCE PROGRAMME . . . 414 12.2.1. Multidisciplinary radiotherapy team . . . . . . . . . . . . . . . . . . 414 12.2.2. Quality system/comprehensive quality assurance programme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416 12.3. QUALITY ASSURANCE PROGRAMME FOR EQUIPMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418 12.3.1. Structure of an equipment quality assurance programme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418 12.3.1.1. Equipment specification . . . . . . . . . . . . . . . . . . . 419 12.3.1.2. Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419

12.3.1.3. Commissioning . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 12.3.1.4. Quality control . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 12.3.2. Uncertainties, tolerances and action levels . . . . . . . . . . . . . 421 12.3.3. Quality assurance programme for cobalt-60 teletherapy machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 12.3.4. Quality assurance programme for linacs . . . . . . . . . . . . . . 425 12.3.5. Quality assurance programme for treatment simulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 12.3.6. Quality assurance programme for computed tomography scanners and computed tomography simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 12.3.7. Quality assurance programme for treatment planning systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430 12.3.8. Quality assurance programme for test equipment . . . . . . 431 12.4. TREATMENT DELIVERY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 12.4.1. Patient charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 12.4.2. Portal imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 12.4.2.1. Portal imaging techniques . . . . . . . . . . . . . . . . . . 436 12.4.2.2. Future developments in portal imaging . . . . . . . 439 12.4.3. In vivo dose measurements . . . . . . . . . . . . . . . . . . . . . . . . . 439 12.4.3.1. In vivo dose measurement techniques . . . . . . . . 440 12.4.3.2. Use of electronic portal imaging systems for in vivo dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . 443 12.4.4. Record and verify systems . . . . . . . . . . . . . . . . . . . . . . . . . . 443 12.5. QUALITY AUDIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 12.5.1. Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 12.5.2. Practical quality audit modalities . . . . . . . . . . . . . . . . . . . . . 446 12.5.2.1. Postal audit with mailed dosimeters . . . . . . . . . 446 12.5.2.2. Quality audit visits . . . . . . . . . . . . . . . . . . . . . . . . 446 12.5.3. What should be reviewed in a quality audit visit? . . . . . . . 447 BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448 CHAPTER 13. BRACHYTHERAPY: PHYSICAL AND CLINICAL ASPECTS . . . . . . . . . . . 451 13.1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451 13.2. PHOTON SOURCE CHARACTERISTICS . . . . . . . . . . . . . . . . . . 455 13.2.1. Practical considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455

13.2.2. Physical characteristics of some photon emitting brachytherapy sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456 13.2.3. Mechanical source characteristics . . . . . . . . . . . . . . . . . . . . 456 13.2.4. Source specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457 13.2.4.1. Specification of g ray sources . . . . . . . . . . . . . . . 457 13.2.4.2. Specification of b ray sources . . . . . . . . . . . . . . . 459 13.3. CLINICAL USE AND DOSIMETRY SYSTEMS . . . . . . . . . . . . . 460 13.3.1. Gynaecology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460 13.3.1.1. Types of source . . . . . . . . . . . . . . . . . . . . . . . . . . . 460 13.3.1.2. Dose specification . . . . . . . . . . . . . . . . . . . . . . . . . 460 13.3.1.3. Source arrangement . . . . . . . . . . . . . . . . . . . . . . 460 13.3.1.4. Applicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461 13.3.1.5. Rectal and bladder dose monitoring . . . . . . . . . 461 13.3.2. Interstitial brachytherapy . . . . . . . . . . . . . . . . . . . . . . . . . . . 461 13.3.2.1. Patterson–Parker system . . . . . . . . . . . . . . . . . . . 461 13.3.2.2. Quimby system . . . . . . . . . . . . . . . . . . . . . . . . . . . 462 13.3.2.3. Paris system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462 13.3.3. Remote afterloading systems . . . . . . . . . . . . . . . . . . . . . . . . 463 13.3.4. Permanent prostate implants . . . . . . . . . . . . . . . . . . . . . . . . 464 13.3.4.1. Choice of radionuclide for prostate implants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465 13.3.4.2. Planning technique: ultrasound or computed tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465 13.3.4.3. Preplanning, seed placement and dose distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465 13.3.4.4. Post-implant dose distributions and evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465 13.3.5. Eye plaques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466 13.3.6. Intravascular brachytherapy . . . . . . . . . . . . . . . . . . . . . . . . . 466 13.4. DOSE SPECIFICATION AND REPORTING . . . . . . . . . . . . . . . . 467 13.4.1. Intracavitary treatments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 13.4.2. Interstitial treatments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 13.5. DOSE DISTRIBUTIONS AROUND SOURCES . . . . . . . . . . . . . 468 13.5.1. AAPM TG 43 algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468 13.5.2. Other calculation methods for point sources . . . . . . . . . . . 471 13.5.3. Linear sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 13.5.3.1. Unfiltered line source in air . . . . . . . . . . . . . . . . . 473

13.5.3.2. Filtered line source in air . . . . . . . . . . . . . . . . . . . 474 13.5.3.3. Filtered line source in water . . . . . . . . . . . . . . . . 475 13.6. DOSE CALCULATION PROCEDURES . . . . . . . . . . . . . . . . . . . . 475 13.6.1. Manual dose calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . 475 13.6.1.1. Manual summation of doses . . . . . . . . . . . . . . . . 475 13.6.1.2. Precalculated dose distributions (atlases) . . . . . 475 13.6.2. Computerized treatment planning . . . . . . . . . . . . . . . . . . . 476 13.6.2.1. Source localization . . . . . . . . . . . . . . . . . . . . . . . . 476 13.6.2.2. Dose calculation . . . . . . . . . . . . . . . . . . . . . . . . . . 476 13.6.2.3. Dose distribution display . . . . . . . . . . . . . . . . . . . 476 13.6.2.4. Optimization of dose distribution . . . . . . . . . . . . 477 13.6.3. Calculation of treatment time . . . . . . . . . . . . . . . . . . . . . . . 477 13.6.3.1. Use of Patterson–Parker tables . . . . . . . . . . . . . 477 13.6.3.2. Choice of reference points . . . . . . . . . . . . . . . . . . 478 13.6.3.3. Decay corrections . . . . . . . . . . . . . . . . . . . . . . . . . 478 13.7. COMMISSIONING OF BRACHYTHERAPY COMPUTER TREATMENT PLANNING SYSTEMS . . . . . . . . . . . . . . . . . . . . . . 479 13.7.1. Check of the reconstruction procedure . . . . . . . . . . . . . . . 479 13.7.2. Check of consistency between quantities and units . . . . . . 479 13.7.3. Computer versus manual dose calculation for a single source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 13.7.4. Check of decay corrections . . . . . . . . . . . . . . . . . . . . . . . . . . 479 13.8. SOURCE COMMISSIONING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480 13.8.1. Wipe tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480 13.8.2. Autoradiography and uniformity checks of activity . . . . . 480 13.8.3. Calibration chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480 13.9. QUALITY ASSURANCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 13.9.1. Constancy check of a calibrated dosimeter . . . . . . . . . . . . 481 13.9.2. Regular checks of sources and applicators . . . . . . . . . . . . . 481 13.9.2.1. Mechanical properties . . . . . . . . . . . . . . . . . . . . . 481 13.9.2.2. Source strength . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 13.9.2.3. Wipe tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482 13.9.3. Checks of source positioning with afterloading devices . . 482 13.9.4. Radiation monitoring around patients . . . . . . . . . . . . . . . . 482 13.9.5. Quality management programme . . . . . . . . . . . . . . . . . . . . 482

13.10. BRACHYTHERAPY VERSUS EXTERNAL BEAM RADIOTHERAPY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483 BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483 CHAPTER 14. BASIC RADIOBIOLOGY . . . . . . . . . . . . . . . . . . . . . . . . 485 14.1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485 14.2. CLASSIFICATION OF RADIATIONS IN RADIOBIOLOGY . 486 14.3. CELL CYCLE AND CELL DEATH . . . . . . . . . . . . . . . . . . . . . . . . 487 14.4. IRRADIATION OF CELLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488 14.4.1. Direct action in cell damage by radiation . . . . . . . . . . . . . . 488 14.4.2. Indirect action in cell damage by radiation . . . . . . . . . . . . 488 14.4.3. Fate of irradiated cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489 14.5. TYPE OF RADIATION DAMAGE . . . . . . . . . . . . . . . . . . . . . . . . . 489 14.5.1. Timescale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489 14.5.2. Classification of radiation damage . . . . . . . . . . . . . . . . . . . 490 14.5.3. Somatic and genetic effects . . . . . . . . . . . . . . . . . . . . . . . . . 490 14.5.4. Stochastic and deterministic (non-stochastic) effects . . . . 491 14.5.5. Acute versus late tissue or organ effects . . . . . . . . . . . . . . . 491 14.5.6. Total body radiation response . . . . . . . . . . . . . . . . . . . . . . . 491 14.5.7. Foetal irradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492 14.6. CELL SURVIVAL CURVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492 14.7. DOSE RESPONSE CURVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494 14.8. MEASUREMENT OF RADIATION DAMAGE IN TISSUE . . . 496 14.9. NORMAL AND TUMOUR CELLS: THERAPEUTIC RATIO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 14.10. OXYGEN EFFECT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498 14.11. RELATIVE BIOLOGICAL EFFECTIVENESS . . . . . . . . . . . . . . 500 14.12. DOSE RATE AND FRACTIONATION . . . . . . . . . . . . . . . . . . . . . 501 14.13. RADIOPROTECTORS AND RADIOSENSITIZERS . . . . . . . . . 503 BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504 CHAPTER 15. SPECIAL PROCEDURES AND TECHNIQUES IN RADIOTHERAPY . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 15.1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 15.2. STEREOTACTIC IRRADIATION . . . . . . . . . . . . . . . . . . . . . . . . . 506 15.2.1. Physical and clinical requirements for radiosurgery . . . . . 506 15.2.2. Diseases treated with stereotactic irradiation . . . . . . . . . 507

15.2.3. Equipment used for stereotactic radiosurgery . . . . . . . . . 507 15.2.4. Historical development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508 15.2.5. Radiosurgical techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 509 15.2.5.1. Gamma Knife . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509 15.2.5.2. Linac based radiosurgery . . . . . . . . . . . . . . . . . . . 509 15.2.5.3. Miniature linac on robotic arm . . . . . . . . . . . . . . 511 15.2.6. Uncertainty in radiosurgical dose delivery . . . . . . . . . . . . . 512 15.2.7. Dose prescription and dose fractionation . . . . . . . . . . . . . . 513 15.2.8. Commissioning of radiosurgical equipment . . . . . . . . . . . . 514 15.2.9. Quality assurance in radiosurgery . . . . . . . . . . . . . . . . . . . . 514 15.2.10. Gamma Knife versus linac based radiosurgery . . . . . . . . . 515 15.2.11. Frameless stereotaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516 15.3. TOTAL BODY IRRADIATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516 15.3.1. Clinical total body irradiation categories . . . . . . . . . . . . . . 516 15.3.2. Diseases treated with total body irradiation . . . . . . . . . . . 517 15.3.3. Technical aspects of total body irradiation . . . . . . . . . . . . . 517 15.3.4. Total body irradiation techniques . . . . . . . . . . . . . . . . . . . . 518 15.3.5. Dose prescription point . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519 15.3.6. Commissioning of total body irradiation procedure . . . . . 519 15.3.7. Test of total body irradiation dosimetry protocol . . . . . . . 521 15.3.8. Quality assurance in total body irradiation . . . . . . . . . . . . 521 15.4. TOTAL SKIN ELECTRON IRRADIATION . . . . . . . . . . . . . . . . . 522 15.4.1. Physical and clinical requirements for total skin electron irradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523 15.4.2. Current total skin electron irradiation techniques . . . . . . 523 15.4.3. Selection of total skin electron irradiation technique . . . . 524 15.4.4. Dose calibration point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525 15.4.5. Skin dose rate at the dose prescription point . . . . . . . . . . . 525 15.4.6. Commissioning of the total skin electron irradiation procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525 15.4.7. Measurement of clinical total skin electron irradiation dose distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526 15.4.8. Quality assurance in total skin electron irradiation . . . . . 526 15.5. INTRAOPERATIVE RADIOTHERAPY . . . . . . . . . . . . . . . . . . . 527 15.5.1. Physical and clinical requirements for intraoperative radiotherapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527 15.5.2. Intraoperative radiotherapy radiation modalities and techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527

15.5.3. Commissioning of an intraoperative radiotherapy programme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528 15.5.4. Quality assurance in intraoperative radiotherapy . . . . . . . 528 15.6. ENDOCAVITARY RECTAL IRRADIATION . . . . . . . . . . . . . . . 529 15.6.1. Physical and clinical requirements for endorectal irradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529 15.6.2. Endorectal treatment technique . . . . . . . . . . . . . . . . . . . . . 530 15.6.3. Quality assurance in endorectal treatments . . . . . . . . . . . . 531 15.7. CONFORMAL RADIOTHERAPY . . . . . . . . . . . . . . . . . . . . . . . . . 531 15.7.1. Basic aspects of conformal radiotherapy . . . . . . . . . . . . . . 531 15.7.2. Multileaf collimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532 15.7.3. Acceptance testing of multileaf collimators . . . . . . . . . . . . 533 15.7.4. Commissioning of multileaf collimators . . . . . . . . . . . . . . . 534 15.7.5. Quality assurance programme for multileaf collimators . 534 15.7.6. Intensity modulated radiotherapy . . . . . . . . . . . . . . . . . . . . 534 15.7.7. Commissioning of intensity modulated radiotherapy systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535 15.7.8. Quality assurance for intensity modulated radiotherapy systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537 15.7.9. Dose verification for intensity modulated radiotherapy treatment plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537 15.8. IMAGE GUIDED RADIOTHERAPY . . . . . . . . . . . . . . . . . . . . . . 538 15.8.1. Cone beam computed tomography . . . . . . . . . . . . . . . . . . . 539 15.8.2. Computed tomography Primatom . . . . . . . . . . . . . . . . . . . 540 15.8.3. Tomotherapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541 15.8.4. BAT system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542 15.8.5. ExacTrac ultrasonic module . . . . . . . . . . . . . . . . . . . . . . . . . 542 15.8.6. CyberKnife . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543 15.9. ADAPTIVE RADIOTHERAPY . . . . . . . . . . . . . . . . . . . . . . . . . . . 544 15.10. RESPIRATORY GATED RADIOTHERAPY . . . . . . . . . . . . . . . 544 15.11. POSITRON EMISSION TOMOGRAPHY/COMPUTED TOMOGRAPHY SCANNERS AND POSITRON EMISSION TOMOGRAPHY/COMPUTED TOMOGRAPHY IMAGE FUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 548

CHAPTER 16. RADIATION PROTECTION AND SAFETY IN RADIOTHERAPY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549 16.1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549 16.2. RADIATION EFFECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550 16.2.1. Deterministic effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550 16.2.2. Stochastic effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550 16.2.3. Effects on the embryo and foetus . . . . . . . . . . . . . . . . . . . . 551 16.3. INTERNATIONAL CONSENSUS AND RADIATION SAFETY STANDARDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551 16.4. TYPES OF RADIATION EXPOSURE . . . . . . . . . . . . . . . . . . . . . . 552 16.5. QUANTITIES AND UNITS USED IN RADIATION PROTECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554 16.5.1. Physical quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554 16.5.2. Radiation protection quantities . . . . . . . . . . . . . . . . . . . . . . 554 16.5.2.1. Organ dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555 16.5.2.2. Equivalent dose . . . . . . . . . . . . . . . . . . . . . . . . . . 555 16.5.2.3. Effective dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556 16.5.2.4. Committed dose . . . . . . . . . . . . . . . . . . . . . . . . . . 557 16.5.2.5. Collective dose . . . . . . . . . . . . . . . . . . . . . . . . . . . 558 16.5.3. Operational quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558 16.5.3.1. Ambient dose equivalent . . . . . . . . . . . . . . . . . . . 558 16.5.3.2. Directional dose equivalent . . . . . . . . . . . . . . . . 558 16.5.3.3. Personal dose equivalent . . . . . . . . . . . . . . . . . . . 559 16.6. BASIC FRAMEWORK OF RADIATION PROTECTION . . . . . 559 16.7. GOVERNMENTAL REGULATION AND NATIONAL INFRASTRUCTURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560 16.8. SCOPE OF THE BASIC SAFETY STANDARDS . . . . . . . . . . . . 561 16.9. RESPONSIBILITIES FOR IMPLEMENTATION OF BASIC SAFETY STANDARDS REQUIREMENTS . . . . . . . 562 16.10. SAFETY IN THE DESIGN OF RADIATION SOURCES AND EQUIPMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562 16.10.1. Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563 16.10.2. Sealed sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565 16.10.3. Safety in the design of facilities and ancillary equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567 16.10.3.1. Manual brachytherapy . . . . . . . . . . . . . . . . . . . . . 567 16.10.3.2. Remote control brachytherapy and external beam radiotherapy . . . . . . . . . . . . . . . . 569

16.11. SAFETY ASSOCIATED WITH ACCEPTANCE TESTS, COMMISSIONING AND OPERATION . . . . . . . . . . . . . . . . . . . . 570 16.11.1. Safe operation of external beam radiotherapy . . . . . . . . . 572 16.11.2. Safe operation of brachytherapy . . . . . . . . . . . . . . . . . . . . . 572 16.11.2.1. Safe operation of manual brachytherapy . . . . . . 574 16.11.2.2. Safe operation of remote control afterloading brachytherapy . . . . . . . . . . . . . . . . . 575 16.12. SECURITY OF SOURCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575 16.13. OCCUPATIONAL EXPOSURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577 16.13.1. Responsibilities and conditions of service . . . . . . . . . . . . . 577 16.13.2. Use of dose constraints in radiotherapy . . . . . . . . . . . . . . 577 16.13.3. Investigation levels for staff exposure in radiotherapy . . . 578 16.13.4. Pregnant workers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578 16.13.5. Classification of areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579 16.13.6. Local rules and supervision . . . . . . . . . . . . . . . . . . . . . . . . . 579 16.13.7. Protective equipment and tools . . . . . . . . . . . . . . . . . . . . . . 580 16.13.8. Individual monitoring and exposure assessment . . . . . . . . 580 16.13.9. Monitoring of the workplace . . . . . . . . . . . . . . . . . . . . . . . . 581 16.13.10. Health surveillance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581 16.13.11. Records . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582 16.14. MEDICAL EXPOSURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583 16.14.1. Responsibilities for medical exposure . . . . . . . . . . . . . . . . . 583 16.14.2. Justification of medical exposure . . . . . . . . . . . . . . . . . . . . . 584 16.14.3. Optimization of exposure and protection . . . . . . . . . . . . . . 584 16.14.4. Calibration of radiotherapy sources and machines . . . . . . 585 16.14.5. Clinical dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587 16.14.6. Quality assurance for medical exposure . . . . . . . . . . . . . . . 587 16.14.7. Constraints for comforters and visitors . . . . . . . . . . . . . . . . 589 16.14.8. Discharge of patients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589 16.14.9. Investigation of accidental medical exposure . . . . . . . . . . 590 16.15. PUBLIC EXPOSURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591 16.15.1. Responsibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591 16.15.2. Access control for visitors . . . . . . . . . . . . . . . . . . . . . . . . . . . 591 16.15.3. Radioactive waste and sources no longer in use . . . . . . . . 591 16.15.4. Monitoring of public exposure . . . . . . . . . . . . . . . . . . . . . . . 592 16.16. POTENTIAL EXPOSURE AND EMERGENCY PLANS . . . . . 592 16.16.1. Potential exposure and safety assessment . . . . . . . . . . . . . 592

16.16.2. Mitigation of consequences: emergency plans . . . . . . . . . . 593 16.16.2.1. Lost source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593 16.16.2.2. Stuck source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594 16.16.2.3. Contamination . . . . . . . . . . . . . . . . . . . . . . . . . . . 595 16.16.2.4. Off-site accidents . . . . . . . . . . . . . . . . . . . . . . . . . 595 16.16.2.5. Patient accidental exposure . . . . . . . . . . . . . . . . . 595 16.17. GENERAL SHIELDING CALCULATIONS . . . . . . . . . . . . . . . . 596 16.17.1. Step one: Design dose in occupied areas (annual dose and weekly dose) . . . . . . . . . . . . . . . . . . . . . . 597 16.17.2. Step two: Calculation of the radiation field (air kerma in air) in the occupied area without shielding . 598 16.17.3. Step three: Attenuation by shielding barriers . . . . . . . . . . 599 16.18. TYPICAL LINAC INSTALLATION . . . . . . . . . . . . . . . . . . . . . . . . 600 16.18.1. Workload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600 16.18.2. Calculation of the primary barrier transmission factor . . . 602 16.18.3. Calculation of the scatter barrier transmission factor . . . . 603 16.18.4. Calculation of the leakage barrier transmission factor . . . 603 16.18.5. Determination of barrier thickness . . . . . . . . . . . . . . . . . . . 604 16.18.6. Consideration of neutron production in a high energy linac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605 16.18.7. Door of a linac room . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605 16.18.8. Other considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606 16.19. SHIELDING DESIGN FOR BRACHYTHERAPY FACILITIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606 BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607 INTERNATIONAL ORGANIZATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 611 ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613 SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 619 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 639

BL AN K

Chapter 1 BASIC RADIATION PHYSICS E.B. PODGORSAK Department of Medical Physics, McGill University Health Centre, Montreal, Quebec, Canada 1.1. INTRODUCTION 1.1.1. Fundamental physical constants (rounded off to four significant figures) ● Avogadro’s number: NA = 6.022 × 1023 atoms/g-atom. 23 ● Avogadro’s number: NA = 6.022 × 10 molecules/g-mole. 8 ● Speed of light in vacuum: c = 299 792 458 m/s (ª3 × 10 m/s). –19 ● Electron charge: e = 1.602 × 10 C. 2 ● Electron rest mass: me– = 0.5110 MeV/c . 2 ● Positron rest mass: me+ = 0.5110 MeV/c . 2 ● Proton rest mass: mp = 938.3 MeV/c . 2 ● Neutron rest mass: mn = 939.6 MeV/c . 2 ● Atomic mass unit: u = 931.5 MeV/c . –34 ● Planck’s constant: h = 6.626 × 10 J·s. ● Permittivity of vacuum: e0 = 8.854 × 10 –12 C/(V·m). ● Permeability of vacuum: m0 = 4p × 10 (V·s)/(A·m). –7 –11 ● Newtonian gravitation constant: G = 6.672 × 10 m3·kg–1·s–2. ● Proton mass/electron mass: mp/me = 1836.0. 11 ● Specific charge of electron: e/me = 1.758 × 10 C/kg. 1.1.2. Important derived physical constants and relationships ● Speed of light in a vacuum: 1 c= ª 3 ¥ 10 8 m/s (1.1) e 0 m0 1

CHAPTER 1 ● Reduced Planck’s constant × speed of light in a vacuum: h c= c = 197.3 MeV◊ fm ª 200 MeV◊ fm (1.2) 2p ● Fine structure constant: e2 1 1 a= = (1.3) 4pe 0 c 137 ● Bohr radius: c 4pe ( c) 2 a0 = = 20 = 0.5292 Å (1.4) a mec 2 e mec 2 ● Rydberg energy: 2 1 1 Ê e 2 ˆ mec 2 ER = mec 2a 2 = Á = 13.61 eV (1.5) 2 2 Ë 4pe 0 ˜ ( c) 2 ¯ ● Rydberg constant: 2 E m c 2a 2 1 Ê e 2 ˆ mec 2 R• = R = e = = 109 737 cm -1 (1.6) 2p c 4p c 4p Á 4pe 0 ˜ ( c) 3 Ë ¯ ● Classical electron radius: e2 re = = 2.818 fm (1.7) 4pe 0 mec 2 ● Compton wavelength of the electron: h lC = = 0.0243 Å (1.8) mec 2

BASIC RADIATION PHYSICS 1.1.3. Physical quantities and units ● Physical quantities are characterized by their numerical value (magnitude) and associated unit. ● Symbols for physical quantities are set in italic type, while symbols for units are set in roman type (e.g. m = 21 kg; E = 15 MeV). ● The numerical value and the unit of a physical quantity must be separated by a space (e.g. 21 kg and not 21kg; 15 MeV and not 15MeV). ● The currently used metric system of units is known as the Système inter- national d’unités (International System of Units), with the international abbreviation SI. The system is founded on base units for seven basic physical quantities: Length l: metre (m). Mass m: kilogram (kg). Time t: second (s). Electric current I: ampere (A). Temperature T: kelvin (K). Amount of substance: mole (mol). Luminous intensity: candela (cd). All other quantities and units are derived from the seven base quantities and units (see Table 1.1). TABLE 1.1. THE BASIC AND SEVERAL DERIVED PHYSICAL QUANTITIES AND THEIR UNITS IN THE INTERNATIONAL SYSTEM OF UNITS AND IN RADIATION PHYSICS Physical Unit Units used in Symbol Conversion quantity in SI radiation physics Length l m nm, Å, fm 1 m = 109 nm = 1010 Å = 1015 fm Mass m kg MeV/c2 1 MeV/c2 = 1.78 × 10–30 kg Time t s ms, ms, ns, ps 1 s = 103 ms = 106 ms = 109 ns = 1012 ps Current I A mA, mA, nA, pA 1 A = 103 mA = 106 mA = 109 nA Charge Q C e 1 e = 1.602 × 10–19 C Force F N 1 N = 1 kg·m·s–2 Momentum p N·s 1 N·s = 1 kg·m·s–1 Energy E J eV, keV, MeV 1 eV = 1.602 × 10–19 J = 10–3 keV 3

CHAPTER 1 1.1.4. Classification of forces in nature There are four distinct forces observed in the interaction between various types of particle (see Table 1.2). These forces, listed in decreasing order of strength, are the strong force, electromagnetic (EM) force, weak force and gravitational force, with relative strengths of 1, 1/137, 10–6 and 10–39, respectively. ● The ranges of the EM and gravitational forces are infinite (1/r2 dependence, where r is the separation between two interacting particles); ● The ranges of the strong and weak forces are extremely short (of the order of a few femtometres). Each force results from a particular intrinsic property of the particles, such as: — Strong charge for the strong force transmitted by massless particles called gluons; — Electric charge for the EM force transmitted by photons; — Weak charge for the weak force transmitted by particles called W and Z0; — Energy for the gravitational force transmitted by hypothetical particles called gravitons. 1.1.5. Classification of fundamental particles Two classes of fundamental particle are known: quarks and leptons. ● Quarks are particles that exhibit strong interactions. They are constit- uents of hadrons (protons and neutrons) with a fractional electric charge (2/3 or –1/3) and are characterized by one of three types of strong charge called colour: red, blue and green. There are six known quarks: up, down, strange, charm, top and bottom. TABLE 1.2. THE FOUR FUNDAMENTAL FORCES IN NATURE Force Source Transmitted particle Relative strength Strong Strong charge Gluon 1 EM Electric charge Photon 1/137 Weak Weak charge W and Z0 10–6 Gravitational Energy Graviton 10–39 4

BASIC RADIATION PHYSICS ● Leptons are particles that do not interact strongly. Electrons (e), muons (m), taus (t) and their corresponding neutrinos (ne, nm, nt) are in this category. 1.1.6. Classification of radiation As shown in Fig. 1.1, radiation is classified into two main categories, non- ionizing and ionizing, depending on its ability to ionize matter. The ionization potential of atoms (i.e. the minimum energy required to ionize an atom) ranges from a few electronvolts for alkali elements to 24.5 eV for helium (noble gas). ● Non-ionizing radiation (cannot ionize matter). ● Ionizing radiation (can ionize matter either directly or indirectly): —Directly ionizing radiation (charged particles): electrons, protons, a particles and heavy ions. —Indirectly ionizing radiation (neutral particles): photons (X rays and g rays), neutrons. Directly ionizing radiation deposits energy in the medium through direct Coulomb interactions between the directly ionizing charged particle and orbital electrons of atoms in the medium. Indirectly ionizing radiation (photons or neutrons) deposits energy in the medium through a two step process: ● In the first step a charged particle is released in the medium (photons release electrons or positrons, neutrons release protons or heavier ions); ● In the second step the released charged particles deposit energy to the medium through direct Coulomb interactions with orbital electrons of the atoms in the medium. Non-ionizing Radiation Directly ionizing (charged particles) electrons, protons, etc. Ionizing Indirectly ionizing (neutral particles) photons, neutrons FIG. 1.1. Classification of radiation. 5

CHAPTER 1 Both directly and indirectly ionizing radiations are used in the treatment of disease, mainly but not exclusively for malignant disease. The branch of medicine that uses radiation in the treatment of disease is called radiotherapy, therapeutic radiology or radiation oncology. Diagnostic radiology and nuclear medicine are branches of medicine that use ionizing radiation in the diagnosis of disease. 1.1.7. Classification of ionizing photon radiation ● Characteristic X rays: resulting from electron transitions between atomic shells. ● Bremsstrahlung: resulting from electron–nucleus Coulomb interactions. ● g rays: resulting from nuclear transitions. ● Annihilation quanta: resulting from positron–electron annihilation. 1.1.8. Einstein’s relativistic mass, energy and momentum relationships m0 m0 m(u ) = = = g m0 (1.9) Êu ˆ 2 1- b 2 1- Á ˜ Ë c¯ E = m(u)c2 (1.10) E0 = m0c2 (1.11) EK = E – E0 = (g – 1)E0 (1.12) E2 = E0 + p2c2 2 (1.13) where u is the particle velocity; c is the speed of light in a vacuum; b is the normalized particle velocity (i.e. b = u/c); m(u) is the particle mass at velocity u; m0 is the particle rest mass (at velocity u = 0); E is the total energy of the particle; E0 is the rest energy of the particle; EK is the kinetic energy of the particle; p is the momentum of the particle. 6

BASIC RADIATION PHYSICS ● For photons, E = hn and E0 = 0; thus using Eq. (1.13) we obtain p = hn/c = h/l, where n and l are the photon frequency and wavelength, respec- tively. 1.1.9. Radiation quantities and units The most important radiation quantities and their units are listed in Table 1.3. Also listed are the definitions of the various quantities and the relationships between the old and the SI units for these quantities. 1.2. ATOMIC AND NUCLEAR STRUCTURE 1.2.1. Basic definitions for atomic structure The constituent particles forming an atom are protons, neutrons and electrons. Protons and neutrons are known as nucleons and form the nucleus of the atom. ● Atomic number Z: number of protons and number of electrons in an atom. ● Atomic mass number A: number of nucleons in an atom (i.e. number of protons Z plus number of neutrons N in an atom: A = Z + N). ● There is no basic relation between A and Z, but the empirical relationship A Z= (1.14) 1.98 + 0.0155 A 2 / 3 furnishes a good approximation for stable nuclei. ● Atomic mass M: expressed in atomic mass units u, where 1 u is equal to 1/12 of the mass of the 12C atom or 931.5 MeV/c2. The atomic mass M is smaller than the sum of the individual masses of constituent particles because of the intrinsic energy associated with binding the particles (nucleons) within the nucleus. ● Atomic g-atom (gram-atom): number of grams that correspond to NA atoms of an element, where NA = 6.022 × 1023 atoms/g-atom (Avogadro’s number). The atomic mass numbers of all elements are defined such that A grams of every element contain exactly NA atoms. For example: 1 g-atom of 60Co is 60 g of 60Co. In 60 g of 60Co (1 g-atom) there is Avogadro’s number of 60Co atoms. 7

CHAPTER 1 TABLE 1.3. RADIATION QUANTITIES, UNITS AND CONVERSION BETWEEN OLD AND SI UNITS Quantity Definition SI unit Old unit Conversion Exposure DQ 10 -4 C 1 esu 10 -4 C X= 2.58 ¥ R= 1 R = 2.58 ¥ (X) Dmair kg air cm 3 airSTP kg air DE ab J erg Dose (D) D= 1 Gy = 1 1 rad = 100 1 Gy = 100 rad Dm kg g Equivalent H = DwR 1 Sv 1 rem 1 Sv = 100 rem dose (H) 1 Ci Activity (A) A = lN 1 Bq = 1 s–1 1 Ci = 3.7 × 1010 s–1 1 Bq = 3.7 ¥ 10 10 DQ is the charge of either sign collected; Dmair is the mass of air; DEab is the absorbed energy; Dm is the mass of medium; wR is the radiation weighing factor; l is the decay constant; N is the number of radioactive atoms; R stands for roentgen; Gy stands for gray; Sv stands for sievert; Bq stands for becquerel; Ci stands for curie; STP stands for standard temperature (273.2 K) and standard pressure (101.3 kPa). ● Number of atoms Na per mass of an element: Na NA = m A ● Number of electrons per volume of an element: Na N N Z = rZ a = rZ A V m A 8

BASIC RADIATION PHYSICS ● Number of electrons per mass of an element: Na Z Z = N m A A Note that (Z/A) ª 0.5 for all elements, with the one notable exception of hydrogen, for which (Z/A) = 1. Actually, (Z/A) slowly decreases from 0.5 for low Z elements to 0.4 for high Z elements. A ● In nuclear physics the convention is to designate a nucleus X as ZX, where A is the atomic mass number and Z is the atomic number; for example, the 60Co nucleus is identified as 60 Co, the 226Ra nucleus as 226 Ra. 27 88 ● In ion physics the convention is to designate ions with + or – superscripts. For example, 4He+ stands for a singly ionized 4He atom and 4He2+ stands 2 2 for a doubly ionized 4He atom, which is the a particle. ● If we assume that the mass of a molecule is equal to the sum of the masses of the atoms that make up the molecule, then for any molecular compound there are NA molecules per g-mole of the compound, where the g-mole (gram-mole or mole) in grams is defined as the sum of the atomic mass numbers of the atoms making up the molecule; for example, a g-mole of water is 18 g of water and a g-mole of CO2 is 44 g of CO2. Thus 18 g of water or 44 g of carbon dioxide contain exactly NA molecules (or 3NA atoms, since each molecule of water and carbon dioxide contains three atoms). 1.2.2. Rutherford’s model of the atom The model is based on the results of an experiment carried out by Geiger and Marsden in 1909 with a particles scattered on thin gold foils. The experiment tested the validity of the Thomson atomic model, which postulated that the positive charges and negative electrons were uniformly distributed over the spherical atomic volume, the radius of which was of the order of a few ångström. Theoretical calculations predict that the probability for an a particle to be scattered on such an atom with a scattering angle exceeding 90º is of the order of 10–3500, while the Geiger–Marsden experiment showed that approximately 1 in 104 a particles was scattered with a scattering angle q > 90º (probability 10–4). From the findings of the Geiger–Marsden experiment, Rutherford in 1911 concluded that the positive charge and most of the mass of the atom are concentrated in the atomic nucleus (diameter a few femtometres) and negative electrons are smeared over on the periphery of the atom (diameter a few ångströms). In a particle scattering the positively charged a particle has a repulsive Coulomb interaction with the more massive and positively charged nucleus. 9

CHAPTER 1 The interaction produces a hyperbolic trajectory of the a particle, and the scattering angle q is a function of the impact parameter b. The limiting case is a direct hit with b = 0 and q = p (backscattering) that, assuming conservation of energy, determines the distance of closest approach Da–N in the backscattering interaction: za Z N e 2 za Z N e 2 E K (a ) = fi Da - N = (1.15) 4pe 0 Da - N 4pe 0 E K (a ) where zα is the atomic number of the a particle; ZN is the atomic number of the scattering material; EK(a) is the initial kinetic energy of the a particle. The repulsive Coulomb force between the a particle (charge +2e) and the nucleus (charge +Ze) is governed by 1/r2 as follows: 2Ze 2 FCoul = (1.16) 4pe 0 r 2 resulting in the following b versus θ relationship: 1 q b= Da - N cot (1.17) 2 2 The differential Rutherford scattering cross-section is then expressed as follows: 2 Ê ds ˆ Ê Da - N ˆ 1 Á = Ë dW ˜ R Á 4 ˜ sin 4 (q /2) (1.18) ¯ Ë ¯ 1.2.3. Bohr’s model of the hydrogen atom Bohr expanded Rutherford’s atomic model in 1913 and based it on four postulates that combine classical, non-relativistic mechanics with the concept of angular momentum quantization. Bohr’s model successfully deals with one- electron entities such as the hydrogen atom, singly ionized helium atom, doubly ionized lithium atom, etc. 10

BASIC RADIATION PHYSICS The four Bohr postulates are as follows: ● Postulate 1: Electrons revolve about the Rutherford nucleus in well defined, allowed orbits (shells). The Coulomb force of attraction FCoul = Ze2/(4pe0r2) between the negative electrons and the positively charged nucleus is balanced by the centrifugal force Fcent = meu2/r, where Z is the number of protons in the nucleus (atomic number), r is the radius of the orbit, me is the electron mass and u is the velocity of the electron in the orbit. ● Postulate 2: While in orbit, the electron does not lose any energy despite being constantly accelerated (this postulate is in contravention of the basic law of nature, which is that an accelerated charged particle will lose part of its energy in the form of radiation). ● Postulate 3: The angular momentum L = meur of the electron in an allowed orbit is quantized and given as L=n , where n is an integer referred to as the principal quantum number and =h/(2p), where h is Planck’s constant. The simple quantization of angular momentum stipulates that the angular momentum can have only integral multiples of a basic value ( ). ● Postulate 4: An atom or ion emits radiation when an electron makes a transition from an initial orbit with quantum number ni to a final orbit with quantum number nf for ni > nf. The radius rn of a one-electron Bohr atom is given by: Ê n2 ˆ Ê n2 ˆ rn = a 0 Á ˜ = 0.529 Å Á ˜ ËZ¯ ËZ¯ (1.19) where a0 is the Bohr radius (a0 = 0.529 Å). The velocity un of the electron in a one-electron Bohr atom is: ÊZˆ c ÊZˆ un = acÁ ˜ = Ë n ¯ 137 Á n ˜ (1.20) Ë ¯ where a is the fine structure constant (a = 1/137). The energy levels for orbital electron shells in monoelectronic atoms (e.g. hydrogen, singly ionized helium and doubly ionized lithium) are given by: 2 2 ÊZˆ ÊZˆ E n = - E R Á ˜ = -13.6 eV Á ˜ (1.21) Ë n¯ Ë n¯ 11

CHAPTER 1 where ER is the Rydberg energy (13.61 eV); n is the principal quantum number (n = 1, ground state; n > 1, excited state); Z is the atomic number (Z = 1 for a hydrogen atom, Z = 2 for singly ionized helium, Z = 3 for doubly ionized lithium, etc.). The wave number k of the emitted photon is given by: 1 Ê 1 1ˆ Ê 1 1ˆ k= = R• Z 2 Á 2 - 2 ˜ = 109 737 cm -1Z 2 Á 2 - 2 ˜ (1.22) l Ë nf ni ¯ Ë nf ni ¯ where R• is the Rydberg constant. Bohr’s model results in the energy level diagram for the hydrogen atom shown in Fig. 1.2. 1.2.4. Multielectron atoms For multielectron atoms the fundamental concepts of the Bohr atomic theory provide qualitative data for orbital electron binding energies and electron transitions resulting in emission of photons. Electrons occupy allowed shells, but the number of electrons per shell is limited to 2n2, where n is the shell number (the principal quantum number). ● The K shell binding energies EB(K) for atoms with Z > 20 may be estimated with the following relationship: E B (K) = E R Z eff = E R (Z - s) 2 = E R (Z - 2) 2 2 (1.23) where Zeff, the effective atomic number, is given by Zeff = Z – s, where s is the screening constant equal to 2 for K shell electrons. ● Excitation of an atom occurs when an electron is moved from a given shell to a higher n shell that is either empty or does not contain a full complement of electrons. ● Ionization of an atom occurs when an electron is removed from the atom (i.e. the electron is supplied with enough energy to overcome its binding energy in a shell). ● Excitation and ionization processes occur in an atom through various possible interactions in which orbital electrons are supplied with a given amount of energy. Some of these interactions are: (i) Coulomb 12

BASIC RADIATION PHYSICS Continuum of electron kinetic energies 0 –0.9 eV Excited n=3 –1.5 eV states n>1 n=2 –3.4 eV Discrete energy levels Electron bound states Ground state n=1 –13.6 eV n=1 FIG. 1.2. Energy level diagram for a hydrogen atom (ground state: n = 1, excited states: n > 1). interaction with a charged particle; (ii) the photoelectric effect; (iii) the Compton effect; (iv) triplet production; (v) internal conversion; (vi) electron capture; (vii) the Auger effect; and (viii) positron annihilation. ● An orbital electron from a higher n shell will fill an electron vacancy in a lower n atomic shell. The energy difference between the two shells will be either emitted in the form of a characteristic photon or it will be transferred to a higher n shell electron, which will be ejected from the atom as an Auger electron. ● Energy level diagrams of multielectron atoms resemble those of one- electron structures, except that inner shell electrons are bound with much larger energies, as shown for a lead atom in Fig. 1.3. ● The number of characteristic photons (sometimes called fluorescent photons) emitted per orbital electron shell vacancy is referred to as fluorescent yield w, while the number of Auger electrons emitted per orbital 13

CHAPTER 1 electron vacancy is equal to (1 – w). The fluorescent yield depends on the atomic number Z of the atom and on the principal quantum number of a shell. For atoms with Z < 10 the fluorescent yield wK = 0; for Z ª 30 the fluorescent yield wK ª 0.5; and for high atomic number atoms wK = 0.96, where wK refers to the fluorescent yield for the K shell (see Fig. 1.9). 1.2.5. Nuclear structure Most of the atomic mass is concentrated in the atomic nucleus consisting of Z protons and (A – Z) neutrons, where Z is the atomic number and A is the atomic mass number of a given nucleus. Continuum of electron kinetic energies 0 n=3 M Eighteen electrons Excited –3 keV states n>1 n=2 L Eight electrons –15 keV Discrete energy levels Electron bound states Ground state n=1 K Two electrons –88 keV n=1 FIG. 1.3. Energy level diagram for a multielectron atom (lead). The n = 1, 2, 3, 4… shells are referred to as the K, L, M, O… shells, respectively. Electronic transitions that end in low n shells are referred to as X ray transitions because the resulting photons are in the X ray energy range. Electronic transitions that end in high n shells are referred to as optical transitions because they result in ultraviolet, visible or infrared photons. 14

BASIC RADIATION PHYSICS ● The radius r of the nucleus is estimated from: r = r0 3 A (1.24) where r0 is a constant (~1.4 fm) assumed equal to ½ of re, the classical electron radius. ● Protons and neutrons are commonly referred to as nucleons and are bound in the nucleus with the strong force. In contrast to electrostatic and gravitational forces, which are inversely proportional to the square of the distance between two particles, the strong force between two nucleons is a very short range force, active only at distances of the order of a few femtometres. At these short distances the strong force is the predominant force, exceeding other forces by several orders of magnitude. ● The binding energy EB per nucleon in a nucleus varies slowly with the number of nucleons A, is of the order of ~8 MeV/nucleon and exhibits a broad maximum of 8.7 MeV/nucleon at A ª 60. For a given nucleus it may be calculated from the energy equivalent of the mass deficit Dm as follows: EB = Dmc 2 /A = [Zm p c 2 + ( A - Z )mn c 2 - Mc 2 ]/A (1.25) nucleon where M is the nuclear mass in atomic mass units u (note that uc2 = 931.5 MeV); 2 mpc is the proton rest energy; mnc2 is the neutron rest energy. 1.2.6. Nuclear reactions Much of the present knowledge of the structure of nuclei comes from experiments in which a particular nuclide A is bombarded with a projectile a. The projectile undergoes one of three possible interactions: (i) elastic scattering (no energy transfer occurs; however, the projectile changes trajectory); (ii) inelastic scattering (the projectile enters the nucleus and is re- emitted with less energy and in a different direction); or (iii) nuclear reaction (the projectile a enters the nucleus A, which is transformed into nucleus B and a different particle b is emitted). 15

CHAPTER 1 ● Nuclear reactions are designated as follows: a+AÆB+b or A(a, b)B (1.26) ● A number of physical quantities are rigorously conserved in all nuclear reactions. The most important of these quantities are charge, mass number, linear momentum and mass–energy. ● The threshold energy for a nuclear reaction is defined as the smallest value of a projectile’s kinetic energy at which a nuclear reaction can take thr place. The threshold kinetic energy EK (a) of projectile a is derived from relativistic conservation of energy and momentum as: (m Bc 2 + m b c 2 ) 2 - (m A c 2 + ma c 2 ) 2 E K (a) = thr (1.27) 2m A c 2 where mA, ma, mB and mb are the rest masses of the target A, projectile a and products B and b, respectively. 1.2.7. Radioactivity Radioactivity is characterized by a transformation of an unstable nucleus into a more stable entity that may be unstable and will decay further through a chain of decays until a stable nuclear configuration is reached. The exponential laws that govern the decay and growth of radioactive substances were first formulated by Rutherford and Soddy in 1902 and then refined by Bateman in 1910. ● The activity A(t) of a radioactive substance at time t is defined as the product of the decay constant l and the number of radioactive nuclei N(t): A(t) = lN(t) (1.28) ● The simplest radioactive decay is characterized by a radioactive parent nucleus P decaying with a decay constant lP into a stable daughter nucleus D: lP P Æ D (1.29) —The number of radioactive parent nuclei NP(t) as a function of time t is governed by the following relationship: 16

BASIC RADIATION PHYSICS N P (t ) = N P (0)e - l Pt (1.30) where NP(0) is the initial number of parent nuclei at time t = 0. —Similarly, the activity of parent nuclei AP(t) at time t is given as: A P (t) = A P (0)e - l Pt (1.31) where AP(0) is the initial activity of parent nuclei at time t = 0. ● The half-life t1/2 of a radioactive substance is the time during which the number of radioactive nuclei decays to half of the initial value NP(0) present at time t = 0: N P (t = t 1 / 2 ) = (1 / 2)N P (0) = N P (0)e - l Pt 1 / 2 (1.32) ● The decay constant lP and half-life (t1/2)P for the parent are thus related as follows: ln 2 lP = (1.33) t 1/ 2 ● The specific activity a is defined as the parent’s activity per unit mass: AP lP N N N A ln 2 a= = = lP A = (1.34) m m A P A P (t 1 / 2 ) P where NA is Avogadro’s number and AP is the parent’s atomic mass number. ● The average (mean) life tP of a radioactive substance represents the average life expectancy of all parent radioactive atoms in the substance at time t = 0: • A P (0) A P (0)t P = Ú A P (0)e - l Pt dt = (1.35) lP 0 ● The decay constant lP and average life tP are thus related as follows: lP = 1/tP (1.36) resulting in the following relationship between (t1/2)P and tP: 17

CHAPTER 1 (t1/2)P = tP ln 2 (1.37) ● A more complicated radioactive decay occurs when a radioactive parent nucleus P decays with a decay constant lP into a daughter nucleus D which in turn is radioactive and decays with a decay constant lD into a stable granddaughter G: lP lD P Æ D Æ G (1.38) —The activity of the daughter A D(t) may then be expressed as: lD A D (t ) = A P (0)(e - l Pt - e - l Dt ) (1.39) lD - lP where AP(0) is the initial activity of the parent nuclei present at time t = 0 (i.e. AP(0) = lPNP(0), where NP(0) is the number of parent nuclei at t = 0). —The maximum activity of daughter nuclei occurs at time tmax given by: ln(l D /l P ) t max = (1.40) lD - lP under the condition that ND = 0 at time t = 0. ● Special considerations in parent Æ daughter Æ granddaughter relation- ships: —For lD < lP or (t1/2)D > (t1/2)P we obtain the following general relationship: AD lD = [1 - e -( l D - l P )t ] (1.41) AP lD - lP —For lD > lP or (t1/2)D < (t1/2)P we obtain transient equilibrium with: AD lD = for t >> tmax (1.42) AP lD - lP —For lD >> lP or (t1/2)D << (t1/2)P we obtain secular equilibrium and AD/AP ª 1 (1.43) 18

BASIC RADIATION PHYSICS 1.2.8. Activation of nuclides Activation of nuclides occurs when a stable parent isotope P is bombarded with neutrons in a nuclear reactor and transforms into a radioactive daughter D that decays into a granddaughter G: sf lD P Æ D Æ G (1.44) The probability for activation is determined by the cross-section s for the nuclear reaction, usually expressed in barns per atom, where 1 barn = 10–24 cm2. ● Activity of the daughter AD(t) is expressed as: sfl D A D (t ) = N (0)(e -sf t - e - l Dt ) (1.45) l D - sf P where NP(0) is the initial number of parent nuclei. ● This result is similar to the P Æ D Æ G relationship above (Eq. (1.39)) in which an unstable parent P decays into an unstable daughter D that in turn decays into granddaughter G. However, the decay constant lP in the P Æ D Æ G decay relationship is replaced by sf, where s is the cross- section for activation of the parent nuclei (cm2/atom) and f is the fluence rate of neutrons in the reactor (cm–2·s–1). ● The time tmax at which the maximum activity AD occurs in the activation process is then, similarly to Eq. (1.40), given by: lD ln sf t max = (1.46) l D - sf ● In situations where sf << lD, the daughter activity relationship of Eq. (1.45) transforms into a simple exponential growth relationship: A D (t) = sf N P (0)(1 - e - l Dt ) (1.47) ● An important example of nuclear activation is the production of the 60Co isotope by bombarding 59Co with thermal neutrons in a nuclear reactor: 59 27 Co +n Æ 60 27 Co +g (1.48) 19

CHAPTER 1 or in shorthand notation 59 Co(n, g)60 Co, with an activation cross-section s 27 27 of 37 × 10–24 cm2/atom (37 barn/atom with 1 barn = 10–24 cm2) and typical reactor neutron fluence rates f of the order of 1013 cm–2·s–1. 1.2.9. Modes of radioactive decay A radioactive parent X with atomic number Z and atomic mass number A decays into a daughter Y through the following possible modes of decay: a, b –, b +, electron capture g and internal conversion. a decay: A- 4 A ZX Æ Z - 2Y + 4 He(a ) 2 (1.49) where 4He(a) is a 4He nucleus referred to as an a particle. An example of a 2 decay is the decay of 226Ra into 222Rn with a half-life of 1600 years: 226 88 Ra Æ 222 86 Rn + 4 He 2 (1.50) b – decay: A ZX Æ A Z +1 Y + b - + ne (1.51) A neutron transforms into a proton, and an electron b – and antineutrino — n e, sharing the available energy, are ejected from the nucleus. An example of b – decay is the decay of 60Co nuclei into excited 60Ni nuclei with a half-life of 5.26 years: 60 27 Co Æ 60 28 Ni * + b - + ne (1.52) b + decay: A ZX Æ A Z -1 Y + b + + ne (1.53) A proton transforms into a neutron, and a positron b + and neutrino ne, sharing the available energy, are ejected from the nucleus. An example of b + decay is the decay of 13N into 13C: 7NÆ 6C+ 13 13 b + +n e (1.54) 20

BASIC RADIATION PHYSICS Electron capture: - A ZX + eK Æ A Z -1 Y +n e (1.55) The nucleus captures one of its own K shell orbital electrons, a proton transforms into a neutron and a neutrino ne is ejected. An example of electron capture is the decay of 125I into 125Te in an excited state, which decays to the 125 Te ground state through g decay and internal conversion: - * 53 I + e K Æ +n e 125 125 (1.56) 52 Te The resulting K shell vacancy is filled with a higher level orbital electron and the transition energy is emitted from the atom in the form of characteristic photons or Auger electrons. g decay: * A ZX Æ A ZX +g (1.57) An excited nucleus AX*, generally produced through b – or b + decay, Z attains its ground state AX through emission of one or several g photons. An Z example of g decay is the transition of the excited 60 Ni*, resulting from the b – 28 decay of 60Co, into stable 60 Ni through an emission of two g rays with energies 28 of 1.17 and 1.33 MeV. Internal conversion: A * - ZX Æ A ZX + eK (1.58) Rather than being emitted as a g photon, the nuclear excitation energy may be transferred to a K shell orbital electron that is ejected with a kinetic energy equal to the excitation energy less the orbital electron binding energy. The resulting K shell vacancy is filled with a higher level orbital electron and the transition energy is emitted in the form of characteristic photons or Auger electrons. An example of internal conversion is the decay of excited 125Te, which results from an electron capture decay of 125I, into stable 125Te through emission of 35 keV g rays (7%) and internal conversion electrons (93%). 21

CHAPTER 1 1.3. ELECTRON INTERACTIONS As an energetic electron traverses matter, it interacts with matter through Coulomb interactions with atomic orbital electrons and atomic nuclei. Through these collisions the electrons may lose their kinetic energy (collision and radiative losses) or change their direction of travel (scattering). Energy losses are described by stopping power; scattering is described by scattering power. The collisions between the incident electron and an orbital electron or nucleus of an atom may be elastic or inelastic. In an elastic collision the electron is deflected from its original path but no energy loss occurs, while in an inelastic collision the electron is deflected from its original path and some of its energy is transferred to an orbital electron or emitted in the form of brems- strahlung. Energetic electrons experience thousands of collisions as they traverse an absorber, hence their behaviour is described by a statistical theory of multiple scattering embracing the individual elastic and inelastic collisions with orbital electrons and nuclei. The type of interaction that the electron undergoes with a particular atom of radius a depends on the impact parameter b of the interaction, defined as the perpendicular distance between the electron direction before the interaction and the atomic nucleus (see Fig. 1.4). Electron trajectory Nucleus Electron cloud FIG. 1.4. Interaction of an electron with an atom, where a is the atomic radius and b is the impact parameter. 22

BASIC RADIATION PHYSICS ● For b >> a the electron will undergo a soft collision with the whole atom and only a small amount of energy will be transferred from the incident electron to orbital electrons. ● For b ª a the electron will undergo a hard collision with an orbital electron and an appreciable fraction of the electron’s kinetic energy will be transferred to the orbital electron. ● For b << a the incident electron undergoes a radiative interaction (collision) with the atomic nucleus. The electron will emit a photon (bremsstrahlung) with energy between zero and the incident electron kinetic energy. The energy of the emitted bremsstrahlung photon depends on the magnitude of the impact parameter b; the smaller the impact parameter, the higher the energy of the bremsstrahlung photon. 1.3.1. Electron–orbital electron interactions ● Coulomb interactions between the incident electron and orbital electrons of an absorber result in ionizations and excitations of absorber atoms: —Ionization: ejection of an orbital electron from the absorber atom; —Excitation: transfer of an orbital electron of the absorber atom from an allowed orbit to a higher allowed orbit (shell). ● Atomic excitations and ionizations result in collisional energy losses and are characterized by collision (ionization) stopping powers. 1.3.2. Electron–nucleus interactions ● Coulomb interactions between the incident electron and nuclei of the absorber atom result in electron scattering and energy loss of the electron through production of X ray photons (bremsstrahlung). These types of energy loss are characterized by radiative stopping powers. ● Bremsstrahlung production is governed by the Larmor relationship, which states that the power P emitted in the form of photons from an accelerated charged particle is proportional to the square of the particle acceleration a and the square of the particle charge q, or: q 2a 2 P= (1.59) 6pe 0 c 3 ● The angular distribution of the emitted photons (bremsstrahlung) is proportional to sin2 q/(1 – b cos q)5, where q is the angle between the acceleration of the charged particle and a unit vector connecting the charge with the point of observation and b is the standard relativistic u/c. 23

CHAPTER 1 ● At small velocities u of the charged particle (b Æ 0) the angular distri- bution goes as sin2 q and exhibits a maximum at q = 90º. However, as the velocity of the charged particle increases from 0 towards c, the angular distribution of the emitted photons becomes increasingly more forward peaked. ● The angle at which the photon emission intensity is maximum can be calculated from the following relationship: È 1 ˘ q max = arccos Í ( 1 + 15 b 2 - 1)˙ (1.60) Î 3b ˚ that for b Æ 0 gives qmax = p/2 and for b Æ 1 gives qmax = 0, indicating that in the diagnostic radiology energy range (orthovoltage beams) most X ray photons are emitted at 90º to the electron path, while in the megavoltage range (linac beams) most photons are emitted in the direction of the electron beam striking the target. ● The energy loss by radiation and the radiative yield g increase directly with the absorber atomic number Z and the kinetic energy of electrons. The radiation yield for X ray targets in the diagnostic radiology energy range (~100 keV) is of the order of 1%, while in the megavoltage energy range it amounts to 10–20%. 1.3.3. Stopping power The inelastic energy losses by an electron moving through a medium with density r are described by the total mass–energy stopping power (S/r)tot, which represents the kinetic energy EK loss by the electron per unit path length x, or: 1 dE K (S/r ) tot = (MeV◊ cm 2 /g) (1.61) r dx (S/r)tot consists of two components: the mass collision stopping power (S/r)col, resulting from electron–orbital electron interactions (atomic excitations and ionizations), and the mass radiative stopping power (S/r)rad, resulting from electron–nucleus interactions (bremsstrahlung production): (S/r)tot = (S/r)col + (S/r)rad (1.62) ● (S/r)col has an important role in radiation dosimetry, since the dose D in the medium may be expressed as: 24

BASIC RADIATION PHYSICS D = f(S/r)col (1.63) where f is the fluence of electrons. ● (S/r)tot is used in the calculation of electron range R as follows: E Ki -1 ÊS ˆ R= Ú 0 Á r (E K )˜ dE K Ë ¯ tot (1.64) where Eki is the initial kinetic energy of the electron. ● Both (S/r)rad and (S/r)tot are used in the determination of radiation yield (also referred to as bremsstrahlung efficiency) Y as: E Ki 1 (S/r ) rad Y= E Ki Ú 0 (S/r ) tot dE K (1.65) ● The stopping power focuses on the energy loss by an electron moving through a medium. When attention is focused on the absorbing medium, one is interested in the linear rate of energy absorption by the absorbing medium as the electron traverses the medium. The rate of energy absorption, called the linear energy transfer (LET), is defined as the average energy locally imparted to the absorbing medium by an electron of specified energy in traversing a given distance in the medium. ● In radiation dosimetry the concept of restricted stopping power (SD/r) is introduced, which accounts for that fraction of the collisional stopping power (S/r)col that includes all the soft collisions plus those hard collisions that result in delta rays with energies less than a cut-off value D. In radiation dosimetry this cut-off energy is usually taken as 10 keV, an energy that allows an electron just to traverse an ionization chamber gap of 1 mm in air. Delta rays are defined as electrons that acquire sufficiently high kinetic energies through hard collisions so as to enable them to carry this energy a significant distance away from the track of the primary particle and produce their own ionizations of absorber atoms. 1.3.4. Mass scattering power When a beam of electrons passes through an absorbing medium, the electrons undergo multiple scattering through Coulomb interactions between the incident electrons and nuclei of the absorber. The angular and spatial spread of a pencil electron beam can be approximated by a Gaussian distri- bution. The multiple scattering of electrons traversing a path length l through an absorbing medium is commonly described by the mean square angle of 25

CHAPTER 1 scattering q 2 that is proportional to the mass thickness rl of the absorber. Analogously to the definition of stopping power, the International Commission on Radiation Units and Measurements (ICRU) defines the mass scattering power T/r as: T 1 dq 2 T q2 = or = (1.66) r r dl r rl The scattering power varies approximately as the square of the absorber atomic number and inversely as the square of the electron kinetic energy. 1.4. PHOTON INTERACTIONS 1.4.1. Types of indirectly ionizing photon radiation Depending on their origin, the indirectly ionizing photon radiations fall into one of the following four categories: ● Bremsstrahlung (continuous X rays), emitted through electron–nucleus interactions. ● Characteristic X rays (discrete), emitted in transitions of orbital electrons from one allowed orbit to a vacancy in another allowed orbit. ● g rays (discrete), emitted through nuclear transitions in g decay. ● Annihilation radiation (discrete, typically 0.511 MeV), emitted through positron–electron annihilation. 1.4.2. Photon beam attenuation The intensity I(x) of a narrow monoenergetic photon beam, attenuated by an attenuator of thickness x, is given as: I ( x) = I (0)e - m ( hn , Z ) x (1.67) where I(0) is the original intensity of the unattenuated beam; m(hn, Z) is the linear attenuation coefficient, which depends on photon energy hn and attenuator atomic number Z. 26

BASIC RADIATION PHYSICS ● The half-value layer (HVL or x1/2) is defined as that thickness of the attenuator that attenuates the photon beam intensity to 50% of its original value: x1/2 = HVL = (ln 2)/m (1.68) ● Similarly, the tenth-value layer (TVL or x1/10) is defined as that thickness of the attenuator that attenuates the photon beam intensity to 10% of its original value: x1/10 = TVL = (ln 10)/m (1.69) ● HVL and TVL are thus related as follows: ln 10 x 1 / 10 = x 1 / 2 = 3.3 x 1 / 2 (1.70) ln 2 ● The mass attenuation coefficient mm, atomic attenuation coefficient am and electronic attenuation coefficient em are proportional to the linear attenuation coefficient m through the following relationships: rN A r N AZ m = rm m = am = m (1.71) A A e where r, Z and A are the density, atomic number and atomic mass number, respectively, of the attenuator. ● Typical units for the linear, mass, atomic and electronic attenuation coefficients are: cm–1, cm2/g, cm2/atom and cm2/electron, respectively, implying that thickness x in the exponent (–mx) must be given in cm, g/cm2, atoms/cm2 and electrons/cm2, respectively. ● For use in radiation dosimetry two additional attenuation coefficients are defined: the energy transfer coefficient mtr and the energy absorption coefficient mab (often designated as men). The two coefficients are related to m as follows: E tr m tr = m (1.72) hn and 27

CHAPTER 1 E ab m ab = m (1.73) hn where E tr is the average energy transferred to charged particles (electrons and positrons) in the attenuator; E ab is the average energy deposited by charged particles in the attenuator. ● The energy transfer coefficient mtr and the energy absorption coefficient mab are related through the radiative fraction g as follows: mab = mtr(1 – g) (1.74) 1.4.3. Types of photon interaction Photons may undergo various possible interactions with the atoms of an attenuator; the probability or cross-section for each interaction depends on the energy hn of the photon and on the atomic number Z of the attenuator. ● The photon interactions may be with a tightly bound electron (i.e. with an atom as a whole (photoelectric effect, coherent scattering)), with the field of the nucleus (pair production) or with an essentially free orbital electron (Compton effect, triplet production). ● In the context of photon interactions, a tightly bound electron is an orbital electron with a binding energy of the order of, or slightly larger than, the photon energy, while a free electron is an electron with a binding energy that is much smaller than the photon energy. ● During the interaction the photon may completely disappear (photo- electric effect, pair production, triplet production) or it may be scattered coherently (coherent scattering) or incoherently (Compton effect). 1.4.4. Photoelectric effect In the photoelectric effect (sometimes referred to as the photoeffect) the photon interacts with a tightly bound orbital electron of an attenuator and disappears, while the orbital electron is ejected from the atom as a photo- electron with a kinetic energy EK given as: EK = hn – EB (1.75) 28

BASIC RADIATION PHYSICS where hn is the incident photon energy and EB is the binding energy of the electron. ● The atomic attenuation coefficient for the photoelectric effect at is proportional to Z4/(hn)3, while the mass attenuation coefficient for the photoelectric effect tm is proportional to (Z/hn)3, where Z is the atomic number of the attenuator and hn is the photon energy. ● In addition to a steady decrease in tm with an increasing hn, the plot of tm versus hn also shows sharp discontinuities in tm when hn equals the binding energy for a particular electronic shell of the attenuator. These discontinuities, called absorption edges, reflect the fact that for hn less than the binding energy photons cannot undergo the photoelectric effect with electrons in that particular shell, while for hn greater than or equal to the binding energy they can. ● The average energy transferred from the photon with energy hn > EB(K) – to electrons (EK)PE in the photoelectric effect is given as follows: tr (E K ) tr = hn - PK w K E B (K) PE (1.76) where EB(K) is the binding energy of the K shell orbital electron (photo- electron), PK is the fraction of all photoelectric effect interactions that occur in the K shell and wK is the fluorescent yield for the K shell. The range of PK is from 1.0 at low atomic numbers Z to 0.8 at high atomic numbers (see Fig. 1.9). 1.4.5. Coherent (Rayleigh) scattering In coherent (Rayleigh) scattering the photon interacts with a bound orbital electron (i.e. with the combined action of the whole atom). The event is elastic in the sense that the photon loses essentially none of its energy and is scattered through only a small angle. Since no energy transfer occurs from the photon to charged particles, Rayleigh scattering plays no role in the energy transfer coefficient; however, it contributes to the attenuation coefficient. ● The atomic cross-section for Rayleigh scattering asR is proportional to (Z/hn) 2 and the mass attenuation coefficient sR/r is proportional to Z/(hn)2. ● In tissue and tissue equivalent materials the relative importance of Rayleigh scattering in comparison with other photon interactions is small, as it contributes only a few per cent or less to the total attenuation coefficient. 29

CHAPTER 1 1.4.6. Compton effect (incoherent scattering) The Compton effect (incoherent scattering) represents a photon interaction with an essentially ‘free and stationary’ orbital electron. The incident photon energy hn is much larger than the binding energy of the orbital electron. The photon loses part of its energy to the recoil (Compton) electron and is scattered as photon hn ¢ through a scattering angle q, as shown schemati- cally in Fig. 1.5. Angle f represents the angle between the incident photon direction and the direction of the recoil electron. ● The change in photon wavelength Dl is given by the well known Compton relationship: Dl = lC(1 – cos q) (1.77) where lC is the Compton wavelength of the electron, expressed as: h lC = = 0.024 Å (1.78) mec ● The relationship for Dl is calculated from equations representing conser- vation of energy and momentum in the Compton process: hn + mec2 = hn ¢ + mec2 + EK (1.79) hn hn ¢ meu = cos q + cos f (1.80) c c Êu ˆ 2 1- Á ˜ Ë c¯ and hn ¢ meu 0= sin q - sin f (1.81) c Êu ˆ 2 1- Á ˜ Ë c¯ where e is the normalized incident photon energy: hn e= mec 2 30

BASIC RADIATION PHYSICS y pn¢ cos q Recoil electron pe sin f me n pe = 2 Ênˆ 1- Á ˜ Ë c¯ Incident photon f q x h pn = c pe cos f pn¢ sin q Scattered photon hn¢ pn¢ = c FIG. 1.5. Schematic diagram of Compton scattering. An incident photon with energy hn interacts with a loosely bound (essentially free) atomic electron. The electron is ejected from the atom as a recoil (Compton) electron with kinetic energy EK and a scattered photon with energy hn¢ = hn – EK is produced (see Eq. (1.79)). and EK is the kinetic energy of the recoil electron. Equation (1.79) represents conservation of energy; Eqs (1.80) and (1.81) represent conservation of momentum along the x axis and y axis, respectively, of Fig. 1.5. ● The scattering angle q and the recoil electron angle f are related through the following relationship: cot f = (1 + e) tan(q/2) (1.82) From Eq. (1.82) it is evident that the range of angle f is between 0 for q = p (photon backscattering) and p/2 for q = 0 (photon forward scattering) for any arbitrary photon energy. For a given q, the higher the incident photon energy, the smaller is the recoil electron angle f. ● The Compton interaction represents a photon interaction with an essentially free and stationary electron (hn >> EB). Consequently, the atomic Compton attenuation coefficient asC depends linearly on the atomic 31

CHAPTER 1 number Z of the attenuator, while esC and sC/r, the electronic and mass Compton attenuation coefficients, respectively, are independent of Z. ● The electronic Compton attenuation coefficient esC steadily decreases with hn from a value of 0.665 × 10–24 cm2/electron at low photon energies to 0.21 × 10–24 cm2/electron at hn = 1 MeV; 0.051 × 10–24 cm2/electron at hn = 10 MeV; and 0.008 × 10–24 cm2/electron at hn = 100 MeV. ● The scattered photon energy hn and the kinetic energy of the Compton electron EK are given as follows: 1 e (1 - cos q ) hn ¢ = hn and E K = hn (1.83) 1 + e (1 - cos q ) 1 + e (1 - cos q ) ● The energy of photons scattered at 90º and 180º is thus given as: hn hn hn ¢(q = 90 o ) = and hn ¢(q = 180 o ) = (1.84) 1+e 1 + 2e which for large incident photon energies (e = hn/(mec2) Æ • results in mec2 and 0.5 mec2 for q = 90º and q = 180º, respectively. ● The maximum (for q = 180º (i.e. photon backscattering)) and mean fractions of the incident photon energy transferred to the Compton recoil electron are given in Fig. 1.6. The mean fraction is used in the determi- nation of the Compton effect contribution to the energy transfer coefficient. ● For example, from Fig. 1.6 we determine that a 1 MeV photon undergoing a Compton backscattering event would result in a recoil electron with a kinetic energy of 800 keV and a backscattered photon with an energy of 200 keV. ● On average, a 1 MeV photon undergoing Compton scattering will produce a 440 keV recoil electron and a 560 keV scattered photon; a 100 keV photon will produce a 15 keV recoil electron and a 85 keV scattered photon; a 10 MeV photon will produce a 6.9 MeV recoil electron and a 3.1 MeV scattered photon; and a 100 MeV photon will produce an 80 MeV recoil electron and a 20 MeV scattered photon. 1.4.7. Pair production In pair production the photon disappears and an electron–positron pair with a combined kinetic energy equal to hn – 2mec2 is produced in the nuclear Coulomb field. 32

BASIC RADIATION PHYSICS 1.0 photon energy given to Compton electron Maximum and mean fraction of incident Maximum fraction 0.8 0.6 Mean fraction 0.4 0.2 0.0 0.01 0.1 1 10 100 Photon energy (MeV) FIG. 1.6. Maximum and mean fractions of incident photon energy transferred to a Compton recoil electron in the photon energy range from 10 keV to 100 MeV. Data are obtained from the National Institute of Science and Technology (NIST) in Washington, DC (www.nist.gov). ● Since mass is produced out of photon energy in the form of an electron– positron pair, pair production has an energy threshold (minimum photon energy required for the effect to happen) of 2mec2 = 1.02 MeV. ● When pair production occurs in the field of an orbital electron, the effect is referred to as triplet production, and three particles (an electron– positron pair and the orbital electron) share the available energy. The threshold for this effect is 4mec2. ● The probability for pair production is zero for photon energies below the threshold energy and increases rapidly with photon energy above the threshold. ● The atomic attenuation coefficient for pair production ak and the mass attenuation coefficient for pair production k/r vary approximately as Z2 and Z, respectively, where Z is the atomic number of the attenuator. 33

CHAPTER 1 1.4.8. Photonuclear reactions Photonuclear reactions (also referred to as photodisintegration reactions) occur when a high energy photon is absorbed by the nucleus of an atom, resulting in an emission of a neutron ((x, n) reaction) or proton ((x, p) reaction) and a transformation of the nucleus into a radioactive reaction product. ● The threshold for a particular photonuclear reaction depends on the reaction and the nucleus and is of the order of 10 MeV or higher for most nuclei (with the exception of the deuteron and 9Be nuclei, for which the threshold is of the order of 2 MeV). ● The probability for photonuclear reactions is much smaller than that for other photon interactions, and their contribution to the total attenuation coefficient amounts to only a few per cent at photon energies above the reaction threshold. ● While photonuclear reactions do not play an active role in photon attenuation considerations, they are of concern in high energy radio- therapy treatment rooms because of the neutron production through the (x, n) reactions and because of the radioactivity that is induced in the treatment room air and in machine components through the (x, n) reaction. Both the neutrons and the radioactivity pose a health hazard to personnel and must be dealt with in the treatment room and treatment machine design. The neutron problem is dealt with special treatment room doors incorporating borated hydrogenous materials to thermalize and absorb the neutrons, the radioactivity with adequate room ventilation (six to eight air changes per hour) and use of machine components with a low reaction cross-section and short half-life of the reaction product. 1.4.9. Contributions to attenuation coefficients For a given photon energy hn and attenuator Z, the attenuation coefficient m, energy transfer coefficient mtr and energy absorption coefficient mab are given as a sum of coefficients for individual photon interactions (the energy absorption coefficient is often designated as men): m = t + sR + sC + k (1.85) PE (E K ) tr (E ) CE PP (E K ) tr m tr = t tr + (s C ) tr + k tr = t + s C K tr + k (1.86) hn hn hn 34

BASIC RADIATION PHYSICS mab = men = mtr(1 – g) (1.87) where g is the radiative fraction, and the average energies transferred to charged particles (electrons and positrons) for the photoelectric effect, the – – Compton effect and pair production are designated as (EK)PE, (EK)CE and tr tr – PP (EK)tr , respectively. – ● (EK)PE may be approximated by hn – PKwKEB(K), where EB(K) is the tr binding energy of the K shell electron, PK is the fraction of all photo- electric effect interactions that occur in the K shell and wK is the fluorescent yield for the K shell. – CE ● (EK)tr is obtained from tabulated values or from the graph shown in Fig. 1.6. – PP 2 ● (EK)tr = hn – 2mec . ● Note that in Rayleigh scattering no energy transfer occurs and therefore Rayleigh scattering contributes neither to the energy transfer coefficient nor to the energy absorption coefficient. The individual components of the attenuation coefficients, when summed, result in the total mass attenuation, mass–energy transfer and mass– energy absorption coefficients as follows: m t sR sC k (1.88) = + + + r r r r r m tr t tr (s C ) tr k tr = + + r r r r 1 Ê hn - PKw K E B (K) (E ) CE hn - 2 m ec 2 ˆ = t + s C K tr + k (1.89) rÁË hn hn hn ˜ ¯ m ab m tr = (1 - g ) (1.90) r r Figure 1.7 shows the mass attenuation coefficient m/r in (a) and the mass– energy transfer coefficient (mtr/r) and mass–energy absorption coefficient (mab/ r) in (b) for lead in the photon energy range from 10 keV to 100 MeV. 35

CHAPTER 1 1000 1000 (a) (b) L edges L edges mass–energy absorption coefficient (cm2/g) Mass–energy transfer coefficient (cm2/g) 100 100 Mass attenuation coefficient (cm2/g) 10 K edge 10 K edge and 1 1 m t r /r sc/r t /r m ab /r m /r m t r /r 0.1 0.1 tt r /r k /r mab /r sR /r 0.01 0.01 sC /r tr kt r /r 0.01 0.1 1 10 100 0.01 0.1 1 10 100 Photon energy (MeV) Photon energy (MeV) FIG. 1.7. Mass attenuation coefficient m/r (a); mass–energy transfer coefficient mtr/r and mass–energy absorption coefficient mab/r (b) for lead in the photon energy range between 10 keV and 100 MeV. The dotted–dashed curves represent contributions of individual effects, while the solid curves represent the sum of the contributions of the individual effects as given by Eq. (1.88) for m/r, Eq. (1.89) for mtr/r and Eq. (1.90) for mab/r. For photon energies below 2 MeV, mtr/r ª mab/r, because the radiative fraction g in this energy region is negligible. Above 2 MeV, g increases with photon energy, causing the divergence between the mass–energy transfer and mass–energy absorption coefficients. 1.4.10. Relative predominance of individual effects The probability for a photon to undergo any one of the various interaction phenomena with an attenuator depends on the energy hn of the photon and on the atomic number Z of the attenuating material. In general, the photoelectric effect predominates at low photon energies, the Compton effect at intermediate energies and pair production at high photon energies. Figure 1.8 shows the regions of relative predominance of the three most important individual effects with hn and Z as parameters. The two curves display the points in the (hn, Z) diagram for which asC = at or asC = ak and thus delineate the regions of photoelectric effect predominance at low photon energies, Compton effect predominance at intermediate energies and pair 36

BASIC RADIATION PHYSICS FIG. 1.8. Regions of relative predominance of the three main forms of photon interaction with matter. The left curve represents the region where the atomic coefficients for the photoelectric effect and Compton effect are equal (at = asC), the right curve is for the region where the atomic Compton coefficient equals the atomic pair production coefficient (asC = ak). production predominance at high photon energies. For example, a 100 keV photon will interact with lead (Z = 82) predominantly through the photo- electric effect and with soft tissue (Zeff = 7.5) predominantly through the Compton effect. A 10 MeV photon, on the other hand, will interact with lead predominantly through pair production and with tissue predominantly through the Compton effect. 1.4.11. Effects following photon interactions In the photoelectric effect, the Compton effect and triplet production, vacancies are produced in atomic shells through the ejection of orbital electrons. For the orthovoltage and megavoltage photons used in the diagnosis 37

CHAPTER 1 and treatment of disease with radiation, the shell vacancies occur mainly in inner atomic shells and are followed by characteristic X rays or Auger electrons, the probability for the former given by the fluorescent yield w (see Fig. 1.9), while the probability for the Auger effect is 1 – w. Pair production and triplet production are followed by the annihilation of the positron with a ‘free’ and stationary electron, producing two annihilation quanta, most commonly with energies of 0.511 MeV each and emitted at 180º from each other to satisfy the conservation of charge, momentum and energy. An annihilation of a positron before it has expended all of its kinetic energy is referred to as annihilation in flight and produces photons with energies exceeding 0.511 MeV. 1.4.12. Summary of photon interactions Table 1.4 summarizes the main characteristics of the photoeffect, Rayleigh scattering, the Compton effect and pair production. 1.0 1.0 PK PK 0.8 0.8 PL Fluorescent yields wK and wL Fractions PK and PL 0.6 0.6 0.4 0.4 wK wL 0.2 0.2 0 0 0 20 40 60 80 Atomic number Z Atomic number Z FIG. 1.9. Fluorescent yields wK for hn > (EB )K and wL for (EB )L < hn < (EB )K as well as lfractions PK for hn > (EB )K and PL for (EB )L < hn < (EB )K against the atomic number Z. Data were obtained from F.H. Attix, Introduction to Radiological Physics and Radiation Dosimetry, Wiley, New York (1986). 38

BASIC RADIATION PHYSICS TABLE 1.4. MAIN CHARACTERISTICS OF THE PHOTOELECTRIC EFFECT, RAYLEIGH SCATTERING, THE COMPTON EFFECT AND PAIR PRODUCTION Photoelectric Rayleigh Compton Pair effect scattering effect production Photon With whole atom With bound With free With nuclear interaction (bound electron) electrons electrons Coulomb field Mode of photon Photon Photon Photon Photon interaction disappears scattered scattered disappears Energy 1 1 Decreases Increases with dependence (hn ) 3 (hn ) 2 with energy energy Threshold No No No 2mec2 Linear t sR sC k attenuation coefficient Particles Photoelectron None Compton Electron– released (recoil) positron pair electron Atomic at µ Z4 asR µ Z2 a sC µZ ak µ Z2 coefficient dependence on Z Mass coefficient t sR k dependence μ Z3 μ Z Independent μ Z r r r on Z Average energy hn – PKwKEB(K) 0 (E K ) CE tr hn – 2mec2 transferred (see Fig. 1.6) Subsequent Characteristic None Characteristic Annihilation effect X ray, X ray, radiation Auger effect Auger effect Significant <20 keV <20 keV 20 keV– >10 MeV energy region 10 MeV for water 39

CHAPTER 1 1.4.13. Example of photon attenuation For 2 MeV photons in lead (Z = 82; A = 207.2 g/g-atom; r = 11.36 g/cm3) the photoelectric effect, coherent scattering, the Compton effect and pair production linear attenuation coefficients are: t = 0.055 cm–1, sR = 0.008 cm–1, sC = 0.395 cm–1 – and k = 0.056 cm–1. The average energy transferred to charged particles (EK)tr = – 1.13 MeV and the average energy absorbed in lead is (EK)ab = 1.04 MeV. Calculate the linear attenuation coefficient m; mass attenuation coefficient mm; atomic attenuation coefficient am; mass–energy transfer coefficient mtr/r; mass–energy absorption coefficient mab/r; and radiative fraction g: m = t + sR + sC + k = (0.055 + 0.008 + 0.395 + 0.056) cm–1 = 0.514 cm–1 (1.91) m 0.514 cm -1 mm = = = 0.0453 cm 2 /g (1.92) r 11.36 g/cm 3 -1 Ê rNA ˆ 207.2 g/g-atom ¥ 0.514 cm -1 am =Á m= Ë A ˜ ¯ 11.36 g/cm 3 ¥ 6.022 ¥ 10 23 atom/g-atom = 1.56 ¥ 10 -23 cm 2 /atom (1.93) m tr (E K ) tr m 1.13 MeV ¥ 0.0453 cm 2 /g = = = 0.0256 cm 2 /g (1.94) r hn r 2 MeV m ab m en (E K ) ab m 1.04 MeV ¥ 0.0453 cm 2 /g = = = = 0.0236 cm 2 /g r r hn r 2 MeV (1.95) (E K ) tr - (E K ) ab (E ) 1.04 MeV g= = 1 - K ab = 1 - = 0.08 0 (1.96) (E K ) tr (E K ) tr 1.13 MeV or 40

BASIC RADIATION PHYSICS m ab /r 0.0236 cm 2 /g g = 1- =1- = 0.08 (1.97) m tr /r 0.0256 cm 2 /g The mass–energy transfer coefficient mtr/r can also be determined using Eq. (1.89) with: hn – PKwKEB = 2 MeV – 0.8 × 0.96 × 0.088 MeV = 1.93 MeV (from Fig. 1.9) (1.98) – (EK)CE = 0.53 × 2 MeV = 1.06 MeV (from Fig. 1.6) tr (1.99) hn – 2mec2 = 2 MeV – 1.02 MeV = 0.98 MeV (1.100) to obtain m tr 1 Ê 1.93 1.06 0.98 ˆ cm 2 cm 2 = Á ¥ 0.055 + ¥ 0.395 + ¥ 0.056˜ = 0.0254 r 11.36 Ë 2 2 2 ¯ g g (1.101) in good agreement with the result obtained in Eq. (1.94). Thus, as shown schematically in Fig. 1.10, a 2 MeV photon in lead will on average: ● Transfer 1.13 MeV to charged particles (electrons and positrons); and ● 0.87 MeV will be scattered through Rayleigh and Compton scattering. Of the 1.13 MeV of energy transferred: ● 1.04 MeV will be absorbed in lead; and ● 0.09 MeV will be re-emitted through bremsstrahlung radiative loss. The radiative fraction g for 2 MeV photons in lead is 0.08. 1.4.14. Production of vacancies in atomic shells There are eight main means of producing vacancies in atomic shells and transforming the atom from a neutral state into an excited positive ion: 41

CHAPTER 1 Bremsstrahlung photon hn¢¢ = 0.09 MeV B Incident photon hn = 2 MeV A Electron track Scattered photon hn¢ = 0.87 MeV FIG. 1.10. Schematic diagram of general photon interactions with an atom. In this example a 2 MeV photon hn interacts with a lead atom. An individual 2 MeV photon, as it encounters a lead atom at point A, may interact with the atom through the photoelectric effect, Rayleigh scattering, the Compton effect or pair production, or it may not interact at all. However, for a large number of 2 MeV photons striking lead, we may state that on average: 1.13 MeV will be transferred at point A to charged particles (mainly to fast energetic electrons, but possibly also to positrons if the interaction is pair production); 0.87 MeV will be scattered through Rayleigh and Compton scattering (hn ¢). Of the 1.13 MeV transferred to charged particles: 1.04 MeV will be absorbed in lead over the fast charged particle tracks, and 0.09 MeV will be emitted in the fform of bremsstrahlung photons (hn¢¢). ● Coulomb interaction (1) of an energetic charged particle with an orbital electron. ● Photon interactions: —Photoelectric effect (2); —Compton effect (3); —Triplet production (4). ● Nuclear decay: —Electron capture (5); —Internal conversion (6). ● Positron annihilation (7). ● Auger effect (8). 42

BASIC RADIATION PHYSICS Note that pair production does not produce shell vacancies. Vacancies in inner atomic shells are not stable; they are followed by emission of character- istic photons or Auger electrons and cascade to the outer shell of the ion. The ion eventually attracts an electron from its surroundings and reverts to a neutral atom. BIBLIOGRAPHY ATTIX, F.H., Introduction to Radiological Physics and Radiation Dosimetry, Wiley, New York (1986). ATTIX, F.H., ROESCH, W.C., TOCHILIN, E., Radiation Dosimetry, Academic Press, New York (1968). EVANS, R.D., The Atomic Nucleus, McGraw-Hill, New York (1955). HALE, J., The Fundamentals of Radiological Science, Thomas, Springfield, IL (1974). JOHNS, H.E., CUNNINGHAM, J.R., The Physics of Radiology, Thomas, Springfield, IL (1984). KASE, K.R., BJARNGARD, B.E., ATTIX, F.H. (Eds), The Dosimetry of Ionizing Radiation, Academic Press, San Diego, CA (1985). KHAN, F., The Physics of Radiation Therapy, 3rd edn, Lippincott, Williams and Wilkins, Baltimore, MD (2003). ROHLF, J.W., Modern Physics from a to Z0, Wiley, New York (1994). JAYARAMAN, S., LANZL, L.H., Clinical Radiotherapy Physics, CRC Press, Boca Raton, FL (1996). 43

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Chapter 2 DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS J.P. SEUNTJENS Department of Medical Physics, McGill University Health Centre, Montreal, Quebec, Canada W. STRYDOM Department of Medical Physics, Medical University of Southern Africa, Pretoria, South Africa K.R. SHORTT Division of Human Health, International Atomic Energy Agency, Vienna 2.1. INTRODUCTION Radiation measurements and investigations of radiation effects require various specifications of the radiation field at the point of interest. Radiation dosimetry deals with methods for a quantitative determination of energy deposited in a given medium by directly or indirectly ionizing radiations. A number of quantities and units have been defined for describing the radiation beam, and the most commonly used dosimetric quantities and their units are defined below. A simplified discussion of cavity theory, the theory that deals with calculating the response of a dosimeter in a medium, is also given. 2.2. PHOTON FLUENCE AND ENERGY FLUENCE The following quantities are used to describe a monoenergetic ionizing radiation beam: particle fluence, energy fluence, particle fluence rate and energy fluence rate. These quantities are usually used to describe photon beams and may also be used in describing charged particle beams. 45

CHAPTER 2 ● The particle fluence F is the quotient dN by dA, where dN is the number of particles incident on a sphere of cross-sectional area dA: dN F= (2.1) dA The unit of particle fluence is m–2. The use of a sphere of cross-sectional area dA expresses in the simplest manner the fact that one considers an area dA perpendicular to the direction of each particle and hence that particle fluence is independent of the incident angle of the radiation. ● Planar particle fluence is the number of particles crossing a plane per unit area and hence depends on the angle of incidence of the particle beam. ● The energy fluence Y is the quotient of dE by dA, where dE is the radiant energy incident on a sphere of cross-sectional area dA: dE Y= (2.2) dA The unit of energy fluence is J/m2. Energy fluence can be calculated from particle fluence by using the following relation: dN Y= E = FE (2.3) dA where E is the energy of the particle and dN represents the number of particles with energy E. Almost all realistic photon or particle beams are polyenergetic, and the above defined concepts need to be applied to such beams. The concepts of particle fluence spectrum and energy fluence spectrum replace the particle fluence and energy fluence, respectively. They are defined respectively as: dF F E (E ) ∫ (E ) (2.4) dE and dY dF Y E (E ) ∫ (E ) = ( E )E (2.5) dE dE where FE(E) and YE(E) are shorthand notations for the particle fluence spectrum and the energy fluence spectrum differential in energy E, respec- tively. Figure 2.1 shows a photon fluence and an energy fluence spectrum generated by an orthovoltage X ray unit with a kVp value of 250 kV and an 46

DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS 0.25 Fluence (arbitrary units) Particle fluence spectrum 0.20 Energy fluence spectrum 0.15 0.10 0.05 50 100 150 200 250 Energy (keV) FIG. 2.1. Photon fluence and energy fluence spectra at 1 m from the target of an X ray machine with a tube potential of 250 kV and added filtration of 1 mm Al and 1.8 mm Cu (target material: W; inherent filtration: 2 mm Be). added filtration of 1 mm Al and 1.8 mm Cu (target material: W; inherent filtration: 2 mm Be). The two spikes superimposed on the continuous bremsstrahlung spectrum represent the Ka and the Kb characteristic X ray lines produced in the tungsten target. The particle fluence rate F is the quotient of dF by dt, where dF is the increment of the fluence in time interval dt: dF F= (2.6) dt with units of m–2◊s–1. The energy fluence rate (also referred to as intensity) is the quotient of dY by dt, where dY is the increment of the energy fluence in the time interval dt: dY Y= (2.7) dt The unit of energy fluence rate is W/m2 or J·m–2·s–1. 47

CHAPTER 2 2.3. KERMA Kerma is an acronym for kinetic energy released per unit mass. It is a non- stochastic quantity applicable to indirectly ionizing radiations such as photons and neutrons. It quantifies the average amount of energy transferred from indirectly ionizing radiation to directly ionizing radiation without concern as to what happens after this transfer. In the discussion that follows we will limit ourselves to photons. The energy of photons is imparted to matter in a two stage process. In the first stage, the photon radiation transfers energy to the secondary charged particles (electrons) through various photon interactions (the photoelectric effect, the Compton effect, pair production, etc.). In the second stage, the charged particle transfers energy to the medium through atomic excitations and ionizations. In this context, the kerma is defined as the mean energy transferred from the indirectly ionizing radiation to charged particles (electrons) in the medium dE tr per unit mass dm: dE tr K= (2.8) dm The unit of kerma is joule per kilogram (J/kg). The name for the unit of kerma is the gray (Gy), where 1 Gy = 1 J/kg. 2.4. CEMA Cema is the acronym for converted energy per unit mass. It is a non- stochastic quantity applicable to directly ionizing radiations such as electrons and protons. The cema C is the quotient of dEc by dm, where dEc is the energy lost by charged particles, except secondary electrons, in collisions in a mass dm of a material: dE c C= (2.9) dm The unit of cema is joule per kilogram (J/kg). The name for the unit of cema is the gray (Gy). 48

DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS 2.5. ABSORBED DOSE Absorbed dose is a non-stochastic quantity applicable to both indirectly and directly ionizing radiations. For indirectly ionizing radiations, energy is imparted to matter in a two step process. In the first step (resulting in kerma), the indirectly ionizing radiation transfers energy as kinetic energy to secondary charged particles. In the second step, these charged particles transfer some of their kinetic energy to the medium (resulting in absorbed dose) and lose some of their energy in the form of radiative losses (bremsstrahlung, annihilation in flight). The absorbed dose is related to the stochastic quantity energy imparted. – The absorbed dose is defined as the mean energy e imparted by ionizing radiation to matter of mass m in a finite volume V by: de D= (2.10) dm – The energy imparted e is the sum of all the energy entering the volume of interest minus all the energy leaving the volume, taking into account any mass– energy conversion within the volume. Pair production, for example, decreases the energy by 1.022 MeV, while electron–positron annihilation increases the energy by the same amount. Note that because electrons travel in the medium and deposit energy along their tracks, this absorption of energy does not take place at the same location as the transfer of energy described by kerma. The unit of absorbed dose is joule per kilogram (J/kg). The name for the unit of absorbed dose is the gray (Gy). 2.6. STOPPING POWER Stopping powers are widely used in radiation dosimetry, but they are rarely measured and must be calculated from theory. For electrons and positrons the Bethe theory is used to calculate stopping powers. The linear stopping power is defined as the expectation value of the rate of energy loss per unit path length (dE/dx) of the charged particle. The mass stopping power is defined as the linear stopping power divided by the density of the absorbing medium. Division by the density of the absorbing medium almost eliminates the dependence of the mass stopping power on mass density, except for the density effect discussed further below. Typical units for the linear and mass stopping powers are MeV/cm and MeV·cm2/g, respectively. 49

CHAPTER 2 Two types of stopping power are known: collision (ionization), resulting from interactions of charged particles with atomic orbital electrons; and radiative, resulting from interactions of charged particles with atomic nuclei. The unrestricted mass collision stopping power expresses the average rate of energy loss by a charged particle in all hard and soft collisions. ● A soft collision occurs when a charged particle passes an atom at a consid- erable distance (i.e. b >> a, where b is the impact parameter and a the atomic radius). The net effect of the collision is that a very small amount of energy is transferred to an atom of the absorbing medium in a single collision. ● In a hard collision where b ª a, a secondary electron (often referred to as a delta electron or historically as a delta ray) with considerable energy is ejected and forms a separate track. ● In the unrestricted mass collision stopping power the maximum energy transfer to an orbital electron allowed due to a hard collision is half of the kinetic energy of the electron (collision of indistinguishable particles) or the full kinetic energy of a positron (collision of distinguishable particles). The theory of the mass collision stopping power for heavy charged particles, electrons and positrons as a result of soft and hard collisions combines the Bethe theory for soft collisions with the stopping power as a result of energy transfers due to hard collisions. The result of this, for a heavy charged particle with mass M and velocity u, where the energy transfer due to hard collisions is limited to 2mec2b2/(1 – b2), where b = u/c, is: S col 4p N A Z re2 mec 2 2 È Ê 2 meu 2 ˆ C˘ = z Í ln Á ˜ - ln(1 - b ) - b - Z ˙ 2 2 (2.11) r A b 2 Î Ë I ¯ Í ˙ ˚ where re is the classical electron radius (2.82 fm); z is the projectile charge in units of electron charge; I is the mean excitation potential of the medium; C/Z is the shell correction. The mean excitation potential I is a geometric mean value of all ionization and excitation potentials of an atom of the absorbing material. Since binding effects influence the exact value of I, calculation models are often inadequate to estimate its value accurately. Hence, I values are usually derived 50

DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS from measurements of stopping powers in heavy charged particle beams, for which the effects of scattering in these measurements is minimal. For elemental materials I varies approximately linearly with Z, with, on average, I = 11.5Z. For compounds, I is calculated assuming additivity of the collision stopping power, taking into account the fraction by weight of each atom constituent in the compound. The shell correction C/Z accounts for the decrease in mass stopping power when the passing particle’s velocity has ceased to be much greater than that of the atomic electrons in the stopping medium, an effect that leads to a violation of the Born approximation, which underlies the derivation of the mass collision stopping power. The electrons in the K shell are the first affected by this, followed by the L shell electrons, etc. C/Z is a function of the medium and of the velocity of the fast charged particle. The following observations can be made about Eq. (2.11): ● The mass stopping power does not depend on the projectile mass and is proportional to the inverse square of the projectile velocity. Note that the term 2meu 2 under the logarithm has no relation to the kinetic energy of any of the particles involved in the collision process. ● The mass stopping power gradually flattens to a broad minimum for kinetic energies EK ª 3mec2. ● The leading factor Z/A is responsible for a decrease of about 20% in stopping power from carbon to lead. The term –ln I causes a further decrease in stopping power with Z. 2 ● In a given medium, the square dependence on the projectile charge (z ) causes heavy charged particles with double the charge to experience four times the stopping power. For electrons and positrons, energy transfers due to soft collisions are combined with those due to hard collisions using the Møller (for electrons) and Bhabba (for positrons) cross-sections for free electrons. The complete mass collisional stopping power for electrons and positrons, according to ICRU Report No. 37, is: S col N A Z p r02 2 mec 2 = [ln(E K /I ) 2 + ln(1 + t / 2) + F ± (t ) - d ] (2.12) r A b2 with F – given for electrons as: F –(t) = (1 – b 2)[1 + t 2/8 – (2t + 1) ln 2] 51

CHAPTER 2 and F + given for positrons as: F +(t) = 2 ln 2 – (b 2/12)[23 + 14/(t + 2) + 10/(t + 2)2 + 4/(t + 2)3] In this equation, t = EK/mec2 and b = u/c. The density effect correction d accounts for the fact that the effective Coulomb force exerted on a fast charged particle by atoms that are distant from the particle track is reduced as a result of the polarization of the medium caused by the charged particle. The density effect affects the soft collision component of the stopping power. It plays a significant role in the values of ratios of the stopping power of a dense material to that of a non-dense material (such as, for example, water to air), and various models for it have been developed. The mass radiative stopping power is the rate of energy loss by electrons or positrons that results in the production of bremsstrahlung. The Bethe– Heitler theory leads to the following formula for the mass radiative stopping power: S rad N Z2 =s0 A (E K + m e c 2 )Br (2.13) r A where s = a(e2/(4pe0mec2))2 = 5.80 × 10–28 cm2/atom, where a is the fine – structure constant and Br is a function of Z and EK, varying between 5.33 and 15 for energies in the range from less than 0.5 MeV to 100 MeV. This factor, together with the increase of the radiative stopping power proportional with EK, is responsible for the increase in total stopping power at energies above 2 MeV as depicted in Fig. 2.2. Note that the Z2 dependence of the mass radiative stopping power in contrast to the Z dependence of the mass collision stopping power makes this mode of energy loss more prominent in high Z materials. The concept of restricted mass collision stopping power is introduced to calculate the energy transferred to a localized region of interest. By limiting the energy transfer to secondary charged (delta) particles to a threshold (often denoted as D), highly energetic secondary particles are allowed to escape the region of interest. The restricted stopping power is lower than the unrestricted stopping power. The choice of the energy threshold depends on the problem at hand. For problems involving ionization chambers a frequently used threshold value is 10 keV (the range of a 10 keV electron in air is of the order of 2 mm). For microdosimetric quantities one usually takes 100 eV as a reasonable threshold value. 52

DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS Unrestricted total stopping power Total mass stopping power (MeV·cm2·g–1) Restricted total stopping power (D = 10 keV) Restricted total stopping power (D = 100 keV) 10 (S/r) (L/r) 1 (L/r) 0.01 0.10 1.00 10.00 Kinetic energy (MeV) FIG. 2.2. Unrestricted S/r and restricted ((L/r)D with D = 10 and 100 keV) total mass stopping powers for carbon (r = 1.70 g/cm3), based on data published in ICRU Report No. 37. Vertical lines indicate the points at which restricted and unrestricted mass stopping powers begin to diverge as the kinetic energy increases. The restricted linear collision stopping power (also referred to as linear energy transfer (LET)) LD of a material, for charged particles, is the quotient of dED by dl, where dED is the energy lost by a charged particle due to soft and hard collisions in traversing a distance dl minus the total kinetic energy of the charged particles released with kinetic energies in excess of D: LD = dED/dl (2.14) The restricted mass collision stopping power is the restricted linear collision stopping power divided by the density of the material. As the threshold for maximum energy transfer in the restricted stopping power increases, the restricted mass stopping power tends to the unrestricted mass stopping power for D Æ EK/2. Note also that since energy transfers to secondary electrons are limited to EK/2, unrestricted and restricted electron mass stopping powers are identical for kinetic energies lower than or equal to 2D. This is indicated in Fig. 2.2 by vertical lines at 20 keV and 200 keV. 53

CHAPTER 2 The total mass stopping power is the sum of the collision mass stopping power and the radiative mass stopping power. Figure 2.2 shows the total unrestricted and restricted (D = 10 keV, 100 keV) electron mass stopping powers for carbon, based on data in ICRU Report No. 37. 2.7. RELATIONSHIPS BETWEEN VARIOUS DOSIMETRIC QUANTITIES 2.7.1. Energy fluence and kerma (photons) The energy transferred to electrons by photons can be expended in two distinct ways: ● Through collision interactions (soft collisions and hard collisions); ● Through radiative interactions (bremsstrahlung and electron–positron annihilation). The total kerma is therefore usually divided into two components: the collision kerma Kcol and the radiative kerma Krad. ● The collision kerma Kcol is that part of kerma that leads to the production of electrons that dissipate their energy as ionization in or near the electron tracks in the medium, and is the result of Coulomb force interac- tions with atomic electrons. Thus the collision kerma is the expectation value of the net energy transferred to charged particles per unit mass at the point of interest, excluding both the radiative energy loss and energy passed from one charged particle to another. ● The radiative kerma Krad is that part of kerma that leads to the production of radiative photons as the secondary charged particles slow down and interact in the medium. These interactions most prominently are bremsstrahlung as a result of Coulomb field interactions between the charged particle and the atomic nuclei, but can also result from annihi- lation in flight. The total kerma K is thus given by the following: K = Kcol + Krad (2.15) 54

DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS The average fraction of the energy transferred to electrons that is lost through radiative processes is represented by a factor referred to as the – – radiative fraction g. Hence the fraction lost through collisions is (1 – g ). A frequently used relation between collision kerma Kcol and total kerma K may be written as follows: – Kcol = K(1 – g ) (2.16) For monoenergetic photons the collision kerma Kcol at a point in a medium is related to the energy fluence Y at that point in the medium by the following: Êm ˆ K col = Y Á en ˜ (2.17) Ë r ¯ where (men/r) is the mass–energy absorption coefficient for the monoenergetic photons in the medium. For polyenergetic beams a formally similar relation exists, but use is made of spectrum averaged quantities. If a photon energy fluence spectrum YE(E) is present at the point of interest, the collision kerma at that point is obtained as follows: E max Êm ˆ Êm ˆ K col = Ú0 Y E (E) Á en ˜ dE = Y Á en ˜ Ë r ¯ Ë r ¯ (2.18) In Eq. (2.18): E max Y= Ú0 Y E ( E ) dE stands for the total (integrated) energy fluence, and: E max Ê m en ˆ 1 m en Á r ˜=Y Ë ¯ Ú 0 Y E (E ) r ( E ) dE is a shorthand notation for the mass–energy absorption coefficient for the medium averaged over the energy fluence spectrum. For monoenergetic photons the total kerma K at a point in a medium is related to the energy fluence Y in the medium by the following: 55

CHAPTER 2 Êm ˆ K = Y Á tr ˜ (2.19) Ë r ¯ where (mtr/r) is the mass–energy transfer coefficient of the medium for the given monoenergetic photon beam. For polyenergetic beams, similarly as above, spectrum averaged mass–energy transfer coefficients can be used in conjunction with total energy fluence to obtain the total kerma. Note that, using Eq. (2.17), one can obtain the frequently used relation between collision kerma in two different materials, material 1 and material 2, as follows: Êm ˆ Y 2 Á en ˜ K col,2 Ë r ¯2 Êm ˆ = ∫ ( Y ) 2,1Á en ˜ (2.20) K col,1 Êm ˆ Ë r ¯ 2,1 Y 1Á en ˜ 1 Ë r ¯1 This equation is often used in circumstances in which the fluence ratio (Y)2,1 can be assumed to be unity through a proper scaling of dimensions (the scaling theorem), for very similar materials or for situations in which the mass of material 2 is sufficient to provide buildup but at the same time small enough so as not to disturb the photon fluence in material 1 (e.g. dose to a small mass of tissue in air). 2.7.2. Fluence and dose (electrons) Under the conditions that (a) radiative photons escape the volume of interest and (b) secondary electrons are absorbed on the spot (or there is a charged particle equilibrium (CPE) of secondary electrons), the absorbed dose to medium Dmed is related to the electron fluence Fmed in the medium as follows: ÊS ˆ Dmed = F med Á col ˜ (2.21) Ë r ¯ med where (Scol/r)med is the unrestricted mass collision stopping power of the medium at the energy of the electron. Owing to electron slowdown in a medium, even for a monoenergetic starting electron kinetic energy EK, there is always present a primary fluence spectrum that ranges in energy from EK down to zero and is commonly denoted by Fmed,E. 56

DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS In this case, the absorbed dose to the medium can be obtained by an integration of Eq. (2.20): E max ÊS ˆ ÊS ˆ Dmed = Ú0 F med,E (E) Á col ˜ Ë r ¯ med (E) dE = F med Á col ˜ Ë r ¯ med (2.22) The right hand side of Eq. (2.21) shows that absorbed dose can be calculated using a formally similar equation as Eq. (2.20) by making use of spectrum averaged collision stopping power and total fluence. Based on Eq. (2.22) and under the same assumptions, for two media, med1 and med2, the ratio of absorbed doses can be calculated as: Dmed Ê S col ˆ 2 = (F) med Á r ˜ (2.23) Dmed 1 2 ,med 1 Ë ¯ med 2 ,med 1 where the shorthand notations: ÊS ˆ (F) med and Á col ˜ 2 ,med 1 Ë r ¯ med 2 ,med 1 are being used for the ratio of the electron fluences (often referred to as the electron fluence ratio) and the collision stopping powers in the media med2 and med1, respectively. The full, realistic electron fluence spectrum consists of primary charged particles that, for example, are the result of a polyenergetic photon beam interacting in the medium. These primary charged particles are slowed down and result in secondary particle fluence. This fluence thus contains charged particles that result from slowing down through soft collisions as well as hard, knock-on collisions. Electrons created as a result of the latter process are designated delta electrons. 2.7.3. Kerma and dose (charged particle equilibrium) Generally, the transfer of energy (kerma) from the photon beam to charged particles at a particular location does not lead to the absorption of energy by the medium (absorbed dose) at the same location. This is due to the non-zero (finite) range of the secondary electrons released through photon interactions. 57

CHAPTER 2 Since radiative photons mostly escape from the volume of interest, one relates absorbed dose usually to collision kerma. In general, however, the ratio of dose and collision kerma is often denoted as: b = D/Kcol (2.24) If radiative photons escape the volume of interest, an assumption is made that b ª 1. Figure 2.3 illustrates the relation between collision kerma and absorbed dose under buildup conditions; under conditions of CPE in part (a) and under conditions of transient charged particle equilibrium (TCPE) in part (b). As a high energy photon beam penetrates the medium, collision kerma is maximal at the surface of the irradiated material because photon fluence is greatest at the surface. Initially, the charged particle fluence, and hence the absorbed dose, increases as a function of depth until the depth of dose maximum zmax is attained. If there were no photon attenuation or scattering in the medium, but yet production of electrons, a hypothetical situation, as illustrated in Fig. 2.3(a), would occur: the buildup region (with b < 1) is followed by a region of complete CPE where D = Kcol (i.e. b = 1). g In the more realistic situation, however, due to photon attenuation and scattering in the medium, a region of TCPE occurs (Fig. 2.3(b)) where there exists an essentially constant relation between collision kerma and absorbed dose. This relation is practically constant since, in high energy photon beams, the average energy of the generated electrons and hence their range does not change appreciably with depth in the medium. In the special case in which true CPE exists (at the depth of maximum dose in the medium), the relation between absorbed dose D and total kerma K is given by: — D = Kcol = K(1 – g ) (2.25) — where g is the radiative fraction, depending on the electron kinetic energy; the — higher the energy, the larger is g. The radiative fraction also depends on the material considered, with higher values of — for higher Z materials. For g electrons produced by 60Co rays in air the radiative fraction equals 0.0032. The buildup of absorbed dose is responsible for the skin sparing effect in the case of high energy photon beams. However, in practice the surface dose is small but does not equal zero because of the electron contamination in the beam due to photon interactions in the media upstream from the phantom or 58

DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS Kcol (a) Relative energy per unit mass b =1 b b <1 D Buildup CPE region zmax Depth in medium Kcol b b =1 (b) b >1 b Relative energy per unit mass b <1 D Buildup TCPE region zmax Depth in medium Zmax FIG. 2.3. Collision kerma and absorbed dose as a function of depth in a medium irradi- ated by a high energy photon beam for (a) the hypothetical case of no photon attenuation or scattering and for (b) the realistic case. 59

CHAPTER 2 due to charged particles generated in the accelerator head and beam modifying devices. 2.7.4. Collision kerma and exposure Exposure X is the quotient of dQ by dm, where dQ is the absolute value of the total charge of the ions of one sign produced in air when all the electrons and positrons liberated or created by photons in mass dm of air are completely stopped in air: dQ X= (2.26) dm The unit of exposure is coulomb per kilogram (C/kg). The unit used for exposure is the roentgen R, where 1 R = 2.58 × 10–4 C/kg. In the SI system of units, roentgen is no longer used and the unit of exposure is simply 2.58 × 10–4 C/kg of air. The average energy expended in air per ion pair formed Wair is the quotient of EK by N, where N is the mean number of ion pairs formed when the initial kinetic energy EK of a charged particle is completely dissipated in air: E Wair = (2.27) N The current best estimate for the average value of Wair is 33.97 eV/ion pair or 33.97 × 1.602 × 1019 J/ion pair: Wair 33.97 (eV/ion pair) ¥ 1.602 ¥ 10 -19 ( J/eV) = = 33.97 J/C (2.28) e 1.602 ¥ 10 -19 (C/ion pair) Multiplying the collision kerma by (e/Wair), the number of coulombs of charge created per joule of energy deposited, gives the charge created per unit mass of air or exposure: Ê e ˆ X = (K col ) air Á ˜ (2.29) Ë Wair ¯ The relation between total kerma and exposure is obtained by combining Eqs (2.25) and (2.29): ÊW ˆ 1 K air = X Á air ˜ (2.30) Ë e ¯ 1- g 60

DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS 2.8. CAVITY THEORY In order to measure the absorbed dose in a medium, it is necessary to introduce a radiation sensitive device (dosimeter) into the medium. Generally, the sensitive medium of the dosimeter will not be of the same material as the medium in which it is embedded. Cavity theory relates the absorbed dose in the dosimeter’s sensitive medium (cavity) to the absorbed dose in the surrounding medium containing the cavity. Cavity sizes are referred to as small, interme- diate or large in comparison with the ranges of secondary charged particles produced by photons in the cavity medium. If, for example, the range of charged particles (electrons) is much larger than the cavity dimensions, the cavity is regarded as small. Various cavity theories for photon beams have been developed, which depend on the size of the cavity; for example, the Bragg– Gray and Spencer–Attix theories for small cavities and the Burlin theory for cavities of intermediate sizes. 2.8.1. Bragg–Gray cavity theory The Bragg–Gray cavity theory was the first cavity theory developed to provide a relation between the absorbed dose in a dosimeter and the absorbed dose in the medium containing the dosimeter. The conditions for application of the Bragg–Gray cavity theory are: (a) The cavity must be small when compared with the range of charged particles incident on it, so that its presence does not perturb the fluence of charged particles in the medium; (b) The absorbed dose in the cavity is deposited solely by charged particles crossing it (i.e. photon interactions in the cavity are assumed negligible and thus ignored). The result of condition (a) is that the electron fluences in Eq. (2.22) are the same and equal to the equilibrium fluence established in the surrounding medium. This condition can only be valid in regions of CPE or TCPE. In addition, the presence of a cavity always causes some degree of fluence pertur- bation that requires the introduction of a fluence perturbation correction factor. Condition (b) implies that all electrons depositing the dose inside the cavity are produced outside the cavity and completely cross the cavity. No secondary electrons are therefore produced inside the cavity and no electrons stop within the cavity. 61

CHAPTER 2 Under these two conditions, according to the Bragg–Gray cavity theory, the dose to the medium Dmed is related to the dose in the cavity Dcav as follows: ÊSˆ Dmed = Dcav Á ˜ (2.31) Ë r ¯ med,cav – where (S /r)med,cav is the ratio of the average unrestricted mass collision stopping powers of the medium and the cavity. The use of unrestricted stopping powers rules out the production of secondary charged particles (or delta electrons) in the cavity and the medium. Although the cavity size is not explicitly taken into account in the Bragg– Gray cavity theory, the fulfilment of the two Bragg–Gray conditions will depend on the cavity size, which is based on the range of the electrons in the cavity medium, the cavity medium and the electron energy. A cavity that qualifies as a Bragg–Gray cavity for high energy photon beams, for example, may not behave as a Bragg–Gray cavity in a medium energy or low energy X ray beam. 2.8.2. Spencer–Attix cavity theory The Bragg–Gray cavity theory does not take into account the creation of secondary (delta) electrons generated as a result of hard collisions in the slowing down of the primary electrons in the sensitive volume of the dosimeter. The Spencer–Attix cavity theory is a more general formulation that accounts for the creation of these electrons that have sufficient energy to produce further ionization on their own account. Some of these electrons released in the gas cavity would have sufficient energy to escape from the cavity, carrying some of their energy with them. This reduces the energy absorbed in the cavity and requires modification of the stopping power of the gas. The Spencer–Attix theory operates under the two Bragg–Gray conditions; however, these conditions now even apply to the secondary particle fluence in addition to the primary particle fluence. The secondary electron fluence in the Spencer–Attix theory is divided into two components based on a user defined energy threshold D. Secondary electrons with kinetic energies EK less than D are considered slow electrons that deposit their energy locally; secondary electrons with energies larger than or equal to D are considered fast (slowing down) electrons and are part of the electron spectrum. Consequently, this spectrum has a low energy threshold of D and a high energy threshold of EK0, where EK0 represents the initial electron kinetic energy. Since the lowest energy in the spectrum is D, the maximum energy loss of a fast electron with kinetic energy EK larger than or equal to 2D 62

DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS cannot be larger than D, and the maximum energy loss of a fast electron with kinetic energy less than 2D cannot be larger than EK/2 (where D £ EK < 2D). The energy deposition must be calculated as the product of LD(EK)/r, the restricted collision stopping power with threshold D, and F e-e ,E , the fast med K electron fluence ranging in energy from D to EK0 (e-e stands for the contri- bution of delta electrons in the slowing down spectrum). Owing to the Bragg–Gray condition, which stipulates that there must not be electron production in the cavity, the electrons with energy D must be capable of crossing the cavity. The threshold value D is hence related to the cavity size and is defined as the energy of the electron with a range equal to the mean chord length across the cavity. The Spencer–Attix relation between the dose to the medium and the dose in the cavity is thus written as: Dmed/Dcav = smed,cav (2.32) where smed,cav is the ratio of the mean restricted mass collision stopping powers of the medium to that of the cavity. Using the medium electron fluence spectrum F e-e E (E K ) , the full med, K expression is: E K0 s med,cav = ÚD F e-e ,E (E K )(L D,med /r )d(E K ) + TE med med K (2.33) E K0 Ú D F e-e E (E K )(L D,cav /r )d(E K ) + TE cav med, K The terms TEmed and TEcav are called the track end terms and account for a part of the energy deposited by electrons with initial kinetic energies between D and 2D. These electrons can have an energy loss that brings their kinetic energy to lower than D. Their residual energy after such events should be deposited on the spot, and these electrons are removed from the spectrum. The track end terms are approximated by Nahum as: S med ( D) TE med = F e-e E ( D) D (2.34) med, K r and S cav ( D) TE cav = F e-e ,E ( D) D (2.35) med K r 63

CHAPTER 2 Note that the unrestricted collision stopping powers can be used here because the maximum energy transfer for an electron with energy less than 2D is less than D. Monte Carlo calculations have shown that the difference between the Spencer–Attix and Bragg–Gray cavity theories is non-negligible yet generally not very significant. Since collision stopping powers for different media show similar trends as a function of particle energy, their ratio for the two media is a very slowly varying function with energy. The value of the stopping power water to air ratio for ionization chambers is only weakly dependent on the choice of the cut-off energy. For Farmer type chambers and for parallel-plate chambers used in radiotherapy physics a nominal value of 10 keV is often used. For a typical ionization chamber used in water, the energy dependence of the stopping power water to air ratio arises mainly from the difference in the density effect correction between the two materials. 2.8.3. Considerations in the application of cavity theory to ionization chamber calibration and dosimetry protocols A dosimeter can be defined generally as any device that is capable of providing a reading that is a measure of the average absorbed dose deposited in its (the dosimeter’s) sensitive volume by ionizing radiation. A dosimeter can generally be considered as consisting of a sensitive volume filled with a given medium, surrounded by a wall of another medium. In the context of cavity theories, the sensitive volume of the dosimeter can be identified as the ‘cavity’, which may contain a gaseous, liquid or solid medium. Gas is often used as the sensitive medium, since it allows a relatively simple electrical means for collection of charges released in the sensitive medium by radiation. The medium surrounding the cavity of an ionization chamber depends on the situation in which the device is used. In an older approach, the wall (often supplemented with a buildup cap) serves as the buildup medium and the Bragg–Gray theory provides a relation between the dose in the gas and the dose in the wall. This is referred to as a thick walled ionization chamber and forms the basis of cavity chamber based air kerma in-air standards and of the Cl based dosimetry protocols of the 1970s. If, however, the chamber is used in a phantom without a buildup material, since typical wall thicknesses are much thinner than the range of the secondary electrons, the proportion of the cavity dose due to electrons generated in the phantom greatly exceeds the dose contribution from the wall, and hence the phantom medium serves as the medium and the wall is treated as a perturbation to this concept. 64

DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS In the case of a thick walled ionization chamber in a high energy photon beam, the wall thickness must be greater than the range of secondary electrons in the wall material to ensure that the electrons that cross the cavity arise in the wall and not in the medium. The Bragg–Gray cavity equation then relates the dose in the cavity to the dose in the wall of the chamber. The dose in the medium is related to the dose in the wall by means of a ratio of the mass– – energy absorption coefficients of the medium and the wall (m en/r)med,wall by assuming that: (a) The absorbed dose is the same as the collision kerma; (b) The photon fluence is not perturbed by the presence of the chamber. The dose to the cavity gas is related to the ionization produced in the cavity as follows: Q Ê W gas ˆ Dgas = (2.36) m Á e ˜ Ë ¯ where Q is the charge (of either sign) produced in the cavity and m is the mass of the gas in the cavity. Spencer–Attix cavity theory can be used to calculate the dose in the medium as: Êm ˆ Êm ˆ Dmed = Dwall Á en ˜ = Dgas s wall,gas Á en ˜ Ë r ¯ med,wall Ë r ¯ med,wall Q Ê W gas ˆ Ê m en ˆ = s (2.37) m Á e ˜ wall,gas Á r ˜ med,wall Ë ¯ Ë ¯ where swall,gas is the ratio of restricted mass collision stopping powers for a cavity wall and gas with threshold D. In practice, there are additional correction factors associated with Eq. (2.37) to satisfy assumptions (a) and (b) made above. A similar equation to Eq. (2.37) is used for air kerma in-air calibrations; however, here the quantity of interest is not the dose to the medium, but the air kerma in air. In this case, a substantial wall correction is introduced to ensure the presence of complete CPE in the wall to satisfy assumption (a) above. In the case of a thin walled ionization chamber in a high energy photon or electron beam, the wall, cavity and central electrode are treated as a 65

CHAPTER 2 perturbation to the medium fluence, and the equation now involves the ratio of restricted collision stopping powers of the medium to that of the gas smed,gas as: Q Ê W gas ˆ Dmed = s p p p p (2.38) m Á e ˜ med,gas fl dis wall cel Ë ¯ where pfl is the electron fluence perturbation correction factor; pdis is the correction factor for displacement of the effective measurement point; pwall is the wall correction factor; pcel is the correction factor for the central electrode. Values for these multiplicative correction factors are summarized for photon and electron beams in typical dosimetry protocols (see Section 9.7 for details). 2.8.4. Large cavities in photon beams A large cavity is a cavity with dimensions such that the dose contribution made by electrons inside the cavity originating from photon interactions outside the cavity can be ignored when compared with the contribution of electrons created by photon interactions within the cavity. For a large cavity the ratio of dose cavity to medium is calculated as the ratio of the collision kerma in the cavity to the medium and is therefore equal to the ratio of the average mass–energy absorption coefficients of the cavity gas – to that of the medium (m /r)gas,med: Dgas Êm ˆ (2.39) = Á en ˜ Dmed Ë r ¯ gas,med where the mass–energy absorption coefficients have been averaged over the photon fluence spectra in the cavity gas (numerator) and in the medium (denominator). 2.8.5. Burlin cavity theory for photon beams Burlin extended the Bragg–Gray and Spencer–Attix cavity theories to cavities of intermediate dimensions by introducing, on a purely phenomeno- logical basis, a large cavity limit to the Spencer–Attix equation using a 66

DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS weighting technique. He provided a formalism to calculate the value of the weighting parameter. The Burlin cavity theory can be written in its simplest form as follows: Dgas Êm ˆ = ds gas,med + (1 - d) Á en ˜ (2.40) Dmed Ë r ¯ gas,med where d is a parameter related to cavity size, approaching unity for small cavities and zero for large cavities; sgas,med is the mean ratio of the restricted mass stopping powers of the cavity and the medium; Dgas is the absorbed dose in the cavity; – (m en/r)gas,med is the mean ratio of the mass–energy absorption coefficients for the cavity and the medium. The Burlin theory effectively requires that: ● The surrounding medium and the cavity medium be homogeneous; ● A homogeneous photon field exist everywhere throughout the medium and the cavity; ● CPE exist at all points in the medium and the cavity that are further than the maximum electron range from the cavity boundary; ● The equilibrium spectra of secondary electrons generated in the medium and the cavity be the same. Burlin provided a method for estimating the weighting parameter d in his theory. It is expressed as the average value of the electron fluence reduction in the medium. Consistent with experiments with b sources he proposed that the electron fluence in the medium F e-e decays, on average, exponentially. The med value of the weighting parameter d in conjunction with the stopping power ratio can be calculated as: L ÚF e-e med e - b l dl 1 - e -b L d= 0 = (2.41) L bL ÚF 0 e-e med dl 67

CHAPTER 2 where b is an effective electron fluence attenuation coefficient that quantifies the reduction in particle fluence from its initial medium fluence value through a cavity of average length L. For convex cavities and isotropic electron fluence distributions, L can be calculated as 4V/S, where V is the cavity volume and S its surface area. Burlin described the buildup of the electron fluence F e-e inside gas the cavity using a similar, complementary equation: L ÚF gas (1 - e e-e -bl ) dl b L - 1 + e -b L 1- d = 0 = (2.42) L bL Ú 0 F e-e dl gas Burlin’s theory is consistent with the fundamental constraint of cavity theory: that the weighting factors of both terms add up to unity (i.e. d and 1 – d). It had relative success in calculating ratios of absorbed dose for some types of intermediate cavities. More generally, however, Monte Carlo calculations show that, when studying ratios of directly calculated absorbed doses in the cavity to absorbed dose in the medium as a function of cavity size, the weighting method is too simplistic and additional terms are necessary to calculate dose ratios for intermediate cavity sizes. For these and other reasons, the Burlin cavity theory is no longer used in practice. 2.8.6. Stopping power ratios Although cavity theory was designed to calculate ratios of absorbed doses, the practical application of the Spencer–Attix cavity theory has always required additional correction factors. Since the central component of the Spencer–Attix cavity theory results in averaging stopping powers, Spencer– Attix dose ratios are often referred to as ‘stopping power ratios’. In photon beams, except at or near the surface, average restricted stopping power ratios of water to air do not vary significantly as a function of depth. Stopping power ratios (with D = 10 keV) under full buildup conditions are shown in Table 2.1. Stopping power ratios not only play a role in the absolute measurement of absorbed dose, they are also relevant in performing accurate relative measurements of absorbed dose in regimes in which the energy of the secondary electrons changes significantly from one point in a phantom to another. An important example of this is apparent from Fig. 2.4, which shows restricted stopping power ratios (D = 10 keV) of water to air for electron beams as a function of depth in water. Note that these curves are for monoenergetic 68

DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS TABLE 2.1. AVERAGE RESTRICTED STOPPING POWER RATIO OF WATER TO AIR, swater,air, FOR DIFFERENT PHOTON SPECTRA IN THE RANGE FROM 60Co g RAYS TO 35 MV X RAYS Photon spectrum swater,air 60 Co 1.134 4 MV 1.131 6 MV 1.127 8 MV 1.121 10 MV 1.117 15 MV 1.106 20 MV 1.096 25 MV 1.093 35 MV 1.084 5 MeV 10 MeV 20 MeV 1.10 30 MeV 40 MeV 1.05 swater,air 1.00 0.95 5 10 15 Depth in water (cm) FIG. 2.4. Restricted collision stopping power water to air ratio (D = 10 keV) as a function of depth for different monoenergetic electron energies. 69

CHAPTER 2 electrons; protocols or codes of practice for electron dosimetry provide fits of stopping power ratios for realistic accelerator beams. However, Fig. 2.4 shows clearly that the accurate measurement of electron beam depth dose curves requires depth dependent correction factors. More detailed information on stopping power ratios is given in Section 9.5. BIBLIOGRAPHY ATTIX, F.H., Introduction to Radiological Physics and Radiation Dosimetry, Wiley, New York (1986). GREENING, J.R., Fundamentals of Radiation Dosimetry, Adam Hilger, Bristol (1981). INTERNATIONAL COMMISSION ON RADIATION UNITS AND MEASUREMENTS, Stopping Powers for Electrons and Positrons, Rep. 37, ICRU, Bethesda, MD (1984). — Fundamental Quantities and Units for Ionizing Radiation, Rep. 60, ICRU, Bethesda, MD (1998). JOHNS, H.E., CUNNINGHAM, J.R., The Physics of Radiology, Thomas, Springfield, IL (1985). KHAN, F.M., The Physics of Radiation Therapy, Lippincott, Williams and Wilkins, Baltimore, MD (2003). 70

Chapter 3 RADIATION DOSIMETERS J. IZEWSKA Division of Human Health, International Atomic Energy Agency, Vienna G. RAJAN Medical Physics and Safety Section, Bhabha Atomic Research Centre, Mumbai, Maharashtra, India 3.1. INTRODUCTION A radiation dosimeter is a device, instrument or system that measures or evaluates, either directly or indirectly, the quantities exposure, kerma, absorbed dose or equivalent dose, or their time derivatives (rates), or related quantities of ionizing radiation. A dosimeter along with its reader is referred to as a dosimetry system. Measurement of a dosimetric quantity is the process of finding the value of the quantity experimentally using dosimetry systems. The result of a measurement is the value of a dosimetric quantity expressed as the product of a numerical value and an appropriate unit. To function as a radiation dosimeter, the dosimeter must possess at least one physical property that is a function of the measured dosimetric quantity and that can be used for radiation dosimetry with proper calibration. In order to be useful, radiation dosimeters must exhibit several desirable characteristics. For example, in radiotherapy exact knowledge of both the absorbed dose to water at a specified point and its spatial distribution are of importance, as well as the possibility of deriving the dose to an organ of interest in the patient. In this context, the desirable dosimeter properties will be characterized by accuracy and precision, linearity, dose or dose rate dependence, energy response, directional dependence and spatial resolution. Obviously, not all dosimeters can satisfy all characteristics. The choice of a radiation dosimeter and its reader must therefore be made judiciously, taking into account the requirements of the measurement situation; for example, in radiotherapy ionization chambers are recommended for beam calibrations 71

CHAPTER 3 (reference dosimetry: see Chapter 9) and other dosimeters, such as those discussed below, are suitable for the evaluation of the dose distribution (relative dosimetry) or dose verification. 3.2. PROPERTIES OF DOSIMETERS 3.2.1. Accuracy and precision In radiotherapy dosimetry the uncertainty associated with the measurement is often expressed in terms of accuracy and precision. The precision of dosimetry measurements specifies the reproducibility of the measurements under similar conditions and can be estimated from the data obtained in repeated measurements. High precision is associated with a small standard deviation of the distribution of the measurement results. The accuracy of dosimetry measurements is the proximity of their expectation value to the ‘true value’ of the measured quantity. Results of measurements cannot be absolutely accurate and the inaccuracy of a measurement result is charac- terized as ‘uncertainty’. The uncertainty is a parameter that describes the dispersion of the measured values of a quantity; it is evaluated by statistical methods (type A) or by other methods (type B), has no known sign and is usually assumed to be symmetrical. The error of measurement is the difference between the measured value of a quantity and the true value of that quantity. ● An error has both a numerical value and a sign. ● Typically, the measurement errors are not known exactly, but they are estimated in the best possible way, and, where possible, compensating corrections are introduced. ● After application of all known corrections, the expectation value for errors should be zero and the only quantities of concern are the uncer- tainties. 3.2.1.1. Type A standard uncertainties If a measurement of a dosimetric quantity x is repeated N times, then the best estimate for x is x, the arithmetic mean value of all measurements xi: 72

RADIATION DOSIMETERS N Âx 1 x= i (3.1) N i =1 The standard deviation sx characterizes the average uncertainty for an individual result xi and is given by: N Â 1 sx = (x - x) 2 (3.2) N - 1 i =1 i The standard deviation of the mean value is given by: N Â (x 1 1 sx = sx = - x)2 (3.3) N N ( N - 1) i =1 i ● The standard uncertainty of type A, denoted uA, is defined as the standard deviation of the mean value, uA = s x . ● The standard uncertainty of type A is obtained by a statistical analysis of repeated measurements and, in principle, can be reduced by increasing the number of measurements. 3.2.1.2. Type B standard uncertainties Type B standard uncertainties uB cannot be estimated by repeated measurements; rather, they are intelligent guesses or scientific judgements of non-statistical uncertainties associated with the measurement. They include influences on the measuring process, application of correction factors or physical data taken from the literature. It is often assumed that type B standard uncertainties have a probability distribution, such as a normal (Gaussian) or a rectangular distribution (equal probability anywhere within the given limits). Type B standard uncertainties can be derived by estimating the limit beyond which the value of the factor is not going to lie, and a fraction of this limit is taken as uB. The fraction is chosen according to the distribution assumed. 3.2.1.3. Combined and expanded uncertainties The equation that determines a dosimetric quantity Q at a point P is of the type: 73

CHAPTER 3 N Q P = M P Fi (3.4) i =1 where M is the reading provided by the dosimetry system and Fi is the correction or conversion coefficient. ● The combined standard uncertainty uC associated with the quantity Q is a quadratic summation of type A (uA) and type B (uB) uncertainties: uC = u A + u B 2 2 (3.5) ● The combined uncertainty is assumed to exhibit a normal distribution and is multiplied by a coverage factor, denoted by k, to obtain the expanded uncertainty U = kuC. The result of the measurement of the quantity Q is then expressed by QP ± U. ● The expanded uncertainty U with the coverage factor k = 2, corre- sponding to the 95% confidence level, is often used to represent the overall uncertainty, which relates to the accuracy of the measurement of the quantity Q. 3.2.2. Linearity Ideally, the dosimeter reading M should be linearly proportional to the dosimetric quantity Q. However, beyond a certain dose range a non-linearity sets in. The linearity range and the non-linearity behaviour depend on the type of dosimeter and its physical characteristics. Two typical examples of response characteristics of dosimetry systems are shown in Fig. 3.1. Curve A first exhibits linearity with dose, then a supralinear behaviour, and finally saturation. Curve B first exhibits linearity and then saturation at high doses. In general, a non-linear behaviour should be corrected for. A dosimeter and its reader may both exhibit non-linear characteristics, but their combined effect could produce linearity over a wider range. 3.2.3. Dose rate dependence Integrating systems measure the integrated response of a dosimetry system. For such systems the measured dosimetric quantity should be independent of the rate of that quantity. 74

RADIATION DOSIMETERS Dosimeter reading A B Dose FIG. 3.1. Response characteristics of two dosimetry systems. Curve A first exhibits linearity with dose, then supralinear behaviour and finally saturation. Curve B first exhibits linearity and then saturation at high doses. Ideally, the response of a dosimetry system M/Q at two different dose rates ((dQ/dt)1 and (dQ/dt)2) should remain constant. In reality, the dose rate may influence the dosimeter readings and appropriate corrections are necessary, for example recombination corrections for ionization chambers in pulsed beams. 3.2.4. Energy dependence The response of a dosimetry system M/Q is generally a function of radiation beam quality (energy). Since the dosimetry systems are calibrated at a specified radiation beam quality (or qualities) and used over a much wider energy range, the variation of the response of a dosimetry system with radiation quality (called energy dependence) requires correction. Ideally, the energy response should be flat (i.e. the system calibration should be independent of energy over a certain range of radiation qualities). In reality, the energy correction has to be included in the determination of the quantity Q for most measurement situations. Ιn radiotherapy, the quantity of interest is the dose to water (or to tissue). As no dosimeter is water or tissue equivalent for all radiation beam qualities, the energy dependence is an important characteristic of a dosimetry system. 75

CHAPTER 3 3.2.5. Directional dependence The variation in response of a dosimeter with the angle of incidence of radiation is known as the directional, or angular, dependence of the dosimeter. Dosimeters usually exhibit directional dependence, due to their constructional details, physical size and the energy of the incident radiation. Directional dependence is important in certain applications, for example in in vivo dosimetry while using semiconductor dosimeters. Therapy dosimeters are generally used in the same geometry as that in which they are calibrated. 3.2.6. Spatial resolution and physical size Since the dose is a point quantity, the dosimeter should allow the determi- nation of the dose from a very small volume (i.e. one needs a ‘point dosimeter’ to characterize the dose at a point). Τhe position of the point where the dose is determined (i.e. its spatial location) should be well defined in a reference coordinate system. Thermoluminescent dosimeters (TLDs) come in very small dimensions and their use, to a great extent, approximates a point measurement. Film dosimeters have excellent 2-D and gels 3-D resolution, where the point measurement is limited only by the resolution of the evaluation system. Ionization chamber type dosimeters, however, are of finite size to give the required sensitivity, although the new type of pinpoint microchambers partially overcomes the problem. 3.2.7. Readout convenience Direct reading dosimeters (e.g. ionization chambers) are generally more convenient than passive dosimeters (i.e. those that are read after due processing following the exposure, for example TLDs and films). While some dosimeters are inherently of the integrating type (e.g. TLDs and gels), others can measure in both integral and differential modes (ionization chambers). 3.2.8. Convenience of use Ionization chambers are reusable, with no or little change in sensitivity within their lifespan. Semiconductor dosimeters are reusable, but with a gradual loss of sensitivity within their lifespan; however, some dosimeters are not reusable (e.g. films, gels and alanine). Some dosimeters measure dose distribution in a single exposure (e.g. films and gels) and some dosimeters are 76

RADIATION DOSIMETERS quite rugged (i.e. handling will not influence sensitivity, for example ionization chambers), while others are sensitive to handling (e.g. TLDs). 3.3. IONIZATION CHAMBER DOSIMETRY SYSTEMS 3.3.1. Chambers and electrometers Ionization chambers are used in radiotherapy and in diagnostic radiology for the determination of radiation dose. The dose determination in reference irradiation conditions is also called beam calibration (see Chapter 9 for details). Ionization chambers come in various shapes and sizes, depending upon the specific requirements, but generally they all have the following properties: ● An ionization chamber is basically a gas filled cavity surrounded by a conductive outer wall and having a central collecting electrode (see Fig. 3.2). The wall and the collecting electrode are separated with a high quality insulator to reduce the leakage current when a polarizing voltage is applied to the chamber. ● A guard electrode is usually provided in the chamber to further reduce chamber leakage. The guard electrode intercepts the leakage current and allows it to flow to ground, bypassing the collecting electrode. It also ensures improved field uniformity in the active or sensitive volume of the chamber, with resulting advantages in charge collection. ● Measurements with open air ionization chambers require temperature and pressure correction to account for the change in the mass of air in the chamber volume, which changes with the ambient temperature and pressure. Graphite Central electrode PTCFE Outer electrode Insulator Aluminium Dural FIG. 3.2. Basic design of a cylindrical Farmer type ionization chamber. 77

CHAPTER 3 Electrometers are devices for measuring small currents, of the order of 10–9 A or less. An electrometer used in conjunction with an ionization chamber is a high gain, negative feedback, operational amplifier with a standard resistor or a standard capacitor in the feedback path to measure the chamber current or charge collected over a fixed time interval, as shown schematically in Fig. 3.3. 3.3.2. Cylindrical (thimble type) ionization chambers The most popular cylindrical ionization chamber is the 0.6 cm3 chamber designed by Farmer and originally manufactured by Baldwin, but now available from several vendors, for beam calibration in radiotherapy dosimetry. Its chamber sensitive volume resembles a thimble, and hence the Farmer type chamber is also known as a thimble chamber. A schematic diagram of a Farmer type thimble ionization chamber is shown in Fig. 3.2; ionization chamber based dosimetry systems are discussed in Section 9.2. Cylindrical chambers are produced by various manufacturers, with active volumes between 0.1 and 1 cm3. They typically have an internal length no greater than 25 mm and an internal diameter no greater than 7 mm. The wall material is of low atomic number Z (i.e. tissue or air equivalent), with the thickness less than 0.1 g/cm2. A chamber is equipped with a buildup cap with a thickness of about 0.5 g/cm2 for calibration free in air using 60Co radiation. The chamber construction should be as homogeneous as possible, although an aluminium central electrode of about 1 mm in diameter is typically Cf Rf - + I V = II Rf (rate mode) Rf = feedback resistor V = (II – t)/Cf (variable to vary sensitivity) (integrated mode) Cf = feedback capacitor (variable to vary sensitivity) FIG. 3.3. Electrometer in feedback mode of operation. 78

RADIATION DOSIMETERS used to ensure flat energy dependence. Construction details of various commercially available cylindrical chambers are given in the IAEA Technical Reports Series (TRS) 277 and TRS 398 codes of practice. The use of the cylindrical chamber in electron and photon beam dosimetry is discussed in Chapter 9. 3.3.3. Parallel-plate (plane-parallel) ionization chambers A parallel-plate ionization chamber consists of two plane walls, one serving as an entry window and polarizing electrode and the other as the back wall and collecting electrode, as well as a guard ring system. The back wall is usually a block of conducting plastic or a non-conducting material (usually Perspex or polystyrene) with a thin conducting layer of graphite forming the collecting electrode and the guard ring system on top. A schematic diagram of a parallel-plate ionization chamber is shown in Fig. 3.4. The parallel-plate chamber is recommended for dosimetry of electron beams with energies below 10 MeV. It is also used for surface dose and depth dose measurements in the buildup region of megavoltage photon beams. Dose measurements in the buildup region of photon beams are discussed in Section 6.13. The characteristics of commercially available parallel-plate chambers and the use of these chambers in electron beam dosimetry are explained in detail in the TRS 381 and TRS 398 codes of practice. Some parallel-plate chambers require significant fluence perturbation correction because they are provided with an inadequate guard width. 3.3.4. Brachytherapy chambers Sources used in brachytherapy are low air kerma rate sources that require chambers of sufficient volume (about 250 cm3 or more) for adequate sensitivity. Well type chambers or re-entrant chambers are ideally suited for calibration and standardization of brachytherapy sources. Figure 3.5 shows a schematic diagram of a well type chamber. Well type chambers should be designed to accommodate sources of the typical sizes and shapes that are in clinical use in brachytherapy and are usually calibrated in terms of the reference air kerma rate. 3.3.5. Extrapolation chambers Extrapolation chambers are parallel-plate chambers with a variable sensitive volume. They are used in the measurement of surface doses in ortho- 79

CHAPTER 3 a Schnitt A–B 3 1 2 3 d m g A B FIG. 3.4. Parallel-plate ionization chamber. 1: the polarizing electrode. 2: the measuring electrode. 3: the guard ring. a: the height (electrode separation) of the air cavity. d: the diameter of the polarizing electrode. m: the diameter of the collecting electrode. g: the width of the guard ring. voltage and megavoltage X ray beams and in the dosimetry of b rays, and low energy X rays. They can also be used in absolute radiation dosimetry when directly embedded into a tissue equivalent phantom. The cavity perturbation for electrons can be eliminated by making measurements as a function of the cavity thickness and then extrapolating to zero thickness. Using this chamber, the cavity perturbation for parallel-plate chambers of finite thickness can be estimated. 80

RADIATION DOSIMETERS Source holder Collecting electrode Outer electrode (HV) Insulator To electrometer FIG. 3.5. Basic design of a brachytherapy well type chamber. 3.4. FILM DOSIMETRY 3.4.1. Radiographic film Radiographic X ray film performs several important functions in diagnostic radiology, radiotherapy and radiation protection. It can serve as a radiation detector, a relative dosimeter, a display device and an archival medium. Unexposed X ray film consists of a base of thin plastic with a radiation sensitive emulsion (silver bromide (AgBr) grains suspended in gelatin) coated uniformly on one or both sides of the base. ● Ionization of AgBr grains, as a result of radiation interaction, forms a latent image in the film. This image only becomes visible (film blackening) and permanent subsequently to processing. ● Light transmission is a function of the film opacity and can be measured in terms of optical density (OD) with devices called densitometers. ● The OD is defined as OD = log10 (I0/I) and is a function of dose. I0 is the initial light intensity and I is the intensity transmitted through the film. ● Film gives excellent 2-D spatial resolution and, in a single exposure, provides information about the spatial distribution of radiation in the area of interest or the attenuation of radiation by intervening objects. 81

CHAPTER 3 ● Τhe useful dose range of film is limited and the energy dependence is pronounced for lower energy photons. The response of the film depends on several parameters, which are difficult to control. Consistent processing of the film is a particular challenge in this regard. ● Typically, film is used for qualitative dosimetry, but with proper calibration, careful use and analysis film can also be used for dose evaluation. ● Various types of film are available for radiotherapy work (e.g. direct exposure non-screen films for field size verification, phosphor screen films used with simulators and metallic screen films used in portal imaging). ● Unexposed film would exhibit a background OD called the fog density (ODf). The density due to radiation exposure, called the net OD, can be obtained from the measured density by subtracting the fog density. ● OD readers include film densitometers, laser densitometers and automatic film scanners. The principle of operation of a simple film densi- tometer is shown in Fig. 3.6. Ideally, the relationship between the dose and OD should be linear, but this is not always the case. Some emulsions are linear, some are linear over a limited dose range and others are non-linear. The dose versus OD curve, known as the sensitometric curve (also known as the characteristic or H&D curve, in honour of Hurter and Driffield, who first investigated the relationship) must therefore be established for each film before using it for dosimetry work. A typical H&D curve for a radiographic film is shown in Fig. 3.7. It has four regions: (1) fog, at low or zero exposures; (2) toe; (3) a linear portion at Log ratio amplifier Isig _ 2.99 Film I0 + (3½ digits DPM) OD = log10 (I0/Isig) FIG. 3.6. Basic film densitometer. 82

RADIATION DOSIMETERS intermediate exposures; and (4) shoulder and saturation at high exposures. The linear portion is referred to as optimum measurement conditions, the toe is the region of underexposure and the shoulder is the region of overexposure. Important parameters of film response to radiation are gamma, latitude and speed: ● The slope of the straight line portion of the H&D curve is called the gamma of the film. ● The exposure should be chosen to make all parts of the radiograph lie on the linear portion of the H&D curve, to ensure the same contrast for all ODs. ● The latitude is defined as the range of exposures over which the ODs will lie in the linear region. ● The speed of a film is determined by giving the exposure required to produce an OD of 1.0 greater than the OD of fog. Typical applications of a radiographic film in radiotherapy are qualitative and quantitative measurements, including electron beam dosimetry, quality control of radiotherapy machines (e.g. congruence of light and radiation fields and the determination of the position of a collimator axis, the so called star 4 (4) Shoulder 3 OD (3) Linear portion 2 1 (1) Fog (2) Toe 0 1 10 100 1000 Exposure (arbitrary units) FIG. 3.7. Typical sensitometric (characteristic H&D) curve for a radiographic film. 83

CHAPTER 3 test), verification of treatment techniques in various phantoms and portal imaging. 3.4.2. Radiochromic film Radiochromic film is a new type of film in radiotherapy dosimetry. The most commonly used is a GafChromic film. It is a colourless film with a nearly tissue equivalent composition (9.0% hydrogen, 60.6% carbon, 11.2% nitrogen and 19.2% oxygen) that develops a blue colour upon radiation exposure. Radiochromic film contains a special dye that is polymerized upon exposure to radiation. The polymer absorbs light, and the transmission of light through the film can be measured with a suitable densitometer. Radiochromic film is self-developing, requiring neither developer nor fixer. Since radio- chromic film is grainless, it has a very high resolution and can be used in high dose gradient regions for dosimetry (e.g. measurements of dose distributions in stereotactic fields and in the vicinity of brachytherapy sources). Dosimetry with radiochromic films has a few advantages over radio- graphic films, such as ease of use; elimination of the need for darkroom facilities, film cassettes or film processing; dose rate independence; better energy characteristics (except for low energy X rays of 25 kV or less); and insensitivity to ambient conditions (although excessive humidity should be avoided). Radiochromic films are generally less sensitive than radiographic films and are useful at higher doses, although the dose response non-linearity should be corrected for in the upper dose region. ● Radiochromic film is a relative dosimeter. If proper care is taken with calibration and the environmental conditions, a precision better than 3% is achievable. ● Data on the various characteristics of radiochromic films (e.g. sensitivity, linearity, uniformity, reproducibility and post-irradiation stability) are available in the literature. 3.5. LUMINESCENCE DOSIMETRY Some materials, upon absorption of radiation, retain part of the absorbed energy in metastable states. When this energy is subsequently released in the form of ultraviolet, visible or infrared light, the phenomenon is called lumines- cence. Two types of luminescence, fluorescence and phosphorescence, are known, which depend on the time delay between stimulation and the emission of light. Fluorescence occurs with a time delay of between 10–10 and 10–8 s; 84

RADIATION DOSIMETERS phosphorescence occurs with a time delay exceeding 10–8 s. The process of phosphorescence can be accelerated with a suitable excitation in the form of heat or light. ● If the exciting agent is heat, the phenomenon is known as thermolumines- cence and the material is called a thermoluminescent material, or a TLD when used for purposes of dosimetry. ● If the exciting agent is light, the phenomenon is referred to as optically stimulated luminescence (OSL). As discussed in Section 1.4, the highly energetic secondary charged particles, usually electrons, that are produced in the primary interactions of photons with matter are mainly responsible for the photon energy deposition in matter. In a crystalline solid these secondary charged particles release numerous low energy free electrons and holes through ionizations of atoms and ions. The free electrons and holes thus produced will either recombine or become trapped in an electron or hole trap, respectively, somewhere in the crystal. The traps can be intrinsic or can be introduced in the crystal in the form of lattice imperfections consisting of vacancies or impurities. Two types of trap are known in general: storage traps and recombination centres. ● A storage trap merely traps free charge carriers and releases them during the subsequent (a) heating, resulting in the thermoluminescence process, or (b) irradiation with light, resulting in the OSL process. ● A charge carrier released from a storage trap may recombine with a trapped charge carrier of opposite sign in a recombination centre (luminescence centre). The recombination energy is at least partially emitted in the form of ultraviolet, visible or infrared light that can be measured with photodiodes or photomultiplier tubes (PMTs). 3.5.1. Thermoluminescence Thermoluminescence is thermally activated phosphorescence; it is the most spectacular and widely known of a number of different ionizing radiation induced thermally activated phenomena. Its practical applications range from archaeological pottery dating to radiation dosimetry. In 1968 Cameron, Suntharalingam and Kenney published a book on the thermoluminescence process that is still considered an excellent treatise on the practical aspects of the thermoluminescence phenomenon. A useful phenomenological model of the thermoluminescence mechanism is provided in terms of the band model for 85

CHAPTER 3 solids. The storage traps and recombination centres, each type characterized with an activation energy (trap depth) that depends on the crystalline solid and the nature of the trap, are located in the energy gap between the valence band and the conduction band. The states just below the conduction band represent electron traps, the states just above the valence band are hole traps. The trapping levels are empty before irradiation (i.e. the hole traps contain electrons and the electron traps do not). During irradiation the secondary charged particles lift electrons into the conduction band either from the valence band (leaving a free hole in the valence band) or from an empty hole trap (filling the hole trap). The system may approach thermal equilibrium through several means: ● Free charge carriers recombine with the recombination energy converted into heat; ● A free charge carrier recombines with a charge carrier of opposite sign trapped at a luminescence centre, the recombination energy being emitted as optical fluorescence; ● The free charge carrier becomes trapped at a storage trap, and this event is then responsible for phosphorescence or the thermoluminescence and OSL processes. 3.5.2. Thermoluminescent dosimeter systems The TLDs most commonly used in medical applications are LiF:Mg,Ti, LiF:Mg,Cu,P and Li2B4O7:Mn, because of their tissue equivalence. Other TLDs, used because of their high sensitivity, are CaSO4:Dy, Al2O3:C and CaF2:Mn. ● TLDs are available in various forms (e.g. powder, chips, rods and ribbons). ● Before they are used, TLDs need to be annealed to erase the residual signal. Well established and reproducible annealing cycles, including the heating and cooling rates, should be used. A basic TLD reader system consists of a planchet for placing and heating the TLD, a PMT to detect the thermoluminescence light emission and convert it into an electrical signal linearly proportional to the detected photon fluence and an electrometer for recording the PMT signal as a charge or current. A basic schematic diagram of a TLD reader is shown in Fig. 3.8. 86

RADIATION DOSIMETERS Electrometer HV Thermoluminescence ~ charge PMT TLD Heater FIG. 3.8. TLD reader. ● The thermoluminescence intensity emission is a function of the TLD temperature T. Keeping the heating rate constant makes the temperature T proportional to time t, and so the thermoluminescence intensity can be plotted as a function of t if a recorder output is available with the TLD measuring system. The resulting curve is called the TLD glow curve. In general, if the emitted light is plotted against the crystal temperature one obtains a thermoluminescence thermogram (Fig. 3.9). ● The peaks in the glow curve may be correlated with trap depths responsible for thermoluminescence emission. ● The main dosimetric peak of the LiF:Mg,Ti glow curve between 180ºC and 260ºC is used for dosimetry. The peak temperature is high enough so as not to be affected by room temperature and still low enough so as not to interfere with black body emission from the heating planchet. ● The total thermoluminescence signal emitted (i.e. the area under the appropriate portion of the glow curve) can be correlated to dose through proper calibration. ● Good reproducibility of heating cycles during the readout is important for accurate dosimetry. ● The thermoluminescence signal decreases in time after the irradiation due to spontaneous emission of light at room temperature. This process is called fading. Typically, for LiF:Mg,Ti, the fading of the dosimetric peak does not exceed a few per cent in the months after irradiation. ● The thermoluminescence dose response is linear over a wide range of doses used in radiotherapy, although it increases in the higher dose region, exhibiting supralinear behaviour before it saturates at even higher doses. 87

CHAPTER 3 1.0 Time after irradiation Normalized thermolumescence signal 1h 0.8 4d 20 d 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350 400 Temperature (˚C) FIG. 3.9. A typical thermogram (glow curve) of LiF:Mg,Ti measured with a TLD reader at a low heating rate. ● TLDs need to be calibrated before they are used (thus they serve as relative dosimeters). To derive the absorbed dose from the thermolumi- nescence reading a few correction factors have to be applied, such as those for energy, fading and dose response non-linearity. ● Typical applications of TLDs in radiotherapy are: in vivo dosimetry on patients (either as a routine quality assurance procedure or for dose monitoring in special cases, for example complicated geometries, dose to critical organs, total body irradiation (TBI), brachytherapy); verification of treatment techniques in various phantoms (e.g. anthropomorphic phantoms); dosimetry audits (such as the IAEA–World Health Organi- zation (WHO) TLD postal dose audit programme); and comparisons among hospitals. 3.5.3. Optically stimulated luminescence systems OSL is based on a principle similar to that of thermoluminescence dosimetry. Instead of heat, light (from a laser) is used to release the trapped energy in the form of luminescence. OSL is a novel technique offering a 88

RADIATION DOSIMETERS potential for in vivo dosimetry in radiotherapy. The integrated dose measured during irradiation can be evaluated using OSL directly afterwards. The optical fibre optically stimulated thermoluminescent dosimeter consists of a small (~1 mm3) chip of carbon doped aluminium oxide (Al2O3:C) coupled with a long optical fibre, a laser, a beam splitter and a collimator, a PMT, electronics and software. To produce OSL, the chip is excited with laser light through an optical fibre, and the resulting luminescence (blue light) is carried back in the same fibre, reflected through 90º by the beam splitter and measured in a PMT. The optical fibre dosimeter exhibits high sensitivity over the wide range of dose rates and doses used in radiotherapy. The OSL response is generally linear and independent of energy as well as the dose rate, although the angular response requires correction. Various experimental set-ups exist, such as pulsed OSL or OSL used in conjunction with radioluminescence. Radioluminescence is emitted promptly at the time of dosimeter irradiation and provides information on the dose rate during irradiation, while OSL provides the integrated dose thereafter. This technique, although not yet used routinely in radiotherapy, may prove to be a valuable tool for in vivo dosimetry in the future. 3.6. SEMICONDUCTOR DOSIMETRY 3.6.1. Silicon diode dosimetry systems A silicon diode dosimeter is a p–n junction diode. The diodes are produced by taking n type or p type silicon and counter-doping the surface to produce the opposite type material. These diodes are referred to as n–Si or p– Si dosimeters, depending upon the base material. Both types of diode are commercially available, but only the p–Si type is suitable for radiotherapy dosimetry, since it is less affected by radiation damage and has a much smaller dark current. Radiation produces electron–hole (e–h) pairs in the body of the dosimeter, including the depletion layer. The charges (minority charge carriers) produced in the body of the dosimeter, within the diffusion length, diffuse into the depleted region. They are swept across the depletion region under the action of the electric field due to the intrinsic potential. In this way a current is generated in the reverse direction in the diode. 89

CHAPTER 3 ● Diodes are used in the short circuit mode, since this mode exhibits a linear relationship between the measured charge and dose. They are usually operated without an external bias to reduce leakage current. ● Diodes are more sensitive and smaller in size than typical ionization chambers. They are relative dosimeters and should not be used for beam calibration, since their sensitivity changes with repeated use due to radiation damage. ● Diodes are particularly useful for measurement in phantoms, for example of small fields used in stereotactic radiosurgery or high dose gradient areas such as the penumbra region. They are also often used for measure- ments of depth doses in electron beams. For use with beam scanning devices in water phantoms, they are packaged in a waterproof encapsu- lation. When used in electron beam depth dose measurements, diodes measure directly the dose distribution (in contrast to the ionization measured by ionization chambers). ● Diodes are widely used in routine in vivo dosimetry on patients or for bladder or rectum dose measurements. Diodes for in vivo dosimetry are provided with buildup encapsulation and hence must be appropriately chosen, depending on the type and quality of the clinical beams. The encapsulation also protects the fragile diode from physical damage. ● Diodes need to be calibrated when they are used for in vivo dosimetry, and several correction factors have to be applied for dose calculation. The sensitivity of diodes depends on their radiation history, and hence the calibration has to be repeated periodically. ● Diodes show a variation in dose response with temperature (this is partic- ularly important for long radiotherapy treatments), dependence of signal on the dose rate (care should be taken for different source to skin distances), angular (directional) dependence and energy dependence even for small variations in the spectral composition of radiation beams (important for the measurement of entrance and exit doses). 3.6.2. MOSFET dosimetry systems A metal-oxide semiconductor field effect transistor (MOSFET), a miniature silicon transistor, possesses excellent spatial resolution and offers very little attenuation of the beam due to its small size, which is particularly useful for in vivo dosimetry. MOSFET dosimeters are based on the measurement of the threshold voltage, which is a linear function of absorbed dose. Ionizing radiation penetrating the oxide generates charge that is permanently trapped, thus causing a change in threshold voltage. The integrated dose may be measured during or after irradiation. MOSFETs 90

RADIATION DOSIMETERS require a connection to a bias voltage during irradiation. They have a limited lifespan. ● A single MOSFET dosimeter can cover the full energy range of photons and electrons, although the energy response should be examined, since it varies with radiation quality. For megavoltage beams, however, MOSFETs do not require energy correction, and a single calibration factor can be used. ● MOSFETs exhibit small axial anisotropy (±2% for 360º) and do not require dose rate corrections. ● Similarly to diodes, single MOSFETs exhibit a temperature dependence, but this effect has been overcome by specially designed double detector MOSFET systems. In general, they show non-linearity of response with the total absorbed dose; however, during their specified lifespan, MOSFETs retain adequate linearity. MOSFETs are also sensitive to changes in the bias voltage during irradiation (it must be stable), and their response drifts slightly after the irradiation (the reading must be taken in a specified time after exposure). ● MOSFETs have been in use for the past few years in a variety of radio- therapy applications for in vivo and phantom dose measurements, including routine patient dose verification, brachytherapy, TBI, intensity modulated radiotherapy (IMRT), intraoperative radiotherapy and radio- surgery. They are used with or without additional buildup, depending on the application. 3.7. OTHER DOSIMETRY SYSTEMS 3.7.1. Alanine/electron paramagnetic resonance dosimetry system Alanine, one of the amino acids, pressed in the form of rods or pellets with an inert binding material, is typically used for high dose dosimetry. The dosimeter can be used at a level of about 10 Gy or more with sufficient precision for radiotherapy dosimetry. The radiation interaction results in the formation of alanine radicals, the concentration of which can be measured using an electron paramagnetic resonance (known also as electron spin resonance) spectrometer. The intensity is measured as the peak to peak height of the central line in the spectrum. The readout is non-destructive. ● Alanine is tissue equivalent and requires no energy correction within the quality range of typical therapeutic beams. It exhibits very little fading for 91

CHAPTER 3 many months after irradiation. The response depends on environmental conditions during irradiation (temperature) and storage (humidity). ● At present, alanine’s potential application for radiotherapy is in dosimetry comparisons among hospitals. 3.7.2. Plastic scintillator dosimetry system Plastic scintillators are a relatively new development in radiotherapy dosimetry. The light generated in the scintillator during its irradiation is carried away by an optical fibre to a PMT located outside the irradiation room. A typical set-up requires two sets of optical fibres, which are coupled to two different PMTs, allowing subtraction of the background Cerenkov radiation from the measured signal. The response of the scintillation dosimeter is linear in the dose range of therapeutic interest. Plastic scintillators are almost water equivalent in terms of electron density and atomic composition. Typically, they match the water mass stopping power and mass energy absorption coefficient to within ±2% for the range of beam energies in clinical use, including the kilovoltage region. Scintillators are nearly energy independent and can thus be used directly for relative dose measurements. ● Plastic scintillation dosimeters can be made very small (about 1 mm3 or less) and yet give adequate sensitivity for clinical dosimetry. Hence they can be used in cases where high spatial resolution is required (e.g. high dose gradient regions, buildup regions, interface regions, small field dosimetry and doses very close to brachytherapy sources). Due to flat energy dependence and small size, plastic scintillators are ideal dosimeters for brachytherapy applications. ● Dosimetry based on plastic scintillators is characterized by good repro- ducibility and long term stability. Scintillators suffer no significant radiation damage (up to about 10 kGy), although the light yield should be monitored when used clinically. ● Plastic scintillators are independent of dose rate and can be used from 10 mGy/min (ophthalmic plaque dosimetry) to about 10 Gy/min (external beam dosimetry). They have no significant directional dependence and need no ambient temperature or pressure corrections. 3.7.3. Diamond dosimeters Diamonds change their resistance upon radiation exposure. When applying a bias voltage, the resulting current is proportional to the dose rate of 92

RADIATION DOSIMETERS radiation. Commercially available diamond dosimeters are designed to measure relative dose distributions in high energy photon and electron beams. The dosimeter is based on a natural diamond crystal sealed in a polystyrene housing with a bias applied through thin golden contacts. ● Diamonds have a small sensitive volume, of the order of a few cubic milli- metres, which allows the measurement of dose distributions with an excellent spatial resolution. ● Diamond dosimeters are tissue equivalent and require nearly no energy correction. Owing to their flat energy response, small physical size and negligible directional dependence, diamonds are well suited for use in high dose gradient regions, for example for stereotactic radiosurgery. ● In order to stabilize their dose response, diamonds should be irradiated prior to each use to reduce the polarization effect. They exhibit some dependence of the signal on the dose rate, which has to be corrected for when measuring a given physical quality (e.g. depth dose). Also, they have an insignificant temperature dependence, of the order of 0.1%/ºC or less. ● High sensitivity and resistance to radiation damage are other important features of diamond dosimeters. They are waterproof and can be used for measurements in a water phantom. 3.7.4. Gel dosimetry systems Gel dosimetry systems are the only true 3-D dosimeters suitable for relative dose measurements. The dosimeter is at the same time a phantom that can measure absorbed dose distribution in a full 3-D geometry. Gels are nearly tissue equivalent and can be moulded to any desired shape or form. Gel dosimetry can be divided into two types: ● Fricke gels based on the well established Fricke dosimetry; ● Polymer gels. In Fricke gels, Fe2+ ions in ferrous sulphate solutions are dispersed throughout gelatin, agarose or PVA matrix. Radiation induced changes are either due to direct absorption of radiation or via intermediate water free radicals. Upon radiation exposure, ferrous ions Fe2+ are converted into ferric ions Fe3+ with a corresponding change in paramagnetic properties that may be measured using nuclear magnetic resonance (NMR) relaxation rates or optical techniques. A 3-D image of the dose distribution is created. A major limitation of Fricke gel systems is the continual post-irradiation diffusion of ions, resulting in a blurred dose distribution. 93

CHAPTER 3 In polymer gel, monomers such as acrylamid are dispersed in a gelatin or agarose matrix. Upon radiation exposure, monomers undergo a polymerization reaction, resulting in a 3-D polymer gel matrix that is a function of absorbed dose that can be evaluated using NMR, X ray computed tomography (CT), optical tomography, vibrational spectroscopy or ultrasound. ● A number of polymer gel formulations are available, including polyacryl- amide gels, generally referred to as PAG gels (e.g. BANG gel), and the new normoxic gels (e.g. MAGIC gel); the latter are not sensitive to the presence of atmospheric oxygen. ● There is a semilinear relationship between the NMR relaxation rate and the absorbed dose at a point in the gel dosimeter. Hence, by mapping the relaxation rates using an NMR scanner, the dose map can be derived by computation and by proper calibration. ● Due to the large proportion of water, polymer gels are nearly water equivalent and no energy corrections are required for photon and electron beams used in radiotherapy. ● No significant dose rate effects in polymer gels have been observed using NMR evaluation, although dose response depends on the temperature at which the dosimeter is evaluated. The strength of the magnetic field during evaluation may also influence the dose response. Care should be taken of post-irradiation effects such as continual polymerization, gelation and strengthening of the gel matrix, which may lead to image distortion. ● Gel dosimetry is a highly promising relative dosimetry technique that may prove particularly useful for dose verification in complex clinical situations (e.g. IMRT), in anatomically shaped phantoms, and for evaluation of doses in brachytherapy, including cardiovascular brachy- therapy. 3.8. PRIMARY STANDARDS Primary standards are instruments of the highest metrological quality that permit determination of the unit of a quantity from its definition, the accuracy of which has been verified by comparison with standards of other institutions of the same level. Primary standards are realized by the primary standards dosimetry laboratories (PSDLs) in about 20 countries worldwide. Regular international comparisons between the PSDLs, and with the Bureau international des poids et mesures (BIPM), ensure international consistency of the dosimetry standards. 94

RADIATION DOSIMETERS Ionization chambers used in hospitals for calibration of radiotherapy beams must have a calibration traceable (directly or indirectly) to a primary standard. Primary standards are not used for routine calibrations, since they represent the unit for the quantity at all times. Instead, the PSDLs calibrate secondary standard dosimeters for secondary standards dosimetry laboratories (SSDLs) that in turn are used for calibrating the reference instruments of users, such as therapy level ionization chambers used in hospitals. 3.8.1. Primary standard for air kerma in air Free-air ionization chambers are the primary standard for air kerma in air for superficial and orthovoltage X rays (up to 300 kV); they cannot function as a primary standard for 60Co beams, since the air column surrounding the sensitive volume (for establishing the electronic equilibrium condition in air) would become very long. This would make the chamber very bulky and the various required corrections and their uncertainties would become problematic. ● At 60Co energy, graphite cavity ionization chambers with an accurately known chamber volume are used as the primary standard. ● The use of the graphite cavity chamber is based on the Bragg–Gray cavity theory. 3.8.2. Primary standards for absorbed dose to water The standards for absorbed dose to water enable therapy level ionization chambers to be calibrated directly in terms of absorbed dose to water instead of air kerma in air. This simplifies the dose determination procedure at the hospital level and improves the accuracy compared with the air kerma based formalism. Standards for absorbed dose to water calibration are now available for 60Co beams in several PSDLs, some of which have extended their calibration services to high energy photon and electron beams from acceler- ators. Ideally, the primary standard for absorbed dose to water should be a water calorimeter that would be an integral part of a water phantom and would measure the dose under reference conditions. However, difficulties in the establishment of this standard have led to the development of a primary standard of absorbed dose in various different ways. At present there are three basic methods used for the determination of absorbed dose to water at the primary standard level: (1) the ionometric method; (2) the total absorption method based on chemical dosimetry; and 95

CHAPTER 3 (3) calorimetry. The three methods are discussed below and in more detail in Chapter 9. 3.8.3. Ionometric standard for absorbed dose to water A graphite cavity ionization chamber with an accurately known active volume, constructed as a close approximation to a Bragg–Gray cavity, is used in a water phantom at a reference depth. Absorbed dose to water at the reference point is derived from the cavity theory using the mean specific energy imparted to the air in the cavity and the restricted stopping power ratio of the wall material to the cavity gas. The BIPM maintains an ionometric standard of absorbed dose to water. 3.8.4. Chemical dosimetry standard for absorbed dose to water In chemical dosimetry systems the dose is determined by measuring the chemical change produced in the medium (the sensitive volume of the dosimeter) using a suitable measuring system. ● The most widely used chemical dosimetry standard is the Fricke dosimeter. ● The Fricke solution has the following composition: 1mM FeSO4 or Fe(NH4)2(SO4)2 + 0.8N H2SO4 air saturated + 1mM NaCl. 2+ ● Irradiation of a Fricke solution oxidizes ferrous ions Fe into ferric ions Fe ; the latter exhibit a strong absorption peak at l = 304 nm, whereas 3+ ferrous ions do not show any absorption at this wavelength. ● Radiation induced ferric ion concentration can be determined using spectro- photometry, which measures the absorbance (in OD units) of the solution. ● The Fricke dosimeter response is expressed in terms of its sensitivity, known as the radiation chemical yield, G value, and defined as the number of moles of ferric ions produced per joule of the energy absorbed in the solution. ● The chemical dosimetry standard is realized by the calibration of a transfer dosimeter in a total absorption experiment and the subsequent application of the transfer dosimeter in a water phantom, in reference conditions. ● The response of the Fricke solution is determined first using the total absorption of an electron beam. An accurate determination of the energy response of the transfer instrument is necessary (i.e. knowing the electron energy, the beam current and the absorbing mass accurately, the total absorbed energy can be determined and related to the change in 96

RADIATION DOSIMETERS absorbance of the Fricke solution). Next, the absorbed dose to water at the reference point in a water phantom is obtained using the Fricke dosimeter as the transfer dosimeter. 3.8.5. Calorimetric standard for absorbed dose to water Calorimetry is the most fundamental method of realizing the primary standard for absorbed dose, since temperature rise is the most direct consequence of energy absorption in a medium. Graphite is in general an ideal material for calorimetry, since it is of low atomic number Z and all the absorbed energy reappears as heat, without any loss of heat in other mechanisms (such as the heat defect). The graphite calorimeter is used by several PSDLs to determine the absorbed dose to graphite in a graphite phantom. The conversion to absorbed dose to water at the reference point in a water phantom may be performed by an application of the photon fluence scaling theorem or by measurements based on cavity ionization theory. ● Graphite calorimeters are electrically calibrated by depositing a known amount of electrical energy into the core. ● Water calorimeters offer a more direct determination of the absorbed dose to water at the reference point in a water phantom. The absorbed dose to water is derived from the measured temperature rise at a point in water, relying on an accurate knowledge of the specific heat capacity. No scaling laws are required, as in the case of graphite calorimetry; however, there are corrections that need to be introduced to compensate for technical complications related to a heat defect due to water radiolysis and heat transport. ● Water calorimeters are calibrated through the calibration of their thermistors in terms of the absolute temperature difference rather than through energy deposition, as is the case for graphite calorimeters. 3.9. SUMMARY OF SOME COMMONLY USED DOSIMETRIC SYSTEMS Radiation dosimeters and dosimetry systems come in many shapes and forms, and they rely on numerous physical effects for storage and readout of the dosimetric signal. The four most commonly used radiation dosimeters are: ● Ionization chambers; ● Radiographic films; 97

CHAPTER 3 ● TLDs; ● Diodes. The strengths and weaknesses of these four dosimeters are summarized in Table 3.1. TABLE 3.1. MAIN ADVANTAGES AND DISADVANTAGES OF THE FOUR COMMONLY USED DOSIMETRIC SYSTEMS Advantage Disadvantage Ionization Accurate and precise Connecting cables required chamber Recommended for beam High voltage supply required calibration Many corrections required for Necessary corrections well high energy beam dosimetry understood Instant readout Film 2-D spatial resolution Darkroom and processing Very thin: does not perturb facilities required the beam Processing difficult to control Variation between films and batches Needs proper calibration against ionization chamber measurements Energy dependence problems Cannot be used for beam calibration TLD Small in size: point dose Signal erased during readout measurements possible Easy to lose reading Many TLDs can be exposed No instant readout in a single exposure Accurate results require care Available in various forms Readout and calibration time Some are reasonably tissue consuming equivalent Not recommended for beam Not expensive calibration Diode Small size Requires connecting cables High sensitivity Variability of calibration with Instant readout temperature No external bias voltage Change in sensitivity with Simple instrumentation accumulated dose Special care needed to ensure constancy of response Cannot be used for beam calibration 98

RADIATION DOSIMETERS BIBLIOGRAPHY ATTIX, F.H., Introduction to Radiological Physics and Radiation Dosimetry, Wiley, New York (1986). CAMERON, J.R., SUNTHARALINGAM, N., KENNEY, G.K., Thermoluminescent Dosimetry, University of Wisconsin Press, Madison, WI (1968). HORTON, J., Handbook of Radiation Therapy Physics, Prentice Hall, New York (1987). INTERNATIONAL ATOMIC ENERGY AGENCY, Absorbed Dose Determination in Photon and Electron Beams, Technical Reports Series No. 277, IAEA, Vienna (1987). — Calibration of Dosimeters Used in Radiotherapy, Technical Reports Series No. 374, IAEA, Vienna (1994). — The Use of Plane Parallel Ionization Chambers in High Energy Electron and Photon Beams, Technical Reports Series No. 381, IAEA, Vienna (1997). — Absorbed Dose Determination in External Beam Radiotherapy, Technical Reports Series No. 398, IAEA, Vienna (2000). INTERNATIONAL ORGANIZATION FOR STANDARDIZATION, Guide to Expression of Uncertainty in Measurement, ISO, Geneva (1992). KHAN, F.M., The Physics of Radiation Therapy, Lippincott, Williams and Wilkins, Baltimore, MD (2003). KLEVENHAGEN, S.C., Physics and Dosimetry of Therapy Electron Beams, Medical Physics Publishing, Madison, WI (1993). VAN DYK, J. (Ed.), Modern Technology of Radiation Oncology: A Compendium for Medical Physicists and Radiation Oncologists, Medical Physics Publishing, Madison, WI (1999). 99

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Chapter 4 RADIATION MONITORING INSTRUMENTS G. RAJAN Medical Physics and Safety Section, Bhabha Atomic Research Centre, Mumbai, Maharashtra, India J. IZEWSKA Division of Human Health, International Atomic Energy Agency, Vienna 4.1. INTRODUCTION Radiation exposure to humans can be broadly classified as internal and external exposure. Sealed sources, which are unlikely to cause internal exposure, are used almost exclusively in radiotherapy. This chapter deals with the monitoring of external exposures. ● External exposure monitoring refers to measuring: — Radiation levels in and around work areas; — Radiation levels around radiotherapy equipment or source containers; — Equivalent doses received by individuals working with radiation. ● Radiation monitoring is carried out: — To assess workplace conditions and individual exposures; — To ensure acceptably safe and satisfactory radiological conditions in the workplace; — To keep records of monitoring, over a long period of time, for the purposes of regulation or good practice. ● Radiation monitoring instruments are used both for area monitoring and for individual monitoring. The instruments used for measuring radiation levels are referred to as area survey meters (or area monitors) and the instruments used for recording the equivalent doses received by individuals working with radiation are referred to as personal dosimeters (or individual dosimeters). All instruments must be calibrated in terms of the appropriate quantities used in radiation protection. 101

CHAPTER 4 4.2. OPERATIONAL QUANTITIES FOR RADIATION MONITORING Recommendations regarding dosimetric quantities and units in radiation protection dosimetry are set forth by the International Commission on Radiation Units and Measurements (ICRU). The recommendations on the practical application of these quantities in radiation protection are established by the International Commission on Radiological Protection (ICRP). The operational quantities are defined for practical measurements both for area and individual monitoring. In radiation protection radiation is charac- terized as either weakly or strongly penetrating, depending on which dose equivalent is closer to its limiting value. In practice, the term ‘weakly penetrating’ radiation usually applies to photons below 15 keV and to b radiation. For the purpose of area monitoring, the ambient dose equivalent H*(d) and directional dose equivalent H¢(d,W) are defined. They link the external radiation field to the effective dose equivalent in the ICRU sphere phantom (see Chapter 16), at depth d, on a radius in a specified direction W. ● For strongly penetrating radiation the depth d = 10 mm is used; the ambient dose equivalent is denoted as H*(10) and the directional dose equivalent as H¢(10,W). ● For weakly penetrating radiation the ambient and directional dose equivalents in the skin at d = 0.07 mm, H*(0.07) and H¢(0.07, W), are relevant, and in the lens of the eye at d = 3 mm, H*(3) and H¢(3,W), are relevant. For individual monitoring the personal dose equivalent Hp(d) is defined, which is the dose equivalent in soft tissue below a specified point on the body at depth d (see also Chapter 16). ● For strongly penetrating radiation the depth d = 10 mm is used and the personal dose equivalent is denoted as Hp(10). ● For weakly penetrating radiation the personal dose equivalent in the skin at d = 0.07 mm, Hp(0.07), and in the lens of the eye at d = 3 mm, Hp(3), are used. ● Hp(d) can be measured with a dosimeter that is worn at the surface of the body and covered with an appropriate layer of tissue equivalent material. 102

RADIATION MONITORING INSTRUMENTS 4.3. AREA SURVEY METERS Radiation instruments used as survey monitors are either gas filled detectors or solid state detectors (e.g. scintillator or semiconductor detectors). A gas filled detector is usually cylindrical in shape, with an outer wall and a central electrode well insulated from each other. The wall is usually made of tissue equivalent material for ionization chamber detectors and of brass or copper for other types of detector. Depending upon the design of the gas filled detector and the voltage applied between the two electrodes, the detector can operate in one of three regions, shown in Fig. 4.1 (i.e. the ionization region B, proportional region C or Geiger–Müller (GM) region E). Regions of recombination and of limited proportionality in the ‘signal versus applied voltage’ plot (regions A and D, respectively, in Fig. 4.1) are not used for survey meters. 1012 Region of GM limited counter region proportionality 1010 Region of Recombination continuous discharge Number of ion pairs collected region 108 Ionization chamber region Proportional 106 region 104 (a) (b) 102 A B C D E F 100 Applied voltage FIG. 4.1. Various regions of operation of a gas filled detector. Region A represents the recombination region, region B the ionization region, region C the proportionality region, region D the region of limited proportionality and region E the GM region. Curve (a) is for 1 MeV b particles, curve (b) for 100 keV b particles. 103

CHAPTER 4 Ionization chambers GM counters Proportional counter FIG. 4.2. Area survey meters commonly used for radiation protection level measure- ments: ionization chambers, a proportional counter and GM counters. ● Survey meters come in different shapes and sizes, depending upon the specific application (see Fig. 4.2). ● The gas is usually a non-electronegative gas in order to avoid negative ion formation by electron attachment, which would increase the collection time in the detector, thus limiting the dose rate that can be monitored. The increase in charge collection time results from the relatively slow mobility of ions, which is about three orders of magnitude smaller than that of electrons. Noble gases are generally used in these detectors. ● b–g survey meters have a thin end window to register weakly penetrating radiation. The g efficiency of these detectors is only a few per cent (as determined by the wall absorption), while the b response is near 100% for b particles entering the detector. ● Owing to their high sensitivity, the tubes of GM based g monitors are smaller in size than ionization chamber type detectors. 104

RADIATION MONITORING INSTRUMENTS ● Depending upon the electronics used, detectors can operate in a ‘pulse’ mode or in the ‘mean level’ or current mode. Proportional and GM counters are normally operated in the pulse mode. ● Owing to the finite resolving time (the time required by the detector to regain its normal state after registering a pulse), these detectors will saturate at high intensity radiation fields. Ionization chambers operating in the current mode are more suitable for higher dose rate measurements. 4.3.1. Ionization chambers In the ionization region the number of primary ions of either sign collected is proportional to the energy deposited by the charged particle tracks in the detector volume. Owing to the linear energy transfer (LET) differences, the particle discrimination function can be used (see Fig. 4.1). Buildup caps are required to improve detection efficiency when measuring high energy photon radiation, but they should be removed when measuring lower energy photons (10–100 keV) and b particles. 4.3.2. Proportional counters In the proportional region there is an amplification of the primary ion signal due to ionization by collision between ions and gas molecules (charge multiplication). This occurs when, between successive collisions, the primary ions gain sufficient energy in the neighbourhood of the thin central electrode to cause further ionization in the detector. The amplification is about 103–104-fold. Proportional counters are more sensitive than ionization chambers and are suitable for measurements in low intensity radiation fields. The amount of charge collected from each interaction is proportional to the amount of energy deposited in the gas of the counter by the interaction. 4.3.3. Neutron area survey meters Neutron area survey meters operate in the proportional region so that the photon background can be easily discriminated against. ● Thermal neutron detectors usually have a coating of a boron compound on the inside of the wall, or the counter is filled with BF3 gas. ● A thermal neutron interacts with a B nucleus causing an (n, a) reaction, 10 and the a particles can easily be detected by their ionizing interactions. ● To detect fast neutrons the same counter is surrounded by a moderator made of hydrogenous material (Fig. 4.3); the whole assembly is then a fast 105

CHAPTER 4 FIG. 4.3. Neutron dose equivalent rate meter with a thermalizing polyethylene sphere with a diameter of 20 cm. neutron counter. The fast neutrons interacting with the moderator are thermalized and are subsequently detected by a BF3 counter placed inside the moderator. ● Filter compensation is applied to reduce thermal range over-response so that the response follows the ICRP radiation weighting factors wR (see Chapter 16). The output is approximately proportional to the dose equivalent in soft tissue over a wide range (10 decades) of neutron energy spectra. 3 ● Other neutron detectors (e.g. those based on He) also function on the same principles. 4.3.4. Geiger–Müller counters The discharge spreads in the GM region throughout the volume of the detector and the pulse height becomes independent of the primary ionization or the energy of the interacting particles. In a GM counter detector the gas 106

RADIATION MONITORING INSTRUMENTS multiplication spreads along the entire length of the anode. Gas filled detectors cannot be operated at voltages beyond the GM region because they continu- ously discharge. Owing to the large charge amplification (nine to ten orders of magnitude), GM survey meters are widely used at very low radiation levels (e.g. in areas of public occupancy around radiotherapy treatment rooms). They are particularly applicable for leak testing and detection of radioactive contamination. GM counters exhibit strong energy dependence at low photon energies and are not suitable for use in pulsed radiation fields. They are considered indicators of radiation, whereas ionization chambers are used for more precise measurements. GM detectors suffer from very long dead times, ranging from tens to hundreds of milliseconds. For this reason, GM counters are not used when accurate measurements are required of count rates of more than a few hundred counts per second. A portable GM survey meter may become paralysed in a very high radiation field and yield a zero reading. Ionization chambers should therefore be used in areas where radiation rates are high. 4.3.5. Scintillator detectors Detectors based on scintillation (light emission) are known as scintil- lation detectors and belong to the class of solid state detectors. Certain organic and inorganic crystals contain activator atoms, emit scintillations upon absorption of radiation and are referred to as phosphors. High atomic number phosphors are mostly used for the measurement of g rays, while plastic scintil- lators are mostly used with b particles. ● Scintillating phosphors include solid organic materials such as anthracene, stilbene and plastic scintillators as well as thallium activated inorganic phosphors such as NaI(Tl) or CsI(Tl). ● A photomultiplier tube (PMT) is optically coupled to the scintillator to convert the light pulse into an electric pulse. Some survey meters use photodiodes in place of PMTs. 4.3.6. Semiconductor detectors Bulk conductivity detectors are formed from intrinsic semiconductors of very high bulk resistivity (e.g. CdS or CdSe). They act like solid state ionization chambers on exposure to radiation and, like scintillation detectors, belong to the class of solid state detectors. 107

CHAPTER 4 Extrinsic (i.e. doped with trace quantities of impurities such as phosphorus or lithium) semiconductors such as silicon or germanium are used to form junction detectors. They too act as solid state ionization chambers on application of a reverse bias to the detectors and on exposure to radiation. The sensitivity of solid state detectors is about 104 times higher than that of gas filled detectors, owing to the lower average energy required to produce an ion pair in solid detector materials compared with air (typically one order of magnitude lower) and the higher density of the solid detector materials compared with air (typically three orders of magnitude higher). These properties facilitate the miniaturization of solid state radiation monitoring instruments. 4.3.7. Commonly available features of area survey meters The commonly available features of area survey meters are: ● A ‘low battery’ visual indication; ● Automatic zeroing, automatic ranging and automatic back-illumination facilities; ● A variable response time and memory to store the data; ● The option of both ‘rate’ and ‘integrate’ modes of operation; ● An analog or digital display, marked in conventional (exposure/air kerma) or ‘ambient dose equivalent’ or ‘personal dose equivalent’ units; ● An audio indication of radiation levels (through the ‘chirp’ rate); ● A resettable/non-resettable alarm facility with adjustable alarm levels; ● A visual indication of radiation with flashing LEDs; ● Remote operation and display of readings. 4.3.8. Calibration of survey meters Protection level area survey meters must be calibrated against a reference instrument that is traceable (directly or indirectly) to a national standards laboratory. A reference instrument for g radiation is generally an ionization chamber (Fig. 4.4) with a measuring assembly. Reference instruments do not indicate directly the dose equivalent H required for calibration of radiation protection monitoring instruments. Rather, they measure basic radiation quantities such as the air kerma in air for photon radiation, and the dose equivalent H is then determined by using appropriate conversion coefficients h: H = hNRMR (4.1) 108

RADIATION MONITORING INSTRUMENTS 1-L ionization chamber Cs-137 irradiator FIG. 4.4. Reference ionization chamber used for the calibration of area survey meters in a 137Cs g beam. where NR is the calibration factor (e.g. in terms of air kerma in air or air kerma rate in air) of the reference chamber under reference conditions; MR is the reading of the reference instrument corrected for influence quantities. A reference instrument is calibrated free in air for the range of reference radiation qualities (defined by the International Organization for Standardi- zation (ISO)). The same reference qualities should be used for the calibration of radiation protection monitoring instruments. 109

CHAPTER 4 Typically, calibration of survey meters in terms of the ambient dose equivalent H*(10) involves three steps: ● The air kerma in air is measured in a reference field, using a reference standard. ● The values of the conversion coefficient: hH* = [H*(10)/(Kair)air] are theoretically available. Using these data for the calibration beam quality, a reference instrument reading can be converted to H*(10). ● The survey monitor being calibrated is then placed at the calibration point and its reading M is determined. The calibration factor in terms of the ambient dose equivalent NH* for the survey monitor is determined from the equation NH* = H*(10)/M. 4.3.9. Properties of survey meters 4.3.9.1. Sensitivity The sensitivity S is defined as the inverse of the calibration coefficient N. Using decade resistances, larger detector volumes or detector gases under higher pressures, a wide range of equivalent dose rates can be covered with ionization chamber based survey meters (e.g. 1 mSv/h–1 Sv/h). Owing to finite resolving time, GM based systems would saturate beyond a few thousand counts per second. Low dead time counters or dead time correction circuits enable these detectors to operate at higher intensity radiation fields. Scintillation based systems are more sensitive than GM counters because of higher g conversion efficiency and dynode amplification. Scintillation based systems are generally used for surveys at very low radiation levels (e.g. contam- ination monitoring and lost source detection surveys). However, they can also be used at higher radiation levels, since their resolving time is quite low (a few microseconds or lower) compared with GM counters. 4.3.9.2. Energy dependence Survey meters are calibrated at one or more beam qualities, but are often used in situations in which the radiation field is complex or unknown. These survey meters should hence have a low energy dependence over a wide energy range. 110

RADIATION MONITORING INSTRUMENTS In the past, survey meters were designed to exhibit a flat energy response that follows exposure or air kerma in air. For measuring the equivalent dose: NH* = [H*(10)/M] = [H*(10)/(Kair)air]/[(Kair)air/M] a meter’s response with energy should vary as the quantity: [H*(10)/(Kair)air] GM counters exhibit strong energy dependence for low energy photons (<80 keV). 4.3.9.3. Directional dependence By rotating the survey monitor about its vertical axis, the directional response of the instrument can be studied. A survey monitor usually exhibits isotropic response, as required for measuring ambient dose equivalent, within ±60º to ±80º with respect to the reference direction of calibration, and typically has a much better response for higher photon energies (>80 keV). 4.3.9.4. Dose equivalent range Survey meters may cover a range from nSv/h to Sv/h, but the typical range in use is mSv/h to mSv/h. 4.3.9.5. Response time The response time of the survey monitor is defined as the RC time constant of the measuring circuit, where R is the decade resistor used and C the capacitance of the circuit. Low dose equivalent ranges would have high R and hence high RC values, and so the indicator movement would be sluggish. It takes at least three to five time constants for the monitor reading to stabilize. 4.3.9.6. Overload characteristics Survey meters must be subjected to dose rates of about ten times the maximum scale range to ensure that they read full scale rather than near zero on saturation. 111

CHAPTER 4 Some survey meters, especially the older models, may read zero on overload (i.e. when the equivalent dose rate exceeds the scale range). Such survey meters should not be used for monitoring, since the worker may wrongly assume that there is no radiation in an area where the radiation field is actually very high. GM survey meters are not suitable for use in pulsed fields, due to the possible overload effect, and ionization chamber based survey meters should be used instead. 4.3.9.7. Long term stability Survey meters must be calibrated in a standards dosimetry laboratory with the frequency prescribed by the regulatory requirements of the country, typically once every three years; they also need calibration immediately after repair or immediately upon detection of any sudden change in response. The long term stability of survey meters must be checked at regular intervals using a long half-life source in a reproducible geometry. 4.3.9.8. Discrimination between different types of radiation End window GM counters have a removable buildup cap to discriminate b from g rays. For b measurements the end cap must be removed to allow b particles to enter the sensitive volume. 4.3.9.9. Uncertainties in area survey measurements The standards laboratory provides, along with the survey monitor calibration, the uncertainty associated with the calibration factor. Subsequent measurements at the user department provide a type A uncertainty. The uncer- tainties due to energy dependence and angular dependence of the detector, and the variation in the user field conditions compared with calibration conditions, contribute to type B uncertainties. These two types of uncertainty are added in quadrature to obtain the combined uncertainty associated with the survey meter measurements. The combined uncertainty is multiplied by the coverage factor k = 2 or k = 3 to correspond to the confidence limits of 95% or 99%, respectively. The uncertainty of measurements with area monitors is typically within ±30% under standard laboratory conditions. 112

RADIATION MONITORING INSTRUMENTS 4.4. INDIVIDUAL MONITORING Individual monitoring is the measurement of the radiation doses received by individuals working with radiation. Individuals who regularly work in controlled areas or those who work full time in supervised areas (see Chapter 16 for the definitions) should wear personal dosimeters to have their doses monitored on a regular basis. Individual monitoring is also used to verify the effectiveness of radiation control practices in the workplace. It is useful for detecting changes in radiation levels in the workplace and to provide information in the event of accidental exposures. ● The most widely used individual monitoring systems are based on thermoluminescence or film dosimetry, although other techniques, such as radiophotoluminescence (RPL) and optically stimulated luminescence (OSL), are in use in some countries. Albedo dosimeters and nuclear track emulsions are used for monitoring fast neutron doses. ● Self-reading pocket dosimeters and electronic personal dosimeters (EPDs) are direct reading dosimeters and show both the instantaneous dose rate and the accumulated dose at any point in time. As explained in Section 4.2, the operational quantity for the individual monitoring of external exposure is the personal dose equivalent Hp(d) with the recommended depth d = 10 mm for strongly penetrating radiation and d = 0.07 mm for weakly penetrating radiation. Personal dosimeters are calibrated in these quantities. 4.4.1. Film badge A special emulsion photographic film in a light-tight wrapper enclosed in a case or holder with windows, with appropriate filters, is known as a film badge (Fig. 4.5). The badge holder creates a distinctive pattern on the film indicating the type and energy of the radiation received. While one filter is adequate for photons of energy above 100 keV, the use of a multiple filter system is necessary for lower energy photons. Since the film is non-tissue equivalent, a filter system must be used to flatten the energy response, especially at lower photon beam qualities, to approximate the response of a tissue equivalent material. 113

CHAPTER 4 Filters A Film Thermoluminescence Filters dosimetry chips C E FIG. 4.5. Personal dosimeters: examples of thermoluminescence dosimetry badges (A, B, C) and film badges (D, E). ● Cumulative doses from b, X, g and thermal neutron radiation are evaluated by measuring the film optical densities (ODs) under different filters and then comparing the results with calibration films that have been exposed to known doses of well defined radiation of different types. ● Film can also serve as a monitor for thermal neutrons. The cadmium window absorbs thermal neutrons and the resulting g radiation blackens the film below this window as an indication of the neutron dose. ● Nuclear track emulsions are used for monitoring of fast neutrons. The neutrons interact with hydrogen nuclei in the emulsion and surrounding material, producing recoil protons by elastic collisions. These particles create a latent image, which leads to darkening of the film along their tracks after processing. ● Films are adversely affected by many external agents, such as heat, liquids and excessive humidity. The latent image on undeveloped film fades with time, limiting possible wearing periods to three months in ideal conditions. 114

RADIATION MONITORING INSTRUMENTS Thermoluminescence dosimetry badges Cs-137 irradiator FIG. 4.6. Calibration of personal dosimeters on a PMMA slab phantom using a standard 137 Cs g beam. 4.4.2. Thermoluminescence dosimetry badge A thermoluminescence dosimetry badge (see Fig. 4.5) consists of a set of thermoluminescent dosimeter (TLD) chips enclosed in a plastic holder with filters. The most frequently used thermoluminescence dosimetry materials (also referred to as phosphors) are LiF:Ti,Mg, CaSO4:Dy and CaF2:Mn. Different badge designs (thermoluminescence dosimetry materials and filters) are in use in different countries. The doses of b, X and g radiation registered by the dosimeter are evaluated by measuring the output under different filters and then comparing the results with calibration curves established for the calibration badge, which has been exposed to known doses under well defined conditions. ● Badges that use high atomic number Z thermoluminescence dosimetry materials are not tissue equivalent and, like film, also require filters to match their energy response to that of tissue. Badges using low Z phosphors do not require such complex filter systems. 115

CHAPTER 4 ● The thermoluminescence signal exhibits fading, but the problem is less significant than for films. ● The badges currently used for b monitoring have a relatively high threshold for b particles (about 50 keV) because of the thickness of the detector and its cover. ● TLDs are convenient for monitoring doses to parts of the body (e.g. eyes, arm or wrist, or fingers) using special types of dosimeter, including extremity dosimeters. ● Various techniques have been used for neutron monitoring, such as using the body as a moderator to thermalize neutrons (similarly to albedo dosimeters) or using LiF enriched with 6Li for enhanced thermal neutron sensitivity due to the (n, a) reaction of thermal neutrons in 6Li. 4.4.3. Radiophotoluminescent glass dosimetry systems Radiophotoluminescent glass dosimeters are accumulation type solid state dosimeters that use the phenomenon of RPL to measure the radiation dose. The material used is silver activated phosphate glass. The dosimeters come in the shape of small glass rods. ● When silver activated phosphate glass is exposed to radiation, stable luminescence centres are created in silver ions Ag+ and Ag++. The readout technique uses pulsed ultraviolet laser excitation. A PMT registers the orange fluorescence emitted by the glass. ● The RPL signal is not erased during the readout, thus the dosimeter can be reanalysed several times and the measured data reproduced. Accumu- lation of the dose is also possible, and may be used for registration of the lifetime dose. ● Commercially available radiophotoluminescent dosimeters typically cover the dose range of 30 mSv to 10 Sv. They have a flat energy response within 12 keV to 8 MeV for Hp(10). ● The RPL signal exhibits very low fading and is not sensitive to the environmental temperature, making it convenient for individual monitoring. 4.4.4. Optically stimulated luminescence systems OSL is now commercially available for measuring personal doses. Optically stimulated luminescent dosimeters contain a thin layer of aluminium oxide (Al2O3:C). During analysis the aluminium oxide is stimulated with 116

RADIATION MONITORING INSTRUMENTS selected frequencies of laser light producing luminescence proportional to the radiation exposure. ● Commercially available badges are integrated, self-contained packets that come preloaded, incorporating an aluminium oxyde (Al2O3) strip sandwiched within a filter pack that is heat sealed. Special filter patterns provide qualitative information about conditions during exposure. ● Optically stimulated luminescent dosimeters are highly sensitive; for example, the Luxel system can be used down to 10 mSv with a precision of ±10 mSv. This high sensitivity is particularly suitable for individual monitoring in low radiation environments. The dosimeters can be used in a wide dose range of up to 10 Sv in photon beams from 5 keV to 40 MeV. ● The dosimeters can be reanalysed several times without losing sensitivity and may be used for up to one year. 4.4.5. Direct reading personal monitors In addition to passive dosimetry badges, direct reading personal dosimeters are widely used: ● To provide a direct readout of the dose at any time; ● For tracking the doses received in day to day activities; ● In special operations (e.g. source loading surveys and handling of radiation incidents or emergencies). Direct reading personal dosimeters fall into two categories: (1) self- reading pocket dosimeters and (2) electronic personal dosimeters (EPDs). Self-reading pocket dosimeters resemble a pen and consist of an ionization chamber that acts as a capacitor. The capacitor is fully charged and reads zero before use. On exposure to radiation for a period of time, the ionization produced in the chamber discharges the capacitor; the exposure (or air kerma) is proportional to the discharge, which can be directly read against light through a built-in eyepiece. However, the use of pocket dosimeters has declined in recent years because of their poor useful range, charge leakage problems and poor sensitivity compared with EPDs. EPDs based on miniature GM counters or silicon detectors are available with a measurement range of down to 30 keV photon energy. — Modern EPDs are calibrated in the personal equivalent dose (i.e. in terms of Hp(10) or Hp(0.07) for both photons and b radiation). EPDs provide an instantaneous display of accumulated equivalent dose at any time. 117

CHAPTER 4 — EPDs have automatic ranging facilities and give a visual and an audio indication (flashing or a chirping frequency proportional to the dose equivalent rate), so that changes in the radiation field can be recognized immediately. — EPDs are very useful in emergency situations for immediate readout of the equivalent doses received. 4.4.6. Calibration of personal dosimeters Personal dosimeters should be calibrated in terms of operational quantities for individual monitoring of external exposure (i.e. the personal dose equivalent Hp(d) with the recommended depth d = 10 mm for strongly penetrating radiation and d = 0.07 mm for weakly penetrating radiation (see Section 4.2)). For calibration, dosimeters should be irradiated on standardized phantoms that provide an approximation of the backscatter conditions of the human body. Three types of phantom are recommended that cover the needs of calibration of whole body dosimeters, wrist or ankle dosimeters and finger dosimeters: a slab phantom to represent a human torso, a pillar phantom for wrist or ankle dosimeters and a rod phantom for finger dosimeters. The standard phantoms are composed of ICRU tissue. The ISO recommends special water phantoms (referred to as ISO slab phantoms), although in practice PMMA phantoms are used with the appropriate corrections. Calibration of personal dosimeters in terms of Hp(d) involves three steps: ● Air kerma in air (Kair)air is measured in a reference field, using a reference ionization chamber calibrated by a standards laboratory. ● [Hp(d)/(Kair)air]slab = hkHp values are theoretically available. Using these data for the calibration beam quality, a reference instrument reading can be converted to [Hp(d)]slab. ● The dosimeter badge being calibrated is then placed at the calibration point on a phantom and its reading M is determined. NHp = Hp(d)/M gives the calibration factor in terms of the personal dose equivalent for the dosimeter badge. 4.4.7. Properties of personal monitors 4.4.7.1. Sensitivity Film and thermoluminescence dosimetry badges can measure equivalent doses as low as 0.1 mSv and up to 10 Sv; optically stimulated luminescent and 118

RADIATION MONITORING INSTRUMENTS radiophotoluminescent dosimeters are more sensitive, with a lower detection limit of 10–30 mSv. Personal dosimeters are generally linear in the dose range of interest in radiation protection. 4.4.7.2. Energy dependence Film exhibits a strong energy dependence and film badges are empirically designed to reduce their energy response to within ±20%. A LiF TLD is nearly tissue equivalent and exhibits acceptable energy dependence characteristics. CaSO4:Dy shows significant energy dependence and its energy response is reduced by empirical adjustments in the badge design. Commercially available radiophotoluminescent dosimeters (e.g. Asahi, PTW and Toshiba) have a flat energy response from 12 keV to 8 MeV, while commercially available optically stimulated luminescent dosimeters (e.g. Landauer) have a flat energy response from 5 keV to 40 MeV. For direct reading pocket dosimeters the energy dependence is within ±20% over the range from 40 keV to 2 MeV. For EPDs containing energy compensated detectors the energy dependence is within ±20% over the energy range from 30 keV to 1.3 MeV. The energy response values quoted above can vary in energy range and in the degree of flatness, depending on the individual monitor material and construction details. 4.4.7.3. Uncertainties in personal monitoring measurements The ICRP has stated that, in practice, it is usually possible to achieve an uncertainty of about 10% at the 95% confidence level (k = 2) for measure- ments of radiation fields in laboratory conditions. However, in the workplace, where the energy spectrum and orientation of the radiation field are generally not well known, the uncertainties in a measurement made with an individual dosimeter will be significantly greater, and may be a factor of one for photons and still greater for neutrons and electrons. The uncertainty in measurements with EPDs is about 10% for low dose rates (2 mSv/h) and increases to 20% for higher dose rates (<100 mSv/h) in laboratory conditions. 4.4.7.4. Equivalent dose range Personal monitors must have as wide a dose range as possible so that they can cover both radiation protection and accidental situations (typically from 10 mSv to about 10 Sv). The dose range normally covered by film and TLDs is 119

CHAPTER 4 from about 100 mSv to 10 Sv and that by optically stimulated luminescent and radiophotoluminescent dosimeters is 10 mSv to 10 Sv. Self-reading pocket dosimeters can measure down to about 50 mSv; the upper dose limit of the available pocket dosimeters is around 200 mSv. EPDs measure in the range from 0.1 mSv to 10 Sv. 4.4.7.5. Directional dependence According to the ICRU, an individual dosimeter must be iso-directional, (i.e. its angular response relative to normal incidence must vary as the ICRU directional dose equivalent quantity H¢(10, W)) (see Section 4.2). The directional dependence must be evaluated and the appropriate corrections derived. 4.4.7.6. Discrimination between different types of radiation Film dosimeters can identify and estimate doses of X rays, g rays, b particles and thermal neutrons. TLDs and optically stimulated luminescent and radiophotoluminescent dosimeters generally identify and estimate doses of X rays and g and b radiation. BIBLIOGRAPHY ATTIX, F.H., Introduction to Radiological Physics and Radiation Dosimetry, Wiley, New York (1986). CLARK, M.J., et al., Dose quantities for protection against external radiations: Guidance on the 1990 recommendations of ICRP, Doc. NRPB 4 3 (1993). FOOD AND AGRICULTURE ORGANIZATION OF THE UNITED NATIONS, INTERNATIONAL ATOMIC ENERGY AGENCY, INTERNATIONAL LABOUR ORGANISATION, OECD NUCLEAR ENERGY AGENCY, PAN AMERICAN HEALTH ORGANIZATION, WORLD HEALTH ORGANIZATION, International Basic Safety Standards for Protection against Ionizing Radiation and for the Safety of Radiation Sources, Safety Series No. 115, IAEA, Vienna (1996). INTERNATIONAL ATOMIC ENERGY AGENCY, Calibration of Radiation Protection Monitoring Instruments, Safety Reports Series No. 16, IAEA, Vienna (2000). 120

RADIATION MONITORING INSTRUMENTS INTERNATIONAL COMMISSION ON RADIATION UNITS AND MEASUREMENTS, Determination of Dose Equivalents Resulting from External Radiation Sources, Rep. 43, ICRU, Bethesda, MD (1988). — Measurement of Dose Equivalents from External Photon and Electron Radiations, Rep. 47, ICRU, Bethesda, MD (1992). — Quantities and Units in Radiation Protection Dosimetry, Rep. 51, ICRU, Bethesda, MD (1993). INTERNATIONAL COMMISSION ON RADIOLOGICAL PROTECTION, Conversion Coefficients for Use in Radiological Protection Against External Radiation, Publication 74, Pergamon Press, Oxford and New York (1997). INTERNATIONAL ORGANIZATION FOR STANDARDIZATION, X and Gamma Reference Radiations for Calibrating Dosemeters and Dose Ratemeters and for Determining their Response as a Function of Energy, ISO 4037. See also High Rate Series of Filtered X-radiations, ISO 4037-1979/Addendum 1(1983); and Low Rate Series of Filtered X-radiations, ISO 4037-1979/Amendment 1-1983 (E), ISO, Geneva (1979). — Reference Beta Radiations for Calibrating Dosimeters and Dose Rate Meters and for Determining their Response as a Function of Beta Radiation Energy, ISO 6980, ISO, Geneva (1984). — Dosimetry of the Reference Radiation Fields Used for Determining the Response of Protection Level Dosimeters and Dose-rate Meters at Photon Energies Between 4 and 9 MeV, ISO/DP 9991, ISO, Geneva (1988). — Dosimetry of X and Gamma Reference Radiations for Radiation Protection over the Energy Range from 9 keV to 1.3 MeV, ISO/DIS 8963, ISO, Geneva (1988). KNOLL, G.F., Radiation Detection and Measurement, Wiley, New York (1979). NATIONAL RADIOLOGICAL PROTECTION BOARD, New Radiation Quantities Recommended by ICRU for Practical Use in Radiation Protection: Their Implementation in the United Kingdom, NRPB, Didcot, UK (1986). 121

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Chapter 5 TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY E.B. PODGORSAK Department of Medical Physics, McGill University Health Centre, Montreal, Quebec, Canada 5.1. INTRODUCTION Since the inception of radiotherapy soon after the discovery of X rays by Roentgen in 1895, the technology of X ray production has first been aimed towards ever higher photon and electron beam energies and intensities, and more recently towards computerization and intensity modulated beam delivery. During the first 50 years of radiotherapy the technological progress was relatively slow and mainly based on X ray tubes, van de Graaff generators and betatrons. The invention of the 60Co teletherapy unit by H.E. Johns in Canada in the early 1950s provided a tremendous boost in the quest for higher photon energies and placed the cobalt unit at the forefront of radiotherapy for a number of years. The concurrently developed medical linacs, however, soon eclipsed cobalt units, moved through five increasingly sophisticated generations and became the most widely used radiation source in modern radiotherapy. With its compact and efficient design, the linac offers excellent versatility for use in radiotherapy through isocentric mounting and provides either electron or megavoltage X ray therapy with a wide range of energies. In addition to linacs, electron and X ray radiotherapy is also carried out with other types of accelerator, such as betatrons and microtrons. More exotic particles, such as protons, neutrons, heavy ions and negative p mesons, all produced by special accelerators, are also sometimes used for radiotherapy; however, most contemporary radiotherapy is carried out with linacs or teletherapy cobalt units. 123

CHAPTER 5 5.2. X RAY BEAMS AND X RAY UNITS Clinical X ray beams typically range in energy between 10 kVp and 50 MV and are produced when electrons with kinetic energies between 10 keV and 50 MeV are decelerated in special metallic targets. Most of the electron’s kinetic energy is transformed in the target into heat, and a small fraction of the energy is emitted in the form of X ray photons, which are divided into two groups: characteristic X rays and bremsstrahlung X rays. 5.2.1. Characteristic X rays Characteristic X rays result from Coulomb interactions between the incident electrons and atomic orbital electrons of the target material (collision loss). In a given Coulomb interaction between the incident electron and an orbital electron, the orbital electron is ejected from its shell and an electron from a higher level shell fills the resulting orbital vacancy. The energy difference between the two shells may either be emitted from the atom in the form of a characteristic photon (characteristic X ray) or transferred to an orbital electron that is ejected from the atom as an Auger electron. ● The fluorescent yield w gives the number of fluorescent (characteristic) photons emitted per vacancy in a shell (0 < w < 1) and ranges from zero _ _ for low Z atoms through 0.5 for copper (Z = 29) to 0.96 for high Z atoms for K shell vacancies, which are the most prominent sources of character- istic X rays. ● The photons emitted through electronic shell transitions have discrete energies that are characteristic of the particular target atom in which the transitions have occurred; hence the term characteristic radiation. 5.2.2. Bremsstrahlung (continuous) X rays Bremsstrahlung X rays result from Coulomb interactions between the incident electron and the nuclei of the target material. During the Coulomb interaction between the incident electron and the nucleus, the incident electron is decelerated and loses part of its kinetic energy in the form of bremsstrahlung photons (radiative loss). 124

TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY ● Photons with energies ranging from zero to the kinetic energy of the incident electron may be produced, resulting in a continuous brems- strahlung spectrum; ● The bremsstrahlung spectrum produced in a given X ray target depends on the kinetic energy of the incident electron as well as on the thickness and atomic number Z of the target. 5.2.3. X ray targets According to the range R of electrons of a given kinetic energy EK in the target material, targets are divided into two main groups: thin and thick. A thin target has a thickness much smaller than R, while the thickness of a thick target is of the order of R. For thin target radiation, the energy radiated is proportional to the product EKZ, where Z is the atomic number of the target. The intensity versus photon energy (photon spectrum) is constant from zero to the kinetic energy EK of the incident electron, and zero for all energies above EK. A thick target may be considered as consisting of a large number of superimposed thin targets. The intensity I(hn) of a thick target spectrum is expressed as: I(hn) = CZ(EK – hn) (5.1) where C is a proportionality constant; hn is the photon energy. X rays are used in diagnostic radiology for diagnosis of disease and in radiation oncology (radiotherapy) for treatment of disease. X rays produced by electrons with kinetic energies between 10 keV and 100 keV are called superficial X rays, those with electron kinetic energies between 100 keV and 500 keV are called orthovoltage X rays, while those with electron kinetic energies above 1 MeV are called megavoltage X rays. Superficial and orthovoltage X rays are produced with X ray tubes (machines), while megavoltage X rays are most commonly produced with linacs and sometimes with betatrons and microtrons. Typical thin and thick target bremsstrahlung spectra originating from 100 keV electrons striking a thin and thick target, respectively, are shown in Fig. 5.1. 125

CHAPTER 5 5.2.4. Clinical X ray beams A typical spectrum of a clinical X ray beam consists of line spectra that are characteristic of the target material and that are superimposed on to the continuous bremsstrahlung spectrum. The bremsstrahlung spectrum originates in the X ray target, while the characteristic line spectra originate in the target and in any attenuators placed into the beam. ● The relative proportion of the number of characteristic photons to bremsstrahlung photons in an X ray beam spectrum varies with the electron beam kinetic energy and atomic number of the target. For example, X ray beams produced in a tungsten target by 100 keV electrons contain about 20% characteristic photons and 80% bremsstrahlung photons, while in the megavoltage range the contribution of characteristic photons to the total spectrum is negligible. FIG. 5.1. Typical thin target (curve 1) and thick target (curves 2, 3 and 4) spectra for an X ray tube in which 100 keV electrons strike the target. Curve (1) is for a thin target producing a constant intensity for photon energies from zero to the kinetic energy of electrons striking the target (100 keV). Curve (2) represents an unfiltered spectrum (inside the X ray tube) for a thick target and a superposition of numerous thin target spectra; the spectrum of curve (3) is for a beam filtered by an X ray tube window (low energy photons are filtered out); the spectrum of curve (4) is for a beam filtered by the X ray tube window and additional filtration. 126

TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY ● In the diagnostic energy range (10–150 kV) most photons are produced at 90º from the direction of electron acceleration, while in the megavoltage energy range (1–50 MV) most photons are produced in the direction of electron acceleration (forward direction: 0º). 5.2.5. X ray beam quality specifiers Various parameters, such as photon spectrum, half-value layer (HVL), nominal accelerating potential (NAP) and beam penetration into tissue equivalent media, are used as X ray beam quality indices (see Sections 9.8.1 and 9.8.2 for details): ● A complete X ray spectrum is very difficult to measure; however, it gives the most rigorous description of beam quality. ● The HVL is practical for beam quality description in the superficial (HVL in aluminium) and orthovoltage (HVL in copper) X ray energy range, but not practical in the megavoltage energy range because in this energy range the attenuation coefficient is only a slowly varying function of beam energy. ● The effective energy of a heterogeneous X ray beam is defined as that energy of a monoenergetic photon beam that yields the same HVL as does the heterogeneous beam. ● The NAP is sometimes used for describing the megavoltage beam quality. The NAP is determined by measuring the ionization ratio in a water phantom at depths of 10 and 20 cm for a 10 × 10 cm2 field at the nominal source to axis distance (SAD) of 100 cm. ● Recent dosimetry protocols recommend the use of tissue–phantom ratios or percentage depth doses (PDDs) at a depth of 10 cm in a water phantom as an indicator of megavoltage beam effective energy (beam quality index). 5.2.6. X ray machines for radiotherapy Superficial and orthovoltage X rays used in radiotherapy are produced with X ray machines. The main components of a radiotherapeutic X ray machine are: an X ray tube; a ceiling or floor mount for the X ray tube; a target cooling system; a control console; and an X ray power generator. A schematic diagram of a typical therapy X ray tube is shown in Fig. 5.2. ● The electrons producing the X ray beams in the X ray tube (Coolidge tube) originate in the heated filament (cathode) and are accelerated in a 127

CHAPTER 5 vacuum towards the target (anode) by an essentially constant potential electrostatic field supplied by the X ray generator. ● The efficiency for X ray production in the superficial and orthovoltage energy range is of the order of 1% or less. Most of the electron kinetic energy deposited in the X ray target (~99%) is transformed into heat and must be dissipated through an efficient target cooling system. ● To maximize the X ray yield in the superficial and orthovoltage energy range the target material should have a high atomic number Z and a high melting point. ● With X ray tubes, the patient dose is delivered using a timer and the treatment time must incorporate the shutter correction time (see Section 6.16), which accounts for the time required for the power supply components to attain the steady state operating conditions. ● The X ray tube current is controlled by a hot filament emission of electrons, which, in turn, is controlled by the filament temperature (thermionic emission). For a given filament temperature the X ray tube current increases with the tube (anode) voltage, first rising linearly with voltage in the space charge limited region and saturating at higher voltages when all electrons emitted from the cathode are pulled to the anode. FIG. 5.2. Typical therapy X ray tube (reprinted from Johns, H.E., and Cunningham, J.R., with permission). 128

TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY ● Research is currently being carried out on cold field emission cathodes produced with carbon nanotubes (CNTs). The CNT based cold cathode X ray technology may lead to more durable as well as miniature and portable X ray sources for industrial and medical applications. 5.3. GAMMA RAY BEAMS AND GAMMA RAY UNITS 5.3.1. Basic properties of gamma rays For use in external beam radiotherapy, g rays are obtained from specially designed and built sources that contain a suitable, artificially produced radioactive material. ● The parent source material undergoes a b decay, resulting in excited daughter nuclei that attain ground state through emission of g rays (g decay). ● The important characteristics of radioisotopes in external beam radio- therapy are: — High g ray energy; — High specific activity; — Relatively long half-life; — Large specific air kerma rate constant GAKR. ● The specific activity a (activity A per mass m of radioactive nuclide) is inversely proportional to the half-life t1/2: A NA ln 2 a= = (5.2) m t 1/2 A where NA is Avogadro’s number (6.022 × 1023 atoms/g-atom); A is the atomic mass number. ● The air kerma rate in air (K air ) air is given by the following relation: A G AKR (K air ) air = (5.3) d2 129

CHAPTER 5 where A is the source activity; d is the distance between the point of interest and the point source. ● The basic physical properties of the two g emitters (60Co and 137Cs) currently used for external beam teletherapy and a potential source for teletherapy units (152Eu) are listed in Table 5.1. Of the three radioiso- topes, 60Co is the most widely used, since it offers the most practical approach to external beam radiotherapy, considering the energy of emitted photons, half-life, specific activity and means of production. 5.3.2. Teletherapy machines Treatment machines incorporating g ray sources for use in external beam radiotherapy are called teletherapy machines. They are most often mounted isocentrically, allowing the beam to rotate about the patient at a fixed SAD. Modern teletherapy machines have SADs of 80 or 100 cm. The main components of a teletherapy machine are: a radioactive source; a source housing, including beam collimator and source movement mechanism; a gantry and stand in isocentric machines or a housing support assembly in stand-alone machines; a patient support assembly; and a machine console. 5.3.3. Teletherapy sources The most widely used teletherapy source uses 60Co radionuclides contained inside a cylindrical stainless steel capsule and sealed by welding. A double welded seal is used to prevent any leakage of the radioactive material. ● To facilitate interchange of sources from one teletherapy machine to another and from one isotope production facility to another, standard source capsules have been developed. ● The typical diameter of the cylindrical teletherapy source is between 1 and 2 cm; the height of the cylinder is about 2.5 cm. The smaller the source diameter, the smaller is its physical penumbra and the more expensive is the source. Often a diameter of 1.5 cm is chosen as a compromise between the cost and penumbra. ● Typical source activities are of the order of 5000–10 000 Ci (185–370 TBq) and provide a typical dose rate at 80 cm from the teletherapy source of the order of 100–200 cGy/min. Often the output of a teletherapy machine 130

TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY TABLE 5.1. PHYSICAL PROPERTIES OF RADIONUCLIDES USED IN EXTERNAL BEAM RADIOTHERAPY Co-60 Cs-137 Eu-152 Half-life (a) 5.3 30 13.4 a b Specific activity (Ci/g) 1100 (~250 ) 80 180a (~150b) Photon energy (MeV) 1.17 and 1.33 0.662 0.6–1.4 Specific g rate constant 1.31 0.33 1.06 G [Rm2/(Ci·h)] Specific air kerma rate constant 309 78 250 GAKR [mGy·m2/(GBq·h)] HVL (cm Pb) 1.1 0.5 1.1 59 151 Means of production Co + n Fission Eu + n in reactor by-product in reactor a Theoretical specific activity: a = (NA ln 2)/(t1/2A). b The practical specific activity is smaller than the theoretical specific activity because the source is not carrier free (i.e. the source contains stable isotopes in addition to radioactive isotopes (e.g. 59Co mixed with 60Co)). is stated in Rmm (roentgens per minute at 1 m) as a rough guide for the source strength. ● Teletherapy sources are usually replaced within one half-life after they are installed; however, financial considerations often result in longer source usage. 60 ● The Co radionuclides in a teletherapy source decay with a half-life of 5.26 years into 60Ni with the emission of electrons (b particles) with a maximum energy of 320 keV and two g rays with energies of 1.17 MeV and 1.33 MeV. The emitted g rays constitute the therapy beam; the electrons are absorbed in the cobalt source or the source capsule, where they produce relatively low energy and essentially negligible brems- strahlung X rays and characteristic X rays. 5.3.4. Teletherapy source housing The housing for the teletherapy source is called the source head, and consists of a steel shell with lead for shielding purposes and a mechanism for bringing the source in front of the collimator opening to produce the clinical g ray beam. 131

CHAPTER 5 ● Currently two methods are in use for moving the teletherapy source from the beam off into the beam on position and back: (i) a source on a sliding drawer and (ii) a source on a rotating cylinder. Both methods incorporate a safety feature in which the beam is terminated automatically in the event of a power failure or emergency. ● When the source is in the beam off position, a light source appears in the beam on position above the collimator opening, allowing an optical visualization of the radiation field, as defined by the machine collimators and any special shielding blocks. ● Some radiation will escape from the unit even when the source is in the beam off position. The head leakage typically amounts to less than 1 mR/h (0.01 mSv/h) at 1 m from the source. International regulations require that the average leakage of a teletherapy machine head be less than 2 mR/h (0.02 mSv/h) at 1 m from the source. 5.3.5. Dose delivery with teletherapy machines The prescribed target dose is delivered with the help of two treatment timers: primary and secondary. The primary timer actually controls the treatment time, the secondary timer serves as a backup timer in case of the primary timer’s failure. The set treatment time must incorporate the shutter error, which accounts for the travel time of the source from the beam off position towards the beam on position at the start of irradiation and for the reverse travel at the end of irradiation. 5.3.6. Collimator and penumbra Collimators of teletherapy machines provide square and rectangular radiation fields typically ranging from 5 × 5 to 35 × 35 cm2 at 80 cm from the source. The geometric penumbra, which results from a finite source diameter, may be minimized by using small diameter sources and by using penumbra trimmers as close as possible to the patient’s skin (see Section 6.9 for further discussion of the penumbra). 5.4. PARTICLE ACCELERATORS Numerous types of accelerator have been built for basic research in nuclear and high energy physics, and most of them have been modified for at 132

TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY least some limited use in radiotherapy. Irrespective of the accelerator type, two basic conditions must be met for particle acceleration: ● The particle to be accelerated must be charged; ● An electric field must be provided in the direction of particle acceler- ation. The various types of accelerator differ in the way they produce the accel- erating electric field and in how the field acts on the particles to be accelerated. As far as the accelerating electric field is concerned there are two main classes of accelerator: electrostatic and cyclic. — In electrostatic accelerators the particles are accelerated by applying an electrostatic electric field through a voltage difference, constant in time, whose value fixes the value of the final kinetic energy of the particle. Since the electrostatic fields are conservative, the kinetic energy that the particle can gain depends only on the point of departure and point of arrival and hence cannot be larger than the potential energy corre- sponding to the maximum voltage drop existing in the machine. The energy that an electrostatic accelerator can reach is limited by the discharges that occur between the high voltage terminal and the walls of the accelerator chamber when the voltage drop exceeds a certain critical value (typically 1 MV). — The electric fields used in cyclic accelerators are variable and non- conservative, associated with a variable magnetic field and resulting in some close paths along which the kinetic energy gained by the particle differs from zero. If the particle is made to follow such a closed path many times over, one obtains a process of gradual acceleration that is not limited to the maximum voltage drop existing in the accelerator. Thus the final kinetic energy of the particle is obtained by submitting the charged particle to the same, relatively small, potential difference a large number of times, each cycle adding a small amount of energy to the kinetic energy of the particle. Examples of electrostatic accelerators used in medicine are superficial and orthovoltage X ray tubes and neutron generators. The best known example of a cyclic accelerator is the linac; other examples are microtrons, betatrons and cyclotrons. 133

CHAPTER 5 5.4.1. Betatron The betatron was developed in 1940 by D.W. Kerst as a cyclic electron accelerator for basic physics research; however, its potential for use in radio- therapy was realized soon after. ● The machine consists of a magnet fed by an alternating current of frequency between 50 and 200 Hz. The electrons are made to circulate in a toroidal (doughnut shaped) vacuum chamber that is placed into the gap between two magnet poles. A schematic diagram of a betatron is given in Fig. 5.3(a). ● Conceptually, the betatron may be considered an analogue of a trans- former: the primary current is the alternating current exciting the magnet and the secondary current is the electron current circulating in the vacuum chamber (doughnut). ● The electrons are accelerated by the electric field induced in the doughnut shape by the changing magnetic flux in the magnet; they are kept in a circular orbit by the magnetic field present. ● In the 1950s betatrons played an important role in megavoltage radio- therapy. However, the development of linacs pushed them into oblivion because of the numerous advantages offered by linacs over betatrons, such as: much higher beam output (up to 10 Gy/min for linacs versus 1 Gy/min for betatrons); larger field size; full isocentric mounting; more compact design; and quieter operation. 5.4.2. Cyclotron The cyclotron was developed in 1930 by E.O. Lawrence for acceleration of ions to a kinetic energy of a few megaelectronvolts. Initially, the cyclotron was used for basic nuclear physics research, but later on found important medical uses in the production of radioisotopes for nuclear medicine as well as in the production of proton and neutron beams for radiotherapy. The recent introduction of positron emission tomography (PET)/computed tomography (CT) machines for use in radiotherapy (see Section 15.10) has dramatically increased the importance of cyclotrons in medicine. PET/CT machines rely on glucose labelled with positron emitting 18F produced by proton cyclotrons. ● In a cyclotron the particles are accelerated along a spiral trajectory guided inside two evacuated half-cylindrical electrodes (referred to as dees because of their D shaped form) by a uniform magnetic field (1 T) 134

TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY that is produced between the pole pieces of a large magnet. Figure 5.3(b) is a diagram of a cyclotron. ● A radiofrequency (RF) voltage with a constant frequency between 10 and 30 MHz is applied between the two electrodes and the charged particle is accelerated while crossing the gap between the two electrodes. ● Inside the electrodes there is no electric field and the particle drifts under the influence of the magnetic field in a semicircular orbit with a constant speed until it crosses the gap again. If, in the meantime, the electric field has reversed its direction, the particle will again be accelerated across the gap, gain a small amount of energy and drift in the other electrode along a semicircle of a larger radius than the former one, resulting in a spiral orbit and a gradual increase in kinetic energy after a large number of gap crossings. 5.4.3. Microtron The microtron is an electron accelerator that combines the features of a linac with a cyclotron. The concept of the microtron was developed by FIG. 5.3. Two cyclic accelerators: (a) a betatron and (b) a cyclotron. 135

CHAPTER 5 V.I. Veksler in 1944, and the machine is used in modern radiotherapy, albeit to a much smaller extent than linacs. Two types of microtron have been developed: circular and racetrack. ● In the circular microtron the electron gains energy from a microwave resonant cavity and describes circular orbits of increasing radius in a uniform magnetic field. To keep the particle in phase with the microwave power, the cavity voltage, frequency and magnetic field are adjusted in such a way that after each passage through the cavity the electrons gain an energy increment, resulting in an increase in the transit time in the magnetic field equal to an integral number of microwave cycles. ● In the racetrack microtron the magnet is split into two D shaped pole pieces that are separated to provide greater flexibility in achieving efficient electron injection and higher energy gain per orbit through the use of multicavity accelerating structures similar to those used in linacs. The electron orbits consist of two semicircular and two straight sections. 5.5. LINACS Medical linacs are cyclic accelerators that accelerate electrons to kinetic energies from 4 to 25 MeV using non-conservative microwave RF fields in the frequency range from 103 MHz (L band) to 104 MHz (X band), with the vast majority running at 2856 MHz (S band). In a linac the electrons are accelerated following straight trajectories in special evacuated structures called accelerating waveguides. Electrons follow a linear path through the same, relatively low, potential difference several times; hence linacs also fall into the class of cyclic accelerators, just like the other cyclic machines that provide curved paths for the accelerated particles (e.g. betatrons). The high power RF fields used for electron acceleration in the acceler- ating waveguides are produced through the process of decelerating electrons in retarding potentials in special evacuated devices called magnetrons and klystrons. Various types of linac are available for clinical use. Some provide X rays only in the low megavoltage range (4 or 6 MV), while others provide both X rays and electrons at various megavoltage energies. A typical modern high energy linac will provide two photon energies (6 and 18 MV) and several electron energies (e.g. 6, 9, 12, 16 and 22 MeV). 136

TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY 5.5.1. Linac generations During the past 40 years medical linacs have gone through five distinct generations, making the contemporary machines extremely sophisticated in comparison with the machines of the 1960s. The five generations introduced the following new features: ● Low energy photons (4–8 MV): straight-through beam; fixed flattening filter; external wedges; symmetric jaws; single transmission ionization chamber; isocentric mounting. ● Medium energy photons (10–15 MV) and electrons: bent beam; movable target and flattening filter; scattering foils; dual transmission ionization chamber; electron cones. ● High energy photons (18–25 MV) and electrons: dual photon energy and multiple electron energies; achromatic bending magnet; dual scattering foils or scanned electron pencil beam; motorized wedge; asymmetric or independent collimator jaws. ● High energy photons and electrons: computer controlled operation; dynamic wedge; electronic portal imaging device (EPID); multileaf collimator (MLC). ● High energy photons and electrons: photon beam intensity modulation with MLC; full dynamic conformal dose delivery with intensity modulated beams produced with an MLC. 5.5.2. Safety of linac installations The complexity of modern linacs raises concerns as to safety of operation from the point of view of patients and operators. The International Electro- technical Commission (IEC) publishes international standards that express, as nearly as possible, an international consensus of opinion on relevant technical subjects; electron linacs are addressed in detail by the IEC. The IEC statement on the safety of linacs (IEC 60601-2-1, p. 13) is as follows: “The use of electron accelerators for radiotherapy purposes may expose patients to danger if the equipment fails to deliver the required dose to the patient, or if the equipment design does not satisfy standards of electrical and mechanical safety. The equipment may also cause danger to persons in the vicinity if the equipment fails to contain the radiation adequately and/or if there are inadequacies in the design of the treatment room.” 137

CHAPTER 5 The IEC document addresses three categories of safety issues — electrical, mechanical and radiation — and establishes specific requirements mainly for the manufacturers of linacs in the design and construction of linacs for use in radiotherapy. It also covers some radiation safety aspects of linac installation in customer’s treatment rooms. 5.5.3. Components of modern linacs Linacs are usually mounted isocentrically and the operational systems are distributed over five major and distinct sections of the machine, the: ● Gantry; ● Gantry stand or support; ● Modulator cabinet; ● Patient support assembly (i.e. treatment table); ● Control console. A schematic diagram of a typical modern S band medical linac is shown in Fig. 5.4. Also shown are the connections and relationships among the various linac components listed above. The diagram provides a general layout of a linac’s components; however, there are significant variations from one commercial machine to another, depending on the final electron beam kinetic energy as well as on the particular design used by the manufacturer. — The length of the accelerating waveguide depends on the final electron kinetic energy, and ranges from ~30 cm at 4 MeV to ~150 cm at 25 MeV. — The main beam forming components of a modern medical linac are usually grouped into six classes: (i) Injection system; (ii) RF power generation system; (iii) Accelerating waveguide; (iv) Auxiliary system; (v) Beam transport system; (vi) Beam collimation and beam monitoring system. 5.5.4. Configuration of modern linacs At megavoltage electron energies the bremsstrahlung photons produced in the X ray target are mainly forward peaked and the clinical photon beam is produced in the direction of the electron beam striking the target. 138

TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY ● In the simplest and most practical configuration, the electron gun and the X ray target form part of the accelerating waveguide and are aligned directly with the linac isocentre, obviating the need for a beam transport system. A straight-through photon beam is produced and the RF power source is mounted in the gantry. ● The simplest linacs are isocentrically mounted 4 or 6 MV machines, with the electron gun and target permanently built into the accelerating waveguide, thereby requiring no beam transport nor offering an electron therapy option. ● Accelerating waveguides for intermediate (8–15 MeV) and high (15–30 MeV) electron energies are too long for direct isocentric mounting and thus are located either in the gantry, parallel to the gantry axis of rotation, or in the gantry stand. A beam transport system is then used to transport the electron beam from the accelerating waveguide to the X ray target. The RF power source in the two configurations is commonly mounted in the gantry stand. Various design configurations for modern isocentric linacs are shown in Fig. 5.5. FIG. 5.4. Medical linac. 139

CHAPTER 5 5.5.5. Injection system The injection system is the source of electrons; it is essentially a simple electrostatic accelerator called an electron gun. ● Two types of electron gun are in use as sources of electrons in medical linacs: — Diode type; — Triode type. ● Both electron gun types contain a heated filament cathode and a perforated grounded anode; in addition, the triode electron gun also incorporates a grid. 140

TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY ● Electrons are thermionically emitted from the heated cathode, focused into a pencil beam by a curved focusing electrode and accelerated towards the perforated anode through which they drift to enter the accel- erating waveguide. ● The electrostatic fields used to accelerate the electrons in the diode gun are supplied directly from the pulsed modulator in the form of a negative pulse delivered to the cathode of the gun. ● In a triode gun, however, the cathode is held at a static negative potential (typically –20 kV). The grid of the triode gun is normally held sufficiently negative with respect to the cathode to cut off the current to the anode. The injection of electrons into the accelerating waveguide is then controlled by voltage pulses, which are applied to the grid and must be synchronized with the pulses applied to the microwave generator. A removable triode gun of a high energy linac is shown in Fig. 5.6(a). FIG. 5.5. Design configurations for isocentric medical linacs. (a) Straight-through beam design; the electron gun and target are permanently embedded into the accelerating waveguide; the machine produces only X rays with energies of 4–6 MV; the RF power generator is mounted in the gantry. (b) The accelerating waveguide is in the gantry parallel to the isocentre axis; electrons are brought to the movable target through a beam transport system; the RF power generator is located in the gantry stand; the machine can produce megavoltage X rays as well as electrons. (c) The accelerating waveguide and RF power generator are located in the gantry stand; electrons are brought to the movable target through a beam transport system; the machine can produce megavoltage X rays as well as electrons. 141

CHAPTER 5 (a) (b) FIG. 5.6. Removable electron triode gun (a) and removable X ray target (b) for a typical high energy linac (Varian Clinac-18), allowing two photon modes and several electron modes. The target is water cooled and mounted with bellows to allow for movement into the pencil electron beam for X ray production and movement out of the pencil beam for electron beam production. 142

TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY 5.5.6. Radiofrequency power generation system The microwave radiation used in the accelerating waveguide to accelerate electrons to the desired kinetic energy is produced by the RF power generation system, which consists of two major components: ● An RF power source; ● A pulsed modulator. The RF power source is either a magnetron or a klystron. Both are devices that use electron acceleration and deceleration in a vacuum for the production of high power RF fields. Both types use a thermionic emission of electrons from a heated cathode and accelerate the electrons towards an anode in a pulsed electrostatic field; however, their design principles are completely different. — The high voltage (~100 kV), high current (~100 A), short duration (~1 s) pulses required by the RF power source (magnetron or klystron) and the injection system (electron gun) are produced by a pulsed modulator. The circuitry of the pulsed modulator is housed in the modulator cabinet, which, depending on the particular linac installation design, is located in the treatment room, in a special mechanical room next to the treatment room or in the linac control room. — A magnetron is a source of high power RF required for electron acceler- ation, while a klystron is an RF power amplifier that amplifies the low power RF generated by an RF oscillator commonly called the RF driver. 5.5.7. Accelerating waveguide Waveguides are evacuated or gas filled metallic structures of rectangular or circular cross-section used in the transmission of microwaves. Two types of waveguide are used in linacs: RF power transmission waveguides and acceler- ating waveguides. The power transmission waveguides transmit the RF power from the power source to the accelerating waveguide in which the electrons are accelerated. ● The electrons are accelerated in the accelerating waveguide by means of an energy transfer from the high power RF fields, which are set up in the accelerating waveguide and are produced by the RF power generators. ● The simplest kind of accelerating waveguide is obtained from a cylindrical uniform waveguide by adding a series of discs (irises) with 143

CHAPTER 5 circular holes at the centre, placed at equal distances along the tube. These discs divide the waveguide into a series of cylindrical cavities that form the basic structure of the accelerating waveguide in a linac. The accelerating waveguide is evacuated to allow free propagation of electrons. The cavities of the accelerating waveguide serve two purposes: — To couple and distribute microwave power between adjacent cavities; — To provide a suitable electric field pattern for the acceleration of electrons. Two types of accelerating waveguide have been developed for the acceleration of electrons: (i) Travelling wave structure; (ii) Standing wave structure. In the travelling wave structure the microwaves enter the accelerating waveguide on the gun side and propagate towards the high energy end of the waveguide, where they either are absorbed without any reflection or exit the waveguide to be absorbed in a resistive load or to be fed back to the input end of the accelerating waveguide. In this configuration only one in four cavities is at any given moment suitable for electron acceleration, providing an electric field in the direction of propagation. In the standing wave structure each end of the accelerating waveguide is terminated with a conducting disc to reflect the microwave power, resulting in a buildup of standing waves in the waveguide. In this configuration, at all times, every second cavity carries no electric field and thus produces no energy gain for the electrons. These cavities therefore serve only as coupling cavities and can be moved out to the side of the waveguide structure, effectively shortening the accelerating waveguide by 50%. A cut-away view of a 6 MV standing wave accelerating waveguide is shown in Fig. 5.7. 5.5.8. Microwave power transmission The microwave power produced by the RF generator is carried to the accelerating waveguide through rectangular uniform S band waveguides that are either evacuated or, more commonly, pressurized with a dielectric gas (Freon or sulphur hexafluoride, SF6) to twice the atmospheric pressure. An important component that must be inserted into the RF power trans- mission circuit between the RF generator and the accelerating waveguide is a 144

TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY FIG. 5.7. Cutaway view of a standing wave accelerating waveguide for a 6 MV linac. The cavities are clearly visible: the accelerating cavities are on the central axis; the coupling cavities are off-side. The electron gun is on the left, the target on the right, both perma- nently embedded. circulator (sometimes referred to as an isolator), which transmits the RF power from the RF generator to the accelerating waveguide but is impervious to reflected radiation moving in the opposite direction, thereby protecting the RF source from the reflected power. 5.5.9. Auxiliary system The linac auxiliary system consists of several services that are not directly involved with electron acceleration, yet make the acceleration possible and the linac viable for clinical operation. The linac auxiliary system comprises four systems: ● A vacuum pumping system producing a vacuum pressure of ~10–6 torr in the accelerating guide and the RF generator; ● A water cooling system used for cooling the accelerating guide, target, circulator and RF generator; ● An optional air pressure system for pneumatic movement of the target and other beam shaping components; ● Shielding against leakage radiation. 145

CHAPTER 5 5.5.10. Electron beam transport In low energy linacs the target is embedded in the accelerating waveguide and no beam transport between the accelerating waveguide and target is required. Bending magnets are used in linacs operating at energies above 6 MeV, where the accelerating waveguides are too long for straight-through mounting. The accelerating waveguide is usually mounted parallel to the gantry rotation axis and the electron beam must be bent to make it strike the X ray target or be able to exit through the beam exit window. Three systems for electron bending have been developed: ● 90º bending; ● 270º bending (achromatic); ● 112.5º (slalom) bending. In medium (10 MV) and high energy (above 15 MV) linacs an electron beam transport system is used for transporting the electron beam from the accelerating waveguide to the X ray target or to the linac exit window for electron beam therapy. The system consists of evacuated drift tubes and bending magnets. In addition, steering coils and focusing coils, used for steering and focusing of the accelerated electron beam, also form components of the beam transport system. 5.5.11. Linac treatment head The linac head contains several components that influence the production, shaping, localizing and monitoring of the clinical photon and electron beams. Electrons originating in the electron gun are accelerated in the acceler- ating waveguide to the desired kinetic energy and then brought, in the form of a pencil beam, through the beam transport system into the linac treatment head, where the clinical photon and electron beams are produced. ● The important components found in a typical head of a fourth or fifth generation linac include: —Several retractable X ray targets; —Flattening filters and electron scattering foils (also called scattering filters); —Primary and adjustable secondary collimators; —Dual transmission ionization chambers; 146

TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY —A field defining light and a range finder; —Optional retractable wedges; —Optional MLC. ● Clinical photon beams are produced with a target–flattening filter combi- nation. ● Clinical electron beams are produced by retracting the target and flattening filter from the electron pencil beam and: —Either scattering the pencil beam with a single or dual scattering foil; or —Deflecting and scanning the pencil beam magnetically to cover the field size required for electron treatment. Special cones (applicators) are used to collimate the electron beams. ● Each clinical photon beam has its own target–flattening filter combi- nation. The flattening filters and scattering foils (if used for electron beams) are mounted on a rotating carousel or sliding drawer for ease of mechanical positioning into the beam, as required. ● The primary collimator defines a maximum circular field, which is then further truncated with an adjustable rectangular collimator consisting of two upper and two lower independent jaws and producing rectangular and square fields with a maximum dimension of 40 × 40 cm2 at the linac isocentre. The IEC recommends that the transmission of the primary X ray beam through the rectangular collimator should not exceed 2% of the open beam value. ● Dual transmission ionization chambers are used for monitoring the photon and electron radiation beam output as well as the radial and transverse beam flatness (see Section 5.5.14). ● The field defining light and the range finder provide convenient visual methods for correctly positioning the patient for treatment using reference marks. The field light illuminates an area that coincides with the radiation treatment field on the patient’s skin, while the range finder is used to place the patient at the correct treatment distance by projecting a centimetre scale whose image on the patient’s skin indicates the vertical distance from the linac isocentre. 5.5.12. Production of clinical photon beams in a linac Clinical photon beams emanating from a medical linac are produced in an X ray target and flattened with a flattening filter. A high energy linac movable target is shown in Fig. 5.6(b). At electron energies below 15 MeV (photon beam energies 15 MV) optimal targets have a high atomic number Z, while at electron energies above 15 MeV (photon beam energies above 15 MV) the optimal targets have a low 147

CHAPTER 5 atomic number Z. Optimal flattening filters have a low Z irrespective of beam energy. 5.5.13. Beam collimation In a typical modern medical linac, the photon beam collimation is achieved with two or three collimator devices: ● A primary collimator; ● Secondary movable beam defining collimators; ● An MLC (optional). In addition to the primary and secondary collimators, clinical electron beams also rely on electron beam applicators (cones) for beam collimation. — The primary collimator defines the largest available circular field size and is a conical opening machined into a tungsten shielding block, with the sides of the conical opening projecting on to edges of the target on one end of the block and on to the flattening filter on the other end. The thickness of the shielding block is usually designed to attenuate the average primary X ray beam intensity to less than 0.1% of the initial value (three tenth-value layers (TVLs)). According to IEC recommendations, the maximum leakage should not exceed 0.2% of the open beam value. — The secondary beam defining collimators consist of four blocks, two forming the upper and two forming the lower jaws of the collimator. They can provide rectangular or square fields at the linac isocentre, with sides of the order of few millimetres up to 40 cm. — Modern linacs incorporate independent (asymmetric) jaws that can provide asymmetric fields, most commonly one half or three quarter blocked fields in which one or two beam edges, respectively, are coincident with the beam central axis. — MLCs are a relatively recent addition to linac dose delivery technology. In principle, the idea behind an MLC is simple; however, building a reliable MLC system presents a substantial technological challenge. — The number of leaves in commercial MLCs is steadily increasing, and models with 120 leaves (60 pairs) covering fields up to 40 × 40 cm2 and requiring 120 individually computer controlled motors and control circuits are currently available. — MLCs are becoming invaluable in supplying intensity modulated fields in conformal radiotherapy, either in the step and shoot mode or in a continuous dynamic mode. 148

TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY — Miniature versions of MLCs (micro MLCs) projecting 1.5–6 mm leaf widths and up to 10 × 10 cm2 fields at the linac isocentre are currently commercially available. They may be used in radiosurgery as well as for head and neck treatments. 5.5.14. Production of clinical electron beams in a linac The majority of higher energy linacs, in addition to providing single or dual photon energies, also provide electron beams with several nominal electron beam energies in the range from 6 to 30 MeV. ● To activate an electron beam mode, both the target and the flattening filter of the X ray beam mode are removed from the electron beam. ● The electron beam currents producing clinical electron beams are two to three orders of magnitude lower than the electron currents producing the clinical photon beams in the linac X ray target. ● The electron pencil beam exits the evacuated beam transport system through a thin window usually made of beryllium, which, with its low atomic number Z, minimizes the pencil beam scattering and brems- strahlung production. ● Two techniques are available for producing clinical electron beams from electron pencil beams: —Pencil beam scattering. The scattering of the electron pencil beam over the relatively large area used in radiotherapy (up to 25 × 25 cm2) is achieved by placing thin foils of high Z material (copper or lead) into the pencil beam at the level of the flattening filter in the X ray mode. —Pencil beam scanning. Electron pencil beam scanning is an alternative, albeit infrequently used, technique for producing clinical electron beams. The technique is usually implemented with two computer controlled magnets, which deflect the pencil beam in two orthogonal planes, thereby scanning the pencil beam across the clinical treatment field. 5.5.15. Dose monitoring system IEC 60601-2-1 specifies in detail the standards for radiation monitors installed in clinical electron linacs. It deals with standards for the type of radiation detectors, display of monitor units (MUs), termination of radiation and monitoring of beam flatness and dose rate. 149

CHAPTER 5 ● Most common dose monitors in linacs are transmission ionization chambers permanently imbedded in the linac clinical photon and electron beams to monitor the beam output continuously during patient treatment. ● Most linacs use sealed ionization chambers to make their response independent of ambient temperature and pressure. ● The customary position of the dose monitor chambers is between the flattening filter or scattering foil and the photon beam secondary collimator. ● For patient safety, the linac dosimetry system usually consists of two separately sealed ionization chambers with completely independent biasing power supplies and readout electrometers. If the primary chamber fails during patient treatment, the secondary chamber will terminate the irradiation, usually after an additional dose of only a few per cent above the prescribed dose has been delivered. ● In the event of a simultaneous failure of both the primary and secondary ionization chambers, the linac timer will shut the machine down with a minimal overdose to the patient. ● The main requirements for the ionization chamber monitors are as follows: —Chambers must have a minimal effect on clinical photon and electron radiation beams; —Chamber response should be independent of ambient temperature and pressure (most linacs use sealed ionization chambers to satisfy this condition); —Chambers should be operated under saturation conditions. ● The primary ionization chamber measures MUs. Typically, the sensitivity of the chamber electrometer circuitry is adjusted in such a way that 1 MU corresponds to a dose of 1 cGy delivered in a water phantom at the depth of dose maximum on the central beam axis when irradiated with a 10 × 10 cm2 field at a source to surface distance (SSD) of 100 cm. ● Once the operator preset number of MUs has been reached, the primary ionization chamber circuitry shuts the linac down and terminates the dose delivery to the patient. Before a new irradiation can be initiated, it is necessary to reset the MU displays to zero. Furthermore, irradiation is not possible until a new selection of MUs has been made. ● In addition to monitoring the primary dose in MUs, the dose monitoring system also monitors other operating parameters such as the beam energy, flatness and symmetry. Measurement of all these additional parameters requires that the ionization chamber electrodes of the primary and secondary chambers be divided into several sectors, with the 150

TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY resulting signals used in automatic feedback circuits to steer the electron beam through the accelerating waveguide, beam transport system and on to the target or scattering foil, thereby ensuring beam flatness and symmetry. The particular design of the ionization chamber electrodes and sectors varies from one manufacturer to another. ● Linacs must be equipped with a monitoring system that continuously displays the machine isocentre dose rate and terminates the beam when the measured dose rate exceeds twice the maximum specified by the technical machine description. ● When the linac is capable of producing more than one beam energy or more than one beam mode (X rays or electrons), after termination of irradiation further irradiation is prevented until the selection of energy and beam mode has been made afresh and entered into the control console. ● Similarly, for linacs capable of stationary as well as moving beam radio- therapy, after termination of irradiation further irradiation is prevented until stationary radiotherapy or moving beam radiotherapy has been selected afresh and entered into the control console. 5.6. RADIOTHERAPY WITH PROTONS, NEUTRONS AND HEAVY IONS External beam radiotherapy is carried out mainly with machines that produce either X rays or electrons. In a few specialized centres around the world, external beam radiotherapy is also carried out with heavier particles, such as: ● Neutrons produced by neutron generators and cyclotrons; ● Protons produced by cyclotrons and synchrotrons; ● Heavy ions (helium, carbon, nitrogen, argon, neon) produced by synchro- cyclotrons and synchrotrons. These particles offer some distinct advantages over the standard X ray and electron modalities, such as: — Considerably lower oxygen enhancement ratio (OER) for neutrons (see Section 14.10); — Improved dose–volume histograms (DVHs) for protons and heavy ions (see Section 7.6). 151

CHAPTER 5 However, equipment for production of protons, neutrons and heavy ions is considerably more expensive than standard radiotherapy equipment, both in capital costs and in maintenance and servicing costs, thus precluding a widespread use in standard radiotherapy departments. The decreasing costs of proton cyclotrons are likely to result in a wider use of proton beam therapy in the future. 5.7. SHIELDING CONSIDERATIONS External beam radiotherapy is carried out mainly with three types of equipment that produces either X rays or electrons: ● X ray machines (superficial and orthovoltage); ● Teletherapy (60Co) machines; ● Linacs. All radiotherapy equipment must be housed in specially shielded treatment rooms in order to protect personnel and the general public in areas adjacent to the treatment rooms. The treatment rooms must comply not only with structural building codes but also with national and international regulations that deal with shielding requirements to render an installation safe from the radiation protection point of view. During the planning stage for a radiotherapy machine installation, a qualified medical physicist determines the required thickness of primary and secondary barriers and provides the information to the architect and structural engineer for incorporation into the architectural drawing for the treatment room. Superficial and orthovoltage X ray therapy rooms are shielded either with ordinary concrete (2.35 g/cm3) or lead. In this energy range the photo- electric effect is the predominant mode of photon interaction with matter, making the use of lead very efficient for shielding purposes. Megavoltage treatment rooms (often referred to as bunkers or vaults because of the large barrier thickness required for shielding) are most commonly shielded with ordinary concrete so as to minimize construction costs. The Compton effect is the predominant mode of photon interaction with shielding material in this energy range. To conserve space, other higher density materials may be used, with the required wall thickness inversely proportional to the density of the shielding material. Thus the use of high density concrete (5 g/cm3) will cut the required thickness of an ordinary concrete barrier by approximately one half; however, it will also increase the construction material cost by a factor of 30. 152

TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY Shielding issues related to linac bunkers are discussed in more detail in Section 16.17. 5.8. COBALT-60 TELETHERAPY UNITS VERSUS LINACS After the inception of radiotherapy soon after the discovery of X rays by Roentgen in 1895, the technology of radiation production was first aimed towards ever higher photon energies and intensities and more recently towards computerization and intensity modulated beam delivery. During the first 50 years of radiotherapy, technological progress was relatively slow and mainly based on X ray tubes, van de Graaff generators and betatrons. The first truly practical megavoltage therapy machine was the 60Co teletherapy machine developed in Canada in the 1950s. The invention of 60Co teletherapy provided a tremendous boost in the quest for higher photon energies and placed the 60Co unit in the forefront of radiotherapy for a number of years, mainly because it incorporated a radioactive source that is charac- terized by features extremely useful for radiotherapy. The important features of 60Co teletherapy machines can be summarized as follows: ● Relatively high energy g ray emission; ● Relatively long half-life; ● Relatively high specific activity; ● Relatively simple means of production. Figure 5.8(a) shows a 60Co teletherapy machine; Fig. 5.8(b) shows a stamp issued by Canada Post commemorating Canada’s role in the development of the 60Co machine. Linacs were developed concurrently by two groups: W.W. Hansen’s group at Stanford University in the USA and D.D. Fry’s group at the Telecommunica- tions Research Establishment in the UK. Both groups were interested in linacs for research purposes and profited heavily from the microwave radar technology developed during World War II, using 3000 MHz as the design frequency. The potential for the use of linacs in radiotherapy became apparent in the 1950s, and the first clinical linac was installed in the 1950s at the Hammersmith Hospital in London. During subsequent years, the linac eclipsed the cobalt unit and became the most widely used radiation source in modern radiotherapy, with several thousand units in clinical practice around the world today. In 153

CHAPTER 5 (a) (b) FIG. 5.8. Cobalt-60 teletherapy machine. (a) Theratron Equinox, a megavoltage external beam therapy system using cobalt technology, manufactured by MDS Nordion, Ottawa, Canada (published with permission from MDS Nordion). (b) Schematic diagram of a cobalt unit depicted on a postage stamp issued by Canada Post in 1988 in honour of H.E. Johns, who invented the 60Co unit in the 1950s (© Canada Post Corporation, 1988; reproduced with permission). contrast to a 60Co unit, which provides essentially only one g energy of 1.25 MeV, a linac can provide either megavoltage electron or X ray therapy with a wide range of energies. Figure 5.9 shows a modern dual energy linac. In comparison with 60Co machines, linacs have become very complex in design: 154

TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY (a) (b) FIG. 5.9. Modern dual photon energy linac manufactured by Varian; the gantry and the patient support assembly are clearly shown. (a) The portal imager is retracted; (b) the portal imager is activated. (Photographs courtesy of Varian Oncology Systems.) 155

CHAPTER 5 — In part because of the multimodality capabilities that have evolved and are available on most modern machines; — In part because of an increased use of computer logic and microproc- essors in the control systems of these machines; — In part because of added features, such as high dose rate modes, multileaf collimation, electron arc therapy and the dynamic treatment option, which is characterized by a controlled motion on the collimators (dynamic wedge), MLC leaves (IMRT), gantry or table while the beam is turned on. Despite the clear technological and practical advantages of linacs over 60 Co machines, the latter still occupy an important place in the radiotherapy armamentarium, mainly because of the considerably lower capital, installation and maintenance costs of 60Co machines compared with linacs. In the developing world, 60Co machines, because of their relatively lower costs, simplicity of design and ease of operation, are likely to play an important role in cancer therapy for the foreseeable future. Many modern features of linacs, such as MLCs, dynamic wedges and dynamic operation, could be installed on modern 60Co machines to allow, at a lower cost, a similar sophistication in treatment as linacs. It is unfortunate that manufacturers of 60Co units are very slow in reacting to new technological developments in radiotherapy, conceding pre-eminence to linac manufacturers even in areas where it would be much easier and more practical to run 60Co machines than linacs. 5.9. SIMULATORS AND COMPUTED TOMOGRAPHY SIMULATORS Simulators and CT simulators are important components of equipment used in radiotherapy. They cover several crucial steps in the radiotherapeutic process that are not related to the actual dose delivery but are nonetheless very important, as they deal with the determination of target location, treatment planning and spatial accuracy in dose delivery. The determination of the target volume that is related to the extent of the disease (see Section 7.2) and its position relative to adjacent critical normal tissues can be achieved with various methods. These range from a simple clinical examination through planar X ray imaging to the use of complex modern imaging equipment such as CT scanners in conjunction with magnetic resonance (MR) and PET scanners. Both simulators and CT simulators incorporate three major systems: the mechanical, X ray tube and imaging equipment. The major steps in the target localization and field design are: 156

TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY ● Acquisition of the patient data set; ● Localization of target and adjacent structures; ● Definition and marking of the patient coordinate system; ● Design of treatment fields; ● Transfer of data to the treatment planning system (TPS); ● Production of an image for treatment verification. The six steps above can be achieved either with a conventional simulator or with a CT simulator; however, the CT simulator provides for the more elegant, reliable and practical means to achieve the six steps, in addition to providing reliable external and internal contours and electron density infor- mation. 5.9.1. Radiotherapy simulator A radiotherapy simulator consists of a diagnostic X ray tube mounted on a rotating gantry, simulating geometries identical to those found on megavoltage therapy machines that are either isocentric teletherapy 60Co units or isocentric linacs. Thus the simulator enjoys the same degrees of freedom as a megavoltage machine, but rather than providing a megavoltage beam for treatment it provides a diagnostic quality X ray beam suitable for imaging, either in the radiographic mode (image recorded on radiographic film) or in the fluoroscopic mode (image recorded on a TV monitor using an image intensifier). A modern simulator should mimic all the mechanical features and geometric field arrangements of various megavoltage machines, ranging from 60 Co machines with an SAD of 80 cm to high energy linacs with an SAD of 100 cm. In megavoltage machines, radiation fields are defined with collimators (upper and lower jaws), while in simulators the rectangular and square fields are defined with delineator wires to enable visualization of the target as well as of healthy tissues adjacent to the target. A modern simulator covers the following processes: ● Tumour and adjacent normal tissue localization; ● Treatment simulation; ● Treatment plan verification; ● Monitoring of treatment. 157

CHAPTER 5 5.9.2. Computed tomography simulator CT simulators are CT scanners equipped with special features that make them useful for certain stages in the radiotherapeutic process. The special features typically are: ● A flat table top surface to provide a patient position during simulation that will be identical to the position during treatment on a megavoltage machine. ● A laser marking system to transfer the coordinates of the tumour isocentre, derived from the contouring of the CT data set, to the surface of the patient. Two types of laser marking systems are used: a gantry mounted laser and a system consisting of a wall mounted moveable sagittal laser and two stationary lateral lasers. ● A virtual simulator consisting of software packages that allow the user to define and calculate a treatment isocentre and then simulate a treatment using digitally reconstructed radiographs (DRRs). A CT simulator essentially obviates the need for conventional simulation by carrying out two distinct functions: — Physical simulation, which covers the first three of the six target locali- zation steps listed above; — Virtual simulation, which covers the last three of the six target localization steps listed above. In CT simulation the patient data set is collected and target localization is carried out using CT images with fluoroscopy and radiography replaced by DRRs. A laser alignment system is used for marking and a virtual simulator software package is used for field design and production of verification images. Transfer of all necessary information to the TPS is achieved electronically. The planar simulation X ray film provides a beam’s eye view (BEV) of the treatment portal but does not provide 3-D information about anatomical structures. CT, on the other hand, provides anatomical information and target definition but does not allow a direct correlation with the treatment portals. A DRR is the digital equivalent of a planar simulation X ray film (see also Section 7.4.8). It is reconstructed from a CT data set using virtual simulation software available on a CT simulator or a TPS and represents a computed radiograph of a virtual patient generated from a CT data set repre- senting the actual patient. Just like a conventional radiograph, the DRR accounts for the divergence of the beam. 158

TREATMENT MACHINES FOR EXTERNAL BEAM RADIOTHERAPY The basic approach to producing a DRR involves several steps: choice of virtual source position; definition of image plane; ray tracing from virtual source to image plane; determination of the CT value for each volume element traversed by the ray line to generate an effective transmission value at each pixel on the image plane; summation of CT values along the ray line (line integration); and grey scale mapping. An extension of the DRR approach is the digitally composited radiograph (DCR), which provides an enhanced visualization of bony landmarks and soft tissue structures. This is achieved by differentially weighting ranges of CT numbers that correspond to different tissues to be enhanced or suppressed in the resulting DCR images. 5.10. TRAINING REQUIREMENTS The increased complexity of radiotherapy equipment demands that equipment be used only by highly trained and competent staff, in order to minimize the potential for accidents. A recent report by the IAEA summarized the lessons learned from accidental exposures in radiotherapy, and a report by the American Association of Physicists in Medicine (AAPM) specifically addressed medical accelerator safety considerations. Of vital importance in the purchase, installation and clinical operation of radiotherapy equipment are the following: (a) Preparation of an equipment specification document; (b) Design of the treatment room and radiation safety; (c) Acceptance testing of equipment; (d) Commissioning of equipment; (e) A quality assurance programme. Items (a), (c) and (d) are addressed in detail in Chapter 10, item (e) is addressed in Chapter 12 and item (b) is addressed in Chapter 16. 159

CHAPTER 5 BIBLIOGRAPHY AMERICAN ASSOCIATION OF PHYSICISTS IN MEDICINE, Medical accelerator safety considerations: Report of AAPM Radiation Therapy Committee Task Group No. 35, Med. Phys. 20 (1993) 1261–1275. COIA, L., SHULTHEISS, T.E., HANKS, G.E., A Practical Guide to CT Simulation, Advanced Medical Publishing, Madison, WI (1995). GREENE, D., WILLIAMS, P.C., Linear Accelerators for Radiation Therapy, Institute of Physics Publishing, Bristol (1997). INTERNATIONAL ATOMIC ENERGY AGENCY, Lessons Learned from Accidental Exposures in Radiotherapy, Safety Reports Series No. 17, IAEA, Vienna (2000). INTERNATIONAL ELECTROTECHNICAL COMMISSION, Medical Electrical Equipment: Particular Requirements for the Safety of Electron Accelerators in the Range 1 MeV to 50 MeV, Rep. 60601-2-1, IEC, Geneva (1998). JOHNS, H.E., CUNNINGHAM, J.R., The Physics of Radiology, Thomas, Springfield, IL (1984). KARZMARK, C.J., NUNAN, C.S., TANABE, E., Medical Electron Accelerators, McGraw-Hill, New York (1993). KHAN, F., The Physics of Radiation Therapy, Lippincott, Williams and Wilkins, Baltimore, MD (2003). PODGORSAK, E.B., METCALFE, P., VAN DYK, J., “Medical accelerators”, The Modern Technology in Radiation Oncology: A Compendium for Medical Physicists and Radiation Oncologists (VAN DYK, J., Ed.), Medical Physics Publishing, Madison, WI (1999) 349–435. 160

Chapter 6 EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS E.B. PODGORSAK Department of Medical Physics, McGill University Health Centre, Montreal, Quebec, Canada 6.1. INTRODUCTION Radiotherapy procedures fall into two main categories: external beam radiotherapy and brachytherapy. In external beam radiotherapy the radiation source is at a certain distance from the patient and the target within the patient is irradiated with an external radiation beam. In brachytherapy (see Chapter 13) radiation sources are placed directly into the target volume (intracavitary or interstitial brachytherapy) or on to a target (surface mould or intraoperative radiotherapy). Most external beam radiotherapy is carried out with photon beams, some with electron beams and a very small fraction with more exotic particles such as protons, heavier ions or neutrons. This chapter deals with external photon beam radiotherapy. Photon external beams are all characterized by the same physical parameters, but fall into various categories depending on their origin, means of production and energy. There are two origins of photon beams: g rays, which originate from radioactive nuclei, and X rays, which originate in a target bombarded with energetic electrons. The X rays from a target consist of bremsstrahlung photons and characteristic photons. X rays are produced either in an X ray tube (super- ficial or orthovoltage X rays) or in a linac (megavoltage X rays). 6.2. QUANTITIES USED IN DESCRIBING A PHOTON BEAM Radiation dosimetry deals with two distinctly different entities: one describes the photon radiation beam itself in terms of the number and energies of photons constituting the photon beam and the other describes the amount of energy the photon beam may deposit in a given medium such as air, water or biological material. 161

CHAPTER 6 6.2.1. Photon fluence and photon fluence rate The photon fluence f is defined as the quotient dN by dA, where dN is the number of photons that enter an imaginary sphere of cross-sectional area dA: dN f (6.1) dA The unit of photon fluence f is cm–2. The photon fluence rate is defined as the photon fluence per unit time: df j= (6.2) dt The unit of photon fluence rate is cm–2·s–1. 6.2.2. Energy fluence and energy fluence rate The energy fluence Y describes the energy flow in a photon beam and is defined as the amount of energy dE crossing a unit area dA: dE <= (6.3) dA The unit of energy fluence Y is MeV/cm2. For a monoenergetic beam, dE is the number of photons dN times their energy hn, and the energy fluence Y in terms of photon fluence f is: Y = fhn (6.4) The energy fluence rate Y is defined as the energy fluence per unit time: dy Y= (6.5) dt The unit of energy fluence rate is MeV·cm–2·s–1. 162

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS 6.2.3. Air kerma in air For a monoenergetic photon beam in air the air kerma in air (Kair)air at a given point away from the source is proportional to the energy fluence Y or photon fluence f as follows: Êm ˆ Êm ˆ (K air ) air = y Á tr ˜ = f hn Á tr ˜ (6.6) Ë r ¯ air Ë r ¯ air where (mtr/r)air is the mass–energy transfer coefficient for air at photon energy hn. Kerma K consists of two components: the collision kerma Kcol and the radiative kerma Krad: K = Kcol + Krad (6.7) For monoenergetic photons in air the collision kerma Kcol is proportional to Y and f through the following relationship: Êm ˆ Êm ˆ K col = y Á ab ˜ = hnf Á ab ˜ (6.8) Ë r ¯ air Ë r ¯ air where (mab/r)air is the mass–energy absorption coefficient for air at photon energy hn. Often in the literature the energy absorption coefficient mab is denoted as men. The mass–energy transfer coefficient (mtr/r) and mass–energy absorption coefficient (mab/r) are related through the following relationship: m ab m tr = (1 - g ) (6.9) r r where g is the radiative fraction (i.e. the fraction of the energy of secondary charged particles (electrons) that is lost to bremsstrahlung rather than being deposited in the medium). For low atomic number Z materials and photon energies below 1 MeV, the radiative fraction g ª 0, (µtr/r) ª (µab/r) and K ª Kcol. 163

CHAPTER 6 6.2.4. Exposure in air col The collision air kerma in air (K air ) air is related to exposure in air X through the following relationship: (K air ) air = X (Wair / e) col (6.10) where (Wair/e), as discussed in Section 9.1.3, is the average energy required to produce an ion pair in dry air (33.97 eV/ion pair). The special unit of exposure is the roentgen (R), while the SI unit is 2.58 × 10–4 C/kg with 1 R = 2.58 × 10–4 C/kg. Thus: Ê C Jˆ Ê cGy ˆ (K air ) air = Á 2.58 ¥ 10 -4 col 33.97 ˜ X = Á 0.876 ˜X (6.11) Ë kg air R C¯ Ë R ¯ with the exposure X given in roentgens. 6.2.5. Dose to small mass of medium in air The concept ‘dose to small mass of medium in air’, also known as ‘dose in free space’, was introduced by Johns and Cunningham to characterize the output of a radiation unit and to gain a reference dose for dosimetric calcula- tions involving tissue–air ratios (TARs) and peak scatter factors (PSFs). The ‘dose to small mass of medium in air’ is designated as D′ and is based on a med measurement of the air kerma in air. The concept has gained widespread use in orthovoltage and 60Co therapy, but is of limited use in megavoltage linac beam therapy. The steps involved in determining the ‘dose to small mass of medium in air’ D′ at point P in a radiation beam from a signal MP measured with an med ionization chamber centred at point P in air are: (1) ( 2) ( 3) ( 4) ( 5) MP Æ XP Æ (K air ) air Æ (K D m ) air Æ (K med ) air Æ Dmed ¢ (6.12) where MP is the signal measured with an ionization chamber at point P and corrected for influence quantities such as air temperature, air pressure and recombination loss (see Section 9.3). The ionization chamber should have an 164

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS appropriate buildup cap and an exposure calibration coefficient in air NX or an air kerma in air calibration coefficient NK. ● Step 1: Determine XP , the exposure at point P, through: XP = M P NX (6.13) ● Step 2: Determine (Kair)air, the air kerma in air at point P, through: cGy (K air ) air = 0.876 XP (6.14) R Alternatively, (Kair)air may be determined from MP directly, if NK for the chamber is known, as follows: (Kair)air = MPNK (6.15) ● Step 3: Determine collision kerma to Dm, an infinitesimal mass of any other material (e.g. water), in air from: Dm Êm ˆ (K D m )air = (K air) air Á ab ˜ (6.16) Ë r ¯ air Dm where ( m ab / r ) air is the ratio of spectrum averaged mass–energy absorption coefficients for Dm and air. ● Step 4: Determine collision kerma to a spherical mass of medium centred around P and having a radius rmed just large enough to provide charged particle equilibrium (CPE) at point P: (Kmed)air = (KDm)air(rmed) (6.17) where k(rmed) is a correction factor accounting for the photon beam attenuation in the spherical mass of medium and approximated as: Êm ˆ - Á ab ˜ rr Ë r ¯ med med k(rmed ) ª e (6.18) (µab/r)med in Eq. (6.18) is the mass–energy absorption coefficient and r is the density of the medium. For water, which is usually chosen as the 165

CHAPTER 6 medium, k(rmed) ª 0.985 for 60Co photons and approximately 1 for lower photon energies. ● Step 5: ‘Dose to small mass of medium in free space’ D′med is obtained from the following relationship: med cGy Ê m ab ˆ Dmed = b (K med ) air = b 0.876 ¢ X k (r ) (6.19) R Á r ˜ air P med Ë ¯ where b is a proportionality constant equal to 1.003, 1.001 and 1.0 for 60 Co, 137Cs and X rays below 350 kVp, respectively. Often b is assumed equal to 1, even for 60Co g rays. The product: med cGy Ê m ab ˆ 0.876 R Á r ˜ air Ë ¯ is usually referred to as the roentgen to cGy conversion factor fmed, and the ‘dose to small mass of medium in air’, assuming that b ª 1, can then be written as: D′ = fmed Xk(rmed) med (6.20) 6.3. PHOTON BEAM SOURCES Photon sources are either isotropic or non-isotropic and they emit either monoenergetic or heterogeneous photon beams. The most common photon sources used in radiation oncology are X ray machines, teletherapy radio- isotope sources and linacs. ● An isotropic photon source produces the same photon fluence rate in all directions, while the photon fluence rate from a non-isotropic source depends on the direction of measurement. ● A plot of number of photons per energy interval versus photon energy is referred to as a photon spectrum. Photon spectra for a monoenergetic and a heterogeneous photon beam are shown in Figs 6.1(a) and (b), respectively. The area under the curve in Fig. 6.1(b) represents the total number of photons in the beam: 166

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS df ( hn ) f= Ú dhn dhn (6.21) ● All photons in a monoenergetic photon beam have the same energy hn (Fig. 6.1(a)). Photons in a heterogeneous X ray beam form a distinct spectrum, with photons present in all energy intervals from 0 to a maximum value hnmax, which is equal to the kinetic energy of electrons striking the target (Fig. 6.1(b)). ● In Fig. 6.1(b) the two spikes in the spectrum represent characteristic photons, while the continuous spectrum from 0 to hnmax represents bremsstrahlung photons. ● g ray sources are usually isotropic and produce monoenergetic photon beams, while X ray targets are non-isotropic sources producing heteroge- neous photon spectra. ● Narrow monoenergetic photon beams will have identical first and second half-value layers (HVLs). In narrow heterogeneous photon beams, on the other hand, the second HVL will be either larger or smaller than the first HVL: larger in the superficial and orthovoltage range because of beam hardening effects and smaller in the high megavoltage range because of beam softening effects. 6.4. INVERSE SQUARE LAW In external beam radiotherapy, photon sources are often assumed to be point sources and the beams they produce are divergent beams, as shown schematically in Fig. 6.2. Let us assume that we have a photon point source S and a square field with side a (area A = a2) at a distance fa from the source. At (a) (b) df df dhn dhn 0 0 hn hnmax hn FIG. 6.1. Typical spectra for (a) monoenergetic and (b) heterogeneous photon beams. 167

CHAPTER 6 a distance fb we then have a square field with side b (area B = b2), and the two fields are geometrically related as follows: a/2 b/2 tg b = = fa fb or (6.22) a fa = b fb where b is the angle between the beam central axis and the geometric beam edge. The photon source S emits photons and produces a photon fluence fA at distance fa and a photon fluence fB at distance fb. Since the total number of Photon source S fa Area A = a2 fb a b Area B = b2 b Central axis FIG. 6.2. Divergent photon beam originating in a photon point source. At distance fa from the source S the field size is A = a2, at distance fb the field size is B = b2. 168

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS photons Ntot crossing area A is equal to the total number of photons crossing area B (assuming no photon interactions take place in air between area A and area B), we can write: Ntot = fAA = fBB and f A B b 2 f b2 = = = (6.23) f B A a 2 f a2 The photon fluence is thus inversely proportional to the square of the distance from the source. For example, if fb = 2fa then the photon fluence at B will be exactly 1/4 of the photon fluence at A (i.e. fB = fA/4). Since at a given point P in air the exposure in air X, air kerma in air (Kair)air and ‘dose to small mass of medium in air’ D′ are directly proportional med to the photon fluence at point P, it is reasonable to conclude that the three quantities X, (Kair)air and D′ all follow this inverse square law behaviour: med 2 X( fa ) (K air ( f a )) air ¢ Dmed ( f a ) Êf ˆ = = =Á b˜ (6.24) X( fb ) (K air ( f b )) air ¢ Dmed ( f b ) Ë f a ¯ 6.5. PENETRATION OF PHOTON BEAMS INTO A PHANTOM OR PATIENT A photon beam propagating through air or a vacuum is governed by the inverse square law; a photon beam propagating through a phantom or patient, on the other hand, is affected not only by the inverse square law but also by the attenuation and scattering of the photon beam inside the phantom or patient. These three effects make the dose deposition in a phantom or patient a complicated process and its determination a complex task. A direct measurement of the dose distribution inside the patient is essentially impossible, yet for a successful outcome of patient radiation treatment it is imperative that the dose distribution in the irradiated volume be known precisely and accurately. This is usually achieved through the use of several functions that link the dose at any arbitrary point inside the patient to the known dose at the beam calibration (or reference) point in a phantom. 169

CHAPTER 6 The functions are usually measured with suitable radiation detectors in tissue equivalent phantoms, and the dose or dose rate at the reference point is determined for, or in, water phantoms for a specific set of reference conditions, such as depth, field size and source to surface distance (SSD), as discussed in detail in Section 9.1. A typical dose distribution on the central axis of a megavoltage photon beam striking a patient is shown in Fig. 6.3. Several important points and regions may be identified. The beam enters the patient on the surface, where it delivers a certain surface dose Ds. Beneath the surface the dose first rises rapidly, reaches a maximum value at depth zmax and then decreases almost exponentially until it reaches a value Dex at the patient’s exit point. The techniques for relative dose measurements are discussed in detail in Section 6.13. Patient Source Dmax = 100 0 zmax zex Dex Ds 0 zmax Depth (z) zex FIG. 6.3. Dose deposition from a megavoltage photon beam in a patient. Ds is the surface dose at the beam entrance side, Dex is the surface dose at the beam exit side. Dmax is the dose maximum often normalized to 100, resulting in a depth dose curve referred to as the percentage depth dose (PDD) distribution. The region between z = 0 and z = zmax is referred to as the dose buildup region. 170

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS 6.5.1. Surface dose For megavoltage photon beams the surface dose is generally much lower than the maximum dose, which occurs at a depth zmax beneath the patient’s surface. In megavoltage photon beams the surface dose depends on the beam energy and field size. The larger the photon beam energy, the lower the surface dose, which for a 10 × 10 cm2 field typically amounts to some 30% of the maximum dose for a cobalt beam, 15% for a 6 MV X ray beam and 10% for an 18 MV X ray beam. For a given beam energy the surface dose increases with the field size. The low surface dose compared with the maximum dose is referred to as the skin sparing effect and represents an important advantage of megavoltage beams over orthovoltage and superficial beams in the treatment of deep seated tumours. Orthovoltage and superficial beams do not exhibit the skin sparing effect, since their dose maximum occurs on the skin surface (i.e. the surface dose is equal to the maximum dose). The surface dose is measured with thin window parallel-plate ionization chambers for both chamber polarities, with the average reading between the positive and negative polarities taken as the surface dose value (see Section 6.13). The surface dose represents contributions to the dose from: ● Photons scattered from the collimators, flattening filter and air; ● Photons backscattered from the patient; ● High energy electrons produced by photon interactions in air and any shielding structures in the vicinity of the patient. 6.5.2. Buildup region The dose region between the surface (depth z = 0) and depth z = zmax in megavoltage photon beams is referred to as the dose buildup region and results from the relatively long range of energetic secondary charged particles (electrons and positrons) that first are released in the patient by photon interactions (photoelectric effect, Compton effect, pair production) and then deposit their kinetic energy in the patient (see Section 2.7.3). ● In the region immediately beneath the patient’s surface, the condition of CPE does not exist and the absorbed dose is much smaller than the collision kerma. However, as the depth z increases, CPE is eventually reached at z = zmax, where z is approximately equal to the range of 171

CHAPTER 6 secondary charged particles and the dose becomes comparable with the collision kerma. ● Beyond zmax both the dose and collision kerma decrease because of the photon attenuation in the patient, resulting in a transient rather than true CPE. 6.5.3. Depth of dose maximum zmax The depth of dose maximum zmax beneath the patient’s surface depends on the beam energy and beam field size. The beam energy dependence is the main effect; the field size dependence is often ignored because it represents only a minor effect. Nominal values for zmax range from zero for superficial and orthovoltage X ray beams, through 0.5 cm for 60Co beams, to 5 cm for 25 MV beams, as shown in Table 6.1. For a given beam energy, the largest zmax occurs for fields of ~5 × 5 cm2. For fields larger than 5 × 5 cm2, zmax decreases because of collimator scatter effects (for cobalt units) and collimator and flattening filter scatter effects (for linacs). For fields smaller than 5 × 5 cm2, zmax decreases because of phantom scatter effects. 6.5.4. Exit dose The dose delivered to the patient at the beam exit point is referred to as the exit dose. As shown schematically in Fig. 6.3, close to the beam exit point the dose distribution curves slightly downwards from the extrapolated dose distribution curve. This relatively small effect is attributed to the missing scatter contribution at the exit point from points beyond the exit dose point. Similarly to the surface dose, the exit dose may be measured with a parallel-plate chamber, in this case with the chamber body orientated towards the source. 6.6. RADIATION TREATMENT PARAMETERS External beam radiotherapy with photon beams is carried out with three types of treatment machine: X ray units, isotope teletherapy units (mainly 60Co units) and linacs. The main parameters in external beam dose delivery with photon beams are the: (a) depth of treatment; (b) field size; (c) SSD in SSD set- ups or source to axis distance (SAD) in SAD (isocentric) set-ups; and (d) photon beam energy. 172

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS TABLE 6.1. TYPICAL DEPTHS OF DOSE MAXIMUM zmax FOR VARIOUS PHOTON BEAM ENERGIES AND A FIELD SIZE OF 5 × 5 cm2 Superficial Orthovoltage Co-60 4 MV 6 MV 10 MV 18 MV 25 MV zmax 0 0 0.5 1 1.5 2.5 3.5 5 (cm) 6.6.1. Radiation beam field size Beams used for radiotherapy have various shapes that usually represent a compromise between the actual target shape and the need for simplicity and efficiency in beam shaping. Four general groups of field shape are used in radiotherapy: square, rectangular, circular and irregular. Square and rectangular fields are usually produced with collimators installed in radiotherapy machines, circular fields with special collimators attached to the treatment machine and irregular fields with custom made shielding blocks or with multileaf collimators (MLCs) attached to the treatment machine. For any arbitrary radiation field an equivalent square or circular field may be found, meaning that the arbitrary field and the equivalent square or circular field will be characterized with similar beam parameters and functions that are of importance in radiation dosimetry. An arbitrary rectangular field with sides a and b will be approximately equivalent to a square radiation field with sides aeq when both fields have the same area/perimeter ratio (Day’s rule): ab a eq 2 = 2(a + b) 4a eq or 2ab a eq = (6.25) a+b An arbitrary square field with sides aeq will be equivalent to a circular field with radius req when both fields have the same area: aeq = p req 2 2 or a eq req = (6.26) p 173

CHAPTER 6 6.6.2. Collimator factor Exposure in air, air kerma in air and ‘dose to small mass of medium in air’ at a given point P in air contain contributions from two components: primary and scatter. ● The primary component is the major component; it comes directly from the source and does not depend on the field size. ● Scatter represents a minor yet non-negligible component; it consists of photons scattered into point P mainly from the collimator but also possibly from the air and the flattening filter of a linac. The scatter component depends on field size A (collimator setting): the larger the field size, the larger the collimator surface available for scattering and consequently the larger the scatter component. Exposure in air X, air kerma in air (Kair)air and ‘dose to small mass of medium in air’ D′ depend on field size A and a parameter referred to as the med collimator factor (CF) (or collimator scatter factor Sc in Khan’s notation, or relative exposure factor (REF) in 1970s notation). The CF is defined as: CF( A, hn ) = S c ( A, hn ) = REF( A, hn ) X ( A, hn ) (K air ( A, hn )) air D¢( A, hn ) = = = (6.27) X (10, hn ) (K air (10, hn )) air D¢(10, hn ) The geometry for the measurement of the CF is shown in Fig. 6.4; Fig. 6.4(a) shows the measurement of D¢(A, hn), while Fig. 6.4(b) shows the measurement of D¢(10, hn). The CF is usually measured with an ionization chamber with a buildup cap of a size large enough to provide maximum dose buildup for the given energy beam. For small fields one may carry out the measurements at large distances from the source so that the buildup cap is fully covered; however, the data are usually corrected back to the nominal SSD of the machine by using the inverse square law. The CF is normalized to 1 for the nominal field of 10 × 10 cm2 at the nominal SSD for the treatment machine. It is larger than 1 for fields A exceeding 10 × 10 cm2 and smaller than 1 for fields A smaller than 10 × 10 cm2. It is usually measured at point P in air with a cylindrical ionization chamber equipped with an appropriate buildup cap and the chamber centre placed at (nominal SSD + zmax) from the source. SSD here stands for the nominal SSD 174

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS (typically 80 or 100 cm for cobalt units and 100 cm for linacs) and zmax for the depth of dose maximum in a phantom for the specific photon beam. In some centres the CF is measured at the machine isocentre. The results are essentially identical to those obtained with measurements carried out at point P in air. 6.6.3. Peak scatter factor The ‘dose to small mass of medium’ D¢P is measured with just enough material around the point of interest P to provide electronic equilibrium (ionization chamber with appropriate buildup cap). D¢P is related to DP, the dose at zmax in a phantom at point P, through the PSF as follows: DP (zmax , A, f , hn ) PSF( A, hn ) = (6.28) DP ( A, hn ) ¢ with the geometry shown in Fig. 6.5. Figure 6.5(a) shows measurement of D¢ P and Fig. 6.5(b) shows measurement of DP. The chamber in part (a) is placed at a distance of f + zmax from the source. At low photon energies zmax = 0, point P is on the surface, and the PSF is referred to as the backscatter factor. The PSF depends on field size A as well as on photon beam energy hn and gives the factor by which the radiation dose at Source Source (a) (b) f = SSD zmax P P A 10 ¥ 10 FIG. 6.4. Geometry for measurement of CF(A, hn). The ‘dose to small mass of water’ is measured at point P in air: in part (a) with field size A, in part (b) with field size 10 × 10 cm2. Parameter f stands for the SSD. 175

CHAPTER 6 point P in air is increased by radiation scattered to point P from the phantom or patient. Typical values for the PSF range from ~1 for small fields of megavoltage beams, through 1.054 for a 10 × 10 cm2 field in a cobalt beam to 1.10 for a 50 × 100 cm2 field in a cobalt beam (used for total body irradiation (TBI)), to 1.50 for a 20 × 20 cm2 field of orthovoltage X rays (HVL = 1 mm of Cu). While backscattering is largest at very low photon energies (classical scattering), the energy of backscattered photons is small at low photon energies, causing a rapid absorption of the scattered photons in the medium. At intermediate and high photon energies the backscattering and side scattering decreases with energy; however, the scattered photons have a higher energy and larger penetrating power. The interrelationship between the amount of backscattering and scattered photon penetration causes the PSF first to increase with beam energy, reaching a peak around HVL ~ 1 mm of Cu, and then to decrease with a further increase in beam energy. The beam quality at which maximum backscatter occurs depends on field size, shifting slightly towards harder radiation with an increase in field size. For a given beam energy hn, the PSF increases with field size, as shown in Fig. 6.6 for a 60Co beam. The scatter factor (SF) (sometimes referred to as relative PSF) for field A is defined as the ratio: PSF( A, hn ) SF( A, hn ) = (6.29) PSF(10, hn ) Source Source (a) (b) f = SSD zmax P P A A FIG. 6.5. Geometry for measurement of the PSF at point P. (a) The measurement of D¢P ; (b) the measurement of DP. The field size A is the same in (a) and (b). 176

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS and thus represents the PSF normalized to 1 for a 10 × 10 cm2 field. In Khan’s notation the scatter factor is referred to as the phantom scatter factor and is denoted as Sp(A). 6.6.4. Relative dose factor For a given photon beam at a given SSD, the dose rate at point P (at depth zmax in a phantom) depends on the field size A; the larger the field size, the larger the dose. The relative dose factor (RDF) (referred to as the total scatter factor (Sc,p) in Khan’s notation, or sometimes the machine output factor) is defined as the ratio of DP(zmax, A, f, hn), the dose at P in a phantom for field A, to DP(zmax, 10, f, hn), the dose at P in a phantom for a 10 × 10 cm2 field: DP (zmax , A, f , hn ) RDF( A, hn ) = S c,p ( A, hn ) = (6.30) DP (zmax , 10, f , hn ) The geometry for measurement of the RDF(A, hn) is shown in Fig. 6.7(a) for the measurement of DP(zmax, A, f, hn) and in Fig. 6.7(b) for the measurement of DP(zmax, 10, f, hn). 1.12 1.10 1.08 PSF 1.06 1.04 1.02 1.00 02 202 402 602 802 Field size (cm2) FIG. 6.6. PSF as a function of field size for a 60Co g ray beam. 177

CHAPTER 6 From the basic definitions of the CF and the SF we can write RDF as the following product: DP (zmax , A, f , hn ) RDF(10, hn ) = DP (zmax , 10, f , hn ) DP ( A, hn )PSF( A, hn ) ¢ = = CF( A, hn ) SF( A, hn ) (6.31) DP (10, hn )PSF(10, hn ) ¢ or in Khan’s notation: Sc,p(A, hn) = Sc(A, hn)Sp(A, hn) (6.32) indicating that the RDF(A) contains two components: scatter from the collimator and scatter from the phantom. Figure 6.8 shows typical values for the RDF(A, hn), CF(A, hn) and SF(A, hn) against field size A for a 60Co beam. All three functions are normalized to 1 for A = 10 × 10 cm2; they are larger than 1 for A > 10 × 10 cm2 and smaller than 1 for A < 10 × 10 cm2. When extra shielding is used on an accessories tray or an MLC is used to shape the radiation field on a patient’s surface into an irregular field B, then the Source Source (a) (b) f = SSD zmax P P A 10 ¥ 10 FIG. 6.7. Geometry for the measurement of the RDF(A). The dose at point P at zmax in a phantom is measured with field A in part (a) and with field 10 × 10 cm2 in part (b). 178

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS RDF(B, hn) is in the first approximation given as: RDF(B, hn) = CF(A, hn)SF(B, hn) (6.33) where field A represents the field set by the machine collimator and field B is the actual irregular field on the patient’s surface. We must note that the behaviour of an MLC as a block or a secondary collimator depends on the MLC design and on the manufacturer in the case of linacs, where the MLC replaces the upper or lower collimator jaws. In this case Eq. (6.33) must be used with caution and its validity should be verified before clinical use. 6.7. CENTRAL AXIS DEPTH DOSES IN WATER: SOURCE TO SURFACE DISTANCE SET-UP 6.7.1. Percentage depth dose Central axis dose distributions inside the patient or phantom are usually normalized to Dmax = 100% at the depth of dose maximum zmax and then 1.100 RDF CF RDF SF 1.050 RDF ( A) = CF( A) ¥ SF ( A) CF SF 1.000 SF CF 0.950 RDF 0 5 10 15 20 25 Side of equivalent square (cm) FIG. 6.8. Typical values for the RDF(A), CF(A) and SF(A) for a 60Co g ray beam as a ifunction of square field size A. All three functions are normalized to 1 for a 10 × 10 cm2 ifield. 179

CHAPTER 6 referred to as the PDD distributions. The PDD is thus defined as follows: PDD(z, A, f , hn ) = 100 DQ /DP = 100 DQ /DP (6.34) where DQ and DQ are the dose and dose rate, respectively, at point Q at depth z on the central axis of the phantom and DP and DP are the dose and dose rate at point P at zmax on the central axis of the phantom. The geometry for PDD definition is shown in Fig. 6.9. Point Q is an arbitrary point at depth z on the beam central axis; point P represents the specific dose reference point at z = zmax on the beam central axis. The PDD depends on four parameters: depth in a phantom z, field size A, SSD (often designated with f ) and photon beam energy hn. The PDD ranges in value from 0 at z Æ • to 100 at z = zmax. The dose at point Q contains two components: primary and scatter. ● The primary component may be expressed as: pri 2 DQ Ê f + zmax ˆ - m eff (z-zmax ) PDD pri = 100 = 100 Á e (6.35) pri DP Ë f +z ˜ ¯ Source f = SSD zmax P z Q A FIG. 6.9. Geometry for PDD measurement and definition. Point Q is an arbitrary point on the beam central axis at depth z, point P is the point at zmax on the beam central axis. The field size A is defined on the surface of the phantom. 180

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS where µeff is the effective linear attenuation coefficient for the primary beam in the phantom material (µeff for a 60Co beam in water is 0.0657 cm–1). ● The scatter component reflects the relative contribution of the scattered radiation to the dose at point Q. As shown in Fig. 6.3, for constant A, f and hn the PDD first increases from the surface to z = zmax and then decreases with a further increase in z. The depth of dose maximum and the surface dose depend on the beam energy; the larger the beam energy, the larger the depth of dose maximum and the lower the surface dose. — For constant z, f and hn the PDD increases with increasing A because of increased scatter contribution to points on the central axis. An example for a 60Co beam is given in Table 6.2. — For constant z, A and hn the PDD increases with increasing f because of a decreasing effect of z on the inverse square factor, which governs the primary component of the photon beam. An example for a 60Co beam is given in Table 6.3. — For constant z, A and f the PDD beyond zmax increases with beam energy because of a decrease in beam attenuation (i.e. because of an increase in beam penetrating power). An example of PDD distributions for 10 × 10 cm2 fields and various megavoltage photon beams is given in Fig. 6.10 and Table 6.4. The size of the buildup region increases with beam energy and the surface dose decreases with beam energy. PDDs for radiotherapy beams are usually tabulated for square fields; however, the majority of fields used in radiotherapy are rectangular or irregularly shaped. The concept of equivalent squares is used to determine the square field that will be equivalent to the given rectangular or irregular field. 6.7.2. Scatter function In radiation dose calculations it is often desirable to separate the scatter component from the total dose at Q: Scatter component at Q = total dose at Q – primary dose at Q = DP PSF( A, hn )PDD(z, A, f , hn ) / 100 - DP PSF(0, hn )PDD(z, 0, f , hn ) / 100 ¢ ¢ 0 (6.36) 181

CHAPTER 6 TABLE 6.2. PERCENTAGE DEPTH DOSES FOR A COBALT-60 BEAM IN WATER FOR VARIOUS FIELD SIZES AND AN SSD OF 100 cm A (cm2) 0×0 5×5 10 × 10 15 × 15 20 × 20 25 × 25 50 × 50 PDD(5, A, 100, Co) 68.2a 76.7 80.4 82.0 83.0 83.4 85.2 a PDD(10, A, 100, Co) 44.7 53.3 58.7 61.6 63.3 64.4 67.3 a PDD(15, A, 100, Co) 29.5 36.5 41.6 44.9 47.1 48.6 49.7 a –1 Calculated using Eq. (6.35) with µeff = 0.0657 cm . TABLE 6.3. PERCENTAGE DEPTH DOSES FOR A COBALT-60 BEAM IN WATER FOR VARIOUS SOURCE TO SURFACE DISTANCES, DEPTH z OF 5 cm IN A PHANTOM AND A FIELD OF A = 10 × 10 cm2 f = SSD (cm) 60 80 100 120 140 PDD(5, 10, f, Co) 76.2 78.8 80.0 81.3 82.3 100.0 SSD = 100 cm 10 ¥ 10 cm2 80.0 25 18 10 6 60.0 4 PDD Co 40.0 20.0 0.0 0 5 10 15 20 Depth in water (cm) FIG. 6.10. PDD curves in water for a 10 × 10 cm2 field at an SSD of 100 cm for various megavoltage photon beams ranging from 60Co g rays to 25 MV X rays. 182

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS TABLE 6.4. PERCENTAGE DEPTH DOSES FOR VARIOUS PHOTON BEAMS IN A WATER PHANTOM WITH A FIELD SIZE A OF 10 × 10 cm2, AN SSD OF 100 cm AND TWO DEPTHS: 5 cm AND 10 cm Photon beam hn Co-60 4 MV 6 MV 10 MV 18 MV 25 MV Nominal zmax (cm) 0.5 1.0 1.5 2.5 3.5 5.0 PDD(5, 10, 100, hn) 80 84 86 92 97 98 PDD(10, 10, 100, hn) 59 65 67 74 80 82 The scatter function S(z, A, f, hn) is then defined as: S(z, A, f , hn ) = PSF( A, hn )PDD(z, A, f , hn ) - PSF(0, hn )PDD(z, 0, f , hn ) (6.37) giving the scatter dose at point Q per 100 cGy of primary dose at point P. Note: PSF(0) = 1 and PDD(z, 0, f, hn) is the primary PDD calculated with Eq. (6.35). Similarly to the PDD, the scatter function S also depends on four parameters: depth z, field size A, SSD f and beam energy hn. ● For constant A, f and hn the scatter function S first increases with z, reaches a peak and then slowly decreases, with a further increase in z. ● For constant z, f and hn, S increases with field size A. ● At z = zmax the scatter function S is given by: S(zmax, A, f, hn) = 100[PSF(A, hn) – 1] (6.38) 6.8. CENTRAL AXIS DEPTH DOSES IN WATER: SOURCE TO AXIS DISTANCE SET-UP When multiple fields are used for the treatment of a particular tumour inside the patient, isocentric (SAD) set-ups are often used because they are more practical in comparison with constant SSD set-ups. Most megavoltage units are mounted isocentrically with an SAD of 80 cm, or more commonly 100 cm, to allow this treatment option. In contrast to SSD set-ups, which rely on PDD distributions, SAD set-ups rely on other functions, such as TARs and tissue–phantom ratios (TPRs), for dosimetric calculations. 183

CHAPTER 6 6.8.1. Tissue–air ratio The TAR(z, AQ, hn) was originally introduced by Johns to simplify dose calculations in rotational radiotherapy, but its use was subsequently expanded to isocentric irradiations with multiple stationary fields. In rotational radio- therapy the radiation source moves in a circle around the axis of rotation, which is usually inside the tumour. During the rotation around the patient the SSD varies with the patient contour; however, the SAD remains constant. TAR(z, AQ, hn) is defined as the ratio of the dose DQ or dose rate DQ at point Q on the central axis in the patient or phantom to the dose D¢Q or dose rate DQ , the ‘dose (rate) to small mass of water in air’, at the same point Q on the beam central axis: DQ DQ TAR(z, AQ , hn ) = = (6.39) ¢ DQ ¢ DQ The geometry for TAR measurement is shown in Fig. 6.11(a) for measurement of DQ in a phantom and in Fig. 6.11(b) for measurement of D¢Q in air. The field size AQ is defined at point Q, which is normally placed in the isocentre of the treatment machine. In contrast to PDD(z, A, f, hn), which depends on four parameters, TAR(z, AQ, hn) depends only on three: depth z, field size AQ at depth z and Source Source (a) (b) SSD SAD P P z Q Q AQ AQ FIG. 6.11. Geometry for measurement and definition of TAR. (a) The dose is determined at point Q in a water phantom; (b) the ‘dose to small mass of water’ is determined at point Q. Point Q is at the machine isocentre at a distance SAD from the source. The beam field size AQ is defined at depth z in the phantom. 184

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS beam energy hn; there is essentially no SSD or SAD dependence in the range of SSDs used clinically (50–150 cm). TARs for various 60Co beams at depths of 5 and 10 cm in water are given in Table 6.5. ● For constant AQ and hn, the TAR decreases with an increasing z beyond zmax. ● For constant z and hn, the TAR increases with increasing AQ. ● For constant z and AQ, the TAR increases with hn. ● For z = zmax, the TAR becomes identical to the PSF: TAR(z = zmax, AQ = AP, hn) = PSF(AP , hn) (6.40) ● The zero area TAR (i.e. TAR(z, 0, hn) may be calculated from TAR(z, 0, hn ) = e - m eff (z-zmax ) (6.41) where µeff is the effective attenuation coefficient for the photon beam hn. A 0 × 0 field is a hypothetical field in which the dose at depth in a phantom is entirely due to primary photons, since the volume that can scatter radiation is zero. TARs are most reliably measured with ionization chambers; however, the measurements are much more cumbersome than those of PDDs. In the case of TARs the depth in water must be measured in such a way that the distance between the ionization chamber and the radiation source remains constant, which is difficult to achieve using automatic techniques. Moreover, the measurement of the ‘dose to small mass of water’ must be carried out with great care in order to ensure full buildup and readings free of radiation scattered into the chamber from the treatment room walls or floor. Since the concept of ‘dose to small mass of medium’ is not recommended for use with megavoltage beams above 60Co and 4 MV, the concept of TAR is not used in the dosimetry of medium and high energy photon beams. For these energies functions are used that are similar to the TAR but that do not suffer the limitations imposed on the measurement of the ‘dose to small mass of medium’. 6.8.2. Relationship between TAR(d, AQ, hv) and PDD(d, A, f, hv) As shown in Fig. 6.12, a simple relationship may be derived between TAR(z, AQ, hn) and the corresponding PDD(z, A, f, hn) from the basic 185

CHAPTER 6 TABLE 6.5. TISSUE–AIR RATIOS FOR A COBALT-60 BEAM IN WATER FOR VARIOUS FIELD SIZES AQ AND TWO DEPTHS IN A PHANTOM: 5 cm AND 10 cm AQ (cm2) 0×0 5×5 10 × 10 15 × 15 20 × 20 25 × 25 TAR(5, AQ, Co) 0.744a 0.864 0.921 0.953 0.974 0.986 a TAR(10, AQ, Co) 0.536 0.654 0.731 0.779 0.809 0.831 a TAR(20, AQ, Co) 0.278 0.354 0.418 0.470 0.509 0.536 a Calculated using Eq. (6.41) with µeff = 0.0657 cm–1. definitions governing the two functions. The basic definitions for the two functions are: DQ TAR(z, AQ , hn ) = (6.42) ¢ DQ DQ PDD(z, A, f , hn ) = 100 (6.43) DP Source f = SSD P zmax A z Q AQ FIG. 6.12. Geometry for the relationship between PDD(z, A, f, hn) and TAR(z, AQ, hn). 186

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS and solving Eqs (6.42) and (6.43) for DQ we obtain: PDD(z, A, f, hn ) DQ = DP = DQ TAR(z, AQ , hn ) ¢ (6.44) 100 DP may now be written as: 2 Ê f +z ˆ DP = DP PSF( A, hn ) = DQ Á ¢ ¢ ˜ PSF( A, hn ) (6.45) Ë f + zmax ¯ and inserted into Eq. (6.44) to yield: TAR(z, AQ , hn ) 2 PDD(z, A, f, hn ) Ê f + z ˆ = PSF( A, hn ) Á f +z ˜ (6.46) 100 Ë max ¯ For the special case of z = zmax, where PDD(zmax, A, f, hn) = 100, Eq. (6.46) shows that the PSF(A, hn) is a special TAR(zmax, A, hn). The range of TARs is therefore from 0 at z ® ¥ to PSF(A, hn) at z = zmax. Since the TAR does not depend on the SSD, a single TAR table for a given photon beam energy may be used to cover all possible SSDs used clinically. Alternatively, PDDs for any arbitrary combination of z, A and f = SSD may be calculated from a single TAR table. Based on Eq. (6.46) we derive the following two relationships for PDDs at two different SSDs (f1 and f2). ● The first relationship assumes an identical field size A at the two SSDs, as shown in Fig. 6.13: 2 Ê f 1 + zmax ˆ PDD(z, A, f 1 , hn ) Ê TAR(z, AQ1 , hn ) ˆ Á f 1 + z ˜ = Á ˜ (6.47) PDD(z, A, f 2 , hn ) Á TAR(z, AQ2 , hn ) ˜ Á f 2 + zmax Ë ¯ ˜ Á f +z Ë ˜ ¯ 2 ● The second relationship assumes the same field size AQ at depth z at the two SSDs, as shown in Fig. 6.14: 187

CHAPTER 6 2 Ê f 1 + zmax ˆ PDD(z, A1 , f 1 , hn ) Ê PSF( A2 , hn ) ˆ Á f 1 + z ˜ = Á ˜ (6.48) PDD(z, A2 , f 2 , hn ) Á PSF( A1 , hn ) ˜ Á f 2 + zmax Ë ¯ ˜ Á f +z Ë ˜ ¯ 2 The relationships in Eqs (6.47) and (6.48) consist of two components each; the inverse square law correction component is the main component of the correction, and is referred to as the Mayneord factor. The second factor, represented by the ratio of TARs or PSFs, is often ignored, because its effect is much smaller than that produced by the Mayneord factor, and the Mayneord factor alone is used for correction of PDDs from one SSD to another. Source Source f2 f1 P z Q A AQ2 AQ1 FIG. 6.13. Derivation of the PDD relationship for two SSDs, with field size A identical for both. Note that the field A on the phantom surface is the same for both SSDs; therefore the fields at depth z differ for the two SSDs but are related through simple geometrical relationships. 188

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS 6.8.3. Scatter–air ratio Just as it was convenient in dealing with PDDs to separate the scattered component from the primary component to obtain the scatter function, it is sometimes useful to separate the primary component of the TAR from the total TAR to obtain the scatter contribution, which, in this case, is referred to as the scatter–air ratio (SAR), defined as: SAR(z, AQ, hn) = TAR(z, AQ, hn) – TAR(z, 0, hn) (6.49) The SAR depends on the same three parameters as the TAR and gives the scatter contribution to the dose at point Q in a phantom per 1 cGy of dose to a small mass of water at point Q in air. Source f2 Source f1 P z Q A1 A2 AQ FIG. 6.14. Derivation of the PDD relationship for two SSDs with field size AQ identical for both. Here the fields A1 and A2 on the phantom surface are related through simple geometrical relationships. 189

CHAPTER 6 6.8.4. Relationship between SAR (d, AQ, hv) and S(z, A, f, hv) Similarly to the relationship between TAR(z, AQ, hn) and PDD(z, A, f, hn), we can derive the relationship between SAR(z, AQ, hn) and S(z, A, f, hn) to obtain: 2 S(z, A, f, hn ) Ê f + z ˆ SAR(z, AQ , hn ) = Á f +z ˜ (6.50) 100 Ë max ¯ It is easy to see that: S(z, A, f, hn) = 100SAR(z, AQ, hn) (6.51) for any z when f ® ¥ and for any f when z ® zmax. 6.8.5. Tissue–phantom ratio and tissue–maximum ratio The TAR concept works well in isocentric set-ups for photon energies of 60 Co and below. For megavoltage X rays produced by high energy linacs, however, the concept breaks down because of difficulties in measuring the ‘dose to small mass of water in air’ at those energies (the required size of the buildup cap for the ionization chamber becomes excessively large). To bypass this problem, the concept of tissue–phantom ratio (TPR) was introduced for use in megavoltage isocentric set-ups. The TPR is defined as follows: DQ DQ TPR(z, AQ , hn ) = = (6.52) DQref DQref where DQ and DQ are the dose and dose rate, respectively, in a phantom at arbitrary point Q on the beam central axis and DQref and DQref are the dose and dose rate, respectively, in a phantom at a reference depth zref (typically 5 or 10 cm) on the beam central axis. The geometry for the measurement of doses DQ and DQref is shown in Fig. 6.15. A special TPR was defined for the reference depth zref equal to the depth of dose maximum zmax, which is referred to as the tissue–maximum ratio (TMR), defined as follows: 190

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS Source Source (a) (b) SSD SAD P Aref A z Q Q zref AQ AQ FIG. 6.15. Geometry for measurement of TPR(d, AQ , hn). (a) The geometry for the meas- urement of DQ at depth z in a phantom; (b) the geometry for the measurement of DQref at depth zref in a phantom. The distance between the source and the point of measurement, as well as the field size at the point of measurement, is the same for (a) and (b). DQ DQ TMR(z, AQ , hν) = = (6.53) DQmax DQmax where DQ and DQ are the dose and dose rate, respectively, at point Q at a depth z in a phantom and DQmax and DQmax are the dose and dose rate, respectively, at point Q at zmax. The geometry for the definition of TMR is the same as in Fig. 6.15, except that zref is now zmax. ● Just like the TAR, the TPR and TMR depend on the three parameters z, AQ, hn, but do not depend on the SAD or SSD. ● The range of TMR is from 0 for z ® ¥ to 1 for z = zmax (i.e. 0 £ TMR(z, AQ, hn) £ 1. ● For constant AQ and hn the TMR decreases with increasing z. ● For constant z and hn the TMR increases with increasing AQ. ● For constant z and AQ the TMR increases with increasing hn. 191

CHAPTER 6 6.8.6. Relationship between TMR(z, AQ, hv) and PDD(z, A, f, hv) As shown in Fig. 6.16, a simple relationship may be derived between TMR(z, AQ, hn) and the corresponding PDD(z, A, f, hn) from the basic definitions governing the two functions. The basic definitions for the two functions are: DQ TMR(z, AQ , hn ) = (6.54) DQmax DQ PDD(z, A, f, hn ) = 100 (6.55) DP Solving Eqs (6.54) and (6.55) for DQ we obtain: PDD(z, A, f, hn ) (6.56) DQ = DP = DQmax TMR(z, AQ , hn ) 100 Source f = SSD zmax P A z Q AQ FIG. 6.16. Geometry for derivation of the relationship between PDD(z, A, f, hn) and TMR(z, AQ, hn). 192

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS and expanding DP and DQmax as follows: 2 Ê f +z ˆ DP = DP PSF( A, hn ) = DQ Á ¢ ¢ ˜ PSF( A, hn ) (6.57) Ë f + zmax ¯ DQmax = DQ PSF(AQ , hn ) ¢ (6.58) we obtain: 2 PDD(z, A, f, hn ) PSF( A, hn ) Ê f + z ˆ TMR(z, AQ , hn ) = (6.59) 100 PSF( AQ , hn ) Á f + zmax ˜ Ë ¯ In the first approximation, ignoring the PSF ratio in Eq. (6.59), we have a very simple approximate relationship between TMR(z, AQ, hn) and PDD(z, A, f, hn) as: 2 PDD(z, A, f, hn ) Ê f + z ˆ TMR(z, AQ , hn ) ª Á f +z ˜ (6.60) 100 Ë max ¯ The error in ignoring the ratio PSF(A, hn)/PSF(AQ, hn) is very small and can be estimated easily for a cobalt beam. For an extreme example, take the case with depth in a phantom d = 20 cm, field size A = 20 × 20 cm2 and SSD f = 100 cm to obtain AQ = 24 × 24 cm2 and PSF(20, Co)/PSF(24, Co) = 1.078/1.083 = 0.995, or a 0.5% error. Errors for smaller fields and shorter SSDs are obviously smaller, making Eq. (6.60) a reasonable and very practical approxi- mation for relating the TMR with the PDD. 6.8.7. Scatter–maximum ratio Similarly to separating TAR(z, AQ, hn) into the primary component TAR(z, 0, hn) and the scatter component SAR(z, AQ, hn), the TMR(z, AQ, hn) can be separated into the primary component TMR(z, 0, hn) and the scatter component, referred to as the scatter–maximum ratio (SMR), defined as follows: SF( AQ , hn ) SMR(z, AQ , hn ) = TMR(z, AQ , hn ) - TMR(z, 0, hn ) (6.61) SF(0, hn ) 193

CHAPTER 6 where SF(AQ, hn) and SF(0, hn) are the scatter factors for fields AQ and 0, respectively, and photon energy hn, as defined in Eq. (6.29). The ratio SF(AQ, hn)/SF(0, hn) is therefore: SF( AQ , hn ) PSF( AQ , hn ) / PSF(10, hn ) = = PSF( AQ , hn ) (6.62) SF(0, hn ) PSF(0, hn ) / PSF(10, hn ) since PSF(0, hn) = 1. For 60Co g rays, SMRs are approximately the same as SARs. However, for megavoltage photon energies above 60Co the SMRs should be calculated from the TMRs using Eq. (6.61) and: TMR(z, 0, hn ) = e - m eff (z-zmax ) (6.63) where µeff is the effective attenuation coefficient for the photon beam hn. 6.9. OFF-AXIS RATIOS AND BEAM PROFILES Dose distributions along the beam central axis give only part of the information required for an accurate dose description inside the patient. Dose distributions in 2-D and 3-D are determined with central axis data in conjunction with off-axis dose profiles. In the simplest form, the off-axis data are given with beam profiles measured perpendicularly to the beam central axis at a given depth in a phantom. The depths of measurement are typically at zmax and 10 cm for verifi- cation of compliance with machine specifications, in addition to other depths required by the particular treatment planning system (TPS) used in the department. An example of typical dose profiles measured at various depths in water for two field sizes (10 × 10 and 30 × 30 cm2) and a 10 MV X ray beam is shown in Fig. 6.17. Combining a central axis dose distribution with off-axis data results in a volume dose matrix that provides 2-D and 3-D information on the dose distri- bution. The off-axis ratio (OAR) is usually defined as the ratio of dose at an off-axis point to the dose on the central beam axis at the same depth in a phantom. Megavoltage X ray beam profiles consist of three distinct regions: central, penumbra and umbra. 194

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS 120 Depth (cm) 2.5 100 5 10 80 Relative dose 60 20 40 30 20 0 –30 –20 –10 0 10 20 30 Distance from central axis axis (cm) FIG. 6.17. An example of beam profiles for two field sizes (10 × 10 cm2 and 30 × 30 cm2) and a 10 MV X ray beam at various depths in water. The central axis dose values are scaled by the appropriate PDD value for the two fields. ● The central region represents the central portion of the profile extending from the beam central axis to within 1–1.5 cm from the geometric field edges of the beam. The geometric field size, indicated by the optical light field, is usually defined as the separation between the 50% dose level points on the beam profile. In the central region, the beam profile for 60 Co beams is affected by the inverse square dose fall-off as well as by increased phantom thickness for off-axis points. For linacs, on the other hand, the central region of the beam profile is affected by the energy of electrons striking the thick target, by the target atomic number and by the flattening filter atomic number and geometric shape. ● In the penumbral region of the dose profile the dose changes rapidly and depends also on the field defining collimators, the finite size of the focal spot (source size) and the lateral electronic disequilibrium. The dose fall- off around the geometric beam edge is sigmoid in shape and extends 195

CHAPTER 6 under the collimator jaws into the penumbral tail region, where there is a small component of dose due to the transmission through the collimator jaws (transmission penumbra), a component attributed to finite source size (geometric penumbra) and a significant component due to in-patient X ray scatter (scatter penumbra). The total penumbra is referred to as the physical penumbra and is the sum of the three individual penumbras: transmission, geometric and scatter. The physical penumbra depends on beam energy, source size, SSD, source to collimator distance and depth in a phantom. ● Umbra is the region outside the radiation field, far removed from the field edges. The dose in this region is generally low and results from radiation transmitted through the collimator and head shielding. Dose profile uniformity is usually measured by a scan along the centre of both major beam axes for various depths in a water phantom. Two parameters that quantify field uniformity are then determined: field (beam) flatness and field (beam) symmetry. 6.9.1. Beam flatness The beam flatness F is assessed by finding the maximum Dmax and minimum Dmin dose point values on the beam profile within the central 80% of the beam width and then using the relationship: Dmax - Dmin F = 100 ¥ (6.64) Dmax + Dmin Standard linac specifications generally require that F be less than 3% when measured in a water phantom at a depth of 10 cm and an SSD of 100 cm for the largest field size available (usually 40 × 40 cm2). Compliance with the flatness specifications at a depth of 10 cm in water results in ‘over-flattening’ at zmax, which manifests itself in the form of ‘horns’ in the profile, and in ‘under-flattening’, which progressively worsens as the depth z increases from 10 cm to larger depths beyond 10 cm, as evident from the profiles for the 30 × 30 cm2 field in Fig. 6.17. The typical limitation on beam horns in the zmax profile is 5% for a 40 × 40 cm2 field at SSD = 100 cm. The over- flattening and under-flattening of the beam profiles is caused by the lower beam effective energies in off-axis directions compared with those in the central axis direction. 196

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS 6.9.2. Beam symmetry The beam symmetry S is usually determined at zmax, which represents the most sensitive depth for assessment of this beam uniformity parameter. A typical symmetry specification is that any two dose points on a beam profile, equidistant from the central axis point, are within 2% of each other. Alternately, areas under the zmax beam profile on each side (left and right) of the central axis extending to the 50% dose level (normalized to 100% at the central axis point) are determined and S is then calculated from: area left - area right S = 100 ¥ (6.65) area left + area right The areas under the zmax profiles can often be determined using an automatic option on the water tank scanning device (3-D isodose plotter). Alternatively, using a planimeter or even counting squares on graph paper with a hard copy of the profile are practical options. 6.10. ISODOSE DISTRIBUTIONS IN WATER PHANTOMS The physical characteristics of radiation beams are usually measured in phantoms under standard conditions that are as follows: ● A homogeneous, unit density phantom; ● A flat phantom surface; ● A perpendicular beam incidence on the phantom. The central axis depth dose data in conjunction with dose profiles contain complete 2-D and 3-D information about a radiation beam. However, this information is difficult to visualize even for a single beam, let alone for a combination of several beams. Planar and volumetric variations in depth doses are usually displayed by means of isodose curves or isodose surfaces, which connect points of equal dose in a volume of interest. The isodose curves and surfaces are usually drawn at regular intervals of absorbed dose and are expressed as a percentage of the dose at a specific reference point. An isodose chart for a given single beam consists of a family of isodose curves usually drawn at regular increments of PDD. Two normalization conventions are in use: 197

CHAPTER 6 — For SSD set-ups, all isodose values are normalized to 100 at point P on the central beam axis. — For SAD set-ups, the isodose values are normalized to 100 at the isocentre. The isodose charts for an SSD set-up are thus plots of PDD values, while isodose charts for an SAD set-up are plots of either TAR or TMR values. For a 60Co beam the dose at any depth is largest on the central beam axis and then decreases towards the beam edges. For megavoltage photon beams the off-axis dose at shallow depths is usually larger than the central axis dose at the same depth, as a consequence of flattening filter design. These filters provide flat beams at a depth of 10 cm in water, and to achieve this they must overcompensate at shallow depths. (Note that the effective beam energy in extreme off-axis directions is lower than the effective beam energy in the direction of the central beam axis.) Figure 6.18 shows an example of isodose charts for a 60Co beam in water: Fig. 6.18(a) shows an SSD set-up (A = 10 × 10 cm2; SSD = 80 cm); Fig. 6.18(b) shows an SAD set-up (AQ = 10 × 10 cm2; SAD = 100 cm; depth of isocentre = 10 cm). FIG. 6.18. Isodose curves for a 60Co g ray beam: (a) for an SSD set-up (A = 10 × 10 cm2; SSD = 80 cm) and (b) for an SAD set-up (AQ=10 × 10 cm2, SAD = 100 cm; depth of isocentre = 10 cm). 198

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS Near the beam edges in the penumbra region the dose decreases rapidly with lateral distance from the beam central axis. This dose fall-off is caused not only by the geometric penumbra but also by the reduced side scatter. Outside the geometric limits of the beam and the penumbra, the dose variation is the result of three components: (i) Scatter from the radiation field; (ii) Leakage through the collimator jaws and machine head housing; (iii) Scatter from the collimation system. Parameters that affect the single beam isodose distribution are beam quality, source size, beam collimation, field size, SSD and source to collimator distance. Isodose charts are measured with ionization chambers, solid state detectors, standard radiographic film and radiochromic film. In addition to direct measurements, isodose charts may also be generated by calculations using various algorithms for treatment planning, most commonly with commercially available TPSs. Treatment by a single photon beam is seldom used except for superficial tumours. Deep seated tumours are usually treated with a combination of two or more beams so as to achieve an acceptable dose distribution within the tumour and the surrounding normal tissues (see Chapter 7). As a rule, the tumour dose is higher than the dose to the surrounding normal tissues, and the dose distri- bution within the tumour should be homogeneous to within +7% and –5% of the prescribed dose, if at all possible. 6.11. SINGLE FIELD ISODOSE DISTRIBUTIONS IN PATIENTS In clinical situations the beam may be obliquely incident on the patient and the patient’s surface may be curved or of irregular shape, requiring corrections for contour irregularities. In addition, some irradiated tissues, such as lung and bone, have densities that differ considerably from that of water, requiring corrections for tissue heterogeneities. Isodose distributions in patients are determined by one of two radically different approaches: ● Correction based algorithms; ● Model based algorithms. 199

CHAPTER 6 Correction based algorithms use depth dose data measured in water phantoms with a flat surface and normal incidence in conjunction with various methods to correct for irregular patient contours and oblique beam incidence, in contrast to the flat surface of a water phantom. They also correct for organ inhomogeneities to account for varying electron densities of organs, in contrast to the uniform electron density of a water phantom. Model based algorithms obviate the correction problem by modelling the dose distributions from first principles and accounting for all geometrical and physical characteristics of the particular patient treatment. Before clinical use both correction algorithms and model based algorithms must be verified experimentally, which often is a difficult task. The relative importance of individual corrections varies with the particular treatment geometry and the position of the target volume inside the patient. For conventional treatment techniques the correction based algorithms work reasonably well and produce reliable dose distributions; however, for the new sophisticated treatments such as 3-D conformal radiotherapy and intensity modulated radiotherapy (IMRT), they become problematic, because of the radical corrections that are required for these techniques. Model based algorithms hold great promise for the future; however, they are currently still under development. 6.11.1. Corrections for irregular contours and oblique beam incidence A radiation beam striking an irregular or sloping patient surface produces an isodose distribution that differs from the standard distributions obtained on flat surfaces with a normal beam incidence. Two approaches are used to address this problem: ● The effect can be corrected through various calculation methods; ● The effect may be compensated for through the use of wedges, bolus materials or compensators. Several methods have been developed to correct standard flat surface/ normal incidence isodose distributions for contour irregularities and oblique angles of beam incidence. The three most commonly used methods, applicable for angles of incidence up to 45º for megavoltage X ray beams and up to 30º for orthovoltage X ray beams, are: — The effective SSD method; — The TAR or TMR method; — The isodose shift method. 200

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS The correction factors for these three methods can be understood with reference to Fig. 6.19, in which an irregular patient contour CC is treated with a beam with an SSD = f. The PDD at point S normalized to dose at point P on the beam central axis is referred to as PDDcorr and is calculated with one of the three methods listed above. 6.11.1.1. Effective source to surface distance method In the effective SSD method, PDDcorr is determined from: 2 Ê f + zmax ˆ PDD corr = PDD¢(z, A, f, hn ) Á ˜ (6.66) Ë f + h + zmax ¯ where PDD¢(z, A, f, hn) is the PDD under standard conditions with the flat surface C¢C¢ and the second term represents an inverse square correction factor. The parameter h is the thickness of missing tissue, while the parameter – h represents the thickness of excess tissue. An assumption is made that the PDD does not depend on the SSD for deviations from the nominal SSD of the Beam central axis C f = SSD C" C" h P C' C' P' z C S Q FIG. 6.19. Geometry used for dose determination at point S in a patient. CC represents the actual patient contour; C¢C¢ and C≤C≤ are flat phantom contours: C≤C≤ at the nominal SSD and C¢C¢ at SSD + h, where h represents the thickness of missing tissue directly above point S. Point P is the point of dose normalization at zmax on the central beam axis. 201

CHAPTER 6 order of h (i.e. h << f). The resulting PDD is normalized to 100 at point P on the central beam axis. Thus in the effective SSD method (see Fig. 6.19): (a) the isodose chart is shifted to the flat surface level at the C¢C¢ contour; (b) the PDD value for point S is read; and (c) the reading is corrected by an inverse square law factor. 6.11.1.2. Tissue–air ratio or tissue–maximum ratio method In the TAR or TMR method, PDDcorr is given as: T (z, AQ , hn ) PDD corr = PDD¢¢(z + h, A, f, hn ) (6.67) T (z + h, AQ , hn ) where AQ is the field size at point S at a distance (f + h + z) from the source. T stands for either the TAR or the TMR, and an assumption is made that TARs and TMRs do not depend on the SSD. PDD≤ represents the PDD value at depth (h + z) for a standard flat phantom with the surface at C≤C≤. h is missing or excessive tissue. For missing tissue h is positive, for excess tissue h is negative. 6.11.1.3. Isodose shift method In the isodose shift method, the value of the dose at S is shifted on a vertical ray line by (h × k), where h is the thickness of the missing or excess tissue and k is a factor depending on beam energy. The factor k is smaller than 1 and has a value of 0.7 for 60Co beams to 5 MV beams, 0.6 for 5–15 MV beams and 0.5 for 15–30 MV beams. For missing tissue h is positive and the isodose is shifted away from the source, while for excess tissue h is negative and the isodose is shifted towards the source. 6.11.2. Missing tissue compensation In addition to techniques to correct for contour irregularities and oblique beam incidence, as discussed in Section 6.11.1, many relatively simple techniques have been devised to compensate for missing tissue, most notably the use of wedges, bolus materials and compensators. 202

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS 6.11.2.1. Wedge filters Wedge filters may be used to even out the isodose surfaces for photon beams striking relatively flat patient surfaces under an oblique beam incidence. Two types of wedge filter are in use: physical wedge filters and dynamic wedge filters. ● Physical wedges are made of lead, brass or steel. When placed in a radiation beam, they cause a progressive decrease in the intensity across the beam and a tilt of isodose curves under normal beam incidence. ● Dynamic wedges provide the wedge effect on isodose curves through a closing motion of a collimator block during irradiation. The wedge angle is defined as the angle through which an isodose curve at a given depth in water (usually 10 cm) is tilted at the central beam axis under the condition of normal beam incidence. Physical wedges are usually available with wedge angles of 15º, 30º, 45º and 60º; dynamic wedges are available with any arbitrary wedge angle in the range 0–60º. The wedge (transmission) factor (WF) is defined as the ratio of doses at zmax in a water phantom on the beam central axis with and without the wedge. Physical wedge filters may alter the X ray beam quality, causing beam hardening at energies of 6–10 MV and beam softening at energies above 15 MV. These effects will affect the central axis PDDs and should be accounted for in treatment planning isodose distribution calculations. 6.11.2.2. Bolus Bolus is a tissue equivalent material placed directly on the skin surface to even out the irregular patient contour and thereby provide a flat surface for normal beam incidence. In principle, the use of bolus is straightforward and practical; however, it suffers a serious drawback: for megavoltage photon beams it results in the loss of the skin sparing effect in the skin under the bolus layer (i.e. skin sparing occurs in the bolus). 6.11.2.3. Compensators Compensators are used to produce the same effect as the bolus yet preserve the skin sparing effect of megavoltage photon beams. They are custom-made devices that mimic the shape of the bolus but are placed in the radiation beam at some 15–20 cm from the skin surface so as not to disrupt the 203

CHAPTER 6 skin sparing properties of the beam. Although compensators may be made of water equivalent materials, they are usually fabricated from lead or special low melting point alloys, such as Cerrobend (Lipowitz’s metal). Since compensators are placed at some distance from the skin surface so as not to affect the skin dose sparing, their shape must be adjusted for: — Beam divergence; — Linear attenuation coefficients of the compensator material relative to that of water; — Reduction in scatter at various depths when the compensator is placed in the radiation beam away from the skin surface rather than in contact with the skin. 6.11.3. Corrections for tissue inhomogeneities Standard isodose charts and depth dose tables are given for uniform density water phantoms. Radiation beams used in patient treatment, however, traverse various tissues that may differ from water in density and atomic number. These tissue inhomogeneities (also referred to as heterogeneities) affect the dose deposition in the patient and may result in isodose distributions that differ considerably from those obtained in water phantoms. The effects of inhomogeneities on radiation dose distributions depend on the amount, density and atomic number of the inhomogeneity, as well as on the quality of the photon beam, and may be separated into two distinct categories: ● Increase or decrease in the attenuation of the primary beam, which affects the distribution of the scattered radiation; ● Increase or decrease of the secondary electron fluence. Three separate regions, in addition to inhomogeneity boundaries, are considered with regard to inhomogeneities: (1) the point of interest P located in front of the inhomogeneity; (2) P inside the inhomogeneity; and (3) P beyond the inhomogeneity. In region (1), in front of the inhomogeneity, especially for megavoltage photon beams, the dose is not affected by the inhomogeneity, since the primary beam in this region is not affected and neither is the scatter component, except close to the boundary. In region (2) the dose is mainly affected by changes in the secondary electron fluence and to a lesser extent by changes in the primary beam attenuation in the inhomogeneity. Under the conditions of electronic equilibrium and for a given photon energy fluence, the ratio of absorbed doses 204

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS in two different media is equal to the ratio of mass–energy absorption coeffi- cients for the two media. Close to the soft tissue–lung interfaces there may be a partial loss of electronic equilibrium and an associated decrease in dose. In region (3), beyond the inhomogeneity, the dose is mainly affected by changes in the primary beam attenuation and to a lesser extent by changes in scatter. Four empirical methods (see Section 7.5.6) are available for correcting the water phantom dose to estimate the dose at points in region (3): — The TAR method; — The power law TAR method; — The equivalent TAR method; — The isodose shift method. Beyond healthy lung (density ~0.3 g/cm3) the dose in soft tissues will increase, while beyond bone (density ~1.6 g/cm3) it will decrease in comparison with dose measured in a uniform phantom. Typical corrections for dose beyond healthy lung are: 4%, 3%, 2% and 1% per centimetre of lung for 60Co g beams and 4, 10 and 20 MV X rays, respec- tively. The shielding effect of bone depends strongly on the beam energy; it is appreciable at low X ray energies because of a strong photoelectric effect presence and essentially negligible in the low megavoltage energy range (mainly Compton effect). At energies above 10 MeV the shielding effect of bone begins to increase with increasing energy because of the increase in the pair production cross-section. 6.11.4. Model based algorithms Model based algorithms for computation of dose distributions in a patient currently fall into one of three categories: ● A relatively simple analytical calculation of first order Compton scatter and its addition to the primary dose at the point of interest. The method is fairly rudimentary as it assumes a parallel beam of monoenergetic photons and ignores heterogeneities and scattering higher than of the first order. ● The convolution–superposition method, which accounts for the indirect nature of dose deposition from photon interactions, separating the primary photon interactions from the transport of scattered photons and charged particles produced through the photoelectric effect (photo- effect), Compton scattering and pair production. 205

CHAPTER 6 ● The Monte Carlo method, which is the most promising of the model based dose computation methods, uses well established probability distri- butions governing the individual interactions of photons and electrons with the patient and their transport through the patient. Monte Carlo simulation is essential in all model based dose computations to charac- terize the clinical beam emanating from the radiation source, but can also be used directly to compute photon dose distributions for a given patient and treatment geometry. The current limitation of direct Monte Carlo calculations is the time required to calculate the large number of histories required to reduce stochastic or random uncertainties to acceptable levels. It is expected that advances in computer technology will, within a few years, reduce Monte Carlo calculation times to acceptable levels, and this will make Monte Carlo methods the standard approach to radio- therapy treatment planning. The electron densities for various tissues of individual patients are obtained with CT scanners or CT simulators and form an essential component of any Monte Carlo based dose distribution calculation. 6.12. CLARKSON SEGMENTAL INTEGRATION Tables for the various dose functions, such as the PDD, TAR, PSF and TMR, etc., are usually given for a series of square fields. Values for these functions when fields are rectangular or circular may be obtained through determining the equivalent square for the rectangular field (Eq. (6.25)) or circular field (Eq. (6.26)) and then using the appropriate tabulated square field data for determining the value of a given dose function. Here, an assumption is made that there is a match between dose functions for rectangular fields and their equivalent square and circular fields. It has been shown experimentally that this assumption is valid for the range of field sizes and beam energies used in radiotherapy. Radiation fields other than square, rectangular or circular are termed irregular fields. An irregular field will also have an equivalent square field and an equivalent circular field that will yield the same value of a given dose function as does the irregular field, but there are no simple means to determine the equivalent square or circle for a given irregular field. However, a technique, referred to as the Clarkson segmental integration, can be used to calculate the appropriate value of any given dose function for the given irregular field based on circular field data. The Clarkson technique resolves the irregular field into sectors of circular beams originating at the point of interest Q in the phantom or patient. For 206

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS manual calculations, sectors with an angular width of 10º are usually used; for computer driven calculations the angular width is 5º or even smaller, in order to improve accuracy. An assumption is made that a sector with a given field radius contributes 1/N of the total circular field value to the value of the given function F for the irregular field at point Q, where N is the number of sectors in a full circle of 360º. The value of a given function F for an irregular field that in general depends on depth z of point Q, shape of the irregular field, SSD = f and beam energy hn is then determined from the following segmental integration relationship: N Â F (z, r , f, hn ) 1 F (z, irregular field, f, hn ) = i (6.68) N i =1 where N is the number of sectors in 360º (for manual calculations N = 36); ri is the radius from point Q to the edge of the field at the centre of sector i; F(z, ri, f, hn) is the value of the dosimetric function F at depth z, SSD = f and beam energy hn for the circular field with radius ri. An example of an irregular field is shown in Fig. 6.20 with two of 36 sectors highlighted: one is a simple sector with radius r1 and the other is a composite sector with three radii: ra, rb and rc. ● The contribution of the simple sector to the sum in Eq. (6.68) is simply equal to: (1/N)F(z, ri, f, hn) ● The composite sector consists of three components to yield the following contribution: (1/N)[F(z, ra, f, hn) – F(z, rb, f, hn) + F(z, rc, f, hn)] to the sum given in Eq. (6.68), with two positive components that are contributed by portions of the radiation field and one negative 207

CHAPTER 6 Q rc 9 rb ra 8 7 6 5 r1 4 3 Segment 2 36 1 FIG. 6.20. An example of a mantle irregular field. Two segments out of 36 are highlighted. The first is simple with radius r1, the seventh is composite with three radii: ra , rb and rc . component that accounts for the missing portion of the radiation field in the segment (sector). Once the value of a dose function for a given irregular field is determined through the Clarkson integration technique, the equivalent square for the irregular field is also established by finding in tabulated square field data the square field that will give the same value for the dose function. The segmental integration technique was originally proposed by Clarkson in the 1940s and developed by Johns and Cunningham in the 1960s for determining the scatter component of the dose at an arbitrary point of interest in the patient, either inside or outside the direct radiation field. For points inside the radiation field the scatter component is added to the primary beam component; for points outside the field the scatter component is added to the radiation transmitted through the shielding blocks, collimator or head shielding of the treatment machine. 208

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS The original implementation of the Clarkson technique was intended for use with orthovoltage and cobalt beams for which the primary dose rate was reasonably flat from the central axis to points near the edge of the field, where it began to decrease. In linac beams, however, the primary dose rate at shallow depths in the patient may actually increase at distances away from the central axis (‘horns’) as a result of flattening filter effects on the radiation beam. A flattening filter correction that depends on depth z in a phantom and radial distance r from the central axis is required to model, for the primary beam component, this increase in the dose rate away from the central beam axis. 6.13. RELATIVE DOSE MEASUREMENTS WITH IONIZATION CHAMBERS Ionization chambers are used in clinical physics not only for photon and electron beam calibration at a reference point in a phantom but also for relative measurements of various parameters and dose functions, such as the CF, the RDF, dose profiles and PDDs, including the surface dose and doses in the buildup region. The dependence of various dose correction factors (such as ionization chamber polarity, ionic recombination, stopping power ratios and fluence correction) on beam energy (i.e. depth in a phantom) should be considered in relative dose measurements, although in many situations the dependence may be ignored. Usually each task of dose determination is carried out with ionization chambers designed for the specific task at hand. For example: ● Doses and dose rates at reference points in a phantom for megavoltage photon beams and electron beams above 10 MeV are measured with relatively large volume (0.6 cm3) cylindrical ionization chambers in order to obtain a reasonable signal and good signal to noise ratio. ● Relative dose distributions (e.g. central axis PDDs and beam profiles) for photon beams beyond zmax and for electron beams are usually measured with small volume (0.1 cm3) ionization chambers in order to obtain good spatial resolution. ● Surface doses and doses in the buildup region for photon beams are measured with parallel-plate ionization chambers incorporating a thin polarizing electrode window (to be able to measure the surface dose) and a small electrode separation (typically 1 mm, for better spatial resolution). 209

CHAPTER 6 ● A typical megavoltage photon beam PDD curve, measured with positive and negative polarities with a parallel-plate ionization chamber in the dose buildup region and beyond, is shown in Fig. 6.21. ● In the buildup region the positive chamber polarity produces a larger signal than the negative polarity. The difference in signals is most pronounced on the phantom surface and then diminishes with depth until it disappears at depths of zmax and beyond. At zmax and beyond this curve is more conveniently measured with small volume cylindrical ionization chamber; the results will match those obtained with a parallel-plate chamber. In the buildup region, however, the cylindrical chamber will read an unrealistically high signal because of its excessive wall thickness. ● In the buildup region, signals for both positive and negative chamber polarities are measured with a parallel-plate ionization chamber, and the average reading between the two polarities is used as the true dose value. Signal averaging eliminates the chamber Compton current that results from photon interactions in the measuring electrode of the chamber. In the dose buildup region, these interactions cause a loss of electrons from the measuring electrode that is not fully compensated by the arrival of Dmax Dose Ds Ds Ds 0 dmax Depth FIG. 6.21. Megavoltage photon beam depth doses measured with a parallel-plate ioniza- tion chamber. In the buildup region the positive polarity produces a higher reading than the negative polarity, beyond zmax both polarities give essentially identical signals. 210

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS electrons from the upper layers of the phantom. The electron difference results in a non-dosimetric current, which is referred to as the Compton current, and causes an increased reading for positive chamber polarity and a decreased reading for negative chamber polarity. ● For depths beyond zmax, both positive and negative chamber polarities yield the same reading, because electronic equilibrium exists on the measuring electrode (as many electrons land on the measuring electrode as are ejected by photon interactions from the measuring electrode). ● Ionic collection efficiency depends not only on the potential difference between the polarizing and measuring electrodes but also on the dose rate in the ionization chamber cavity. Therefore, in principle, when measuring depth doses, one should account for the change in ionic collection efficiency as a function of depth in a phantom. However, in practice, since ionic recombination loss in well behaved chambers is 2% or less, the changes in ionic recombination with depth are ignored when measuring relative depth doses. ● In general, stopping power ratios water to air and chamber correction factors are also depth dependent, and this dependence, according to the particular situation and accuracy required, might have to be accounted for when measuring depth doses with ionization chambers: — In photon beams, since the restricted stopping power ratio water to air is essentially independent of depth at depths larger than zmax, the signal corrected for the polarity effect can be treated as an indication of the relative dose to water. At depths shallower than zmax, the restricted stopping power ratio water to air varies by up to 2%, depending on field size and energy, a variation that is usually ignored. — In electron beams, the restricted stopping power ratio water to air varies significantly as a function of depth, requiring a correction to the measured ionization curve when relative dose is to be determined. For realistic beams as a function of depth z and energy (parametrized by R50) the stopping power ratio water to air is given by the following fit (Burns et al.): water Ê Lˆ Á r˜ (z, R 50 ) Ë ¯ air a + b(ln R 50 ) + c(ln R 50 ) 2 + d(z/R 50 ) = (6.69) 1 + e(ln R 50 ) + f (ln R 50 ) 2 + g(ln R 50 ) 3 + h(z / R 50 ) 211

CHAPTER 6 with the following values for the parameters: a = 1.0752; b = –0.50867; c = 0.088670; d = –0.08402; e = –0.42806; f = 0.064627; g = 0.003085; and h = –0.12460. ● Finally, in electron beams, for unguarded chambers (such as Farmer type thimble chambers), the fluence perturbation correction factor also varies as a function of energy at depth (by up to 5% in the range between zmax and the bremsstrahlung tail for a 20 MeV electron beam). Well guarded parallel-plate ionization chambers are therefore better suited for measurement of relative depth doses in electron beams than are thimble chambers. 6.14. DELIVERY OF DOSE WITH A SINGLE EXTERNAL BEAM Outputs for X ray machines and isotope units are usually given in centigray per minute (cGy/min) at zmax in a phantom, while outputs for linacs are given in centigray per monitor unit (cGy/MU) at zmax in a phantom. Transmission ionization chambers in linacs are usually adjusted such that the beam output corresponds to 1 cGy/MU at zmax for a 10 × 10 cm2 field at SSD = 100 cm (i.e. DP (zmax , 10, 100, hn ) = 1 cGy/MU (Fig. 6.9)). DP (zmax , A, 100, hn ), the dose rate at point P for an arbitrary field size A, is then obtained from DP (zmax , 10, 100, hn ) as follows (see Eq. (6.30)): DP (zmax , A, 100, hn ) = DP (zmax , 10, 100, hn ) ¥ RDF( A, hn ) (6.70) The number of monitor units MU (in MUs) required to deliver a tumour dose TD at point Q (Fig. 6.9) using a single SSD field with field A is calculated from Eq. (6.34) recognizing that DQ = TD = (TD) /(MU) , where TD is the tumour dose rate: TD MU = (6.71) DP (zmax , 10, 100, hn ) ¥ RDF( A, hn ) ¥ PDD(z, A, f, hn ) Similarly, for an SAD set-up (Fig. 6.15) the number of monitor units MUl to deliver a tumour dose TD at point Q with a single isocentric beam with field size AQ may be calculated using Eq. (6.52) recognizing that DQ = TD = (TD) /(MU ) and that DQmax (zmax , AQ , SAD = 100, hn ) may be approximated as: 212

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS DQmax (zmax , AQ , 100 SAD , hn ) 2 Ê f + z ref ˆ ª DP (zmax , 10, 100 SSD , hn ) ¥ RDF( A, hn ) ¥ Á (6.72) Ë f ˜ ¯ to obtain: TD MU = DP (zmax , 10, 100 SSD , hn ) ¥ RDF( A, hn ) ¥ TPR(z, AQ , hn ) 2 Ê f ˆ ¥Á ˜ (6.73) Ë f + z ref ¯ 6.15. EXAMPLE OF DOSE CALCULATION Given D(15, 15, 80, Co) calculate D(10, 20, 140, Co), where D(15, 15, 80, Co) = D (z, A, f, Co) stands for the dose rate in cGy/min at point Q in a water phantom at a depth z = 15 cm on the central axis of a cobalt beam with a field size A = 15 × 15 cm2 and SSD = f = 80 cm. The problem ties together the various basic functions and parameters that are routinely used in external beam radiotherapy and may be solved using either the SSD approach (with PDDs) or the SAD approach (with TARs). The two approaches, of course, should yield the same end result. The steps involved · · in going from D(15, 15, 80, Co) to D(10, 20, 140, Co) are given below for the SSD and the SAD approaches. SSD approach (6.74) SAD approach (6.75) D(15, 15, 80, Co) D(15, 15, 80, Co) 100 1 Ø ¥ Ø ¥ PDD(15,15,80,Co) TAR(15, 17.8, Co) D(0.5, 15, 80, Co) ¢ D95 (17.8, Co) 1 95 2 Ø ¥ Ø ¥ PSF(15, Co) 80.5 2 213

CHAPTER 6 ¢ D80.5 (15 80 , Co) ¢ D80.5 (15 80 , Co) CF(11.4, Co) CF(11.4,Co) Ø ¥ Ø ¥ CF(15, Co) CF(15, Co) ¢ D80.5 (11.4 80 , Co) ¢ D80.5 (11.4 80 , Co) 80.5 2 80.5 2 Ø ¥ Ø ¥ 140.5 2 150 2 ¢ D140.5 (20 140 , Co) ¢ D150 (21.4 150 , Co) Ø ¥ PSF(20,Co) Ø ¥ TAR(10, 21.4, Co) D(0.5, 20, 140,Co) D(10, 20, 140, Co) Ø ¥ PDD(10, 20, 140, Co) / 100 D(10, 20, 140, Co) ¢ where D140.5 (20 140 , Co) stands for the ‘dose rate to small mass of water’ at a distance of 140.5 cm from the source with the collimator set to give 20 × 20 cm2 at 140 cm from the source, corresponding to 11.4 × 11.4 cm2 at 80 cm from the source. The general answer for the SSD approach is: D(10, 20, 140, Co) D(15, 15, 80, Co) PDD(10, 20, 140, Co) PSF(20,Co) CF(11.4,Co) 80.5 2 = ¥ ¥ ¥ PDD(15, 15, 80, Co) PSF(15, Co) CF(15, Co) 140.5 2 PDD(10, 20, 140, Co) RDF(20, Co) CF(11.4, Co) 80.5 2 = ¥ ¥ ¥ PDD(15, 15, 80, Co) RDF(15, Co) CF(20,Co) 140.5 2 (6.76) 214

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS The general answer for the SAD approach is: D(10, 20, 140, Co) TAR(10, 21.4, Co) CF(11.4, Co) 95 2 = ¥ ¥ (6.77) D(15, 15, 80, Co) TAR(15, 17.8, Co) CF(15, Co) 150 2 Both answers with standard 60Co machine data (see, for example, Br. J. Radiol. Suppl. 25) will yield for the ratio of the two dose rates 0.505 within ±1%. ¢ In Eq. (6.74) we go to D80.5 (11.4, Co) from D(0.5, 15, 80, Co) following a ¢ path that leads through D80.5 (15 80 ,Co) as follows: 1 CF(11.4, Co) D80.5 (11.4, Co) = D(0.5, 15, 80, Co) ¥ ¢ ¥ (6.78) PSF(15, Co) CF(15, Co) F ¢ We can also attain D80.5 (11.4, Co) by going in a phantom from ¢ D(0.5, 15, 80, Co) to D(0.5, 11.4, 80, Co) and then to D80.5 (11.4 80 , Co) as follows: D(0.5, 15, 80, Co) RDF(11.4, Co) Ø ¥ RDF(15, Co) D(0.5, 11.4, 80, Co) 1 Ø ¥ PSF(11.4, Co) ¢ D80.5 (11.4 80 , Co) (6.79) Both paths, of course, will give identical end results, since, as can be shown using Eqs (6.29) and (6.31): 1 CF(11.4, Co) RDF(11.4, Co) 1 ¥ = ¥ (6.80) PSF(15, Co) CF(15, Co) RDF(15, Co) PSF(11.4, Co) 6.16. SHUTTER CORRECTION TIME In radiotherapy machines that use an electrical timer for measuring the dose delivery (radiotherapy X ray machines and teletherapy radioisotope machines), account must be taken of possible end effects (shutter correction 215

CHAPTER 6 time) resulting from switching the beam on and off. In X ray machines the beam output builds up from zero to its full value as the generating voltage builds up in the first few seconds of the treatment. In isotope machines the source is moved into position at the start of the treatment and is returned to its safe position at the end of the treatment. The shutter correction time ts is defined as the time that must be added to or subtracted from the calculated treatment time Tc to deliver accurately the prescribed dose to the patient. For a given therapy machine the shutter correction time is typically determined by measuring two doses (D1 and Dn) at a given point P (e.g. at zmax in a phantom): ● D1 is measured with a relatively long exposure time T (of the order of 5 min), contains one end effect and is given by D1 = D(T + t s ) or D = D1 /(T + t s ). ● Dn is measured cumulatively with n dose segments, each having an exposure time T/n. The dose Dn thus contains n end effects; the cumulative beam-on time is again equal to T, and Dn is given by Dn = D(T + nt s ) or D = Dn /(T + nt s) . · Solving the equation for the true dose rate D = D1/(T+ts) = Dn/(T + nts) for the shutter correction time ts gives: ts = (Dn – D1)T/(nD1 – Dn) (6.81) In Eq. (6.81) ts > 0 for Dn > D1; ts = 0 for Dn = D1; and ts < 0 for Dn < D1. The time set on the timer will be (Tc – ts). Typical shutter correction times are of the order of 1 s. BIBLIOGRAPHY BRITISH JOURNAL OF RADIOLOGY, Central Axis Depth Dose Data for Use in Radiotherapy, Suppl. 25 (1996). BURNS, D.T., DING, G.X., ROGERS, D.W.O., R50 as beam quality specifier for selecting stopping power ratios and reference depths for electrons, Med. Phys. 23 (1996) 383–388. HENDEE, W.R., IBBOTT, G.S., Radiation Therapy Physics, Mosby, St. Louis, MI (1996). 216

EXTERNAL PHOTON BEAMS: PHYSICAL ASPECTS JOHNS, H.E., CUNNINGHAM, J.R., The Physics of Radiology, Thomas, Springfield, IL (1984). KHAN, F.M., The Physics of Radiation Therapy, Lippincott, Williams and Wilkins, Baltimore, MD (2003). WILLIAMS, J.R., THWAITES, D.I. (Eds), Radiotherapy Physics in Practice, Oxford University Press, Oxford (2000). 217

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Chapter 7 CLINICAL TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY W. PARKER, H. PATROCINIO Department of Medical Physics, McGill University Health Centre, Montreal, Quebec, Canada 7.1. INTRODUCTION External photon beam radiotherapy is usually carried out with more than one radiation beam in order to achieve a uniform dose distribution inside the target volume and an as low as possible a dose in healthy tissues surrounding the target. ICRU Report No. 50 recommends a target dose uniformity within +7% and –5% of the dose delivered to a well defined prescription point within the target. Modern photon beam radiotherapy is carried out with a variety of beam energies and field sizes under one of two set-up conventions: a constant source to surface distance (SSD) for all beams or an isocentric set-up with a constant source to axis distance (SAD). ● In an SSD set-up, the distance from the source to the surface of the patient is kept constant for all beams, while for an SAD set-up the centre of the target volume is placed at the machine isocentre; ● Clinical photon beam energies range from superficial (30–80 kVp), through orthovoltage (100–300 kVp), to megavoltage energies (60Co– 25 MV); ● Field sizes range from small circular fields used in radiosurgery, through standard rectangular and irregular fields, to very large fields used for total body irradiation (TBI). 7.2. VOLUME DEFINITION Volume definition is a prerequisite for meaningful 3-D treatment planning and for accurate dose reporting. ICRU Reports No. 50 and 62 define and describe several target and critical structure volumes that aid in the treatment planning process and that provide a basis for comparison of 219

CHAPTER 7 treatment outcomes. The following volumes have been defined as principal volumes related to 3-D treatment planning: gross tumour volume (GTV), clinical target volume (CTV), internal target volume (ITV) and planning target volume (PTV). Figure 7.1 shows how the different volumes are related to each other. 7.2.1. Gross tumour volume “The Gross Tumour Volume (GTV) is the gross palpable or visible/ demonstrable extent and location of malignant growth” (ICRU Report No. 50). The GTV is usually based on information obtained from a combination of imaging modalities (computed tomography (CT), magnetic resonance imaging (MRI), ultrasound, etc.), diagnostic modalities (pathology and histological reports, etc.) and clinical examination. 7.2.2. Clinical target volume “The clinical target volume (CTV) is the tissue volume that contains a demonstrable GTV and/or sub-clinical microscopic malignant disease, which has to be eliminated. This volume thus has to be treated adequately in order to achieve the aim of therapy, cure or palliation” (ICRU Report No. 50). Organ at risk FIG. 7.1. Graphical representation of the volumes of interest, as defined in ICRU Reports No. 50 and 62. 220

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY The CTV often includes the area directly surrounding the GTV, which may contain microscopic disease and other areas considered to be at risk and requiring treatment (e.g. positive lymph nodes). The CTV is an anatomical– clinical volume and is usually determined by the radiation oncologist, often after other relevant specialists such as pathologists or radiologists have been consulted. The CTV is usually stated as a fixed or variable margin around the GTV (e.g. CTV = GTV + 1 cm margin), but in some cases it is the same as the GTV (e.g. prostate boost to the gland only). There can be several non-contiguous CTVs, which may require different total doses to achieve treatment goals. 7.2.3. Internal target volume The ITV consists of the CTV plus an internal margin. The internal margin is designed to take into account the variations in the size and position of the CTV relative to the patient’s reference frame (usually defined by the bony anatomy); that is, variations due to organ motions such as breathing and bladder or rectal contents (ICRU Report No. 62). 7.2.4. Planning target volume “The planning target volume (PTV) is a geometrical concept, and it is defined to select appropriate beam arrangements, taking into consideration the net effect of all possible geometrical variations, in order to ensure that the prescribed dose is actually absorbed in the CTV” (ICRU Report No. 50). The PTV includes the internal target margin (ICRU Report No. 62) and an additional margin for set-up uncertainties, machine tolerances and intra- treatment variations. The PTV is linked to the reference frame of the treatment machine and is often described as the CTV plus a fixed or variable margin (e.g. PTV = CTV + 1 cm). Usually a single PTV is used to encompass one or several CTVs to be targeted by a group of fields. The PTV depends on the precision of such tools as immobilization devices and lasers, but does not include a margin for the dosimetric characteristics of the radiation beam (i.e. penumbral areas and buildup region), as these will require an additional margin during treatment planning and shielding design. 221

CHAPTER 7 7.2.5. Organ at risk The organ at risk is an organ whose sensitivity to radiation is such that the dose received from a treatment plan may be significant compared with its tolerance, possibly requiring a change in the beam arrangement or a change in the dose. Specific attention should be paid to organs that, although not immediately adjacent to the CTV, have a very low tolerance dose (e.g. the eye lens during nasopharyngeal or brain tumour treatments). Organs with a radiation tolerance that depends on the fractionation scheme should be outlined completely to prevent biasing during treatment plan evaluation. 7.3. DOSE SPECIFICATION A clearly defined prescription or reporting point along with detailed information regarding total dose, fractional dose and total elapsed treatment days allows for proper comparison of outcome results. Several dosimetric end points have been defined in ICRU Reports No. 23 and 50 for this purpose: ● Minimum target dose from a distribution or a dose–volume histogram (DVH). ● Maximum target dose from a distribution or a DVH. ● Mean target dose: the mean dose of all calculated target points (difficult to obtain without computerized planning). ● The ICRU reference point dose is located at a point chosen to represent the delivered dose using the following criteria: — The point should be located in a region where the dose can be calculated accurately (i.e. no buildup or steep gradients). — The point should be in the central part of the PTV. — The isocentre (or beam intersection point) is recommended as the ICRU reference point. ● Specific recommendations are made with regard to the position of the ICRU reference point for particular beam combinations: — For a single beam: the point on the central axis at the centre of the target volume. — For parallel opposed equally weighted beams: the point on the central axis midway between the beam entrance points. — For parallel opposed unequally weighted beams: the point on the central axis at the centre of the target volume. 222

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY — For other combinations of intersecting beams: the point at the inter- section of the central axes (insofar as there is no dose gradient at this point). 7.4. PATIENT DATA ACQUISITION AND SIMULATION 7.4.1. Need for patient data Patient data acquisition is an important part of the simulation process, since reliable data are required for treatment planning purposes and allow for a treatment plan to be properly carried out. The type of gathered data varies greatly, depending on the type of treatment plan to be generated (e.g. manual calculation of parallel opposed beams versus a complex 3-D treatment plan with image fusion). General considerations include: ● Patient dimensions are almost always required for treatment time or monitor unit (MU) calculations, whether read with a calliper, from CT slices or by other means; ● The type of dose evaluation dictates the amount of patient data required (e.g. DVHs require more patient information than a point dose calculation of organ dose); ● Landmarks such as bony or fiducial marks are required to match positions in the treatment plan with positions on the patient. 7.4.2. Nature of patient data The patient information required for treatment planning varies from rudimentary to very complex, ranging from distances read on the skin, through manual determination of contours, to acquisition of CT information over a large volume, or even image fusion using various imaging modalities. 7.4.2.1. Two dimensional treatment planning A single patient contour, acquired using lead wire or plaster strips, is transcribed on to a sheet of graph paper, with reference points identified. Simulation radiographs are taken for comparison with port films during treatment. For irregular field calculations, points of interest can be identified on a simulation radiograph, and SSDs and depths of interest can be determined at 223

CHAPTER 7 simulation. Organs at risk can be identified and their depths determined on simulator radiographs. 7.4.2.2. Three dimensional treatment planning A CT data set of the region to be treated, with a suitable slice spacing (typically 0.5–1 cm for the thorax, 0.5 cm for the pelvis and 0.3 cm for the head and neck), is required. An external contour (representative of the skin or immobilization mask) must be drawn on every CT slice used for treatment planning. The tumour and target volumes are usually drawn on CT slices by the radiation oncologist. Organs at risk and other structures should be drawn in their entirety if DVHs are to be calculated. Figure 7.2 shows the typical outlining of target volume and organs at risk for a prostate treatment plan on one CT slice. MRI or other studies are required for image fusion. With many contem- porary treatment planning systems (TPSs), the user can choose to ignore inhomogeneities (often referred to as heterogeneities), perform bulk FIG. 7.2. Contours of GTV, CTV, PTV and organs at risk (bladder and rectum) have been drawn on this CT slice for a prostate treatment plan. 224

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY corrections on outlined organs or use the CT data themselves (with an appropriate conversion to electron density) for point to point correction. Simulator radiographs or digitally reconstructed radiographs (DRRs) are used for comparison with portal films. 7.4.3. Treatment simulation Patient simulation was initially developed to ensure that the beams used for treatment were correctly chosen and properly aimed at the intended target. At present, treatment simulation has a more expanded role in the treatment of patients, consisting of: ● Determination of the patient treatment position; ● Identification of the target volumes and organs at risk; ● Determination and verification of the treatment field geometry; ● Generation of simulation radiographs for each treatment beam for comparison with treatment port films; ● Acquisition of patient data for treatment planning. The simplest form of simulation involves the use of port films obtained on the treatment machine prior to treatment in order to establish the treatment beam geometry. However, it is neither efficient nor practical to perform simulations on treatment units. Firstly, these machines operate in the megavoltage range of energies and therefore do not provide adequate quality radiographs for a proper treatment simulation, and, secondly, there is a heavy demand for the use of these machines for actual patient treatments, so using them for simulation is often considered an inefficient use of resources. There are several reasons for the poor quality of port films obtained on treatment machines, such as the following: — Most photon interactions with biological material in the megavoltage energy range are Compton interactions that are independent of atomic number and produce scattered photons that reduce contrast and blur the image. — The large size of the radiation source (either the focal spot for a linac or the diameter of radioactive source in an isotope unit) increases the detrimental effects of beam penumbra on the image quality. — Patient motion during the relatively long exposures required and the constraints on radiographic technique and equipment may contribute to poor image quality. 225

CHAPTER 7 For the above reasons, dedicated equipment for radiotherapy simulation has been developed. Conventional simulation systems are based on treatment unit geometry in conjunction with diagnostic radiography and fluoroscopy systems. Modern simulation systems are based on CT or MR imagers and are referred to as CT simulators or MR simulators. The clinical aspects of treatment simulation, be it with a conventional or CT simulator, rely on the positioning and immobilization of the patient as well as on the data acquisition and beam geometry determination. 7.4.4. Patient treatment position and immobilization devices Depending on the patient treatment position or the precision required for beam delivery, patients may or may not require an external immobilization device for their treatment. Immobilization devices have two fundamental roles: ● To immobilize the patient during treatment; ● To provide a reliable means of reproducing the patient’s position from simulation to treatment, and from one treatment to another. The simplest immobilization means include masking tape, Velcro belts or elastic bands. The basic immobilization device used in radiotherapy is the head rest, shaped to fit snugly under the patient’s head and neck area, allowing the patient to lie comfortably on the treatment table. Figure 7.3 shows common headrests used for patient comfort and immobilization during treatment. Modern radiotherapy generally requires additional immobilization accessories during the treatment of patients. FIG. 7.3. Headrests used for patient positioning and immobilization in external beam radiotherapy. 226

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY Patients to be treated in the head and neck or brain areas are usually immobilized with a plastic mask that, when heated, can be moulded to the patient’s contour. The mask is affixed directly on to the treatment table or to a plastic plate that lies under the patient, thereby preventing movement. A custom immobilization mask is shown in Fig. 7.4. For treatments to the thoracic or pelvic area, a variety of immobilization devices are available. Vacuum based devices are popular because of their reusability. Basically, a pillow filled with tiny Styrofoam balls is placed around the treatment area and a vacuum pump evacuates the pillow, leaving the patient’s form as an imprint on the pillow. The result is that the patient can be positioned snugly and precisely on the pillow prior to every treatment. Another system, similar in concept, uses a chemical reaction between reagents in the pillow to form a rigid mould of the patient. Special techniques, such as stereotactic radiosurgery, require such high precision that conventional immobilization techniques are inadequate. In radiosurgery, a stereotactic frame is attached to the patient’s skull by means of screws and is used for target localization, patient set-up on the treatment machine and patient immobilization during the entire treatment procedure. The frame is bolted to the treatment table, thereby providing complete immobilization during the treatment. FIG. 7.4. Plastic mask used for immobilization of brain and head and neck patients. 227

CHAPTER 7 7.4.5. Patient data requirements In cases where only the dose along the central axis of the beam is sought (e.g. treatments with a direct field, or parallel and opposed fields, and a flat beam incidence), only the SSD is required, since a simple hand calculation for beam-on time or linac MUs may suffice. Simple algorithms, such as Clarkson integration, may be used to determine the dosimetric effects of there being blocks in the fields, and to calculate the dose to off-axis points if their coordinates and SSD are measured. Since only point doses are calculated, the patient shape or contour off-axis is not required. For simple computerized 2-D treatment planning, the patient’s shape is represented by a single transverse skin contour through the central axis of the beams. This contour may be acquired by using lead wire or a plaster cast at the time of simulation. The patient data requirements for more sophisticated TPSs, such as those used in conformal treatment planning, are more elaborate than those for 2-D treatment planning. They include the following: ● The external shape of the patient must be outlined in all areas where the beams enter and exit (for contour corrections) and in the adjacent areas (to account for scattered radiation); ● The targets and internal structures must be outlined in order to determine their shape and volume for dose calculation; ● The electron densities for each volume element in the dose calculation matrix must be determined if a correction for heterogeneities is to be applied; ● The attenuation characteristics of each volume element are required for image processing. The nature and complexity of the data required for sophisticated treatment planning limits the use of manual contour acquisition. At the very best, patient external contour information can be obtained through this method. Transverse CT scans contain all the information required for complex treatment planning and form the basis of CT simulation in modern radiotherapy treatment. 228

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY 7.4.6. Conventional treatment simulation 7.4.6.1. Simulators Simulators provide the ability to mimic most treatment geometries attainable on megavoltage treatment units and to visualize the resulting treatment fields on radiographs or under fluoroscopic examination of the patient. They consist of a gantry and table arrangement similar to that found on isocentric megavoltage treatment units, with the exception that the radiation source in a simulator is a diagnostic quality X ray tube rather than a high energy linac or a cobalt source. Some simulators have a special attachment that allows them to collect patient cross-sectional information similarly to a CT scanner; the combination is referred to as a CT simulator. Figure 7.5 shows a photograph of a conventional treatment simulator. The photons produced by the X ray tube are in the kilovoltage range and are preferentially attenuated by higher Z materials such as bone through photoelectric interactions. The result is a high quality diagnostic radiograph with limited soft tissue contrast but with excellent visualization of bony landmarks and high Z contrast agents. A fluoroscopic imaging system may also be included and would be used from a remote console to view the patient’s anatomy and to modify beam placement in real time. FIG. 7.5. A conventional treatment simulator has the capability to reproduce most treatment geometries available on radiotherapy treatment units. Simulators use a diag- nostic X ray tube and fluoroscopic system to image the patient. 229

CHAPTER 7 7.4.6.2. Localization of the target volume and organs at risk For the vast majority of sites the disease is not visible on the simulator radiographs, and therefore the block positions can be determined only with respect to anatomical landmarks visible on the radiographs (usually bony structures or lead wire clinically placed on the surface of the patient). 7.4.6.3. Determination of the treatment beam geometry Typically, the patient is placed on the simulator table and the final treatment position of the patient is verified using the fluoroscopic capabilities of the simulator (e.g. the patient is straight on the table). The position of the treatment isocentre, beam geometry (i.e. the gantry, table angles, etc.) and field limits are determined with respect to the anatomical landmarks visible under fluoroscopic conditions. Once the final treatment geometry has been established, radiographs are taken as a matter of record and are used to determine shielding requirements for the treatment. Shielding can be drawn directly on the films, which may then be used as the blueprint for the construction of the blocks. A typical simulator radiograph is shown in Fig. 7.6. Treatment time port films are compared with these radiographs periodi- cally to ensure the correct set-up of the patient during the treatments. 7.4.6.4. Acquisition of patient data After proper determination of the beam geometry, patient contours may be taken at any plane of interest to be used for treatment planning. Although more sophisticated devices exist, the simplest and most widely available method for obtaining a patient contour is through the use of lead wire. Typically, the wire is placed on the patient on a transverse plane parallel to the isocentre plane. The wire is shaped to the patient’s contour and the shape is then transferred to a sheet of graph paper. Some reference to the room coordinate system must be marked on the contour (e.g. laser position) in order to relate the position of the beam geometry to the patient. 7.4.7. Computed tomography based conventional treatment simulation 7.4.7.1. Computed tomography based patient data acquisition With the growing popularity of CT in the 1990s, the use of CT scanners in radiotherapy became widespread. Anatomical information on CT scans is 230

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY presented in the form of transverse slices, which contain anatomical images of very high resolution and contrast, based on the electron density. CT images provide excellent soft tissue contrast, allowing for greatly improved tumour localization and definition in comparison with conventional simulation. Patient contours can be obtained easily from the CT data — in particular, the patient’s skin contour, target and any organs of interest. Electron density information, useful in the calculation of dose inhomogeneities due to the differing composition of human tissues, can also be extracted from the CT data set. The target volume and its position are identified with relative ease on each transverse CT slice. The position of each slice and therefore the target can be related to bony anatomical landmarks through the use of scout or pilot images obtained at the time of CT scanning. Shown in Fig. 7.7 is a CT slice through a patient’s neck used in CT based conventional simulation. FIG. 7.6. A typical simulator radiograph for a head and neck patient. The field limits and shielding are clearly indicated on the radiograph. 231

CHAPTER 7 FIG. 7.7. A CT image through a patient’s neck. The target volume has been marked on the film by the physician. Pilot or scout films relate CT slice position to anteroposterior (AP) and lateral radiographic views of the patient at the time of scanning (see Fig. 7.8). They are obtained by keeping the X ray source in a fixed position and moving the patient (translational motion) through the stationary slit beam. The result is a high definition radiograph that is divergent on the transverse axis but non- divergent on the longitudinal axis. The target position relative to the bony anatomy on the simulator radiographs may then be determined through comparison with the CT scout or pilot films, keeping in mind the different magnifications between the simulator films and scout films. This procedure allows for a more accurate determination of tumour extent and therefore more precise field definition at the time of simulation. If the patient is CT scanned in the desired treatment position prior to simulation, the treatment field limits and shielding parameters may be set with respect to the target position as determined from the CT slices. 7.4.7.2. Determination of the treatment beam geometry The treatment beam geometry and any shielding required can now be determined indirectly from the CT data. The result is that the treatment port 232

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY more closely conforms to the target volume, reducing treatment margins around the target and increasing healthy tissue sparing. 7.4.8. Computed tomography based virtual simulation 7.4.8.1. Computed tomography simulator Dedicated CT scanners for use in radiotherapy treatment simulation and planning are known as CT simulators. The components of a CT simulator include: a large bore CT scanner (with an opening of up to 85 cm to allow for a larger variety of patient positions and the placement of treatment accessories during CT scanning); room lasers, including a movable sagittal laser, allowing for patient positioning and marking; a flat table top to more closely match radiotherapy treatment positions; and a powerful graphics workstation, allowing for image manipulation and formation. An example of a modern CT simulator is shown in Fig. 7.9. 7.4.8.2. Virtual simulation Virtual simulation is the treatment simulation of patients based solely on CT information. The premise of virtual simulation is that the CT data can be manipulated to render synthetic radiographs of the patient for arbitrary geometries. These radiographs, DRRs, can be used in place of simulator radiographs to determine the appropriate beam parameters for treatment. The FIG. 7.8. Pilot or scout images relate slice position to radiographic landmarks. 233

CHAPTER 7 FIG. 7.9. A dedicated radiotherapy CT simulator. Note the flat table top and the large bore (85 cm diameter). The machine was manufactured by Marconi, now Philips. advantage of virtual simulation is that anatomical information may be used directly in the determination of treatment field parameters. 7.4.8.3. Digitally reconstructed radiographs DRRs are produced by tracing ray lines from a virtual source position through the CT data of the patient to a virtual film plane. The sum of the attenuation coefficients along any one ray line gives a quantity analogous to optical density (OD) on a radiographic film. If the sums along all ray lines from a single virtual source position are then displayed on to their appropriate positions on the virtual film plane, the result is a synthetic radiographic image based wholly on the 3-D CT data set that can be used for treatment planning. Figure 7.10 provides an example of a typical DRR. 7.4.8.4. Beam’s eye view Beam’s eye views (BEVs) are projections of the treatment beam axes, field limits and outlined structures through the patient on to the corresponding 234

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY FIG. 7.10. A DRR. Note that grey levels, brightness and contrast can be adjusted to provide an optimal image. virtual film plane, and are frequently superimposed on to the corresponding DRRs, resulting in a synthetic representation of a simulation radiograph. Field shaping is determined with respect to both the anatomy visible on the DRR and the outlined structures projected by the BEVs (see Fig. 7.11). Multiplanar reconstructions (MPRs) are images formed from reformatted CT data. They are effectively CT images through arbitrary planes of the patient. Although typically sagittal or coronal MPR cuts are used for planning and simulation, MPR images through any arbitrary plane may be obtained. 7.4.8.5. Virtual simulation procedure A CT simulation begins by placing the patient on the CT simulator table in the treatment position. The patient position is verified on the CT pilot or scout scans. Prior to being scanned, it is imperative that patients be marked with a reference isocentre. Typically, a position near the centre of the proposed scan volume is chosen, radio-opaque fiducial markers are placed on the anterior and lateral aspects of the patient (with the help of the room lasers to ensure proper alignment) and the patient is tattooed to record the position of the fiducial markers to help with the subsequent patient set-up on the treatment machine. 235

CHAPTER 7 FIG. 7.11. A DRR with superimposed BEV for a lateral field of a prostate patient. This reference isocentre position can be used as the origin for a reference coordinate system from which the actual treatment isocentre position can be determined through translational motions of the table. The treatment isocentre can be identified on the patient through table motions and the use of a movable sagittal laser. Target structures and organs of interest can be outlined directly on the CT images using tools available in the virtual simulation software. DRRs and BEVs created from the CT information and outlined data are used to simulate the treatment. The determination of the treatment beam geometry and shielding is carried out with respect to the target position and critical organ location. Standard beam geometries (e.g. four field box, parallel opposed pair and lateral 236

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY oblique beams) can be used together with conformal shielding to increase the healthy tissue sparing. Alternatively, more unorthodox beam combinations can be used to maximize healthy tissue sparing in the event that a critical organ or structure is in the path of a beam. It is imperative that when choosing beam geometries consideration be given to the prospective dose distributions. Additionally, the physical limitations of the treatment unit and its accessories with respect to patient position must be considered. For example, care must be taken that the gantry position does not conflict with the patient position. Once a reasonable beam arrangement has been found, the field limits and shielding design may be obtained. Since the precise target location is known, the determination of the shielding design and treatment field limits becomes a matter of choosing an appropriate margin to account for physical and geometric beam effects such as beam penumbra. Once the relevant treatment parameters have been obtained, the treatment beam geometry, the CT data including contours and the electron density information are transferred to the TPS for the calculation of the dose distribution. 7.4.9. Conventional simulator versus computed tomography simulator The increased soft tissue contrast in combination with the axial anatomical information available from CT scans provides the ability to localize very precisely the target volumes and critical structures. The CT simulation phase allows for accurate identification and delineation of these structures directly on to the CT data set. This ability, in conjunction with the formation of DRRs and BEVs on which organs and targets are projected on to synthetic representations of simulator radiographs, allows the user to define treatment fields with respect to the target volume and critical structure location. By contrast, conventional simulation requires knowledge of tumour position with respect to the visible landmarks on the diagnostic quality simulator radiographs. Since these radiographs provide limited soft tissue contrast, the user is restricted to setting field limits with respect to either the bony landmarks evident on the radiographs or anatomical structures visible with the aid of contrast agents such as barium. Another important advantage of the CT simulation process over the conventional simulation process is the fact that the patient is not required to stay after the scanning has taken place. The patient only stays the minimum time necessary to acquire the CT data set, and this provides the obvious advantage that the radiotherapy staff may take their time in planning the 237

CHAPTER 7 FIG. 7.12. A DRR with superimposed BEV for a vertex field of a brain patient. This treatment geometry would be impossible to simulate on a conventional simulator. treatment as well as trying different beam configurations without the patient having to wait on the simulator table. A CT simulator allows the user to generate DRRs and BEVs even for beam geometries that were previously impossible to simulate conventionally. Vertex fields, for example, obviously are impossible to plan on a conventional simulator because the film plane is in the patient (see Fig. 7.12). There is some debate over whether there is a place in the radiotherapy clinic for a conventional simulator if a CT simulator is in place. Aside from the logistics and economics of having to CT scan every patient, there are certain sites where the use of CT simulation is not necessary (e.g. cord compression and bone and brain metastases). In addition, it is useful to perform a fluoro- scopic simulation of patients after CT simulation in order to verify the isocentre position and field limits as well as to mark the patient for treatment. When patient motion effects such as breathing are of particular concern, a conventional simulation may be preferable. 7.4.10. Magnetic resonance imaging for treatment planning The soft tissue contrast offered by MRI in some areas, such as the brain, is superior to that of CT, and allows small lesions to be seen with greater ease. 238

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY MRI alone, however, cannot be used for radiotherapy simulation and planning, for several reasons: ● The physical dimensions of the MRI scanner and its accessories limit the use of immobilization devices and compromise treatment positions; ● Bone signal is absent and therefore DRRs cannot be generated for comparison with portal films; ● There is no electron density information available for heterogeneity corrections on the dose calculations; ● MRI is prone to geometrical artefacts and distortions that may affect the accuracy of the dose distribution calculation and the treatment. Many modern virtual simulation systems and TPSs have the ability to combine the information from different imaging studies using the process of image fusion or registration. CT–MR image registration or fusion combines the accurate volume definition from MR with the electron density information available from CT. The MR data set is superimposed on the CT data set through a series of trans- lations, rotations and scaling. This process allows the visualization of both studies side by side in the same imaging plane even if the patient has been scanned in a completely different treatment position. An example of CT–MR image fusion is presented in Fig. 7.13. (a) (b) FIG. 7.13. (a) An MR image of a patient with a brain tumour. The target has been outlined and the result was superimposed on the patient’s CT scan (b). Note that the particular target is clearly seen on the MR image but only portions of it are observed on the CT scan. 239

CHAPTER 7 7.4.11. Summary of simulation procedures Tables 7.1–7.3 summarize the conventional and virtual simulation processes. TABLE 7.1. SUMMARY OF THE CONVENTIONAL SIMULATION PROCEDURE FOR A TYPICAL PATIENT (SIX STEPS) Step Conventional simulation procedure 1 Determination of patient treatment position with fluoroscopy 2 Determination of beam geometry 3 Determination of field limits and isocentre 4 Acquisition of contour 5 Acquisition of BEV and set-up radiographs 6 Marking of patient TABLE 7.2. SUMMARY OF THE PROCEDURE FOR A TYPICAL PATIENT COMPUTED TOMOGRAPHY SIMULATION (NINE STEPS) Step CT simulation procedure 1 Determination of patient treatment position with pilot/scout films 2 Determination and marking of reference isocentre 3 Acquisition of CT data and transfer to virtual simulation workstation 4 Localization and contouring of targets and critical structures 5 Determination of treatment isocentre with respect to target and reference isocentre 6 Determination of beam geometry 7 Determination of field limits and shielding 8 Transfer of CT and beam data to the TPS 9 Acquisition of BEV and set-up DRRs 240

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY TABLE 7.3. GOALS OF PATIENT TREATMENT SIMULATION, AND THE TOOLS AVAILABLE FOR ACHIEVING THE GOALS IN CONVENTIONAL AND COMPUTED TOMOGRAPHY SIMULATION Conventional Goal of patient simulation CT simulation simulation Treatment position Fluoroscopy Pilot/scout views Identification of target volume Bony landmarks From CT data Determination of beam geometry Fluoroscopy BEV/DRR Shielding design Bony landmarks Conformal to target Contour acquisition Manual From CT data 7.5. CLINICAL CONSIDERATIONS FOR PHOTON BEAMS 7.5.1. Isodose curves Isodose curves are lines that join points of equal dose. They offer a planar representation of the dose distribution and easily show the behaviour of one beam or a combination of beams with different shielding, wedges, bolus, etc. Isodose curves can be measured in water directly or can be calculated from PDD and beam profile data. A set of isodose curves is valid for a given treatment machine, beam energy, SSD and field size. While isodose curves can be made to display the actual dose in grays, it is more common to present them normalized to 100% at a fixed point. Two such common point normalizations are as follows: ● Normalization to 100% at the depth of dose maximum on the central axis; ● Normalization at the isocentre. Figure 7.14 shows isodose curves superimposed on a transverse contour of a patient for the same beam. Figure 7.14(a) illustrates a distribution normalized at the depth of dose maximum zmax; the distribution in Fig. 7.14(b) is normalized at the isocentre. 7.5.2. Wedge filters Three types of wedge filter are currently in use: manual, motorized and dynamic. 241

CHAPTER 7 ● A physical wedge is an angled piece of lead or steel that is placed in the beam to produce a gradient in radiation intensity. Manual intervention is required to place physical wedges on the treatment unit’s collimator assembly. ● A motorized wedge is a similar device, a physical wedge integrated into the head of the unit and controlled remotely. ● A dynamic wedge produces the same wedged intensity gradient by having one jaw close gradually while the beam is on. A typical isodose distribution for a wedged beam is shown is Fig. 7.15. (a) (b) FIG. 7.14. A single 18 MV photon beam incident on a patient contour. Isodose curves are for (a) a fixed SSD beam normalized at the depth of dose maximum zmax and (b) an isocentric beam normalized at the isocentre. FIG. 7.15. Isodose curves for a wedged 6 MV photon beam. The isodoses have been normalized to zmax with the wedge in place. 242

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY (a) (b) FIG. 7.16. Treatment plans illustrating two uses of wedge filters. In (a) two 15º wedges are used to compensate for the decreased thickness anteriorly. In (b) a wedged pair of beams is used to compensate for the hot spot that would be produced, with a pair of open beams at 90º to each other. The following applies to all wedges: ● The thick end of the wedge is called the heel: the dose is lowest underneath this end. The other end is called the toe. ● The wedge angle is commonly defined as the angle between the 50% isodose line and the perpendicular to the beam central axis. Wedge angles in the range from 10º to 60º are commonly available. There are two main uses of wedges: — Wedges can be used to compensate for a sloping surface, as, for example, in nasopharyngeal treatments, in which wedges are used to compensate for decreased thickness anteriorly, as shown in Fig. 7.16. Figure 7.16(a) shows two wedged beams in a parallel opposed configuration, with the wedges used to compensate for missing tissue. Figure 7.16(b) shows two wedged beams at 90º to one another, with the wedges compensating for the hot spot near the surface. — A wedge pair of beams is also useful in the treatment of relatively low lying lesions, in which two beams are placed at an angle (of less than 180º) called the hinge angle (see Fig. 7.17). The optimal wedge angle (assuming a flat patient surface) may be estimated from: 90º – 1/2 (hinge angle). The wedge factor (WF) is defined as the ratio of dose at a specified depth (usually zmax) on the central axis with the wedge in the beam to the dose under 243

CHAPTER 7 the same conditions without the wedge. This factor is used in MU calculations to compensate for the reduction in beam transmission produced by the wedge. The WF depends on the depth and field size. 7.5.3. Bolus Bolus is a tissue equivalent material placed in contact with the skin to achieve one or both of the following: increase the surface dose and/or compensate for missing tissue. To increase the surface dose, a layer of uniform thickness bolus is often used (0.5–1.5 cm), since it does not significantly change the shape of the isodose curves at depth. Several flab-like materials have been developed commercially for this purpose; however, cellophane wrapped wet towels or gauze offer low cost substitutes. To compensate for missing tissue or a sloping surface, a custom made bolus can be built that conforms to the patient’s skin on one side and yields a flat perpendicular incidence to the beam (see Fig. 7.18). The result is an isodose distribution that is identical to that produced on a flat phantom; however, skin sparing is not maintained. A common material used for this kind of bolus is wax, which is essentially tissue equivalent and when heated is malleable and can be fitted precisely to the patient’s contour. Bolus can also be used to compensate for lack of scatter, such as near the extremities or the head during TBI. Saline or rice bags can be used as bolus in these treatments. FIG. 7.17. A wedge pair of 6 MV beams incident on a patient. The hinge angle is 90º (orthogonal beams), for which the optimal wedge angle would be 45º. However, the addi- tional obliquity of the surface requires the use of a higher wedge angle of 60º. 244

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY (a) (b) Compensator Wax bolus Patient Patient FIG. 7.18. Difference between a bolus and a compensating filter. In (a) a wax bolus is placed on the skin, producing a flat radiation distribution. Skin sparing is lost with bolus. In (b) a compensator achieving the same dose distribution as in (a) is constructed and attached to the treatment unit. Due to the large air gap, skin sparing is maintained. 7.5.4. Compensating filters A compensating filter or compensator achieves the same effect on the dose distribution as a shaped bolus but does not cause a loss of skin sparing. Compensating filters can be made of almost any material, but metals such as lead are the most practical and compact. They are usually placed in a shielding slot on the treatment unit head and can produce a gradient in two dimensions (such compensators are more difficult to make and are best suited for a computer controlled milling machine). The closer to the radiation source the compensator is placed, the smaller the compensator. It is a simple case of demagnification with respect to the patient and source position to compensate for beam divergence. The dimensions of the compensator are simply scaled in length and width by the ratio of the SSD to the distance from the source to the compensator, as shown schematically in Fig. 7.18. The thickness of the compensator is determined on a point by point basis depending on the reduction of the dose that is required at a certain depth of interest in the patient. The thickness of compensator x along the ray line above that point can be solved from the attenuation law I/I0 = exp(–mx), where m is the linear attenuation coefficient for the radiation beam and material used to construct the compensator. 245

CHAPTER 7 The reduction in beam output through a custom compensator at zmax on the central axis needs to be measured and accounted for in MU/time calculations. The use of compensating filters instead of bolus is generally more laborious and time consuming. Additionally, the resulting dose distribution cannot be readily calculated on most TPSs without measurement of the beam profile under the compensator and additional beam data entry into the TPS. Bolus, on the other hand, can be considered part of the patient contour, thus eliminating the need for measurement. The major advantage of a compensating filter over bolus is the preservation of the skin sparing effect. 7.5.5. Corrections for contour irregularities Measured dose distributions apply to a flat radiation beam incident on a flat homogeneous water phantom. To relate such measurements to the actual dose distribution in a patient, corrections for irregular surface and tissue inhomogeneities have to be applied. Three methods for contour correction are used: the isodose shift method, the effective attenuation coefficient method and the tissue–air ratio (TAR) method. 7.5.5.1. Isodose shift method A simple method, called the isodose shift method, can be used, in the absence of computerized approaches, for planning on a manual contour. The method is illustrated in Fig. 7.19. ● Grid lines are drawn parallel to the beam central axis all across the field. ● The tissue deficit (or excess) h is the difference between the SSD along a gridline and the SSD on the central axis. TABLE 7.4. PARAMETER k USED IN THE ISODOSE SHIFT METHOD FOR CORRECTING ISODOSE DISTRIBUTIONS FOR AN IRREGULAR SURFACE Photon energy (MV) k (approximate) <1 0.8 60 Co–5 0.7 5–15 0.6 15–30 0.5 >30 0.4 246

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY ● k is an energy dependent parameter given in Table 7.4 for various photon beam energies. ● The isodose distribution for a flat phantom is aligned with the SSD central axis on the patient contour. ● For each gridline, the overlaid isodose distribution is shifted up (or down) such that the overlaid SSD is at a point k × h above (or below) the central axis SSD. ● The depth dose along the given gridline in the patient can now be read directly from the overlaid distribution. Central axis Patient surface k¥h h 90% 80% 70% 60% FIG. 7.19. Application of the isodose shift method for contour irregularity correction. The isodoses shown join the dose points calculated using the method (shown as solid black circles). 247

CHAPTER 7 7.5.5.2. Effective attenuation coefficient method A second method uses a correction factor known as the effective attenuation coefficient. The correction factor is determined from the attenuation factor exp(–mx), where x is the depth of missing tissue above the calculation point and m is the linear attenuation coefficient of tissue for a given energy. For simplicity, the factors are usually precalculated and supplied in graphical or tabular form. 7.5.5.3. Tissue–air ratio method The TAR correction method is also based on the attenuation law, but takes the depth of the calculation point and the field size into account. Generally, the correction factor CF as a function of depth z, thickness of missing tissue h and field size A is given by: TAR(z - h, AQ ) CF = (7.1) TAR(z, AQ ) 7.5.6. Corrections for tissue inhomogeneities In the most rudimentary treatment planning process, isodose charts and PDD tables are applied under the assumption that all tissues are water equivalent. In actual patients, however, the photon beam traverses tissues, such as fat, muscle, lung, air and bone, with varying densities and atomic numbers. Tissues with densities and atomic numbers different from those of water are referred to as tissue inhomogeneities or heterogeneities. Inhomogeneities in the patient result in: ● Changes in the absorption of the primary beam and associated scattered photons; ● Changes in electron fluence. The importance of each effect depends on the position of the point of interest relative to the inhomogeneity. In the megavoltage range the Compton interaction dominates and its cross-section depends on the electron density (in electrons per cubic centimetre). The following four methods correct for the presence of inhomogeneities within certain limitations: the TAR method; the Batho power law method; the equivalent TAR method; and the isodose shift method. A sample situation is shown in Fig. 7.20, in which a layer of tissue of 248

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY z1 r1 = 1 z2 r = re z3 r3 = 1 P FIG. 7.20. An inhomogeneity nested between two layers of water equivalent tissue. Point P is on the central axis of the beam. electronic density re relative to water is located between two layers of water equivalent tissue. 7.5.6.1. Tissue–air ratio method The dose at an arbitrary point P below the inhomogeneity is corrected by: TAR(z¢, rd ) (7.2) CF = TAR(z, rd ) where: z¢ = z1 + rez2 + z3 and z = z1 + z2 + z3 This method does not account for the position relative to the inhomogeneity. It also assumes that the homogeneity is infinite in lateral extent. 249

CHAPTER 7 7.5.6.2. Batho power law method The Batho power law method was initially developed by Batho and later generalized by Sontag and Cunningham. The dose at an arbitrary point P below the inhomogeneity is corrected by: TAR(z 3 , rd ) r 3 - r 2 (7.3) CF = TAR(z, rd ) 1- r 2 where, similarly to Eq. (7.2): z = z1 + z2 +z3 This method accounts for the position relative to the inhomogeneity. It still assumes that the homogeneity is infinite in lateral extent. 7.5.6.3. Equivalent tissue–air ratio method The equivalent TAR method is similar to the TAR method outlined above, with the exception that the field size parameter is modified as a function of the relative density to correct for the geometrical position of the inhomogeneity with respect to the calculation point. The new dose at arbitrary point P is corrected by: TAR(z ¢, rd ) ¢ (7.4) CF = TAR(z, rd ) where: z¢ = z1 + rez2 + z3 and z = z1 + z2 +z3 7.5.6.4. Isodose shift method The isodose shift method for the dose correction due to the presence of inhomogeneities is essentially identical to the isodose shift method outlined in the previous section for contour irregularities. 250

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY Isodose shift factors for several types of tissue have been determined for isodose points beyond the inhomogeneity. The factors are energy dependent but do not vary significantly with field size. The factors for the most common tissue types in a 4 MV photon beam are: air cavity: –0.6; lung: –0.4; and hard bone: 0.5. The total isodose shift is the thickness of inhomogeneity multiplied by the factor for a given tissue. Isodose curves are shifted away from the surface when the factor is negative. 7.5.7. Beam combinations and clinical application Single photon beams are of limited use in the treatment of deep seated tumours, since they give a higher dose near the entrance at the depth of dose maximum than at depth. The guidelines for the use of a single photon beam in radiotherapy are as follows: ● A reasonably uniform dose to the target (±5%); ● A low maximum dose outside the target (<110%); ● No organs exceeding their tolerance dose. Single fields are often used for palliative treatments or for relatively superficial lesions (depth < 5–10 cm, depending on the beam energy). For deeper lesions, a combination of two or more photon beams is usually required to concentrate the dose in the target volume and spare the tissues surrounding the target as much as possible. 7.5.7.1. Weighting and normalization Dose distributions for multiple beams can be normalized to 100%, just as for single beams: at zmax for each beam or at the isocentre for each beam. This implies that each beam is equally weighted. A beam weighting is applied at the normalization point for the given beam. A wedged pair with zmax normalization weighted 100:50% will show one beam with the 100% isodose at zmax and the other one with 50% at zmax. A similar isocentric weighted beam pair would show the 150% isodose at the isocentre. 7.5.7.2. Fixed source to surface distance versus isocentric techniques Fixed SSD techniques require moving the patient such that the skin is at the correct distance (nominal SSD) for each beam orientation. Isocentric techniques require placing the patient such that the target (usually) is at the 251

CHAPTER 7 FIG. 7.21. A parallel opposed beam pair is incident on a patient. Note the large rectan- gular area of relatively uniform dose (<15% variation). The isodoses have been normal- ized to 100% at the isocentre. This beam combination is well suited to a large variety of treatment sites (e.g. lung, brain, head and neck). isocentre. The machine gantry is then rotated around the patient for each treatment field. Dosimetrically, there is little difference between these two techniques: fixed SSD arrangements are usually used at a greater SSD (i.e. the machine isocentre is on the patient’s skin) than isocentric beams and therefore have a slightly higher PDD at depth. Additionally, beam divergence is smaller with SSD due to the larger distance. These advantages are small and, with the exception of very large fields exceeding 40 × 40 cm2, the advantages of a single set-up point (i.e. the isocentre) greatly outweigh the dosimetric advantage of SSD beams. 7.5.7.3. Parallel opposed beams Parallel opposed beams overcome the difficulty of a decreasing dose gradient due to each individual beam. A decrease in the depth dose of one beam is partially compensated by an increase in the other. The resulting distri- bution has a relatively uniform distribution along the central axis. Figure 7.21 shows a distribution for parallel opposed beams normalized to the isocentre. For small separations (<10 cm), low energy beams are well suited, since they have a sharp rise to a maximum dose and a relatively flat dose plateau in the region between both maximums. 252

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY For large separations (>15 cm), higher energy beams provide a more homogeneous distribution, whereas low energy beams can produce significant hot spots at the zmax locations of the two beams (>30%). Many anatomical sites, such as lung lesions and head and neck lesions, can be adequately treated with parallel opposed beams. 7.5.7.4. Multiple coplanar beams Multiple coplanar beams can be planned using a 2-D approach on a single plane, but their use allows for a higher dose in the beam intersection region. Common field arrangements include (see the two examples in Fig. 7.22): ● Wedge pair. Two beams with wedges (often orthogonal) are used to achieve a trapezoid shaped high dose region. This technique is useful in relatively low lying lesions (e.g. maxillary sinus and thyroid lesions). ● Four field box. A technique of four beams (two opposing pairs at right angles) producing a relatively high dose box shaped region. The region of highest dose now occurs in the volume portion that is irradiated by all four fields. This arrangement is used most often for treatments in the pelvis, where most lesions are central (e.g. prostate, bladder and uterus). ● Opposing pairs at angles other than 90º also result in the highest dose around the intersection of the four beams; however, the high dose area here has a rhombic shape. (a) (b) FIG. 7.22. Comparison of different beam geometries. A four field box (a) allows for a very high dose to be delivered at the intersection of the beams. A three field technique (b), however, requires the use of wedges to achieve a similar result. Note that the latter can produce significant hot spots near the entrance of the wedged beams and well outside the targeted area. 253

CHAPTER 7 ● Occasionally, three sets of opposing pairs are used, resulting in a more complicated dose distribution, but also in a spread of the dose outside the target over a larger volume (i.e. in more sparing of tissues surrounding the target volume). ● Three field box. A technique similar to a four field box for lesions that are closer to the surface (e.g. rectum). Wedges are used in the two opposed beams to compensate for the dose gradient in the third beam. 7.5.7.5. Rotational techniques Rotational techniques produce a relatively concentrated region of high dose near the isocentre, but also irradiate a greater amount of normal tissue to lower doses than fixed field techniques. The target is placed at the isocentre, and the machine gantry is rotated about the patient in one or more arcs while the beam is on. A typical distribution achieved with two rotational arcs is shown in Fig. 7.23. It is a useful technique used mainly for prostate, bladder, cervix and pituitary lesions, particularly boost volumes. The dose gradient at the edge of the field is not as sharp as that for multiple fixed field treatments. Skipping an angular region during the rotation allows the dose distribution to be pushed away from the region; however, this often requires that the isocentre be moved closer to this skipped area so that the resulting high dose region is centred on the target . FIG. 7.23. Isodose curves for two bilateral arcs of 120º each. The isodoses are tighter along the angles avoided by the arcs (anterior and posterior). The isodoses are normal- ized at the isocentre. Pelvic lesions such as prostate have been popular sites for the appli- cation of arc techniques. 254

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY The MU/time calculation uses the average TMR or TAR for the entire range of angles that the gantry covers during each arc. 7.5.7.6. Multiple non-coplanar beams Non-coplanar beams arise from non-standard table angles coupled with gantry angulations; they may be useful when there is inadequate critical structure sparing from a conventional coplanar beam arrangement. Dose distri- butions from non-coplanar beam combinations yield similar dose distributions to conventional multiple field arrangements. Care must be taken when planning the use of non-coplanar beams to ensure that no collisions occur between the gantry and the patient or table. Non-coplanar beams are most often used for treatments of the brain as well as of head and neck disease, where the target volume is frequently surrounded by critical structures. Non-coplanar arcs are also used, the best known example being the multiple non-coplanar converging arcs technique used in radiosurgery. 7.5.7.7. Field matching Field matching at the skin is the easiest field junctioning technique. However, due to beam divergence, this will lead to significant overdosing of tissues at depth and is only used in regions where tissue tolerance is not compromised. For most clinical situations field matching is performed at depth. To produce a junction dose similar to that in the centre of open fields, beams must be junctioned such that their diverging edges match at the desired depth (i.e. their respective 50% isodose levels add up at that depth). For two adjacent fixed SSD fields of different lengths L1 and L2, the surface gap g required to match the two fields at a depth z is (see Fig. 7.24): Ê z ˆ Ê z ˆ GAP = 0.5L1Á + 0.5L2 Á (7.5) Ë SSD ˜ ¯ Ë SSD ˜ ¯ For adjacent fields with isocentric beams and a sloping surface, a similar expression can be developed using similar triangle arguments. 255

CHAPTER 7 7.6. TREATMENT PLAN EVALUATION After the dose calculations are performed by dosimetrists or medical physicists on a computer or by hand, a radiation oncologist evaluates the plan. The dose distribution may be obtained for: ● A few significant points within the target volume; ● A grid of points over a 2-D contour or image; ● A 3-D array of points that covers the patient’s anatomy. The treatment plan evaluation consists of verifying the treatment portals and the isodose distribution for a particular treatment: — The treatment portals (usually through simulation radiographs or DRRs) are verified to ensure that the desired PTV is targeted adequately. — The isodose distribution (or the other dose tools discussed in this section) is verified to ensure that target coverage is adequate and that critical structures surrounding the PTV are spared as necessary. The following tools are used in the evaluation of the planned dose distri- bution: (i) Isodose curves; (ii) Orthogonal planes and isodose surfaces; (iii) Dose distribution statistics; (iv) Differential DVHs; (v) Cumulative DVHs. Beam 1 Beam 2 SSD L1 L2 z FIG. 7.24. Two adjacent fields matched at a depth z. 256

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY 7.6.1. Isodose curves Isodose curves, of which several examples were given in Section 7.5, are used to evaluate treatment plans along a single plane or over several planes in the patient. The isodose covering the periphery of the target is compared with the isodose at the isocentre. If the ratio is within a desired range (e.g. 95– 100%), the plan may be acceptable provided that critical organ doses are not exceeded. This approach is ideal if the number of transverse slices is small. 7.6.2. Orthogonal planes and isodose surfaces When a larger number of transverse planes are used for calculation (such as with a CT scan) it may be impractical to evaluate the plan on the basis of axial slice isodose distributions alone. In such cases, isodose distributions can also be generated on orthogonal CT planes, reconstructed from the original axial data. Sagittal and coronal plane isodose distributions are available on most 3-D TPSs, and displays on arbitrary oblique planes are becoming increas- ingly common. An alternative way to display isodoses is to map them in three dimensions and overlay the resulting isosurface on a 3-D display featuring surface renderings of the target and/or other organs. An example of such a display is shown in Fig. 7.25. While such displays can be used to assess target coverage, they do not convey a sense of distance between the isosurface and the anatomical volumes and give no quantitative volume information. 7.6.3. Dose statistics In contrast to the previous tools, the plan evaluation tools described here do not show the spatial distribution of dose superimposed on CT slices or on anatomy that has been outlined based on CT slices. Instead, they provide quantitative information on the volume of the target or critical structure and on the dose received by that volume. From the matrix of doses to each volume element within an organ, key statistics can be calculated. These include: ● The minimum dose to the volume; ● The maximum dose to the volume; ● The mean dose to the volume; ● The dose received by at least 95% of the volume; ● The volume irradiated to at least 95% of the prescribed dose. 257

CHAPTER 7 The final two statistics are only relevant for a target volume. Organ dose statistics such as these are especially useful in dose reporting, since they are simpler to include in a patient chart than the DVHs described below. 7.6.4. Dose–volume histograms A 3-D treatment plan consists of dose distribution information over a 3-D matrix of points over the patient’s anatomy. DVHs summarize the information contained in the 3-D dose distribution and are extremely powerful tools for quantitative evaluation of treatment plans. In its simplest form a DVH represents a frequency distribution of dose values within a defined volume that may be the PTV itself or a specific organ in the vicinity of the PTV. Rather than displaying the frequency, DVHs are usually displayed in the form of ‘per cent volume of total volume’ on the ordinate against the dose on the abscissa. FIG. 7.25. A 3-D plot of the prescription isodose (white wireframe) is superimposed on the target volume, with the bladder and the rectum shown. The individual beams are also shown. 258

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY Two types of DVH are in use: ● Direct (or differential) DVHs; ● Cumulative (or integral) DVHs. The main drawback of DVHs is the loss of spatial information that results from the condensation of data when DVHs are calculated. 7.6.4.1. Direct dose–volume histogram To create a direct DVH, the computer sums the number of voxels with an average dose within a given range and plots the resulting volume (or more frequently the percentage of the total organ volume) as a function of dose. An example of a direct DVH for a target is shown in Fig. 7.26(a). The ideal DVH for a target volume would be a single column indicating that 100% of the volume receives the prescribed dose. For a critical structure, the DVH may contain several peaks, indicating that different parts of the organ receive different doses. In Fig. 7.26(b) an example of a DVH for a rectum in the treatment of the prostate using a four field box technique is shown. 7.6.4.2. Cumulative dose–volume histogram Traditionally, physicians have sought to answer questions such as: “How much of the target is covered by the 95% isodose line?” In 3-D treatment planning this question is equally relevant and the answer cannot be extracted directly from a direct DVH, since it would be necessary to determine the area (a) (b) 120 120 100 100 Volume (%) Volume (%) 80 80 60 60 40 40 20 20 0 0 0 10 20 30 40 50 0 10 20 30 40 50 Dose (Gy) Dose (Gy) FIG. 7.26. Differential DVHs for a four field prostate treatment plan for (a) the target volume and (b) the rectum. The ideal target differential DVHs would be infinitely narrow peaks at the target dose for the PTV and at 0 Gy for the critical structure. 259

CHAPTER 7 under the curve for all dose levels above 95% of the prescription dose. For this reason, cumulative DVH displays are more popular. ● The computer calculates the volume of the target (or critical structure) that receives at least the given dose and plots this volume (or percentage volume) versus dose; ● All cumulative DVH plots start at 100% of the volume for 0 Gy, since all of the volume receives at least no dose. For the same organs as indicated in the example of Fig. 7.26, Fig. 7.27 shows the corresponding cumulative DVH (both structures are now shown on the same plot). While displaying the per cent volume versus dose is more popular, it is useful in some circumstances to plot the absolute volume versus dose. For example, if a CT scan does not cover the entire volume of an organ such as the lung, and the unscanned volume receives very little dose, then a DVH showing the percentage volume versus dose for that organ will be biased, indicating that a larger percentage of the volume receives dose. Furthermore, in the case of some critical structures, tolerances are known for irradiation of fixed volumes specified in cubic centimetres. 7.6.5. Treatment evaluation Treatment evaluation consists of: ● Verifying the treatment portals (through port films or on-line portal imaging methods) and comparing these with simulator radiographs or DRRs; (a) (b) 120 120 100 100 Volume (%) 80 Volume (%) 80 60 60 40 40 Target Target 20 20 Critical structure Critical structure 0 0 0 10 20 30 40 50 0 10 20 30 40 50 Dose (Gy) Dose (Gy) FIG. 7.27. Cumulative DVHs for the same four field prostate treatment plan used in Fig. 7.26. The ideal cumulative DVHs are shown in (b). 260

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY ● Performing in vivo dosimetry through the use of diodes, thermolumi- nescent dosimeters (TLDs) and other detectors. The latter methods are complex, often difficult to use in vivo and are beyond the scope of this section. Portal imaging, either through port films or on-line systems, provides relatively simpler ways of ensuring that the treatment has been successfully delivered. 7.6.5.1. Port films A port film is usually an emulsion type film, often still in its light-tight paper envelope, that is placed in the radiation beam beyond the patient. Depending on the sensitivity to radiation (or speed), port films can be used in one of two ways: ● Localization: a fast film (requiring only a few centigrays to expose) is placed in each beam at the beginning or end of the treatment to verify that the patient installation is correct for the given beam. ● Verification: a slow film is placed in each beam and left there for the duration of the treatment. In this case any patient or organ movement during treatment will most likely affect the quality of the film. Fast films generally produce a better image and are recommended for verifying small or complex beam arrangements. Slow films are recommended for larger fields, for example where as many as four films may be required to verify the treatment delivery. Localization films used in radiotherapy do not require intensifying screens such as those used in diagnostic radiology. Instead, a single thin layer of a suitable metal (such as copper or aluminium) is used in front of the film (beam entry side) to provide electronic buildup, which will increase the efficiency of the film. A backing layer is sometimes used with double emulsion films to provide backscatter electrons. Since there is no conversion of X rays to light photons, as in diagnostic films, the films need not be removed from the envelope. Port films can be taken either in single or double exposure techniques. — Single exposure: the film is irradiated with the treatment field alone. This technique is well suited to areas where the anatomical features can clearly be seen inside the treated field. Practically all verification films are single exposure. 261

CHAPTER 7 — Double exposure: the film is irradiated with the treatment field first, then the collimators are opened to a wider setting (usually 5–10 cm beyond each field limit) and all shielding is removed. A second exposure of typically 1–2 MUs is then given to the film. The resulting image shows not only the treated field but also some of the surrounding anatomy, which may be useful in verifying the beam position. Figure 7.28 shows a typical double exposure port film. 7.6.5.2. On-line portal imaging On-line portal imaging systems consist of a suitable radiation detector, usually attached through a manual or semirobotic arm to the linac, and are capable of transferring the detector information to a computer that will process it and convert it to an image. These systems use a variety of detectors, all producing computer based images of varying degrees of quality. FIG. 7.28. Port film for a lateral field used in a treatment of the maxillary sinus. This double exposure radiograph allows the physician to visualize both the treatment field and the surrounding anatomy. 262

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY Currently these systems include: ● Fluoroscopic detectors; ● Ionization chamber detectors; ● Amorphous silicon detectors. Fluoroscopic portal imaging detectors have the following characteristics: — They work on the same principle as a simulator image intensifier system. — The detector consists of a combination of a metal plate and fluorescent phosphor screen, a 45º mirror and a television camera. — The metal plate converts incident X rays to electrons and the fluorescent screen converts electrons to light photons. — The mirror deflects light to the TV camera, reducing the length of the imager, and the TV camera captures a small fraction (<0.1%) of the deflected light photons to produce an image. — They have good spatial resolution (depending on phosphor thickness). — They require only a few MUs to produce an image. — They use technology that has been used in many other fields. Matrix ionization chamber detectors have the following characteristics: (i) They are based on a grid of ionization chamber type electrodes that measure ionization from point to point. (ii) The detector consists of two metal plates, 1 mm apart, with the gap filled with isobutene. Each plate is divided into 256 electrodes and the plates are orientated such that the electrodes on one plate are at 90º to the electrodes on the other. (iii) A voltage is applied between two electrodes across the gap and the ionization at the intersection is measured. By selecting each electrode on each plate in turn, a 2-D ionization map is obtained and converted to a greyscale image of 256 × 256 pixels. (iv) The maximum image size is usually smaller than that of fluoroscopic systems. Amorphous silicon detectors have the following characteristics: (a) They have a solid state detector array consisting of amorphous silicon photodiodes and field effect transistors arranged in a large rectangular matrix. 263

CHAPTER 7 (b) They use a metal plate–fluorescent phosphor screen combination like the fluoroscopic systems. Light photons produce electron–hole pairs in the photodiodes, whose quantity is proportional to the intensity, allowing an image to be obtained. (c) They produce an image with a greater resolution and contrast than the other systems. 7.7. TREATMENT TIME AND MONITOR UNIT CALCULATIONS Treatment time and MU calculations are an important component of the dose delivery process since they determine the number of MUs (for linacs) and time (for isotope teletherapy and orthovoltage machines) of beam-on for each individual beam of the treatment plan. The patient treatments are carried out with either a fixed SSD or an isocentric technique. Each of the two techniques is characterized with a specific dose distribution and treatment time or MU calculation. The fixed SSD technique results in an isodose distribution that is governed by PDDs resulting from a well defined dose delivery to points P at the depth of dose maximum for each of the beams in the treatment plan. The weight (W) ranging from 0 to 1.0 applied for a given beam actually determines the dose delivered to point P for the particular beam. W = 1 implies a dose of 100 cGy to point P, W = 0.65 implies a dose of 65 cGy to point P, etc. The isocentric technique, on the other hand, results in a dose distribution that is most often governed by TMRs normalized in such a way that each beam of the treatment plan delivers a prescribed fraction of the total dose at the isocentre. Other functions, such as TARs or tissue–phantom ratios (TPRs), are also sometimes used in isocentric dose distribution calculations. Calculations of treatment time or MUs for both the fixed SSD and the isocentric technique depend on the basic treatment machine output calibration, which is discussed in Chapter 9. For megavoltage photon machines, the output is most commonly stipulated in cGy/MU for linacs and in cGy/min for cobalt units under conditions that may be summarized as follows: ● Measured in a water phantom; ● Measured on the central axis of the radiation beam; ● Stated for point P at the depth of maximum dose; 2 ● Measured with a field size of 10 × 10 cm ; ● Measured at the nominal SSD f of the unit (most commonly 100 cm). 264

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY FIG. 7.29. Fixed SSD isodose distribution for a three field treatment of the prostate. · The output may be designated by D(zmax, 10,¦, hv) and is used directly in meter-set calculations involving fixed SSD techniques. · For cobalt units the output D(zmax, 10,¦, hv) is measured and quoted as the dose rate in cGy/min. The sensitivity of linac monitor chambers, on the · other hand, is usually adjusted in such a way that D(zmax, 10,¦, hv) = 1 cGy/MU. · When used in isocentric calculations, D(zmax, 10,¦, hv) must be corrected by the inverse square factor (ISF) unless the machine is actually calibrated at the isocentre: 2 Ê f + zmax ˆ (7.6) ISF = Á ˜ Ë f ¯ 7.7.1. Treatment time and monitor unit calculations for a fixed source to surface distance set-up Figure 7.29 shows a typical dose distribution obtained for a three field prostate boost treatment with a fixed SSD (100 cm) technique on a 6 MV linac. The three treatment fields have the following characteristics: 265

CHAPTER 7 ● Anterior field: 7.5 × 7.5 cm2 open field with W = 1.0. 2 ● Left posterior oblique (LPO) field: 6.5 × 7.5 cm wedged field with W = 0.8 and WF = 0.53. 2 ● Right posterior oblique (RPO) field: 6.5 × 7.5 cm wedged field with W = 0.8 and WF = 0.53. The dose D(Q) of 200 cGy is prescribed at the ICRU reference point, located at the intersection of the three fields. As shown in Fig. 7.29, the isodose line (IL) through the ICRU reference point is 152%, the maximum dose is 154% and the 150% isodose curve completely covers the PTV. The PTV dose is thus between +2% and –2% of the D(Q) dose, fulfilling well the recommendation that the target doses should lie between +7% and _5% of the dose prescribed at the ICRU reference point. The dose distribution shown in Fig. 7.29 delivers a dose of 152 cGy to the ICRU reference point Q under the following conditions: — A dose of 100 cGy is delivered at a point PA (W = 1 for the anterior field); — A dose of 80 cGy is delivered at a point PLPO (W = 0.8 for the LPO field); — A dose of 80 cGy is delivered at a point PRPO (W = 0.8 for the RPO field). Thus to obtain the prescribed dose of 200 cGy rather than 152 cGy at point Q, doses of D(PA) = 131.6 cGy, D(PLPO) = 105.3 cGy and D(PRPO) = 105.3 cGy should be delivered to points PA, PLPO and PRPO, respectively. The doses at points P for individual beams are often referred to as the given doses for a particular field in the fixed SSD treatment plan and are determined as follows: D(Q) ¥ 100 ¥ WA 200 cGy ¥ 100 ¥ 1.0 D(PA ) = = = 131.6 cGy (7.7) IL 152 D(Q) ¥ 100 ¥ WLPO 200 cGy ¥ 100 ¥ 0.8 D(PLPO ) = = = 105.3 cGy (7.8) IL 152 D(Q) ¥ 100 ¥ WRPO 200 cGy ¥ 100 ¥ 0.8 D(PRPO ) = = = 105.3 cGy (7.9) IL 152 The next step is to calculate the linac monitor chamber setting in MUs required for the delivery of the given doses for each of the three fields consti- tuting the fixed SSD treatment plan. The given dose rates for points PA, PLPO and PRPO are obtained by multiplying the basic linac output with the RDF(A), 266

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY where A refers to the appropriate field size (see Section 6.6.4), and any other applicable transmission factors (such as the WF or the tray factor). The monitor settings MU for points PA, PLPO and PRPO are calculated as follows: D(PA) MU (A) = D(zmax , 10, 100, hn ) ¥ RDF(A, hn ) 131.6 cGy MU(A) = = 134 MU (7.10) 1.0 cGy/MU ¥ 0.98 D(PLPO) MU (LPO) = D(zmax , 10, 100, hn ) ¥ RDF(A, hn ) ¥ WF 105.3 cGy MU(LPO) = = 205 MU (7.11) 1.0 cGy/MU ¥ 0.97 ¥ 0.53 D(PRPO) MU (RPO) = D(zmax , 10, 100, hn ) ¥ RDF(A, hn ) ¥ WF 105.3 cGy MU(RPO) = = 205 MU (7.12) 1.0 cGy/MU ¥ 0.97 ¥ 0.53 7.7.2. Monitor unit and treatment time calculations for isocentric set-ups Figure 7.30 shows a typical isodose distribution obtained for a three field prostate boost treatment with an isocentric (100 cm) technique on a 6 MV linac. For the isocentric distribution, all field sizes (AQ) are defined at the isocentre, and wedges are used for the two oblique fields, as in the fixed SSD example: ● Anterior 8 × 8 cm2 open field with W = 1.0; 2 ● LPO and RPO 7 × 8 cm fields both with W = 0.7, and WF = 0.53. A dose DQ of 200 cGy is prescribed at the ICRU reference point, which is located at the treatment isocentre. The IL at this point is 240% (sum of the weights in per cent), the maximum dose in the distribution is 242% and the 235% isodose completely covers the PTV. 267

CHAPTER 7 The dose distribution shown in Fig. 7.30 that delivers a dose of 240 cGy to the ICRU reference point Q is achieved under the following conditions: — 100 cGy is delivered by the anterior field at the isocentre (W = 1); — 70 cGy is delivered by the LPO field at the isocentre (W = 0.7); — 70 cGy is delivered by the RPO field at the isocentre (W = 0.7). Thus to obtain the prescribed dose of 200 cGy at point Q, doses of 83.4 cGy, 58.3 cGy and 58.3 cGy should be delivered by the respective beams at the isocentre. These doses are obtained by considering the relative weight of each beam, such that: D(Q) ¥ 100 ¥ WA 200 cGy ¥ 100 ¥ 1.0 D(Q) A = = = 83.4 cGy (7.13) IL 240 D(Q) ¥ 100 ¥ WLPO 200 cGy ¥ 100 ¥ 0.7 D(Q) LPO = = = 58.3 cGy (7.14) IL 240 FIG. 7.30. Isocentric isodose distribution for a three field treatment of the prostate. 268

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY D(Q) ¥ 100 ¥ WRPO 200 cGy ¥ 100 ¥ 0.7 D(Q) RPO = = = 58.3 cGy (7.15) IL 240 To calculate the linac monitor chamber setting in MUs, it is first necessary to calculate the doses from each beam at the isocentre at a depth of maximum dose D(Qmax), where SSD = SAD –zmax. The TMR is obtained for each field and used in the calculation as follows: D(Q) A 83.4 cGy D(Q max ) A = = = 97.2 cGy (7.16) TMR(8 ¥ 8, 11.5) 0.72 D(Q) LPO 58.3 cGy D(Q max ) LPO = = = 108.3 cGy (7.17) TMR(7 ¥ 8, 18.5) 0.54 D(Q) RPO 58.3 cGy D(Q max ) RPO = = = 108.3 cGy (7.18) TMR(7 ¥ 8, 18.5) 0.54 Once the dose at D(Qmax) is known for each beam it is possible to · calculate the MU setting (MU) from the basic linac output D(zmax, 10,¦, hv) multiplied by the RDF(AQ), the ISF and other transmission factors as applicable, such that: D(Q max ) A MU (A) = D(zmax , 10, 100, hn ) ¥ ISF ¥ RDF(8 ¥ 8) 97.2 cGy MU(A) = 2 = 96 MU (7.19) Ê 101.5 ˆ 1.0 cGy/MU ¥ Á ¥ 0.982 Ë 100 ˜ ¯ D(Q max ) LPO MU (LPO) = D(zmax , 10, 100, hn ) ¥ ISF ¥ RDF(7 ¥ 8) ¥ WF 108.3 cGy MU(LPO) = 2 = 203 MU (7.20) Ê 101.5 ˆ 1.0 cGy/MU ¥ Á ¥ 0.975 ¥ 0.53 Ë 100 ˜ ¯ 269

CHAPTER 7 D(Q max ) RPO MU (RPO) = D(zmax , 10, 100, hn ) ¥ ISF ¥ RDF(7 ¥ 8) ¥ WF 108.3 cGy MU(RPO) = 2 = 203 MU (7.21) Ê 101.5 ˆ 1.0 cGy/MU ¥ Á ¥ 0.975 ¥ 0.53 Ë 100 ˜ ¯ 7.7.3. Normalization of dose distributions It is important to note that dose distributions can be normalized in a variety of different ways. The ICRU recommends normalization of the dose distribution to 100% at the prescription point Q. Clearly, the calculation of MUs must reflect the normalization technique employed for each particular case. ● If the dose distribution is normalized to 100% at the isocentre, an adjustment must be made to the calculation when calculating the relative dose contribution to the isocentre from each beam. ● For the isocentric example above, the isodose value at the isocentre is simply the sum of the absolute weights of each beam. If the dose distri- bution was normalized to 100% at the isocentre, with D(Q) = 200 cGy and a prescription isodose value (IL) of 100%, the relative contribution for beam A would amount to: D(Q) ¥ 100 Ê WA ˆ D(Q) A = ¥Á ˜ IL Ë WA + WLPO + WRPO ¯ 200 cGy ¥ 100 Ê 1.0 . ˆ D(Q) A = ¥Á = 83.4 cGy Ë 1.0 + 0.7 + 0.7 ˜ (7.22) 100 ¯ The remainder of the calculation remains the same. 7.7.4. Inclusion of output parameters in the dose distribution Modern TPSs give the user the ability to take into account several dosimetric parameters in the dose distribution affecting the beam output, thereby relieving the need to correct the beam output when performing the 270

TREATMENT PLANNING IN EXTERNAL PHOTON BEAM RADIOTHERAPY monitor setting calculation. Obviously, large errors in monitor calculations could occur if the outputs were corrected without need. Frequently, for example, the isodose values in a dose distribution may already include: ● Inverse square law factors for extended distance treatments; ● Effects on dose outputs from blocks in the field; or ● Tray factors and WFs. It is of the utmost importance to know exactly what the isodose lines mean on a dose distribution obtained from a given TPS. 7.7.5. Treatment time calculation for orthovoltage and cobalt-60 units Treatment time calculations for orthovoltage units and 60Co teletherapy units are carried out similarly to the above examples, except that machine outputs are stated in cGy/min and the treatment timer setting in minutes replaces the monitor setting in MUs. A correction for shutter error should be included in the time set. BIBLIOGRAPHY BENTEL, G.C., Radiation Therapy Planning, McGraw-Hill, New York (1996). BENTEL, G.C., NELSON, C.E., NOELL, K.T., Treatment Planning and Dose Calculation in Radiation Oncology, Pergamon Press, New York (1989). HENDEE, W.R., IBBOTT, G.S., Radiation Therapy Physics, Mosby, St. Louis, MI (1996). INTERNATIONAL COMMISSION ON RADIATION UNITS AND MEASUREMENTS, Measurement of Absorbed Dose Measured in a Phantom Irradiated by a Single Beam of X or Gamma Rays, Rep. 23, ICRU, Bethesda, MD (1973). — Prescribing, Recording and Reporting Photon Beam Therapy, Rep. 50, ICRU, Bethesda, MD (1993). — Prescribing, Recording and Reporting Photon Beam Therapy (Supplement to ICRU Report 50), Rep. 62, ICRU, Bethesda, MD (1999). 271

CHAPTER 7 JOHNS, H.E., CUNNINGHAM, J.R., The Physics of Radiology, Thomas, Springfield, IL (1985). KHAN, F.M., The Physics of Radiation Therapy, 3rd edn, Lippincott, Williams and Wilkins, Baltimore, MD (2003). KHAN, F.M., POTTISH, R.A., Treatment Planning in Radiation Oncology, Williams and Wilkins, Baltimore, MD (1998). MOULD, R.F., Radiotherapy Treatment Planning, Adam Hilger, Bristol (1981). WILLIAMS, J.R., THWAITES, D.I., Radiotherapy Physics in Practice, Oxford Univ. Press, Oxford (1993). 272

Chapter 8 ELECTRON BEAMS: PHYSICAL AND CLINICAL ASPECTS W. STRYDOM Department of Medical Physics, Medical University of Southern Africa, Pretoria, South Africa W. PARKER, M. OLIVARES Department of Medical Physics, McGill University Health Centre, Montreal, Quebec, Canada 8.1. CENTRAL AXIS DEPTH DOSE DISTRIBUTIONS IN WATER Megavoltage electron beams represent an important treatment modality in modern radiotherapy, often providing a unique option in the treatment of superficial tumours (less than 5 cm deep). Electrons have been used in radio- therapy since the early 1950s, first produced by betatrons and then by microtrons and linacs. Modern high energy linacs typically provide, in addition to two megavoltage photon energies, several electron beam energies in the range from 4 to 22 MeV. 8.1.1. General shape of the depth dose curve The general shape of the central axis depth dose curve for electron beams differs from that of photon beams (see Fig. 8.1). Figure 8.1(a) shows depth doses for various electron beam energies and Fig. 8.1(b) shows depth doses for 6 and 15 MV X ray beams. Typically, the electron beam central axis depth dose curve exhibits a high surface dose (compared with megavoltage photon beams), and the dose then builds up to a maximum at a certain depth referred to as the electron beam depth of dose maximum zmax. Beyond zmax the dose drops off rapidly and levels off at a small low level dose component referred to as the bremsstrahlung tail. These features offer a distinct clinical advantage over the conventional X ray modalities in the treatment of superficial tumours. 273

CHAPTER 8 110 110 100 (a) 100 (b) 90 90 80 80 70 70 PPD (%) PPD (%) 60 60 50 50 15 MV 40 40 30 6 9 12 18 MeV 30 6 MV 20 20 10 10 0 0 0 5 10 0 5 10 15 20 25 Depth in water (cm) Depth in water (cm) FIG. 8.1. Typical central axis PDD curves in water for a 10 × 10 cm2 field size and an SSD of 100 cm for (a) electron beams with energies of 6, 9, 12 and 18 MeV and (b) photon beams with energies of 6 and 15 MV. A typical high energy linac may produce electron beams with discrete energies in the range from 4 to 25 MeV. Electron beams can be considered almost monoenergetic as they leave the accelerator; however, as the electron beam passes through the accelerator exit window, scattering foils, monitor chambers, collimators and air, the electrons interact with these structures, resulting in: ● A broadening of the beam’s electron energy spectrum; ● Bremsstrahlung production contributing to the bremsstrahlung tail in the electron beam percentage depth dose (PDD) distribution. On initial contact with the patient, the clinical electron beam has an – incident mean energy E0 that is lower than the electron energy inside the accelerator. The ratio of the dose at a given point on the central axis of an electron beam to the maximum dose on the central axis multiplied by 100 is the PDD, which is normally measured for the nominal treatment distance (i.e. the distance between the accelerator exit window and the patient’s skin) and depends on field size and electron beam energy. 8.1.2. Electron interactions with an absorbing medium As electrons travel through a medium, they interact with atoms by a variety of Coulomb force interactions that may be classified as follows: 274

ELECTRON BEAMS: PHYSICAL AND CLINICAL ASPECTS ● Inelastic collisions with atomic electrons, resulting in ionization and excitation of atoms and termed collisional or ionizational loss; ● Elastic collisions with atomic nuclei, resulting in elastic scattering that is characterized by a change in direction but no energy loss; ● Inelastic collisions with atomic nuclei, resulting in bremsstrahlung production and termed radiative loss; ● Elastic collisions with atomic electrons. The kinetic energy of electrons is lost in inelastic collisions that produce ionization or is converted to other forms of energy, such as photon energy or excitation energy. In elastic collisions kinetic energy is not lost; however, the electron’s direction may be changed or the energy may be redistributed among the particles emerging from the collision. The typical energy loss for a therapy electron beam, averaged over its entire range, is about 2 MeV/cm in water and water-like tissues. The rate of energy loss for collisional interactions depends on the electron energy and on the electron density of the medium. The rate of energy loss per gram per square centimetre, MeV·g–1·cm–2 (called the mass stopping power), is greater for low atomic number materials than for high atomic number materials. This is because high atomic number materials have fewer electrons per gram than lower atomic number materials and, moreover, high atomic number materials have a larger number of tightly bound electrons that are not available for this type of interaction. The rate of energy loss for radiative interactions (bremsstrahlung) is approximately proportional to the electron energy and to the square of the atomic number of the absorber. This means that X ray production through radiative losses is more efficient for higher energy electrons and higher atomic number materials. When a beam of electrons passes through a medium the electrons suffer multiple scattering, due to Coulomb force interactions between the incident electrons and predominantly the nuclei of the medium. The electrons will therefore acquire velocity components and displacements transverse to their original direction of motion. As the electron beam traverses the patient, its mean energy decreases and its angular spread increases. The scattering power of electrons varies approximately as the square of the atomic number and inversely as the square of the kinetic energy. For this reason high atomic number materials are used in the construction of scattering foils used for the production of clinical electron beams in a linac. The scattering power variations in heterogeneous tissues are also responsible for the production of local hot and cold spots. 275

CHAPTER 8 8.1.3. Inverse square law (virtual source position) In contrast to a photon beam, which has a distinct focus located at the accelerator X ray target, an electron beam appears to originate from a point in space that does not coincide with the scattering foil or the accelerator exit window. The term ‘virtual source position’ was introduced to indicate the virtual location of the electron source. The effective source to surface distance (SSD) for electron beams (SSDeff) is defined as the distance from the virtual source position to the point of the nominal SSD (usually the isocentre of the linac). The inverse square law may be used for small SSD differences from the nominal SSD to make corrections to the absorbed dose for variations in air gaps between the patient surface and the applicator. There are various methods to determine the SSDeff. One commonly used method consists of measuring the dose at various distances from the electron applicator by varying the gap between the phantom surface and the applicator (with gaps ranging from 0 to 15 cm). In this method, doses are measured in a phantom at the depth of maximum dose zmax, with the phantom first in contact with the applicator (zero gap) and then at various distances g from the applicator. Suppose I0 is the dose with zero gap (g = 0) and Ig is the dose with gap distance g. It follows then from the inverse square law that: 2 I 0 Ê SSD eff + zmax + g ˆ = (8.1) I g Á SSD eff + zmax ˜ Ë ¯ or I0 g = +1 (8.2) I g SSD eff + zmax A plot of I0 / Ig against the gap distance g will give a straight line with a slope of: 1 SSD eff + zmax and the SSDeff will then be given by: 1 SSD eff = - zmax (8.3) slope 276

ELECTRON BEAMS: PHYSICAL AND CLINICAL ASPECTS Although the effective SSD is obtained from measurements at zmax, its value does not change with the depth of measurement. However, the effective SSD changes with beam energy, and has to be measured for all energies available in the clinic. 8.1.4. Range concept A charged particle such as an electron is surrounded by its Coulomb electric field and will therefore interact with one or more electrons or with the nucleus of practically every atom it encounters. Most of these interactions individually transfer only minute fractions of the incident particle’s kinetic energy, and it is convenient to think of the particle as losing its kinetic energy gradually and continuously in a process often referred to as the continuous slowing down approximation (CSDA). The path length of a single electron is the total distance travelled along its actual trajectory until the electron comes to rest, regardless of the direction of movement. The projected path range is the sum of individual path lengths projected on to the incident beam direction (i.e. the central axis). The CSDA range (or the mean path length) for an electron of initial kinetic energy E0 can be found by integrating the reciprocal of the total stopping power: E0 -1 È S( E ) ˘ RCSDA = Ú 0 Í r ˙ dE Î ˚ tot (8.4) The CSDA range is purely a calculated quantity that represents the mean path length along the electron’s trajectory and not the depth of penetration in a defined direction. The CSDA range for electrons in air and water is given in Table 8.1 for various electron kinetic energies. The following two concepts of range are also defined for electron beams: maximum range and practical range. The maximum range Rmax (cm or g/cm2) is defined as the depth at which extrapolation of the tail of the central axis depth dose curve meets the brems- strahlung background, as shown in Fig. 8.2. It is the largest penetration depth of electrons in the absorbing medium. The maximum range has the drawback of not giving a well defined measurement point. The practical range Rp (cm or g/cm2) is defined as the depth at which the tangent plotted through the steepest section of the electron depth dose curve intersects with the extrapolation line of the background due to bremsstrahlung, as shown in Fig. 8.2. 277

CHAPTER 8 TABLE 8.1. CSDA RANGES IN AIR AND WATER FOR VARIOUS ELECTRON ENERGIES Electron energy CSDA range in air CSDA range in water (MeV) (g/cm2) (g/cm2) 6 3.255 3.052 7 3.756 3.545 8 4.246 4.030 9 4.724 4.506 10 5.192 4.975 20 9.447 9.320 30 13.150 13.170 The depths R90 and R50 (cm or g/cm2) are defined as depths on the electron PDD curve at which the PDDs beyond zmax attain values of 90% and 50%, respectively. The depth Rq (cm or g/cm2) is defined as the depth where the tangent through the dose inflection point intersects the maximum dose level, as shown in Fig. 8.2. It is evident that the CSDA range is of marginal usefulness in character- izing the depth of penetration of electrons into an absorbing medium. 100 90 Rq PDD (%) 50 0 R90 R50 Rp Rmax Depth in water (cm) FIG. 8.2. Typical electron beam PDD curve illustrating the definition of Rq, Rp, Rmax, R50l and R90. 278

ELECTRON BEAMS: PHYSICAL AND CLINICAL ASPECTS Scattering effects, predominantly between the incident electrons and nuclei of the absorbing medium, cause electrons to follow very tortuous paths, resulting in large variations in the actual path of electrons in the absorbing medium. 8.1.5. Buildup region (depths between the surface and zmax (i.e. 0 £ z £ zmax)) The dose buildup in electron beams is much less pronounced than that of megavoltage photon beams and results from the scattering interactions that the electrons experience with atoms of the absorber. Upon entry into the medium (e.g. water), the electron paths are approximately parallel. With depth their paths become more oblique with regard to the original direction, due to multiple scattering, resulting in an increase in electron fluence along the beam central axis. In the collision process between electrons and atomic electrons, it is possible that the kinetic energy acquired by the ejected electron is large enough (hard collision) to cause further ionization. In such a case, these electrons are referred to as secondary electrons or d rays, and they also contribute to the buildup of dose. As seen in Fig. 8.1, the surface dose of electron beams (in the range from 75% to 95%) is much higher than the surface dose for photon beams, and the rate at which the dose increases from the surface to zmax is therefore less pronounced for electron beams than for photon beams. Unlike in photon beams, the per cent surface dose for electron beams increases with electron energy. This can be explained by the nature of electron scatter. At lower energies, electrons are scattered more easily and through larger angles. This causes the dose to build up more rapidly and over a shorter distance, as shown in Fig. 8.3. The ratio of surface dose to maximum dose is therefore lower for lower energy electrons than for higher energy electrons. In contrast to the behaviour of megavoltage photon beams, the depth of maximum dose in electron beams zmax does not follow a specific trend with electron beam energy; rather, it is a result of the machine design and accessories used. 8.1.6. Dose distribution beyond zmax (z > zmax) Scattering and continuous energy loss by electrons are the two processes responsible for the sharp drop-off in the electron dose at depths beyond zmax. Bremsstrahlung produced in the head of the accelerator, in the air between the accelerator window and the patient, and in the irradiated medium is responsible for the tail in the depth dose curve. 279

CHAPTER 8 PDD (%) 100 50 20 MeV 15 MeV 12 MeV 9 MeV 6 MeV 4 MeV 0 5 10 Depth (cm) FIG. 8.3. Central axis PDD curves for a family of electron beams from a high energy linac. All curves are normalized to 100% at zmax. The range of electrons increases with increasing electron energy. The electron dose gradient is defined as follows: G = Rp/(Rp – Rq) The dose gradient for lower electron energies is steeper than that for higher electron energies, since the lower energy electrons are scattered at a greater angle away from their initial directions. The stopping powers at low and high energy also affect the dose gradient. The bremsstrahlung contamination (e.g. the tail sections of Fig. 8.1(a)) depends on electron beam energy and is typically less than 1% for 4 MeV and less than 4% for 20 MeV electron beams for an accelerator with dual scattering foils. 280

ELECTRON BEAMS: PHYSICAL AND CLINICAL ASPECTS 8.2. DOSIMETRIC PARAMETERS OF ELECTRON BEAMS 8.2.1. Electron beam energy specification Owing to the complexity of the spectrum, there is no single energy parameter that will fully characterize an electron beam. Several parameters are used to describe a beam, such as the most probable energy Ep,0 on the phantom – surface, the mean energy E0 on the phantom surface, and R50, the depth at which the absorbed dose falls to 50% of the maximum dose. The most probable energy Ep,0 on the phantom surface is empirically related to the practical range Rp in water as follows: 2 Ep,0 = 0.22 + 1.09Rp + 0.0025Rp (8.5) where Ep,0 is in megaelectronvolts and Rp is in centimetres. – The mean electron energy E0 at the phantom surface is related to the half- value depth R50 as follows: – E0 = CR50 (8.6) where C = 2.33 MeV/cm for water. The depth R50 is the beam quality index in electron beam dosimetry as specified in IAEA TRS 398. R50 is calculated from the measured R50,ion, the depth at which the ionization curve falls to 50% of its maximum, by: R50 = 1.029R50,ion – 0.06 (g/cm2) (for R50,ion £ 10 g/cm2) (8.7) R50 = 1.059R50,ion – 0.37 (g/cm2) (for R50,ion > 10 g/cm2) (8.8) – Ez, the mean energy at a depth z in a water phantom, is related to the practical range Rp by the Harder equation as follows: – – Ez = E0 (1 – z/Rp) (8.9) 8.2.2. Typical depth dose parameters as a function of energy Some typical values for electron depth dose parameters as a function of energy are shown in Table 8.2. These parameters should be measured for each electron beam before it is put into clinical service. 281

CHAPTER 8 TABLE 8.2. TYPICAL DEPTH DOSE PARAMETERS OF ELECTRON BEAMS – Energy R90 R80 R50 Rp E0 Surface dose (MeV) (cm) (cm) (cm) (cm) (MeV) (%) 6 1.7 1.8 2.2 2.9 5.6 81 8 2.4 2.6 3.0 4.0 7.2 83 10 3.1 3.3 3.9 4.8 9.2 86 12 3.7 4.1 4.8 6.0 11.3 90 15 4.7 5.2 6.1 7.5 14.0 92 18 5.5 5.9 7.3 9.1 17.4 96 8.2.3. Percentage depth dose Typical central axis PDD curves for various electron beam energies are shown in Fig. 8.3 for a field size of 10 × 10 cm2. When diodes are used in PDD measurements, the diode signal represents the dose directly, because the stopping power ratio water to silicon is essentially independent of electron energy and hence depth. If an ionization chamber is used in the determination of electron beam depth dose distributions, the measured depth ionization distribution must be converted to a depth dose distribution by using the appropriate stopping power ratios water to air at depths in a phantom. For more information on the ionization chamber measurements see IAEA TRS 398. 8.2.3.1. Percentage depth doses for small electron field sizes When the distance between the central axis and the field edge is more than the lateral range of scattered electrons, lateral scatter equilibrium exists and the depth dose for a specific electron energy will be essentially independent of the field dimensions, as shown in Fig. 8.4 for field sizes larger than 10 × 10 cm2 and an electron energy of 20 MeV. With decreasing field size the decreasing degree of lateral electronic equilibrium will be present at the central axis, and the depth dose and output factors will show large sensitivity to field shape and size (see also Section 8.3.2), as shown in Fig. 8.4 for a 20 MeV electron beam and field sizes smaller than 10 × 10 cm2. When the length of one side of the electron field decreases to below the Rp value for a given electron energy, the depth of dose maximum decreases and 282

ELECTRON BEAMS: PHYSICAL AND CLINICAL ASPECTS 100 4 – 4 cm2 6 – 6 cm2 10 – 10 cm2 15 – 15 cm2 20 – 20 cm2 PDD (%) 25 – 25 cm2 50 20 MeV 0 5 10 Depth (cm) FIG. 8.4. PDD curves for different field sizes for a 20 MeV electron beam from a linac. It is clearly illustrated that for field sizes larger than the practical range of the electron beam (Rp is about 10 cm for this 20 MeV electron beam), the PDD curve remains essentially unchanged. the relative surface dose increases with decreasing field size. The Rp, on the other hand, is independent of electron beam field size, as also shown in Fig. 8.4, and depends only on electron beam energy. 8.2.3.2. Percentage depth doses for oblique beam incidence The distributions in Fig. 8.3 are given for normal (perpendicular) beam incidence on the phantom or patient surface. For oblique beam incidences with angles a between the beam central axis and the normal to the phantom or patient surface exceeding 20º, there are significant changes to the PDD charac- teristics of the electron beam, in contrast to the behaviour observed in photon beams. 283

CHAPTER 8 a a PDD (%) a D (zmax) a D (zmax) a a Depth in phantom (cm) FIG. 8.5. PDD curves for various beam incidences for a (a) 9 MeV and (b) 15 MeV electron beam. a = 0 represents normal beam incidence. The inset shows the geometry of the experimental set-up and the doses at zmax for various angles a relative to the dose at zmax for a = 0. Figure 8.5 illustrates the effect of the beam incidence angle a on PDD distributions. Angle a = 0 represents normal incidence. The larger the angle a, the shallower is zmax and the larger is the dose at zmax. All dose values are normalized to 100% at zmax for a = 0. For small angles of incidence a, the slope of the PDD curve decreases and the practical range is essentially unchanged from that for normal beam incidence. When the angle of incidence a exceeds 60º, the PDD looses its characteristic shape and the definition of Rp can no longer be applied. For large angles of incidence, the dose at zmax increases significantly. This effect is due to the increased electron fluence through the central axis from the oblique beam angle. 8.2.4. Output factors An important parameter that determines the electron beam output is the collimator jaw setting. For each electron applicator (cone) there is an associated jaw setting that is generally larger than the field size defined by the applicator (electron beam cone). Such an arrangement minimizes the variation of collimator scatter and therefore the output variation with field size is kept reasonably small. Typical electron applicator sizes are 6 × 6, 10 × 10, 15 × 15, 20 × 20 and 25 × 25 cm2. 284

ELECTRON BEAMS: PHYSICAL AND CLINICAL ASPECTS The output factor for a given electron energy is the ratio of the dose for any specific field size (applicator size) to the dose for a 10 × 10 cm2 reference applicator, both measured at zmax in a phantom at an SSD of 100 cm. The square field defined by the applicator will not adequately shield all normal tissues in most clinical situations. For this reason collimating blocks fabricated from lead or a low melting point alloy are routinely inserted into the end of the applicator to shape the fields. Output factors must also be measured for these irregular fields shaped by cut-outs. For small field sizes this extra shielding will affect the PDD and the output factors due to lack of lateral scatter. The change in zmax as well as changes in the PDDs with small field sizes must be accounted for when measuring output factors. 8.2.5. Therapeutic range R90 The depth of the 90% dose level (R90 (cm)) beyond zmax is defined as the therapeutic range for electron beam therapy. The R90 depth should, if possible, coincide with the distal treatment margin. This depth is approximately given by E/4 in centimetres of water, where E is the nominal energy in megaelectron- volts of the electron beam. R80 (cm), the depth that corresponds to the 80% PDD beyond zmax, is also a frequently used parameter for defining the therapeutic range, and can be approximated by E/3 in centimetres of water. 8.2.6. Profiles and off-axis ratios A typical dose profile for a 6 MeV electron beam and a 25 × 25 cm2 field at zmax is shown in Fig. 8.6. The off-axis ratio (OAR) relates the dose at any point in a plane perpendicular to the beam direction to the dose on the central axis in that plane. A plot of the OAR against the distance from the central axis is referred to as a dose profile. 8.2.7. Flatness and symmetry The specification for the flatness of electron beams according to the IEC is given at zmax and consists of two requirements: ● The flatness specification requires that the distance between the 90% dose level and the geometrical beam edge should not exceed 10 mm along the major axes and 20 mm along the diagonals; 285

CHAPTER 8 Relative dose (%) –20 –15 –10 5 0 5 10 15 20 Distance (cm) FIG. 8.6. Dose profile at depth zmax for a 12 MeV electron beam and 25 × 25 cm2 field. ● The maximum value of the absorbed dose anywhere within the region bounded by the 90% isodose contour should not exceed 1.05 times the absorbed dose on the axis of the beam at the same depth. The specification for symmetry of electron beams according to the IEC at zmax is that the cross-beam profile should not differ by more than 3% for any pair of symmetric points with respect to the central ray. 8.3. CLINICAL CONSIDERATIONS IN ELECTRON BEAM THERAPY 8.3.1. Dose specification and reporting Electron beam therapy is usually applied for the treatment of superficial or subcutaneous disease. Treatments are usually delivered with a single direct 286

ELECTRON BEAMS: PHYSICAL AND CLINICAL ASPECTS electron field at a nominal SSD of 100 cm. The dose specification for treatment is commonly given at a depth that lies at, or beyond, the distal margin of the disease, and the energy chosen for the treatment depends on the depth of the lesion to be treated. To maximize healthy tissue sparing beyond the tumour, while at the same time providing relatively homogeneous target coverage, treatments are usually prescribed at either zmax, R90 or R80. If the treatment dose is specified at either R80 or R90, the skin dose will often be higher than the prescription dose. The maximum dose to the patient could be up to 20% higher than the prescribed dose. The maximum dose should therefore always be reported for electron beam therapy. 8.3.2. Small field sizes For field sizes larger than the practical range of the electron beam, the PDD curve remains constant with increasing field size, since the electrons from the periphery of the field are not scattered sufficiently to contribute to the central axis depth dose. When the field is reduced below that required for lateral scatter equilibrium, the dose rate decreases, zmax moves closer to the surface and the PDD curve becomes less steep (see Fig. 8.4). Therefore, for all treatments involving small electron beam field sizes, the beam output as well as the full PDD distribution must be determined for a given patient treatment. 8.3.3. Isodose curves Isodose curves (see Fig. 8.7) are lines passing through points of equal dose. Isodose curves are usually drawn at regular intervals of absorbed dose and are expressed as a percentage of the dose at a reference point, which is normally taken as the zmax point on the beam central axis. As an electron beam penetrates a medium, the beam expands rapidly below the surface, due to scattering. However, the individual spread of the isodose curves varies depending on the isodose level, energy of the beam, field size and beam collimation. A particular characteristic of electron beam isodose curves is the bulging of the low value curves (<20%) as a direct result of the increase in electron scattering angle with decreasing electron energy. At energies above 15 MeV, electron beams exhibit a lateral constriction of the higher value isodose curves (>80%). Isodose curves for a 9 and 20 MeV electron beam are shown in Fig. 8.7. The phenomena of bulging and constricting isodose curves are clearly visible. 287

CHAPTER 8 0.00 1.00 2.00 90% 3.00 4.00 10% 5.00 9 MeV 6.00 7.00 –8.00 –6.00 –4.00 –2.00 0.00 2.00 4.00 6.00 8.00 0.00 2.00 20 MeV 4.00 90% 6.00 8.00 10% 10.00 –6.00 –4.00 –2.00 0.00 2.00 4.00 6.00 8.00 FIG. 8.7. Measured isodose curves for 9 and 20 MeV electron beams. The field size is 10 × 10 cm2 and SSD = 100 cm. Note the bulging low value isodose lines for both beam energies. The 80% and 90% isodose lines for the 20 MeV beam exhibit a severe lateral constriction. The abscissa and the ordinate represent distance from the central axis and depth in a water phantom, respectively, measured in centimetres. The term penumbra generally defines the region at the edge of a radiation beam over which the dose rate changes rapidly as a function of distance from the beam central axis. The physical penumbra of an electron beam may be defined as the distance between two specified isodose curves at a specified depth. A penumbra defined in this way is a rapidly varying function of depth. 288

ELECTRON BEAMS: PHYSICAL AND CLINICAL ASPECTS The ICRU has recommended that the 80% and 20% isodose lines be used in the determination of the physical penumbra, and that the specified depth of measurement be R85/2, where R85 is the depth of the 85% dose level beyond zmax on the electron beam central axis. The low value isodose lines (e.g. below the 50% isodose line) diverge with increasing air gap between the patient and the end of the applicator (cone), while the high value isodose lines converge towards the central axis. This means that the penumbra will increase if the distance from the applicator increases. 8.3.4. Field shaping Field shaping for electron beams is always achieved with electron applicators (cones), which may be used alone or in conjunction with shielding blocks or special cut-outs. 8.3.4.1. Electron applicators Normally the photon beam collimators on the accelerator are too far from the patient to be effective for electron field shaping. After passing through the scattering foil, the electrons scatter sufficiently with the other components of the accelerator head, and in the air between the exit window and the patient, to create a clinically unacceptable penumbra. Electron beam applicators or cones are usually used to collimate the beam, and are attached to the treatment unit head such that the electron field is defined at distances as small as 5 cm from the patient. Several cones are provided, usually in square field sizes ranging from 5 × 5 cm2 to 25 × 25 cm2. 8.3.4.2. Shielding and cut-outs For a more customized field shape, a lead or metal alloy cut-out may be constructed and placed on the applicator as close to the patient as possible. Standard cut-out shapes may be preconstructed and ready for use at the time of treatment. Custom cut-out shapes may also be designed for patient treatment. Field shapes may be determined from conventional or virtual simulation, but are most often prescribed clinically by the physician prior to the first treatment. The lead thickness required for the shielding of various electron energies with transmissions of 50%, 10% and 5% is given in Table 8.3. As a rule of thumb, simply divide the practical range Rp by 10 to obtain the approximate thickness of lead required for shielding (<5% transmission). 289

CHAPTER 8 TABLE 8.3. LEAD THICKNESS (mm) REQUIRED FOR VARIOUS TRANSMISSION LEVELS FOR A 12.5 × 12.5 cm2 ELECTRON FIELD Transmission Energy (MeV) (%) 6 8 10 12 14 17 20 50 1.2 1.8 2.2 2.6 2.9 3.8 4.4 10 2.1 2.8 3.5 4.1 5.0 7.0 9.0 5 3.0 3.7 4.5 5.6 7.0 8.0 10.0 8.3.4.3. Internal shielding For certain treatments, such as treatments of the lip, buccal mucosa, eyelids or ear lobes, it may be advantageous to use an internal shield to protect the normal structures beyond the target volume. Care must be taken to consider the dosimetric effects of placing lead shielding directly on the patient’s surface. A high dose may inadvertantly be delivered to healthy tissue in contact with the shield owing to electron backscattering from the shield. This dose enhancement can be appreciable and may reach levels of 30–70%, but drops off exponentially with distance from the interface on the entrance side of the beam. Aluminium or acrylic materials have been used around lead shields to absorb the backscattered electrons. Often, these shields are dipped in wax to form a 1 or 2 mm coating around the lead. This not only protects the patient from the toxic effects of the lead, but also absorbs any scattered electrons, which are usually low in energy. 8.3.4.4. Extended source to surface distance treatments In clinical situations in which a set-up at the nominal SSD is precluded, an extended SSD might be used, although, as a general rule, such treatments should be avoided unless absolutely necessary. Extending the SSD typically produces a large change in output, a minimal change in PDD and a significant change in beam penumbra. The beam penumbra can be restored by placing collimation on the skin surface. The inside edge of the skin collimation has to be well within the penumbra cast by the normal treatment collimator. Clinical electron beams are not produced at a single source position in the head of the linac, but rather as an interaction of a pencil beam with the scattering foil and other components. 290

ELECTRON BEAMS: PHYSICAL AND CLINICAL ASPECTS In general, the inverse square law, as used for photon beams, cannot be applied to electron beams without making a correction. A virtual source position for electron beams can be determined experi- mentally as the point in space that appears to be the point source position for the electron beam. An ‘effective’ SSD, based on the virtual source position, is used when applying the inverse square law to correct for a non-standard SSD. 8.3.5. Irregular surface correction A frequently encountered situation in electron beam therapy is that where the end of the treatment cone is not parallel to the skin surface of the patient. This could result in an uneven air gap, and corrections would have to be made to the dose distribution to account for the sloping surface. Corrections to isodose lines can be applied on a point by point basis through the use of the following equation: 2 Ê SSD eff + z ˆ D(SSD eff + g, z) = D0 (SSD eff , z) Á ˜ ¥ OF (q , z) (8.10) Ë SSD eff + g + z ¯ where SSDeff is the effective SSD; g is the air gap; z is the depth in the patient; q is the obliquity angle between the tangent to the skin surface and the beam central axis; D0(SSDeff, z) is the dose at depth z for a beam incident normally on a flat phantom; OF(q, z) is a correction factor for the obliquity of the beam that tends to unity for beams of perpendicular incidence. This factor may either be measured or looked up in the literature. 8.3.6. Bolus Bolus, made of a tissue equivalent material such as wax, is often used in electron beam therapy for the following purposes: ● To increase the surface dose; ● To flatten out irregular surfaces; ● To reduce the electron beam penetration in some parts of the treatment field. 291

CHAPTER 8 For very superficial lesions, the practical range of even the lowest energy beam available from a linac may be too large to provide adequate healthy tissue sparing beyond the tumour depth. To overcome this problem, a tissue equivalent bolus material of specified thickness is placed on the surface of the patient with the intent to shorten the range of the beam in the patient. Bolus may also be used to define more precisely the range of the electron beam. The difference between the available electron beam energies from a linac is usually no less than 3 or 4 MeV. If the lower energy is not penetrating enough and the next available energy is too penetrating, bolus may be used with the higher energy beam to fine tune the electron beam range. Bolus can also be used to shape isodose lines to conform to tumour shapes. Sharp surface irregularities, where the electron beam may be incident tangentially, give rise to a complex dose distribution with hot and cold spots. Tapered bolus around the irregularity may be used to smooth out the surface and reduce the dose inhomogeneity. Although labour intensive, the use of bolus for electron beam treatments is very practical, since treatment planning software for electron beams is limited and empirical data are normally collected only for standard beam geometries. The use of computed tomography (CT) for treatment planning enables accurate determination of the tumour shape and depth and the patient contour. If a wax bolus can be constructed such that the total distance from the surface of the bolus to the required treatment depth is constant along the length of the tumour, then the shape of the resulting isodose curves should approximate the shape of the tumour (see Fig. 8.8). 8.3.7. Inhomogeneity corrections The dose distribution from an electron beam can be greatly affected by the presence of tissue inhomogeneities such as lung or bone. The dose within these inhomogeneities is difficult to calculate or measure, but the effect on the distribution beyond the inhomogeneity is quantifiable. 8.3.7.1. Coefficient of equivalent thickness The simplest correction for tissue inhomogeneities involves the scaling of the inhomogeneity thickness by its density relative to water, and the determi- nation of a coefficient of equivalent thickness (CET). The CET of a material is given by its electron density relative to the electron density of water and is essentially equivalent to the mass density of the 292

ELECTRON BEAMS: PHYSICAL AND CLINICAL ASPECTS Bolus Target 90% 10% FIG. 8.8. Construction of a custom bolus to conform isodose lines to the shape of the target. inhomogeneity; for example, lung has an approximate density of 0.25 g/cm3 and a CET of 0.25. Thus a thickness of 1 cm of lung is equivalent to 0.25 cm of tissue. Solid bone has a CET of approximately 1.6. The CET can be used to determine an effective depth in water equivalent tissue zeff through the following expression: zeff = z – t(1 – CET) (8.11) where z is the actual depth of the point in the patient and t is the thickness of the inhomogeneity. Figure 8.9 illustrates the effect of a lung inhomogeneity on the PDD curve of an electron beam. 8.3.7.2. Scatter perturbation (edge) effects If an electron beam strikes the interface between two materials either tangentially or at a large oblique angle, the resulting scatter perturbation will affect the dose distribution at the interface. The lower density material will receive a higher dose, due to the increased scattering of electrons from the higher density side. 293

CHAPTER 8 Tissue Lung inhomogeneity Tissue 100 PDD (%) 50 0 5 10 Depth (cm) FIG. 8.9. Effect of a 5 cm lung inhomogeneity on a 15 MeV, 10 × 10 cm2 electron beam PDD. The dashed curve represents the PDD in tissue without the inhomogeneity present. Edge effects need to be considered in the following situations: ● Inside a patient, at the interfaces between internal structures of different density; ● On the surface of the patient, in regions of sharp surface irregularity; ● On the interface between lead shielding and the surface of the patient, if the shielding is placed superficially on the patient or if it is internal shielding. The enhancement in dose at the tissue–metal interface is dependent on the beam energy at the interface and on the atomic number of the metal. In the case of a tissue–lead interface, the electron backscatter factor (EBF) is empirically given by: EBF = 1 + 0.735e -0.052 E d (8.12) – where Ed is the average energy of the electrons incident on the interface. This equation, given by Klevenhagen, represents the best fit to the experimental data. 294

ELECTRON BEAMS: PHYSICAL AND CLINICAL ASPECTS 8.3.8. Electron beam combinations Electron beams may be abutted to adjacent electron fields or to adjacent photon fields. 8.3.8.1. Matched (abutted) electron fields When abutting electron fields, it is important to take into consideration the dosimetric characteristics of electron beams at depth. The large penumbra and bulging isodose lines make hot spots and cold spots in the target volume practically unavoidable. Contiguous electron beams should be parallel to each other, in order to avoid significant overlapping of the high value isodose curves at depth. In general, it is best to avoid adjacent electron fields, but if treatment with these fields is absolutely necessary, some basic film dosimetry should be carried out at the junction prior to treatment to verify that no hot or cold spots in dose are present. 8.3.8.2. Matched photon and electron fields Electron–photon field matching is easier than electron–electron field matching. A distribution for photon fields is usually available from a treatment planning system (TPS), and the location of the electron beam treatment field as well as the associated hot and cold spots can be determined relative to the photon field treatment plan. The matching of electron and photon fields on the skin will produce a hot spot on the photon side of the treatment. 8.3.9. Electron arc therapy Electron arc therapy is a special radiotherapeutic technique in which a rotational electron beam is used to treat superficial tumour volumes that follow curved surfaces. While the technique is well known and accepted as clinically useful in the treatment of certain tumours, it is not widely used because it is relatively complicated and its physical characteristics are poorly understood. The dose distribution in the target volume depends in a complicated fashion on the electron beam energy, field width, depth of the isocentre, source to axis distance (SAD), patient curvature, tertiary collimation and field shape as defined by the secondary collimator. The excellent clinical results achieved by the few pioneers in this field during the past two decades have certainly stimulated an increased interest in electron arc therapy, both for curative treatments and for palliation. In fact, 295

CHAPTER 8 manufacturers of linacs now offer the electron arc therapy mode as one of the standard treatment options. While this option is usually purchased with a new linac, since it is relatively inexpensive, it is rarely used clinically because of the technical difficulties involved. Two approaches to electron arc therapy have been developed: the simpler is referred to as electron pseudo arc and is based on a series of overlapping stationary electron fields, and the other uses a continuous rotating electron beam. The calculation of dose distributions in electron arc therapy is a complicated procedure and usually cannot be performed reliably with the algorithms used for standard stationary electron beam treatment planning. The angle b concept offers a semiempirical technique for treatment planning for electron arc therapy. The characteristic angle b for an arbitrary point A on the patient’s surface (Fig. 8.10) is measured between the central axes of two rotational electron beams positioned in such a way that at point A the frontal edge of one beam crosses the trailing edge of the other beam. The angle b is uniquely determined by three treatment parameters: f, the SAD; di, the depth of the isocentre; and w, the field width. Electron beams with combinations of di and w that give the same characteristic angle b actually exhibit very similar radial PDDs, even though they may differ considerably in individual di and w (see Fig. 8.11). Thus the PDDs for rotational electron beams depend only on the electron beam energy and on the characteristic angle b. a b f A di I w FIG. 8.10. Arc therapy geometry: f is the SAD; di is the depth of the isocentre; w is the field width defined at the isocentre; a is the arc angle or the angle of treatment; and b is the characteristic angle for the particular treatment geometry. 296

ELECTRON BEAMS: PHYSICAL AND CLINICAL ASPECTS Photon contamination is of concern in electron arc therapy, since the photon contribution from all beams is added at the isocentre and the isocentre might be placed on a critical structure. Figure 8.12 shows a comparison between two dose distributions measured with film in a humanoid phantom. Figure 8.12(a) is for a small b of 10º (i.e. a small field width) and clearly exhibits a large photon dose at the isocentre, while Fig. 8.12(b) was taken for a large b of 100º and exhibits a low photon dose at the isocentre. In arc therapy the isocentre bremsstrahlung dose is inversely proportional to the characteristic angle b. 100 80 di = 20 cm di = 10 cm w = 9.0 cm w = 7.7 cm di = 15 cm di = 15 cm 60 w = 6.3 cm w = 12.3 cm di = 10 cm di = 18 cm w = 3.9 cm w = 15.4 cm 40 20 b = 20° b = 40° Relative dose (%) (a) (b) 100 di = 10 cm di = 15 cm 80 w = 8 cm w = 14.1 cm di = 15 cm di = 10 cm w = 22.3 cm w = 16.6 cm 60 di = 15 cm w = 25.9 cm 40 20 b = 80° b = 100° (c) (d) 0 0 2 4 6 0 2 4 6 Depth d (cm) FIG. 8.11. Radial PDDs in electron arc therapy measured in a phantom for various combinations of w and di, giving characteristic angles b of (a) 20º, (b) 40º, (c) 80º and (d) 100º. The electron beam energy is 9 MeV. 297

CHAPTER 8 (a) (b) FIG. 8.12. Dose distributions for a 15 MeV rotational electron beam with an isocentre depth di of 15 cm, (a) for a b of 10º and (b) for a b of 100º. One of the technical problems related to electron arc treatment involves the field shape of the moving electron beam defined by secondary collimators. For the treatment of sites that can be approximated with cylindrical geometry (e.g. the chest wall), the field width can be defined by rectangular photon collimators. When treating sites that can only be approximated with a spherical geometry (e.g. the scalp), a custom built secondary collimator defining a non- rectangular field of appropriate shape has to be used to provide a homogeneous dose in the target volume. 8.3.10. Electron therapy treatment planning The complexity of electron–tissue interactions does not make electron beams well suited to conventional treatment planning algorithms. Electron beams are difficult to model, and look-up table type algorithms do not predict well the dose for oblique incidences or tissue interfaces. The early methods of electron dose distribution calculations were empirical and based on water phantom measurements of PDDs and beam profiles for various field sizes, similarly to the Milan–Bentley method developed in the late 1960s for use in photon beams. Inhomogeneities were accounted for by scaling the depth dose curves using the CET technique. This technique provides useful parameterization of the electron depth dose curve but has nothing to do with the physics of electron transport, which is dominated by the theory of multiple scattering. The Fermi–Eyges multiple scattering theory considers a broad electron beam as being made up of many individual pencil beams that spread out laterally in tissue, approximately as a Gaussian function, with the amount of spread increasing with depth. The dose at a particular point in tissue is calculated by an addition of contributions of spreading pencil beams. 298

ELECTRON BEAMS: PHYSICAL AND CLINICAL ASPECTS The pencil beam algorithm can account for tissue inhomogeneities, patient curvature and irregular field shape. Rudimentary pencil beam algorithms deal with lateral dispersion but ignore angular dispersion and backscattering from tissue interfaces. Subsequent analytical advanced algorithms refined the multiple scattering theory through applying both the stopping powers and the scattering powers but nevertheless generally fail to provide accurate dose distributions in general clinical conditions. The most accurate way to calculate electron beam dose distributions is through Monte Carlo techniques. The main drawback of the current Monte Carlo approach as a routine dose calculation engine is its relatively long calculation time. However, with ever increasing computer speeds combined with decreasing hardware costs, it can be expected that in the near future Monte Carlo based electron dose calculation algorithms will become available for routine clinical applications. BIBLIOGRAPHY INTERNATIONAL ATOMIC ENERGY AGENCY, The Use of Plane Parallel Ionization Chambers in High Energy Electron and Photon Beams, Technical Reports Series No. 381, IAEA, Vienna (1997). — Absorbed Dose Determination in External Beam Radiotherapy, Technical Reports Series No. 398, IAEA, Vienna (2000). INTERNATIONAL COMMISSION ON RADIATION UNITS AND MEASUREMENTS, Radiation Dosimetry: Electron Beams with Energies Between 1 and 50 MeV, Rep. 35, ICRU, Bethesda, MD (1984). JOHNS, H.E., CUNNINGHAM, J.R., The Physics of Radiology, Thomas, Springfield, IL (1985). KHAN, F.M., The Physics of Radiation Therapy, Lippincott, Williams and Wilkins, Baltimore, MD (2003). KLEVENHAGEN, S.C., Physics and Dosimetry of Therapy Electron Beams, Medical Physics Publishing, Madison, WI (1993). VAN DYK, J. (Ed.), Modern Technology of Radiation Oncology: A Compendium for Medical Physicists and Radiation Oncologists, Medical Physics Publishing, Madison, WI (1999). 299

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Chapter 9 CALIBRATION OF PHOTON AND ELECTRON BEAMS P. ANDREO Department of Medical Radiation Physics, University of Stockholm, Karolinska Institute, Stockholm, Sweden J.P. SEUNTJENS, E.B. PODGORSAK Department of Medical Physics, McGill University Health Centre, Montreal, Quebec, Canada 9.1. INTRODUCTION Modern radiotherapy relies on accurate dose delivery to the prescribed target volume. The ICRU has recommended an overall accuracy in tumour dose delivery of ±5%, based on an analysis of dose response data and on an evaluation of errors in dose delivery in a clinical setting. Considering all uncer- tainties involved in the dose delivery to the patient, the ±5% accuracy recom- mendation is by no means easy to attain. Before clinical use, the output of photon and electron beams produced by external beam radiotherapy machines must be calibrated. This basic output calibration is but one, albeit very important, of the links constituting the chain representing an accurate dose delivery to the patient. The other links refer to: the procedures for measurement of relative dose data, equipment commis- sioning and quality assurance; treatment planning; and the actual patient set-up on the treatment machine. ● The basic output for a radiotherapy machine is usually stated as the dose rate for a point P at a reference depth zref (often the depth of dose maximum zmax) in a water phantom for a nominal source to surface distance (SSD) or source to axis distance (SAD) and a reference field size (often 10 × 10 cm2) on the phantom surface or the isocentre. The output for kilovoltage X ray generators and teletherapy units is usually given in Gy/min, while for clinical accelerators it is given in Gy/MU. ● For superficial and orthovoltage beams and occasionally for beams produced by teletherapy radioisotope machines, the basic beam output 301

CHAPTER 9 may also be stated as the air kerma rate in air (Gy/min) at a given distance from the source and for a given nominal collimator or applicator setting. The basic output calibration of photon and electron beams is carried out with radiation dosimeters and special radiation dosimetry techniques. Radiation dosimetry refers to a determination by measurement and/or calculation of the absorbed dose or some other physically relevant quantity, such as air kerma, fluence or equivalent dose, at a given point of interest in a given medium. A radiation dosimeter is defined as any device that is capable of providing a reading M that is a measure of the dose D deposited in the dosimeter’s sensitive volume V by ionizing radiation. — A dosimeter that produces a signal from which the dose in its sensitive volume can be determined without requiring calibration in a known field of radiation is referred to as an absolute dosimeter; — Dosimeters requiring calibration in a known radiation field are called relative dosimeters. The basic output calibration of a clinical radiation beam, by virtue of a direct measurement of dose or dose rate in water under specific reference conditions, is referred to as reference dosimetry. Three types of reference dosimetry technique are currently known: (a) Calorimetry; (b) Fricke dosimetry; (c) Ionization chamber dosimetry. These dosimeters can be used as absolute dosimeters but are seldom used as such in clinics, because their use in absolute dosimetry is cumbersome and, moreover, calibration in a known radiation field offers certain advantages, such as traceabilty to a standards laboratory. When an absolute dosimeter is used independently, it relies on its own accuracy instead of referring to a standard in common with other radiation users. 9.1.1. Calorimetry Calorimetry is the most fundamental of the three reference dosimetry techniques, since it relies on basic definitions of either electrical energy or temperature. In principle, calorimetric dosimetry is simple; in practice, 302

CALIBRATION OF PHOTON AND ELECTRON BEAMS however, the need for measuring extremely small temperature differences makes the technique very complex and relegates it to sophisticated standards laboratories. Two main types of absorbed dose calorimeter are currently used in standards laboratories: ● Graphite calorimeters; ● Sealed water calorimeters. In graphite calorimeters the average temperature rise is measured in a body that is thermally insulated from surrounding bodies (‘jackets’) by evacuated vacuum gaps. Gap corrections and dose transfer procedures are used in conjunction with graphite calorimeters to allow for the transfer of absorbed dose from graphite to water. In stagnant sealed water calorimeters use is made of the low thermal diffusivity of water, which enables the temperature rise to be measured directly at a point in (continuous) water. Dose transfer procedures are not needed, but the measurement and analysis are complicated by the presence of conductive heat loss (or gain) and by the heat defect induced by radiolysis. 9.1.2. Fricke dosimetry The energy of ionizing radiation absorbed in certain media produces a chemical change in the absorbing medium, and the amount of this chemical change may be used as a measure of absorbed dose. The best known chemical radiation dosimeter is the Fricke dosimeter, which relies on oxidation of ferrous ions into ferric ions in an irradiated ferrous sulphate solution. The amount of ferric ion produced in the solution is measured by absorption spectrometry with ultraviolet light at 304 nm, which is strongly absorbed by the ferric ion. Fricke dosimetry (sometimes referred to as chemical dosimetry or ferrous sulphate dosimetry) depends on an accurate knowledge of the radiation chemical yield of ferric ions, measured in moles produced per 1 J of energy absorbed in the solution. The chemical yield is related to an older parameter, the G value, defined as the number of ferric molecules produced in the ferrous sulphate solution by 100 eV of absorbed energy. An accurate value of the chemical yield is difficult to ascertain because the chemical yield is affected to a certain degree by the energy of the radiation, dose rate and temperature of the solution during irradiation and readout. The best G value for 60Co g rays is 15.6 molecules per 100 eV, corresponding to a chemical yield of 1.607 × 10–6 mol/J. The typical dynamic range for ferrous sulphate Fricke dosimeters is from a few 303

CHAPTER 9 grays to about 400 Gy, making Fricke dosimetry impractical for routine use in a clinic. 9.1.3. Ionization chamber dosimetry The ionization chamber is the most practical and most widely used type of dosimeter for accurate measurement of machine output in radiotherapy. It may be used as an absolute or a relative dosimeter. Its sensitive volume is usually filled with ambient air and the dose related or dose rate related measured quantities are the ionization charge Q or ionization current I, respectively, produced by radiation in the chamber sensitive air mass mair. Charge Q and air mass mair are related to absorbed dose in air Dair by: Q Ê Wair ˆ Dair = mair Á e ˜ (9.1) Ë ¯ where (Wair/e) is the mean energy required to produce an ion pair in air per unit charge (the current value for dry air is 33.97 eV/ion pair or 33.97 J/C). The subsequent conversion of the air cavity dose Dair to dose to medium (usually water) Dw is based on the Bragg–Gray or Spencer–Attix cavity theories (see Chapter 2 and Section 9.4 in this chapter). The sensitive air volume or mass in an ionization chamber is determined: ● Directly by measurement (the chamber becomes an absolute dosimeter under special circumstances); ● Indirectly through calibration of the chamber response in a known radiation field (the chamber is used as a relative dosimeter). 9.1.4. Mean energy expended in air per ion pair formed It is generally assumed that a constant value of (Wair/e) can be used for the complete photon and electron energy range used in radiotherapy dosimetry. However, there is no direct experimental support for such an assumption, as the data available have been obtained only from measurements with 60Co and 137 Cs g ray beams and 2 MV X rays. The value (Wair/e) = (33.85 ± 0.15) J/C early recommended by the ICRU came from a weighted mean value of the available experimental data, obtained mainly from absorbed dose measurements using a graphite calorimeter and a graphite ionization chamber in a graphite phantom. The two methods for deriving the absorbed dose to graphite must yield the same dose value, and one obtains: 304

CALIBRATION OF PHOTON AND ELECTRON BEAMS Dcalorimetry (Wair /e) = (9.2) (Q/mair )s graphite,air where Q is the charge collected in air mass mair and corrected for influence quantities; and sgraphite,air is the ratio of collision stopping powers for graphite and air calculated for the photon or electron beam energy used. This method of evaluation requires a change in (Wair/e) when the stopping power ratio sgraphite,air is changed. Following the introduction of new electron stopping power data by the ICRU in 1984, the value of (Wair/e) has been modified to (33.97 ± 0.06) J/C for dry air. Analysis of the available experimental data at higher energies, mainly for electron beams, has suggested that energy dependence in (Wair/e) cannot be ruled out, but experimental uncertainties, and the use of different stopping power ratios over the years, do not allow a definitive conclusion to be reached on this question. It is known that the (Wair/e) value for air at a temperature of 20ºC, pressure of 101.325 kPa and 50% relative humidity is 0.6% lower than that for dry air at the same temperature and pressure, resulting in a value of 33.77 J/C instead of 33.97 J/C. Thus for the same amount of energy available for creating charge, 0.6% more charge will be created in air at 50% relative humidity than in dry air (at 20ºC and 101.325 kPa). 9.1.5. Reference dosimetry with ionization chambers Three types of ionization chamber may be used in reference dosimetry as absolute dosimeters: ● Standard free air ionization chambers; ● Cavity ionization chambers; ● Phantom embedded extrapolation chambers. 9.1.5.1. Standard free air ionization chambers Standard free air ionization chambers measure the air kerma in air according to its definition by collecting all ions produced by the radiation beam that result from the direct transfer of energy from photons to primary electrons in a defined volume of air. Determination of the air kerma in air or air kerma rate in air requires accurate knowledge of (Wair/e). For practical reasons related to the range of charge carriers in air, the use of the standard free air ionization chamber is limited to photon energies below 0.3 MeV. 305

CHAPTER 9 9.1.5.2. Cavity ionization chambers Cavity ionization chambers measure the air kerma in air for energies in the range from 0.6 to 1.5 MeV by making use of the Bragg–Gray cavity relationship. Analogously to standard free air ionization chambers, ions are collected in air, but this time inside a cavity with a known cavity volume surrounded by a graphite wall thick enough to provide full buildup of secondary electrons. The Bragg–Gray equation relates the dose to air in the cavity of known volume to the dose to medium in which the secondary electron spectrum is being built up (i.e. the graphite wall (for the thick walled chambers used in primary standards dosimetry laboratories (PSDLs)). The absorbed dose to the wall is related to the collision air kerma in air through the mass– energy absorption coefficient ratio, wall to air. The collision air kerma in air is related to the total air kerma in air by correcting for the fractional energy expended in radiative interactions. In addition to the need for an accurate knowledge of the sensitive air volume, wall correction factors are required to account for the effect of photon attenuation and scattering in the chamber wall. An accurate knowledge of (Wair/e) as well as the cavity volume and radiative fraction is required to determine the air kerma (rate) in air. Finally, standards laboratories implement additional correction factors such as the point source non-uniformity correction factor and factors that account for deviations from the Spencer– Attix cavity theory. 9.1.5.3. Phantom embedded extrapolation chambers Phantom embedded extrapolation chambers are uncalibrated variable air volume extrapolation chambers built as an integral part of a water equivalent phantom in which the dose is measured, and can serve as radiation dosimeters in the measurement of absorbed dose for megavoltage photon and electron beams. Standard dosimetry protocols are based on the Bragg–Gray or Spencer–Attix cavity theories (see Chapter 2 for details), which provide a simple linear relationship between the dose at a given point in the medium and the ratio Q/m, where Q is the ionization charge collected in mass m of air in the measuring cavity inside the medium. In extrapolation chambers, the ratio Q/m is constant and may be replaced in the cavity relationship by the derivative dQ/dm, which can be measured accurately through a controlled variation in the electrode separation. The conversion of cavity dose to dose to medium is based on the Spencer–Attix cavity theory. As in the case of the standard free air ionization chamber and the cavity ionization chamber, extrapolation chamber dosimetry relies on an accurate knowledge of the value of (Wair/e). 306

CALIBRATION OF PHOTON AND ELECTRON BEAMS 9.1.6. Clinical beam calibration and measurement chain The theoretical aspects of the three reference dosimetry techniques discussed above are all well understood; however, none of the three techniques, for one reason or another, is practical for routine clinical use. Clinical photon and electron beams are therefore most commonly calibrated with ionization chambers that are used as relative dosimeters and have calibration coefficients determined either in air or in water and are traceable to a national PSDL. The chamber calibration coefficient essentially obviates the need for an accurate knowledge of the chamber sensitive air volume. The standard ISO 31-0, on quantities and units, has provided guidelines with regard to the use of the terms ‘coefficient’ and ‘factor’. The former should be used for a multiplier possessing dimensions; the latter should be reserved for a dimensionless multiplier. For consistency, the widely disseminated practice of using the term ‘calibration factor’ is updated here to using ‘calibration coefficient’. The traceability of a calibration coefficient to a national PSDL implies that: ● The chamber was calibrated directly at the PSDL in terms of the air kerma in air or absorbed dose to water; or ● The chamber was calibrated directly at an accredited dosimetry calibration laboratory (ADCL) or secondary standards dosimetry laboratory (SSDL) that traces its calibration to a PSDL; or ● The chamber calibration coefficient was obtained through a cross- calibration with another ionization chamber (user’s secondary standard), the calibration coefficient of which was measured directly at a PSDL, an ADCL or an SSDL. 9.1.7. Dosimetry protocols The procedures to be followed when calibrating a clinical photon or electron beam are described in international or national radiation dosimetry protocols or dosimetry codes of practice; the choice of which protocol to use is largely left to individual radiotherapy departments. Dosimetry protocols are generally issued by national or regional organizations such as the American Association of Physicists in Medicine (AAPM) (North America), Institution of Physics and Engineering in Medicine and Biology (IPEMB) (UK), Deutsches Institut für Normung (DIN) (Germany), Nederlandse Commissie voor Stralingsdosimetrie (NCS) (the Netherlands and Belgium) and Nordic Association of Clinical Physics (NACP) (Scandinavia), or by international bodies such as the IAEA. This procedure ensures a high level of consistency in 307

CHAPTER 9 dose determination among different radiotherapy clinics in a given country and between one country and another. 9.2. IONIZATION CHAMBER BASED DOSIMETRY SYSTEMS As shown schematically in Fig. 9.1, ionization chamber based dosimetry systems are in principle quite simple and consist of three main components: ● A suitable ionization chamber; ● An electrometer; ● A power supply. The circuitry of a simple ionization chamber based dosimetry system resembles a capacitor (ionization chamber) connected to a battery (power supply), with the electrometer measuring the ‘capacitor’ charging or discharging current. 9.2.1. Ionization chambers Ionization chambers incorporate three electrodes, which define the chamber sensitive air volume. The sensitive air volume is typically of the order Polarizing Sensitive (biasing) volume electrode V Guard electrode Measuring (collecting) electrode A FIG. 9.1. Circuitry of an ionization chamber based dosimetry system. A represents the electrometer, V the power supply. The ionization chamber is usually connected to the electrometer through a shielded low noise triaxial cable, with the central wire carrying the signal from the measuring electrode to the electrometer, the first shield connecting the guard electrode to ground and the outer shield connecting the polarizing electrode to the power supply. 308

CALIBRATION OF PHOTON AND ELECTRON BEAMS of 0.1 to 1 cm3 in ionization chambers used for the calibration of clinical photon and electron beams. The three electrodes are the: ● Polarizing electrode, which is connected directly to the power supply. ● Measuring electrode, which is connected to ground through the low impedance electrometer to measure the charge or current produced in the chamber sensitive volume. ● Guard electrode, which is directly grounded and serves two purposes: it defines the chamber sensitive volume and prevents the measurement of chamber leakage currents. Two types of ionization chamber are used in routine beam calibration: — Cylindrical (often referred to as thimble) chambers; — Parallel-plate (sometimes called end window or plane-parallel) chambers. The more common cylindrical chambers are used in the calibration of orthovoltage and megavoltage X ray beams and electron beams of 10 MeV and above, while parallel-plate chambers are used in calibrations of superficial X ray beams, in calibrations of low energy electron beams and in surface dose measurements as well as dose measurements in the buildup region of megavoltage photon beams. Examples of typical ionization chambers used in radiotherapy are given in Fig. 9.2. Air is usually used as the sensitive gas in an ionization chamber. The initial event of interaction of indirectly ionizing radiation with the chamber is characterized by a release of high energy electrons in the chamber wall or phantom through the photoelectric effect, Compton effect or pair production. Some of these electrons enter the chamber sensitive volume and ionize air molecules, producing positive ions and low energy electrons in the chamber sensitive volume. The low energy electrons attach themselves to electro- negative oxygen molecules in air, forming negative ions. Thus in an air based ionization chamber the charged particles collected are the positive and negative ions (ion pairs) rather than positive ions and electrons. 9.2.2. Electrometer and power supply An ionization chamber is essentially a capacitor in which leakage current or leakage charge is induced through the action of the radiation beam. The charge or current that is induced in the chamber is very small and must be measured by a very sensitive charge or current measuring device (electrometer). The power supply in ionization chamber/electrometer circuits 309

CHAPTER 9 FIG. 9.2. Examples of typical ionization chambers used in radiotherapy: (a) cylindrical ionization chambers used for relative dosimetry; (b) pinpoint mini-chamber and 60Co buildup cap; (c) Farmer type cylindrical chamber (top) with a 60Co buildup cap (bottom); (d) parallel plate Roos type electron beam ionization chamber. is either a stand-alone unit or forms an integral part of the electrometer. In either case it is important that one can change the magnitude and polarity of the voltage produced by the power supply, so that the ion collection efficiency of the chamber may be determined for a particular radiation beam (see Section 9.3). 9.2.3. Phantoms Water is the standard phantom material for dosimetry measurements of photon and electron beams; however, dosimetric measurements are often carried out in more practical solid materials, such as polystyrene, Lucite, A-150 tissue equivalent plastic, Solid Water (WT1), Solid Water (RMI-457), Plastic Water or Virtual Water, that mimic water in terms of three parameters: mass density, number of electrons per gram and effective atomic number. The effective atomic number Zeff depends on the atomic composition of the mixture as well as on the type and quality of the radiation beam. For low energy photons, for which the photoelectric effect is dominant over the Compton process and pair production events cannot occur, Zeff of a mixture is defined by: 310

CALIBRATION OF PHOTON AND ELECTRON BEAMS Z eff = 3.5 Âa Z i i 3.5 i (9.3) where ai is the mass fraction of constituent element i; Zi is the atomic number of constituent element i. Using Eq. (9.3) we obtain a Zeff of 7.8 for air and 7.5 for water. For megavoltage photon and electron beams Zeff of a mixture is defined by: Z i2 Â ai Ai Z eff = i (9.4) Â Zi ai i Ai where ai is the mass fraction of constituent element i; Zi is the atomic number of constituent element i; Ai is the atomic mass of constituent element i. Water is the most universal soft tissue substitute material, useful in both photon and electron beam measurements. Plastic solid materials are often used in phantom measurements; however, they are not universal tissue substitutes, since not all three required equivalency parameters for plastics can be matched adequately with those of water. For photon beams, tissue equivalency or water equivalency implies a match in mass–energy absorption coefficient, mass stopping power and mass scattering power. For a phantom to be water equivalent for electron dosimetry, it must match the linear stopping power and the linear scattering power of water. This is approximately achieved if the phantom material has the same electron density and the same atomic number as water. Generally, water is recommended as the phantom material for the calibration of megavoltage photon and electron beams. The depth of calibration for megavoltage X ray beams is 10 cm, while for electron beams it is at a reference depth zref. The margin on the phantom around the nominal field size must be at least 5 cm of water in all directions, and there should be at least 10 cm of water beyond the chamber to provide adequate scattering conditions. 311

CHAPTER 9 For kilovoltage X ray beams, the current plastics used in dosimetry cannot be considered truly water equivalent, and their use for calibration of X ray beam output should be approached with care. 9.3. CHAMBER SIGNAL CORRECTION FOR INFLUENCE QUANTITIES For each ionization chamber, reference conditions are described by a set of influence quantities for which a chamber calibration coefficient is valid without any further corrections. Influence quantities are defined as quantities that are not the subject of a measurement but yet influence the quantity being measured. Examples of influence quantities in ionization chamber dosimetry are: ● Ambient air temperature, pressure and humidity; ● Applied chamber voltage and polarity; ● Chamber leakage currents; ● Chamber stem effects. If the chamber is used under conditions that differ from the reference conditions, then the measured signal must be corrected for the influence quantities to obtain the correct signal. 9.3.1. Air temperature, pressure and humidity effects: kT,P The mass of air contained in the sensitive volume of the chamber is equal to rairVeff, where rair is the air density and Veff is the effective sensitive volume of the chamber. Since most ionization chambers are open to the ambient atmosphere, the air density rair is a function of the atmospheric pressure, temperature and humidity, and so is the charge collected by the chamber, as both the air density and the collected charge are correlated. It is common practice to fix the value of rair to certain conditions and convert the chamber reading to these conditions. Most standards laboratories use the value of 1.2930 kg/m3 for the dry air density value at standard conditions of 0ºC and 101.325 kPa. Considering air as an ideal gas, the density rair(T, P) at an arbitrary temperature T (ºC) and pressure P (kPa) is then given by: 273.2 P r air (T, P ) = r air (0 oC, 101.325 kPa) (9.5) (273.2 + T ) 101.325 312

CALIBRATION OF PHOTON AND ELECTRON BEAMS When calibrating an ionization chamber, the charge measured by the chamber depends on the air temperature, pressure and humidity, and therefore the calibration coefficient must be given for stated reference values of these parameters. At most standards laboratories the chamber signal is corrected to normal conditions of 20ºC (22ºC in North America) and 101.325 kPa, but no correction is applied for humidity. Instead, the relative humidity during calibration is controlled within the range from 45% to 55%, so that the calibration coefficient applies for relative humidities around 50%. In the user’s beam, the correction factor for air temperature and air pressure kT,P is given as : (273.2 + T ) P0 k T, P = (9.6) (273.2 + T0 ) P and is applied to convert the measured signal to the reference conditions used for the chamber calibration at the standards laboratory. Note that P and T (ºC) are chamber air pressure and temperature, respectively, at the time of measurement, while P0 and T0 (ºC) are the normal conditions used in the standards laboratory. The temperature of the air in a chamber cavity should be taken as that of the phantom, which is not necessarily the same as the temperature of the surrounding air. For measurements in a water phantom the chamber waterproof sleeve should be vented to the atmosphere in order to obtain a rapid equilibrium between the ambient air and the air in the chamber cavity. (Wair/e) and stopping powers that are used in dosimetry protocols are stated for dry air but are affected by chamber air humidity. This results in an overall humidity correction factor of 0.997 for a 60Co beam, correcting measurements at the 50% humidity level to those that would be obtained under dry air conditions and consisting of a 0.994 correction to the (Wair/e) dry air value of 33.97 J/C and a 1.003 correction to stopping powers. 9.3.2. Chamber polarity effects: polarity correction factor kpol Under identical irradiation conditions the use of polarizing potentials of opposite polarity in an ionization chamber may yield different readings, a phenomenon that is referred to as the polarity effect. For most ionization chamber types, the effect is practically negligible at phantom depths exceeding the depth of dose maximum in megavoltage photon beams, but in the buildup region of megavoltage photon beams and in electron beams, notably at low energies, as well as in very low energy X ray beams, the effect may be significant. 313

CHAPTER 9 In electron beams the polarity effect is considered a charge balance effect that depends on the energy and angular distribution of the incident radiation, measurement depth in a phantom and field size. The polarity effect may actually change its sign with depth in a phantom. When a chamber is used in a beam that produces a measurable polarity effect, the true reading is taken to be the mean of the absolute values of readings taken at the two polarities. The polarity correction factor kpol is thus given by the following relationship: M+ + M- k pol = (9.7) 2M where M+ and M– are the chamber signals obtained under identical irradiation conditions at positive and negative chamber polarities, respectively, and M is the signal obtained at the polarity used routinely (either positive or negative). If the polarity effect for a particular chamber is larger than 3%, the chamber should not be used for absolute dose measurement. Whenever the polarity has been changed, charge equilibrium and stable operating conditions should be re-established by preirradiating the chamber and waiting several minutes before the next measurement. 9.3.3. Chamber voltage effects: recombination correction factor ksat The response of a given ionization chamber depends not only on the radiation dose, dose rate and chamber polarity but also on the voltage applied between the measuring and collecting electrodes of the chamber. The charges produced in the chamber by radiation may differ from the charges that are actually collected, and these discrepancies (charge losses or excess charges) occur as a result of constraints imposed by the physics of ion transport in the chamber sensitive volume and the chamber electrical design. Charge losses in the chamber are caused by ion recombination; excess charges are caused by charge multiplication and electrical breakdown. Both charge recombination and charge multiplication are influenced by the potential applied to the ionization chamber. A plot of chamber response (i.e. current I or charge Q against the applied voltage V for a constant dose rate or dose, respectively) is called a saturation curve, first rising linearly with voltage at low voltages, then reaching a saturation at high voltages and eventually breaking down at even higher voltages. A sketch of a typical saturation curve is shown in Fig. 9.3. 314

CALIBRATION OF PHOTON AND ELECTRON BEAMS Q(V) Near- Breakdown Linear saturation Saturation region region region Qsat 0 Voltage V FIG. 9.3. Typical saturation curve for an ionization chamber. The saturation charge is represented by Qsat and is used in dosimetry protocols as the appropriate parameter describing the radiation signal. Ionization chambers are usually operated in the near- saturation region and Qsat is calculated by dividing the measured signal by the collection efficiency f. The ratio Q(V)/Qsat or I(V)/Isat, where Qsat and Isat are the saturation values of Q and I, respectively, is referred to as the collection efficiency f of the ionization chamber at the applied voltage V. In radiation dosimetry, ionization chambers are commonly used in the near-saturation region where f > 0.98, or even in the saturation region, where f ª 1. In saturation, all charges produced by radiation are collected and produce directly the Qsat and Isat for use in dosimetry protocols. When the chamber is used below saturation, some of the charges produced by radiation actually recombine and are lost to the dosimetric signal. This charge loss occurs through three different mechanisms: ● General recombination: opposite charges from different tracks collide and recombine. ● Initial recombination: opposite charges from same tracks collide and recombine. ● Ionic diffusion loss: charges diffuse against the electric field. For studies of ionic recombination losses, ionizing radiations are placed into three categories: 315

CHAPTER 9 — Continuous radiation (e.g. cobalt beams and orthovoltage X rays); — Pulsed beams (e.g. non-scanned linac X ray beams and electrons); — Scanned pulsed beams (e.g. scanned linac beams). The ionic recombination correction factor ksat (labelled Pion in the AAPM TG 21 and TG 51 notation and equal to 1/f in recombination theory) accounts for the loss of ions in the chamber sensitive volume due to initial recombi- nation, general recombination and diffusion against the electric field. General recombination is by far the predominant of the three effects. c According to Boag, in the near-saturation region f g the collection efficiency for general recombination in a continuous radiation beam may be written as: Q 1 f gc = = (9.8) Qsat Lg 1+ V2 or 1 1 L g /Qsat 1 lg = + 2 = + 2 (9.9) Q Qsat V Qsat V and in a pulsed beam: Q V Ê Cˆ f gp = = ln Á 1 + ˜ (9.10) Qsat C Ë V ¯ or 1 1 C/Qsat 1 C¢ = + = + (9.11) Q Qsat 2V Qsat V where Lg, C and C¢ are constants, Q is the measured signal and Qsat is the saturation value of the signal. The relationship for 1/Q suggests a linear behaviour when plotted against 1/V2 for continuous beams (Eq. (9.9)) and against 1/V for pulsed beams (Eq. (9.11)), with 1/Qsat the intercept of the linear plot with the ordinate (i.e. for 1/V Æ 0 or V Æ •) . Assuming the predominance of general recombination and based on the linear relationship of 1/Q with either 1/V2 in continuous radiation or 1/V in pulsed radiation, one can determine the collection efficiencies f g and f p for c g continuous and pulsed beams, respectively, with the so called two voltage technique. Chamber signals M are determined under the same irradiation conditions at two voltages, the normal operating voltage VN and a lower 316

CALIBRATION OF PHOTON AND ELECTRON BEAMS voltage VL. The collection efficiencies at the normal chamber operating voltage VN are then expressed as: 2 M N Ê VN ˆ - MN M L Á VL ˜ Ë ¯ f gc (VN ) = = 2 (9.12) M sat ÊV ˆ 1- Á N ˜ ËV ¯ L for continuous beams and M N VN - MN M VL f gp (VN ) = = L (9.13) M sat VN 1- VL as an approximation for pulsed beams, where MN is the chamber signal determined at the normal operating voltage VN; ML is the chamber signal determined at a lower voltage VL; Msat is the saturation signal at V = •. The polarity effect will change with the voltage, and both MN and ML should be corrected for this effect using Eq. (9.7). For pulsed and pulsed–scanned megavoltage radiation beams, dosimetry protocols recommend that the recombination correction factor ksat(VN) be determined: (i) Assuming a linear relationship between 1/M and 1/V; (ii) Using the two voltage technique and the following quadratic polynomial: 2 MN ÊM ˆ k sat (VN ) = a 0 + a1 + a2 Á N ˜ (9.14) ML Ë ML ¯ where ai are constants tabulated for pulsed and pulsed–scanned beams (see, for example, IAEA TRS 398, p. 52). For ksat(VN) £ 1.03 (i.e. f ≥ 0.97) the recombination correction factor may be approximated to within 0.1% using the following relationship obtained from general recombination theory: 317

CHAPTER 9 MN -1 M k sat (VN ) = 1 + L (9.15) VN -1 VL where, as defined above, MN and ML are the chamber signals obtained with the normal applied potential VN and low applied potential VL, respectively. The ratio VN/VL should be equal to or larger than 3, and VN must not be too large in order to ensure that charge multiplication effects do not contribute to the measured chamber signal. It is important to re-establish charge equilibrium after the bias voltage has been changed. This can be achieved by preirradiating the chamber with a dose of 2 to 5 Gy before the next measurement. 9.3.4. Chamber leakage currents Leakage currents present a difficult challenge in the design of ionization chamber based dosimetric systems. Their effects on the true radiation induced currents are minimized with guard electrodes, low noise triaxial cables and sophisticated electrometers. Leakage currents fall into three categories: ● Intrinsic (dark) leakage currents; ● Radiation induced leakage currents; ● Mechanical stress induced and friction induced spurious cable currents. No matter how well an ionization chamber dosimetric system is designed, there will always be a small, non-radiation related signal present when the system is in a ready mode to respond to radiation. This intrinsic (dark) current results from surface and volume leakage currents flowing between the polarizing and measuring electrodes of the ionization chamber. In a well designed ionization chamber system the intrinsic leakage currents are at least two orders of magnitude lower than the measured radiation induced signals, and are thus either negligible or can be suppressed from the actual radiation signal. Electric leakage in the ionization chamber and electrometer may also occur as a consequence of the irradiation of insulators and chamber parts, cables and electronics of the measuring equipment. This is termed post- irradiation leakage, an effect that continues after the irradiation has ceased and commonly decreases exponentially with time. 318

CALIBRATION OF PHOTON AND ELECTRON BEAMS IEC 60731 recommends that within 5 s after the end of a 10 min irradiation the leakage current should have decreased to ±1.0% or less of the ionization current produced in the measuring volume during the irradiation (i.e. it will fall to the intrinsic leakage current level of the dosimetric system). Another effect in insulators, which received considerable attention in the mid-1980s, is the charge accumulation in non-conductive plastic phantoms. This charge accumulation causes a very large electric field around the chamber directing the flow of electrons towards the chamber cavity, yielding an increased signal and an erroneous result for the collection efficiency. Mechanical stress on cable insulators can also cause a leakage current, and for this reason unnecessary bending and twisting of the cables should be avoided. 9.3.5. Chamber stem effects Irradiating the chamber stem often cannot be avoided, but it results in a different type of leakage current, which is generally referred to as the stem effect. Two mechanisms have been described by the IEC, namely stem scatter and stem leakage: ● Stem scatter arises from the effect of scattered radiation in the stem that reaches the chamber volume. This effect can be determined using a dummy stem, and the chamber is irradiated successively with and without the presence of the dummy stem; the ratio of the readings allows a correction factor for the effect to be determined. ● Stem leakage arises as a consequence of a direct irradiation of this chamber volume as well as of the insulators and cables in the chamber. The effect can be determined by irradiating a chamber twice with a narrow rectangular field, once in a parallel orientation and then perpen- dicularly to the chamber central axis. A correction factor can be derived as above. 9.4. DETERMINATION OF ABSORBED DOSE USING CALIBRATED IONIZATION CHAMBERS For practical reasons, outputs of clinical photon and electron beams are usually measured with ionization chambers that have calibration coefficients traceable to a standards laboratory and are thus used as relative dosimeters. Before such a chamber is used in radiotherapy machine output calibration, the user must identify a dosimetry protocol (code of practice) appropriate for the 319

CHAPTER 9 given radiation beam. A dosimetry protocol provides the formalism and the data to relate a calibration of a chamber at a standards laboratory to the measurement of absorbed dose to water under reference conditions in the clinical beam. Two types of dosimetry protocol are available: ● Protocols based on air kerma in air calibration coefficients; ● Protocols based on absorbed dose to water calibration coefficients. Most current megavoltage dosimetry protocols rely on chamber calibration coefficients determined in 60Co beams at standards laboratories. It is expected that the use of megavoltage beam calibration qualities (X rays and electrons), today available only in a few PSDLs, will become more widespread in the future. Conceptually, both types of protocol are similar and are based on several steps in the process of determining the absorbed dose or dose rate from a charge or current measurement, respectively, with an ionization chamber. The first step in the use of dosimetry protocols involves the determination of the chamber signal MQ through correction of the measured chamber charge or current for influence quantities known to affect the measured chamber signal, as discussed in Section 9.3. The subscript Q denotes the quality index of the beam being calibrated, as discussed in Section 9.8. It should be noted that the formalisms presented here, based on a 60Co calibration coefficient, work well for megavoltage photon and electron beams. The calibration of superficial and orthovoltage X ray beams, on the other hand, relies on different principles and the chamber calibration coefficient should be obtained for the particular X ray beam quality that is being calibrated. The physics of kilovoltage dosimetry is discussed in more detail in Section 9.10. 9.4.1. Air kerma based protocols Air kerma based protocols use the air kerma in air calibration coefficient NK,Co obtained for a local reference ionization chamber in a 60Co beam at a standards laboratory. Routine ionization chambers are then cross-calibrated with the reference ionization chamber in a local 60Co beam. Two steps are involved in an air kerma based protocol for the calibration of megavoltage photon and electron beams: ● The cavity air calibration coefficient ND,air is calculated from the NK,Co calibration coefficient. 320

CALIBRATION OF PHOTON AND ELECTRON BEAMS ● Absorbed dose to water is determined using the Bragg–Gray relationship in conjunction with the chamber signal MQ and the cavity air calibration coefficient ND,air. In a 60Co beam at a standards laboratory the mean absorbed dose to air in the cavity is determined from the total air kerma in air (Kair)air using the relationship: Dair = (Kair)air(1 – g)kmkattkcel (9.16) where g is the fraction of the total transferred energy expended in radiative inter- actions on the slowing down of secondary electrons in air; km is a correction factor for the non-air equivalence of the chamber wall and buildup cap needed for an air kerma in air measurement; katt is a correction factor for photon attenuation and scatter in the chamber wall; kcel is a correction factor for the non-air equivalence of the central electrode of the cylindrical ionization chamber. The cavity air calibration coefficient ND,air is defined as: ND,air = Dair/MQ (9.17) where MQ is the chamber signal corrected for influence quantities. The air kerma in air calibration coefficient NK,Co is defined as: NK,Co = (Kair)air/MQ (9.18) If the electrometer device has its readout in nano-coulombs, both the cavity calibration coefficient and the air kerma in air calibration coefficient are given in units of cGy/nC. By dividing the left and right hand sides of Eq. (9.16) by the corrected chamber signal in the calibration beam MQ, the cavity air calibration coefficient can be determined from the air kerma in air calibration coefficient, determined at the 60Co beam quality, using the relationship: ND,air = NK,Co(1 – g)kmkattkcel (9.19) The cavity air calibration coefficient is also directly related to the effective volume Veff of the chamber by: 321

CHAPTER 9 Dair 1 Wair 1 Wair (9.20) N D,air = = = M Q mair e r airVeff e where (Wair/e) is the average energy required to produce an ion pair in air; mair is the mass of air in the chamber cavity; rair is the air density at standard conditions of temperature and pressure; Veff is the effective air volume in the chamber collecting ions. Equation (9.20) shows clearly that ND,air is a characteristic of the dosimetric device and depends only on the effective mass of air in the chamber cavity and does not depend on radiation quality as long as (Wair/e) is independent of the radiation quality. Hence the ND,air calibration coefficient determined at the 60Co beam quality at the standards laboratory is also valid at the user’s megavoltage beam quality Q. If the effective chamber cavity volume Veff were accurately known, the ND,air calibration coefficient could in principle be determined using Eq. (9.20). This is the case for cavity ionization chambers used to establish the air kerma in air for cobalt units at standards laboratories (see Section 9.1.4). For typical ionization chambers used in the clinic, however, Veff is not known with sufficient accuracy and ND,air must be determined from the air kerma in air calibration coefficient NK,Co using Eq. (9.19). The absorbed dose to air Dair,Q in the air cavity can be converted into absorbed dose to medium (e.g. water) Dw,Q by making use of the Bragg–Gray cavity relationship. With a known value of ND,air for a specific chamber, the fully corrected chamber signal MQ at a point in a phantom allows determination of the absorbed dose to water as follows: Dw,Q = Dair,Q(sw,air)QpQ = MQND,air(sw,air)QpQ (9.21) where (sw,air)Q is the ratio of restricted collision stopping powers of water to air; pQ is a perturbation correction factor accounting for perturbations caused by the chamber inserted into the medium, as discussed in detail in Section 9.7. 322

CALIBRATION OF PHOTON AND ELECTRON BEAMS 9.4.2. Absorbed dose to water based protocols All dosimetry protocols aim at determination of the quantity absorbed dose to water. It is therefore logical to provide ionization chambers directly with a calibration coefficient in terms of this quantity, rather than in terms of the air kerma in air, if at all possible. Recent developments have provided support for a change in the quantity used at present to calibrate ionization chambers and provide calibration coefficients in terms of absorbed dose to water ND,w for use in radiotherapy beams. Many PSDLs now provide ND,w calibrations in 60Co g ray beams and some laboratories have already extended these calibration procedures to high energy photon and electron beams. The absorbed dose to water Dw,Q0 at the reference depth zref in water for a reference beam of quality Q0 and in the absence of the chamber is directly given by: Dw,Q0 = MQ0ND,w,Q0 (9.22) where MQ0 is the fully corrected chamber reading under the reference conditions used in the standards laboratory and ND,w,Q0 is the calibration coefficient in terms of the absorbed dose to water of the chamber obtained from the standards laboratory. When a chamber is used in a beam of quality Q that differs from the quality Q0 that was used in its calibration, the absorbed dose to water is given by: Dw,Q0 = MQ0ND,w,Q0kQ,Q0 (9.23) where the factor kQ,Q0 corrects for the differences between the reference beam quality Q0 and the actual user quality Q. The beam quality correction factor kQ,Q0 is defined as the ratio, at beam qualities Q and Q0, of the calibration coefficients in terms of absorbed dose to water of the ionization chamber: N D,w ,Q k Q,Q0 = (9.24) N D,w ,Q0 Currently, the common reference quality Q0 used for the calibration of ionization chambers is the 60Co g radiation, and the symbol kQ,Co, abbreviated to kQ, is often used for the beam quality correction factor. At some PSDLs high energy photon and electron beams are directly used for calibration purposes and the symbol kQ,Q0 is used in these cases, with Q0 323

CHAPTER 9 specifying the calibration beam. Ideally, the beam quality correction factor should be measured directly for each chamber at the same quality as the user’s beam. However, this is not achievable in most standards laboratories. Such measurements can be performed only in laboratories having access to the appropriate beam qualities; for this reason the technique is at present restricted to a few PSDLs around the world, as the procedure requires the availability of an energy independent dosimetry system, such as a calorimeter, operating at these beam qualities. When no experimental data are available, or when it is difficult to measure kQ,Q0 directly for realistic clinical beams, the correction factors can, in many cases, be calculated theoretically. By comparing Eq. (9.24) with the ND,air formalism given above, kQ,Q0 can be written as: ( s w,air ) Q pQ k Q,Q0 = (9.25) ( s w,air ) Q0 pQ0 including the following ratios, at beam qualities Q and Q0: ● Spencer–Attix water to air restricted stopping power ratios sw,air; ● The perturbation factors pQ and pQ0 for departures from the ideal Bragg– Gray detector conditions. The calculations of kQ,Q0 are based on exactly the same data used in the calculations in the air kerma based approach, but the parameters are used as ratios, which have reduced uncertainties compared with individual values. Most protocols provide a modified formalism for electron beams for use when a chamber is cross-calibrated (i.e. does not have a direct ND,w,Co calibration coefficient). The details can be found in the IAEA TRS 398 and AAPM TG 51 protocols. A still frequently used quantity is the exposure calibration coefficient NX, which is related to the air kerma in air calibration coefficient NK through the following relationship: Wair 1 (9.26) NK = NX e 1- g where g is the fraction of the energy loss in air expended in radiative interac- tions (the radiative fraction). For 60Co g rays in air g = 0.003, for superficial X rays in air g < 0.0002. Typical units of NX and NK are R/nC and Gy/nC, respectively. A typical unit for both ND,air and ND,w is Gy/nC. 324

CALIBRATION OF PHOTON AND ELECTRON BEAMS FIG. 9.4. Steps involved in ionization chamber based reference dosimetry: (a) air kerma in air based, (b) absorbed dose to water based. A schematic summary of the steps involved in air kerma in air based and absorbed dose to water based calibration routes is given in Fig. 9.4. The physics and characteristics of stopping power ratios and perturbation correction factors are discussed in more detail in Sections 9.5 and 9.7. The air kerma in air based formalism as well as the absorbed dose to water based formalism for the determination of absorbed dose to water in reference conditions includes stopping power ratios and correction factors for perturbation effects, the latter being detector dependent. Some of the analytical models available for the calculation of perturbation correction factors also include mass–energy absorption coefficient ratios. Although ideally the formalism in terms of absorbed dose to water is based on experimentally determined quantities, the approach most common today relies on theoretically determined beam quality factors kQ,Q0, which are also based on stopping power ratios (see Section 9.5) and perturbation correction factors (see Section 9.7). 325

CHAPTER 9 9.5. STOPPING POWER RATIOS The determination of absorbed dose in a medium using an ionization chamber is based on the Bragg–Gray principle relating the absorbed dose at a point in the medium (water) Dw to the mean absorbed dose in the detector (air) – Dair through a proportionality factor that classically has been identified as the ratio of the mass (collision) stopping powers water to air: – Dw = Dairsw,air (9.27) The key Bragg–Gray assumption is that the electron fluence present in the detector is identical to that in the (undisturbed) medium at the point of interest in the water phantom. The gas filled ionization chamber in a high energy photon or electron beam behaves to a good approximation as a Bragg– Gray detector. Any deviations from perfect Bragg–Gray behaviour are accounted for by perturbation factors, which are discussed in detail in Section 9.7. The stopping power ratio applies to the electron spectrum at the point of interest in the undisturbed medium and is independent of the detector (except for the minor influence of the Spencer–Attix cut-off). 9.5.1. Stopping power ratios for electron beams The most important characteristic of the water/air stopping power ratios for monoenergetic electrons is their strong dependence on energy and depth, as shown in Fig. 9.5, resulting mainly from the considerable variation in energy spectra at the various depths in water. Until lately, the selection of stopping power ratios for the user’s beam in electron dosimetry protocols has relied on the use of monoenergetic data using Harder’s procedure based on the characterization of the electron beam – through the mean electron energy at the phantom surface E0 together with depth of measurement z. Clinical beams are, however, far from monoenergetic and monodirectional at the phantom surface and even less so at depths in a phantom. – The validity of the sw,air (E0,z) selection procedure has been reviewed in detail in the IAEA protocol for parallel-plate ionization chambers (IAEA TRS 381) and a conclusion was reached that, even for beams with large energy and angular spread, the maximum error produced by such a procedure is always within 1%. For most beams used in clinical practice, even for those with a certain degree of photon contamination, the agreement was within the estimated uncertainty of the calculated stopping power ratios, being of the order of 0.6%. 326

CALIBRATION OF PHOTON AND ELECTRON BEAMS 1. 15 1 3 5 7 Electron energy (MeV) 10 14 18 20 25 1. 10 30 40 Stopping power ratio sw,air 50 1. 05 1. 00 0. 95 0. 90 0 4 8 12 16 20 24 Depth in water (cm) FIG. 9.5. Depth variation of the ratio of the mean restricted mass stopping powers off water and air sw,air for a cut-off energy D of 10 keV, derived from Monte Carlo generated electron spectra for monoenergetic, plane-parallel broad electron beams. Stopping power ratios for realistic electron beams, obtained by simulating in detail the treatment head of some clinical accelerators, have become available and are used in the most recent dosimetry protocols based on standards of absorbed dose to water. However, it has been verified that no dramatic changes occur in electron beam dosimetry solely due to this improvement in the calculation of stopping power ratios. 9.5.2. Stopping power ratios for photon beams The most important characteristic of the depth variation of the stopping power ratios of monoenergetic photons is that the ratios are almost constant beyond the depth of dose maximum (i.e. in the region of the transient electronic equilibrium), as Fig. 9.6 clearly shows. The range of variation of the stopping power ratio data with energy is also much smaller than in the case of electrons with similar energies. In the case of photon bremsstrahlung spectra produced by clinical accelerators the constancy of the stopping power ratio is 327

CHAPTER 9 1.15 00.1 01 02 03 Stopping power ratio sw,air 1.10 05 07 010 1.05 015 020 030 040 1.00 050 Photon energy (MeV) 0.95 0 10 20 30 40 50 Depth in water (cm) FIG. 9.6. Depth variation of the ratio of the mean restricted mass stopping powers off water and air sw,air for a cut-off energy D of 10 keV, derived from Monte Carlo generated electron spectra for monoenergetic, plane-parallel monoenergetic and plane-parallel photon beams. reached at shallower depths, due to the presence of low energy photons in the spectrum. 9.6. MASS–ENERGY ABSORPTION COEFFICIENT RATIOS The role of spectrum averaged mass–energy absorption coefficient ratios in modern dosimetry protocols is mainly restricted to their use in calculating perturbation and other correction factors for ionization chambers in 60Co and high energy photon beams. In general, they are associated with the fraction of energy deposited within a detector due to electrons generated by photon inter- actions in the detector material itself. Depending on the medium, the photon fluence spectra may change appreciably with depth or material thickness, and they also depend on the field size of the incident beam. It has been shown that the effects of spectral changes within a phantom on the mean mass–energy absorption coefficients are of importance only for large field sizes or for low energy photon beams, for which there is a more than 0.5% variation in (men/r)w,m, the ratio of mass–energy absorption coefficients, for tissue-like materials (m) with respect to water (w) because of this effect. 328

CALIBRATION OF PHOTON AND ELECTRON BEAMS A consistent set of mass–energy absorption coefficient ratios for photon dosimetry used in most dosimetry protocols was given in the IAEA TRS 277 protocol. These data have not yet been superseded by any other new set of data. 9.7. PERTURBATION CORRECTION FACTORS For a detector to behave as a Bragg–Gray cavity, the electron fluence in the sensitive medium of the detector must be identical to that at a specified point in the uniform medium. The only possible true Bragg–Gray detector would be an exceedingly small air bubble; all protocols for absolute dose deter- mination are, in fact, based on air filled ionization chambers. For megavoltage photon radiation the Bragg–Gray conditions are adequately fulfilled for air cavities of the size encountered in practical ionization chambers (i.e. the ranges in air of the secondary electrons generated in megavoltage photon beams are much greater than the cavity dimensions). However, an ionization chamber does not consist only of an air cavity. There will always be a wall that, in general, is not perfectly medium equivalent. Often this wall is made of graphite, whereas the medium is water. Moreover, for cylindrical chambers there must be a central electrode, which is frequently made of aluminium, and there may be other materials around the chamber, such as a stem for cylindrical chambers and a back wall in the case of parallel- plate designs. All of these features can introduce deviations from perfect Bragg–Gray behaviour. These deviations are generally dealt with by introducing one or more correction factor, often known as perturbation factors, into the expression for the absorbed dose (i.e. the factor pQ in Eq. (9.21)). This overall factor is often written as a product of four perturbation factors, each one accounting for a different effect, assumed to be independent of the others, as follows: pQ = (pdis pwall pcel pcav)Q (9.28) where pdis is a factor that accounts for the effect of replacing a volume of water with the chamber cavity (cylindrical chambers); pwall is a factor that corrects the response of the ionization chamber for the non-water equivalence of the chamber wall and any waterproofing material; 329

CHAPTER 9 pcel is a factor that corrects the response of the chamber for the effect of the central electrode during in-phantom measurements; pcav is a factor that corrects the response of the ionization chamber for effects related to the air cavity, predominantly the in-scattering of electrons, which makes the electron fluence inside a cavity different from that in water in the absence of the cavity. The word perturbation here means a perturbation by the detector of the electron fluence fmed(P) present at the point of interest P in a uniform medium where the relevant fluence in the detector, inevitably a mean value over a finite ¯ volume f det, is that which gives rise to the signal (i.e. the fluence in the air in the case of an ionization chamber). Sections 9.7.1–9.7.4 deal with the four different sources of the Bragg– Gray cavity perturbation. The emphasis here is on the physics of these correction factors. A complete account of numerical values for the particular chamber and radiation quality of interest can be taken from the particular protocol being followed, and a concise summary of the protocol recommenda- tions is given in Section 9.9. 9.7.1. Displacement perturbation factor pdis and effective point of measurement An ionization chamber placed into a phantom will displace a certain volume of the phantom medium. Even if the chamber wall is medium equivalent, one still must consider the effect of the volume occupied by the air cavity. In general the dimensions of this volume are not negligible compared with any changes in the radiation field and hence in the dose distribution. For example, the dose may change by a few per cent within a distance equal to the diameter of the chamber. Clearly the chamber reading will be affected by this ‘missing’ medium. In simple terms one can expect that the reduced attenuation, in the case of photon beams, will result in a higher chamber reading compared with that in a very small ‘air bubble’ situated at the centre of the detector. However, there is another effect: the missing material means that there is less scatter. This will counterbalance the first effect. The net result is still generally an increase in the signal that results in a correction factor known as the displacement perturbation factor, usually denoted by pdis, which will thus be less than unity. The value of pdis will in general depend on both the radiation quality and the physical dimensions of the air cavity in the direction of the beam, as well as on the depth of measurement. In photon beams pdis will be practically constant beyond the depth of dose maximum, due to the exponential fall-off in dose; 330

CALIBRATION OF PHOTON AND ELECTRON BEAMS however, in the buildup region it will vary in a complicated fashion with depth. For a Farmer chamber, which has an internal radius of 3 mm, the value is close to 0.988 in a 60Co beam. The correction for displacement can be viewed in an alternative way. Instead of applying a factor to correct the chamber reading by assuming that the chamber is positioned so that its centre is at the depth of interest, a shift in the position of the chamber can be made. For a cylindrical chamber the electrons enter the wall at various depths, generally forward of its centre, and hence the electron fluence in the air cavity is representative of that existing at some point in the uniform medium shifted forward of the chamber centre. In fact, it was found that the readings of different chambers could be brought into coincidence with one another by performing shifts depending on the chamber dimensions. Thus the concept of the effective point of measurement Peff was developed. The newer absorbed dose to water based dosimetry protocols favour the pdis approach. However, air kerma in air based protocols use the Peff concept in preference to pdis. The IAEA TRS 277 protocol recommended a shift of 0.5r for 60 Co g rays, increasing to 0.75r for all higher energy photon beams. More recent reviews of the experimental evidence on the magnitude of the shift led the IAEA to recommend a single value of 0.6r for all high energy photon beams (IAEA TRS 398), as indicated schematically by the parameter zc in Fig. 9.7(a). In electron beams the use of pdis is impractical, since the depth dose curve is very irregular in shape, in contrast to the quasi-exponential decrease in photon beams at depths beyond the buildup region. Since pdis would vary rapidly and in an irregular way with depth in an electron beam, the Peff concept is universally employed in electron beams. ● For cylindrical chambers the recommended shift is 0.5r (IAEA TRS 277 and IAEA TRS 398). ● For parallel-plate chambers Peff is assumed to be situated in the centre of the inside face of the front wall, as illustrated in Fig. 9.7; this is logical since, in a well guarded chamber, it can be assumed that all the electrons entering the sensitive air volume do so through the front window. 9.7.2. Chamber wall perturbation factor pwall Compliance with the Bragg–Gray conditions implies that the electron fluence in the sensitive volume of the detector is identical (strictly in magnitude, energy and angular distribution) to that present in the undisturbed medium at the position of interest. However, an ionization chamber has a wall 331

CHAPTER 9 (a) Peff zref zc (b) (c) Peff zref FIG. 9.7. (a) In most NK based dosimetry protocols the effective point of measurement off a cylindrical ionization chamber is positioned at the reference depth zref , where the absorbed dose is required; the chamber centre is deeper than zref a distance zc . (b) Except in electron and heavy ion beams, in ND,w based protocols the centre of a cylindrical chamber is positioned at the reference depth zref and the absorbed dose is determined at this position. (c) For plane-parallel chambers all protocols position the effective point off measurement (front of the air cavity) at the reference depth zref . that in general is not made of medium equivalent material. In the case of photon beams the electron fluence in the air cavity in an ionization chamber, assumed cylindrical with a wall of a typical thickness, will consist partly of electrons generated in the (uniform) medium surrounding the wall that have travelled through the wall and partly of electrons generated by photon interactions with the wall material. Quite clearly the number and energy distribution of these wall generated secondary electrons will be characteristic of photon interactions with the material of the wall and not of the medium, as demanded by Bragg–Gray conditions. 332

CALIBRATION OF PHOTON AND ELECTRON BEAMS For ionization chambers with walls of intermediate thickness, in practical use in radiotherapy an approximate empirical two-component expression is in common use: a s wall,air ( m en /r ) w,wall + (1 - a )s w,air p wall = (9.29) s w,air where a is the fraction of the dose to the air in the cavity due to electrons generated in the chamber wall; thus if this is zero, pwall reduces to unity as expected. An additional small correction has been implemented for the case when a waterproofing sleeve is used, where Eq. (9.29) is extended to a three- component model, with a third term tssleeve,air(men/r)w,sleeve, where t is the fraction of the ionization due to electrons generated in the sheath, as follows: a s wall,air ( m en /r ) w,wall + t s sleeve,air ( m en /r ) w,sleeve + (1 - a - t )s w,air p wall = s w,air (9.30) with a and t the fractional contributions to ionization resulting from photon interactions in the wall and sleeve, respectively. The two parameters a and t can be estimated for 60Co beams from the thickness of the wall twall and the waterproofing sleeve tsleeve (g/cm2), if present, using: a = 1 – exp(–11.88twall) (9.31) and t = exp(–11.88twall) – exp[–11.88(twall + tsleeve)] (9.32) For high energy beams, the fractional ionizations a and t are derived from the data given by the IAEA TRS 398 protocol. In the case of electron beams, it is generally assumed that the effect of the chamber wall is negligible. 9.7.3. Central electrode perturbation pcel Cylindrical chambers have a central electrode, which is usually made of aluminium but can be made of graphite. The central electrode will produce an increase in the chamber signal compared with what would be obtained in an air 333

CHAPTER 9 bubble, and a correction for the non-air equivalence of the electrode is in principle necessary; this is denoted by pcel. The effect of a central electrode made of graphite has been shown to be practically negligible in photon beams but decreases with energy from 1.008 to 1.004 for a 1 mm diameter aluminium electrode. In electron beams the effect is negligible for graphite, and never greater than 0.2% at any energy (5–20 MeV) or depth for a 1 mm diameter aluminium electrode. 9.7.4. Cavity or fluence perturbation correction pcav An ionization chamber introduces a low density heterogeneity into a medium. In an electron beam, density changes can cause hot or cold spots as a result of electron scattering. The reason for this is clear from Fig. 9.8, attributed to Harder. As a result of (elastic nuclear) scattering, the angular distribution of electrons broadens with depth; a low density cavity will consequently scatter out fewer electrons than are scattered in, resulting in an increase in the electron fluence towards the downstream end of the cavity in comparison with the fluence in a uniform medium at that depth. R T i m FIG. 9.8. Perturbation of the electron fluence caused by a gas filled cavity in a solid or liquid phantom. Electron tracks are idealized to emphasize the effects being shown. The dominance of in-scattering over out-scattering gives rise to an increase in the fluence towards the back of the cavity, and hence this produces an increase in the chamber signal. 334

CALIBRATION OF PHOTON AND ELECTRON BEAMS All modern air kerma in air based dosimetry protocols include values of perturbation factors determined experimentally. The magnitude of the in-scattering perturbation exceeds 3% for Farmer type chambers for Ez, the electron energy at depth z, below 8 MeV. This is one of the principal reasons why parallel-plate chambers are recommended in low energy electron beams. In a parallel-plate chamber the diameter of the air cavity (typically between 13 and 20 mm) is deliberately made very much greater than its thickness (the electrode spacing), which is 2 mm in almost all commercial designs. Thus most of the electrons enter the air cavity through the front face of the chamber and only a small fraction through the side walls. Furthermore, well designed parallel-plate chambers have a relatively wide guard ring, 3 mm or more, which ensures that almost no electrons entering through the short side walls can contribute to the chamber signal. Conse- quently, in-scattering is virtually eliminated. The electron fluence in the sensitive volume of such a chamber is therefore that existing in the uniform medium at the depth of the inside face of the front window, which is the position of the effective point of measurement Peff. For cylindrical chambers this guarding capability is virtually absent and the electron fluence is signifi- cantly perturbed. For these chambers the cavity perturbation correction factor pcav is given by: – – pcav (E0, r) = 1 – 0.02155r exp(–0.1224 Ez) (9.33) – where r is the cavity inner radius in millimetres and Ez is the mean electron energy at depth z as obtained from the Harder relationship (see Eq. (9.36)). In photon beams there is generally charged particle equilibrium (CPE) (or a very good approximation to it), and therefore no change in either the energy or the angular distribution of the secondary electrons with position in the irradiated medium. The electron fluence perturbation effect is therefore negligible in photon beams. However, in the buildup region in photon beams, where there is no CPE, significant perturbation effects have been demon- strated. 9.8. BEAM QUALITY SPECIFICATION The signal (current or charge) that is produced by an ionization chamber and measured by an electrometer must be multiplied by factors correcting for influence quantities (see Section 9.3) and the various dosimetric physical quantities described in the previous sections to yield the absorbed dose to water at a reference point in water, the quantity in terms of which radiotherapy 335

CHAPTER 9 machine output is specified. Some of these quantities depend upon photon or electron beam energy, thus the beam quality needs to be specified for dosimetric calculations. The most logical means to characterize the quality of a clinical radiation beam is to state its spectral distribution. However, since beam spectra are difficult to measure directly and cumbersome to determine in an absolute sense with Monte Carlo techniques, other, more practical, approaches to beam quality specification have been developed. These approaches are specific to three distinct ionizing radiation beam categories: ● Kilovoltage (superficial and orthovoltage) X ray beams; ● Megavoltage X ray beams; ● Megavoltage electron beams. 9.8.1. Beam quality specification for kilovoltage photon beams For low energy photon beams the quality of the beam is most conven- iently expressed in terms of the half-value layer (HVL) of the beam, with HVL representing the thickness of an attenuator that decreases the measured air kerma rate in air to half of its original value. To minimize the effects of radiation scattered in the attenuator the HVL must be measured under ‘good geometry’ conditions that imply the use of: ● A narrow beam geometry to minimize scattering from the attenuator; ● A reasonable distance between the attenuator and the measuring device (ionization chamber) to minimize the number of scattered photons reaching the detector; ● An ionization chamber with air equivalent walls and with a flat photon energy response for the spectrum of radiations comprising the beam. For superficial X ray beams (10–100 kVp) HVLs are usually given in millimetres of pure aluminium (typical HVLs from 0.01 to 10 mm of aluminium), while for orthovoltage X ray beams (above 100 kVp) HVLs are usually given in millimetres of pure copper (typical HVLs from 0.5 to 4 mm of copper). The specification of beam quality in terms of the HVL is really a very crude beam specification, since it tells little about the energy distribution of the photons present in the beam. However, the beam specification through the HVL provides a general idea of the effective energy of the photon beam, which may be used to assess the beam penetration into tissue and to determine the appropriate values of the quantities used in dosimetry protocols. 336

CALIBRATION OF PHOTON AND ELECTRON BEAMS Since two beams with widely differing potentials can have similar HVLs, due to the marked effect of different filtrations, it is customary to state, in addition to the HVL, the X ray potential and total filtration used in generating a given X ray beam. Often low energy X ray beams are also characterized by stating their homogeneity coefficient k, which is defined as the ratio between the first and second HVL (i.e. = HVL1/HVL2). For heterogeneous low energy X ray beams HVL2 > HVL1, resulting in k < 1; for monochromatic beams, on the other hand, HVL2 = HVL1 and k = 1. Another quantity that is often used in beam quality specification is the equivalent or effective photon energy, defined as the quantum energy of a monoenergetic beam having an HVL equal to HVL1 of the heterogeneous beam being specified. 9.8.2. Beam quality specification for megavoltage photon beams In the megavoltage photon energy range, HVLs vary little with photon energy, making HVLs unsuitable for beam quality specification. Other indices were therefore developed, relating to the energy of the electron beam as it strikes the target (nominal accelerating potential (NAP)) and to radiation beam attenuation as the beam penetrates into water or tissue. Older radiation protocols were based on the NAP, while the recent ones are based on quantities that are related to beam penetration into water, such as the tissue–phantom ratio (TPR) or percentage depth dose (PDD). A considerable improvement was made to air kerma in air based dosimetry protocols when stopping power ratios and mass–energy absorption coefficient ratios were correlated with clinically measured ionization ratios, such as the TPR20,10, rather than with NAPs. The parameter TPR20,10 is defined as the ratio of doses on the beam central axis at depths of 20 cm and 10 cm in water obtained with a constant source to detector distance of 100 cm and a field size of 10 × 10 cm2 at the position of the detector. The TPR20,10 is a measure of the effective attenuation coefficient describing the approximately exponential decrease of a photon depth dose curve beyond the depth of maximum dose zmax, and, more impor- tantly, it is independent of electron contamination of the incident photon beam. The TPR20,10 can be related to the measured PDD20,10 using the following relationship: TPR20,10 = 1.2661PDD20,10 – 0.0595 (9.34) 337

CHAPTER 9 where PDD20,10 is the ratio of PDDs at depths of 20 cm and 10 cm for a field of 10 × 10 cm2 defined at the water phantom surface with an SSD of 100 cm. This empirical relationship was obtained from a sample of almost 700 linacs. Other beam quality indices have been proposed for megavoltage photon dosimetry; they are, in most cases, related to the depth of maximum dose zmax, making them susceptible to the electron contamination of the beam at this depth in a water phantom. Based on PDD distributions, a widely disseminated recommendation for specifying the quality of high energy photon beams was made in British Journal of Radiology Supplement 17, which defined a parameter d80 as the depth of the 80% depth dose for a 10 × 10 cm2 field at an SSD of 100 cm. British Journal of Radiology Supplement 17 clearly points out that electron contamination of the photon beam should be considered a practical shortcoming of the d80 method. The use of TPR20,10 as a photon beam quality index has also been endorsed by the recent British Journal of Radiology Supplement 25, although other beam quality specifiers, such as the PDD(10), are also considered. The parameter PDD(10), the PDD at 10 cm depth in water, determined under the same conditions of field size and SSD as the parameter d80, has in principle the same limitation with regard to the effect of electron contami- nation as d80. A recommendation has been made that a 1 mm thin lead foil be used in measurements to remove the unknown electron contamination from the reading at zmax and to replace it by a known amount of electron contami- nation to arrive at the PDD with the presence of the lead foil, PDD(10)Pb. A correction formula is provided to convert PDD(10)Pb into PDD(10)x, the PDD at a depth of 10 cm in water in a pure photon beam excluding the electron contamination at zmax. The advantages and limitations of the different photon beam quality indices have been discussed at great lengths in the scientific literature. The general conclusion is that there is no unique beam quality index that works satisfactorily in all possible conditions for the entire energy range of megavoltage photon energies used in radiotherapy and for all possible linacs used in hospitals and standards laboratories. Most recent dosimetry protocols based on in-water calibrations of ionization chambers use the TPR20,10 as the beam quality index (IPEM, IAEA TRS 398, etc.); the AAPM TG 51 protocol, however, uses the PDD(10)x. For a user in a hospital or clinic there is no advantage of one specifier (index) over the other, as both lead to the same dose conversion factors and hence yield the same dose to water in the user’s beam. However, the choice of the beam quality index should not be governed by user preference but should follow the 338

CALIBRATION OF PHOTON AND ELECTRON BEAMS dosimetry protocol used in order to ensure uniformity and consistency in radiotherapy dosimetry. 9.8.3. Beam quality specification for megavoltage electron beams Electron beams are essentially monoenergetic when exiting the accelerator waveguide; however, the electron beam striking the phantom or patient surface at a nominal SSD exhibits a spectrum that results from the energy spread caused by interactions between electrons and air as well as inter- actions between electrons and the linac components, such as the collimator, scattering foil, ionization chamber and treatment cone. A typical electron beam PDD distribution is shown in Fig. 9.9. Until lately, the quality of clinical electron beams has been specified in – practically all dosimetry protocols by E0, the mean electron energy of the incident spectrum striking the phantom surface. This beam quality index was derived from measurement of the half-value depth R50, defined as the depth at which the electron beam depth dose decreases to 50% of its maximum value. 100 PDD (%) 50 0 R100 R50 Rp Depth z FIG. 9.9. Typical electron beam depth dose distribution with R100 the depth of dose maximum, R50 the depth of the 50% dose and Rp the practical range of electrons. The dose beyond Rp is contributed by the bremsstrahlung contamination of the electron beam produced in the linac components, air and water phantom. 339

CHAPTER 9 – The empirical relationship between E0 and R50 is: – E0 = CR50 (9.35) where C is a constant (2.33 MeV/cm); R50 is the half-value depth in centimetres. Strictly speaking, Eq. (9.35) is valid only for large field sizes (broad beams), for electron energies between 5 and 30 MeV, and for R50 determined from depth dose distributions measured in water with a constant source to chamber distance. The criterion for a broad beam is satisfied when the depth dose distribution is independent of field size, and this is achieved for field sizes exceeding 12 × 12 cm2 for electron beam energies below 15 MeV and at least 20 × 20 cm2 for energies above 15 MeV. – The mean energy at depth z in a phantom, Ez, is also a quantity of general use in electron beam dosimetry. An empirical relationship, originally proposed for the most probable energy of an electron spectrum at a depth z in a water phantom, has been recommended by many electron dosimetry protocols to – determine Ez according to: – – Ez = E0(1 – z/Rp) (9.36) where Rp is the practical range of the electron beam defined as the depth where the tangent at the steepest point (the inflection point) on the almost straight descending portion of the depth dose curve meets the extrapolated brems- strahlung background. Equation (9.36) is only an acceptable approximation of the mean energy at depth in water for electron beams with incident energies of less than 10 MeV or for small depths at higher energies. In other situations the mean electron – – – energy Ez is obtained from tabulated data of Ez/E0 versus the scaled depth z/Rp (IAEA TRS 277). Much of the available data for electron dosimetry that were originally – given in terms of Ez determined from Eq. (9.36) have been recast to Monte – Carlo determined Ez in recent dosimetry protocols. When R50 and Rp have been determined in a plastic phantom rather than in water, the electron ranges in plastic Rpl should be converted into ranges in water as follows: Rwater = RplCpl (9.37) 340

CALIBRATION OF PHOTON AND ELECTRON BEAMS where Cpl is a material dependent scaling factor that was defined by the IAEA TRS 381 protocol as the ratio of average electron penetrations in water and plastic and is equivalent to the effective density of the AAPM TG 25 dosimetry protocol. PDD distributions for clinical electron beams are most commonly determined from ionization measurements carried out in water or water equivalent phantoms with diodes or ionization chambers. ● Percentage depth ionization curves measured with a diode represent the PDD curve, since the mass collision stopping power ratios silicon to water are essentially constant with depth in a phantom (i.e. with electron beam energy). ● Percentage depth ionization curves measured with an ionization chamber, on the other hand, must be corrected for gradient effects as well as for variations in mass collision stopping power ratios water to air with electron energy when determining the PDDs from ionization measure- ments. R50 may be determined from I50, the 50% value on the percentage depth ionization curve measured with an ionization chamber in water, as follows: R50 = 1.029I50 (cm) – 0.06 cm (for 2 cm £ I50 £ 10 cm) (9.38) and R50 = 1.059I50 (cm) – 0.37 cm (for I50 > 10 cm) (9.39) – – E0 and Ez are determined from the measured R50 and Rp, respectively, and their use in electron beam dosimetry should be considered an approxi- mation that facilitates the selection of dosimetric quantities and correction coefficients, rather than being an accurate statement on the energy parameters of clinical electron beams. To avoid potential misunderstandings of the meaning of the energy based relationships, the recent dosimetry protocols use R50 directly as a beam quality index for selecting stopping power ratios and reference depths. This parallels the long standing practice in photon dosimetry in which beam qualities are expressed in terms of the penetration of the beam into a water phantom. The choice of R50 as the beam quality index is a change from the previous practice of specifying beam quality in terms of the mean energy at the phantom – surface. Since E0 is normally derived from R50, this change in beam quality index is merely a simplification that avoids the need for a conversion to energy. 341

CHAPTER 9 By choosing a specific reference depth zref for the calibration in water the stopping power ratio water to air has been shown to depend only on R50. The recent dosimetry protocols based on in-water calibration by the IAEA (TRS 398) and the AAPM (TG 51) have endorsed this approach, and all data are expressed in terms of R50. The reference depth zref for electron beam calibration in water is expressed in terms of R50 as follows: zref = 0.6R50 (cm) – 0.1 cm (9.40) The reference depth in water is close to the depth of dose maximum zmax – for beams with R50 < 4 cm (E0 < 10 MeV); however, for beams with R50 ≥ 4 cm, zref is deeper than zmax. This choice of reference depth may be less convenient than that recommended in previous protocols, since for a given linac no two reference beams will have the same reference depth. However, the new reference depth defined by Eq. (9.40) has been shown to reduce significantly machine to machine variations in chamber calibration coefficients, and the gained accuracy justifies its use. 9.9. CALIBRATION OF MEGAVOLTAGE PHOTON AND ELECTRON BEAMS: PRACTICAL ASPECTS This section summarizes the practical aspects of the recommendations made in air kerma in air based and absorbed dose to water based codes of practice or protocols for the calibration of megavoltage photon and electron beams. For numerical values on the various correction and conversion factors we refer to the IAEA TRS 277 or the IAEA TRS 398 protocols. For background on the physical meaning of the factors we refer to the previous sections. 9.9.1. Calibration of megavoltage photon beams based on the air kerma in air calibration coefficient NK,Co A cylindrical ionization chamber is used at a given depth z in a water phantom (typically z is 5 or 10 cm). The calibration is based on an air kerma in air calibration coefficient NK,Co obtained in a 60Co beam at a standards laboratory. Beam quality is specified with a ratio of TPRs, TPR20 at depths of 20 cm and 10 cm in water or with the PDD at a depth of 10 cm in water with electron contamination removed, PDD(10)x, as discussed in Section 9.8.2. 342

CALIBRATION OF PHOTON AND ELECTRON BEAMS The Bragg–Gray or Spencer–Attix cavity theory is used to determine the absorbed dose Dw(z) or dose rate at the point of interest at depth z in the water phantom from the measured signal MQ (charge or current) as follows: Dw(z) = MQND,airsw,airpwallpcel (9.41) where MQ is the chamber current or charge corrected for influence quantities and measured at beam quality Q; ND,air is related to NK through Eq. (9.19); sw,air is the restricted stopping power ratio between water and air averaged over the electron slowing down spectrum resulting from the photon spectrum; pwall is the wall correction factor that accounts for the non-equivalence of the medium and wall; pcel is the central electrode correction factor that accounts for scatter and absorption of radiation on the central electrode (the factor was ignored in the AAPM TG 21 protocol but introduced in the IAEA TRS 277 and subsequent IAEA dosimetry protocols). In the IAEA air kerma in air based protocols, the displacement effect resulting from the insertion of an air cavity into a phantom is accounted for by defining an effective point of measurement while the cavity perturbation effect is negligible. For cylindrical chambers in high energy photon beams the effective point of measurement is located 0.6r upstream of the chamber centre, r being the cavity inner radius. For the purpose of absorbed dose measurements, in the absorbed dose to water based protocols the point of measurement is defined as the centre of the chamber and the displacement effects are accounted for by the introduction of the ‘gradient correction factor’ equivalent to pdis. The cavity fluence perturbation correction factor pcav is unity in high energy photon beams. 9.9.2. Calibration of megavoltage photon beams based on the dose to water calibration coefficient ND,w,Co A cylindrical ionization chamber is used at a given depth z in a water phantom (typically z is 10 cm). The calibration is based on a dose to water chamber calibration coefficient ND,w,Co obtained from a standards laboratory 343

CHAPTER 9 with the chamber irradiated with a 60Co beam at a reference depth zref in a water phantom. The absorbed dose to water Dw,Co at a given depth in a phantom in a cobalt beam in the absence of the ionization chamber is given by: Dw,Co = McoND,w,Co (9.42) where Mco is the chamber signal (charge or current) corrected for influence quantities, as discussed in Section 9.3. When the ionization chamber is used in a beam quality Q different from the 60Co used in its calibration, the absorbed dose to water is given by: Dw,Q = MQND,w,CokQ,Co (9.43) where the correction factor kQ,Co corrects for the effects of the difference between the reference 60Co beam quality (Co) and the actual user beam quality Q, and the chamber signal MQ has been corrected to the reference values of influence quantities, other than beam quality, for which the calibration coefficient is valid. The beam quality Q of megavoltage photon beams is specified, as discussed in Section 9.8.2, either with a ratio of TPRs (TPR20,10(Q)) or with the PDD (PDD(10, 10 × 10, SSD, Q)x. The IAEA TRS 398 dosimetry protocol recommends the use of the ratio of TPRs, while the AAPM TG 51 protocol recommends the use of PDDx , for megavoltage photon beam quality specification. Despite considerable polemics on the merits of each of the two approaches, in practice they both give essentially the same results for the megavoltage photon beams currently used in clinical practice. The beam quality correction factor kQ,Co is defined as the ratio, at the beam qualities Q and Co, of the calibration coefficients in terms of the absorbed dose to water of the ionization chamber: N D,w,Q k Q,Co = (9.44) N D,w,Co Ideally, the beam quality correction factors should be measured directly for each ionization chamber at the same quality as the user’s beam. In practice, this is generally not possible, so the factors are calculated theoretically assuming the validity of Bragg–Gray cavity theory and using the ND,air concept (see Section 9.4). 344

CALIBRATION OF PHOTON AND ELECTRON BEAMS 9.9.3. Calibration of megavoltage electron beams based on the air kerma in air calibration coefficient NK,Co For electron beams with energies equal to or above 10 MeV a cylindrical or a parallel-plate ionization chamber is used at a reference depth in a water phantom (usually close to zmax). For electron energies below 10 MeV a parallel- plate ionization chamber must be used. The calibration is based on air kerma in air calibration coefficient NK obtained in a 60Co beam at the standards laboratory, but for parallel-plate chambers a cross-calibration against a cylindrical chamber allows a direct determination of the ND,air coefficient. – E0, the mean electron energy on a phantom surface, is used for specifying the electron beam quality (Eq. (9.35)). The Spencer–Attix cavity relationship is used to determine the absorbed dose at the reference point in a water phantom as follows: Dw(z) = MQND,airsw,airpcavpcel (9.45) where MQ is the corrected measured chamber current or charge. ND,air is related to NK through Eq. (9.19). sw,air is the restricted stopping power ratio between water and air. pcav is the cavity fluence perturbation correction factor accounting for the in- scattering effect as discussed in Section 9.7. It is unity for well guarded parallel-plate chambers and is given by Eq. (9.33) for Farmer type cylindrical chambers. pcel is the central electrode correction factor that accounts for scatter and absorption of radiation on the central electrode of a cylindrical chamber. The factor was ignored in the AAPM TG 21 protocol but was taken into account in the IAEA TRS 277 and subsequent IAEA protocols, as well as in the AAPM TG 51 protocol. For parallel-plate chambers the effective point of measurement is located on the inner surface of the window at its centre, and no gradient correction is required. For cylindrical ionization chambers, on the other hand, the effective point of measurement is located 0.5r upstream from the chamber centre. In the AAPM protocols, in the latter case, the point of measurement is defined as the centre of the chamber and the gradient effects are to be accounted for by the introduction of the gradient or displacement correction factor pdis. 345

CHAPTER 9 The wall correction factor pwall is considered unity in electron beam dosimetry. 9.9.4. Calibration of high energy electron beams based on the dose to water calibration coefficient ND,w,Co The output calibration is based on a dose to water chamber calibration coefficient ND,w,Co obtained from a standards laboratory with the chamber irradiated in a reference beam of quality Q0. This reference quality is most commonly a 60Co g ray beam (ND,w,Co), but may also be an electron beam. Parallel-plate ionization chambers are recommended for all electron beam qualities and must be used for electron beams of energies below 10 MeV. At electron energies equal or above 10 MeV the use of cylindrical chambers is allowed. The reference point for parallel-plate chambers is taken to be on the inner surface of the entrance window, at the centre of the window. Water is recommended as the reference medium. The water phantom should extend to at least 5 cm beyond all four sides of the largest field size employed. For electron energies below 10 MeV a plastic phantom may be used, but all depths must be scaled appropriately. The beam quality index for electron beams is R50 , the half-value depth in water, measured with a field size of at least 10 × 10 cm2 for R50 £ 7 g/cm2 and at least 20 × 20 cm2 for R50 > 7 g/cm2. The preferred choice of detector for the measurement of R50 is a well guarded parallel-plate ionization chamber, the preferred choice of phantom medium is water. Output calibration is carried out in a water phantom at a reference depth zref with a field of 10 × 10 cm2. The reference depth is given by: zref = 0.6R50 – 0.1 g/cm2 (9.46) with R50 given in g/cm2. This depth is close to the depth of dose maximum zmax at beam qualities R50 < 4 g/cm2 (E0 £ 10 MeV); at higher beam energies it is deeper than zmax. The absorbed dose to water at the reference depth zref in an electron beam of quality Q, in the absence of the chamber, is given by: Dw,Q = MQND,w,CokQ,Co (9.47) where MQ is the chamber signal corrected for influence quantities; 346

CALIBRATION OF PHOTON AND ELECTRON BEAMS ND,w,Co is the calibration coefficient in terms of absorbed dose to water for the chamber irradiated in a 60Co beam at a standards laboratory; kQ,Co is a chamber correction factor for differences between the reference beam quality (Co) and the actual electron beam quality Q. Calculated values of kQ,Co against R50 are available in dosimetry protocol documents for a wide variety of parallel-plate and cylindrical ionization chambers. They are tabulated directly in the IAEA TRS 398 protocol or ¢ determined as a product of conversion and correction factors termed kecal, kR50 and Pgr in the AAPM TG 51 protocol. 9.10. KILOVOLTAGE DOSIMETRY During the past 30 years there has been a great deal of development in the dosimetry of high energy (i.e. megavoltage photon and electron) beams. The dosimetry of kilovoltage X ray beams (low and medium energy or ortho- voltage X ray beams), on the other hand, remained more or less static in that period until the late 1980s. Despite this, kilovoltage beams are still in widespread use for the treatment of superficial lesions. The IAEA TRS 277 protocol devoted a separate, detailed section to kilovoltage X rays, setting out a new air kerma in air based formalism, and this has recently been followed by several national dosimetry protocols on kilovoltage X ray dosimetry. Note that the second edition of the IAEA TRS 277 protocol provided substantial changes to the numerical data given in the original publication of 1987. 9.10.1. Specific features of kilovoltage beams When kilovoltage X rays interact with a medium, the secondary electrons have extremely short ranges due to their low initial energy coupled with the rapid increase of the collision stopping power at subrelativistic energies. This results in several important differences between kilovoltage and megavoltage beams as far as radiation dosimetry is concerned: ● The Bragg–Gray principle can no longer be applied to such beam qualities (i.e. the electron fluence in the air cavity of the ionization chamber is not exclusively determined by electron interactions in the surrounding medium); ● Owing to the short electron ranges, absorbed dose can be equated to the collision kerma to a very good approximation; 347

CHAPTER 9 ● Radiative losses can be ignored in low atomic number materials, so that absorbed dose and kerma are essentially equivalent. An ionization chamber calibration coefficient in kilovoltage X rays is determined with reference to a free air ionization chamber at a set of kilovoltage radiation qualities, in contrast to a single air kerma in air calibration coefficient at 60Co for megavoltage beams. Since the wall thickness of a typical cylindrical ionization chamber is larger than the range of secondary electrons created in it, CPE is established in the wall without a buildup cap. For this reason, and since the chamber calibration coefficient is given in terms of air kerma in air, the calibrated chamber acts as a kerma detector even when used in a phantom. The amount of photon scatter in a tissue equivalent phantom at kilovoltage energies is much larger than in high energy photon beams. This fact makes ratios of mass–energy absorption coefficients and, to a lesser extent, other, detector related dosimetric quantities depth and field size dependent. Kilovoltage beam quality is specified differently than megavoltage beam quality. As discussed in Section 9.8, for kilovoltage beams the beam quality is specified in terms of the HVL, generally expressed in millimetres of aluminium or, at the top end of the energy range, in millimetres of copper. It should be noted that beams with widely differing tube potentials may have similar HVLs, due to the marked effect of different filtrations. Thus the user determines the HVL of the beams of interest and then chooses NK values for the calibrated chamber for the beam using the calibration curve supplied by the standards laboratory. 9.10.2. Air kerma based in-phantom calibration method (medium energies) For medium energy X ray beams, typically above 100 kV, various dosimetry protocols recommend that the dose be determined at a depth in a water phantom, similarly to recommendations for megavoltage beam qualities. The various dosimetry protocols differ, however, in their specification of the reference depth. The IAEA TRS 277 protocol followed early recommendations of the ICRU and specifies a depth of 5 cm in water. The UK protocol (IPEMB, 1996) chose instead a depth of 2 cm in water for the reference depth, considering this to be much more representative of clinical practice; this has also been adopted in several other recent protocols. The formalism for the determination of the absorbed dose to water is: 348

CALIBRATION OF PHOTON AND ELECTRON BEAMS Dw,Q = MQNK,Q[(men/r)w,air]Q pQ (9.48) where, for the HVL of the user’s beam (Q): MQ is the instrument reading corrected for influence quantities (see Section 9.3); NK,Q is the air kerma in air chamber calibration coefficient for beam quality Q; (men/r)w,air is the mass–energy absorption coefficient ratio water to air for the photon spectrum at the depth of measurement in water and for the field size of the user’s beam; pQ is an overall perturbation correction factor, which is not to be confused with the pQ factor of Eq. (9.28) and which consists of multi- plicative components of a different nature than those involved in Eq. (9.28). For a detailed description of these components please refer to, for example, the AAPM TG 61 protocol. There is only a weak dependence on field size or depth in the values of (men/r)w,air in general and in the pQ values for Farmer type chambers. Cylindrical chambers of the Farmer type are commonly used at this energy range. All recent kilovoltage dosimetry protocols agree to within about 1.5% in the deter- mination of the absorbed dose to water at 2 cm depth in a water phantom. 9.10.3. Air kerma based backscatter method (low and medium photon energies) Clinically, for these beams, the dose is most often prescribed for the skin surface (strictly just below the surface, where CPE is established). This has led to the most important and widely used method of determining the absorbed dose. The principle is straightforward. A chamber is positioned free in air (i.e. with no phantom involved) at a position corresponding to the centre of the field on the patient’s skin surface. The reading of the (calibrated) chamber yields the air kerma in air (Kair)air. This is then converted into dose to water at the surface of a phantom at the field size of interest. The energy or quality range for this method differs slightly from protocol to protocol, but all of the protocols denote it by the term low energy; in the IAEA TRS 277 protocol this range is 10–160 kV. The theoretical route is as follows: 349

CHAPTER 9 ● The air kerma in air (Kair)air is converted into water kerma in air (Kw)air through the mass–energy absorption coefficient ratio water to air, but still under free in air conditions (i.e. for the primary spectrum); this has the advantage that (men/r)w,air is independent of field size. ● Next, the backscatter factor (BSF) converts the water kerma in air (Kw)air into the water kerma in water (Kw)w at the surface of a water phantom. The formalism for this procedure is: Dw,Q = M freeair,Q N K,Q BSF[( m en /r ) w,air ] free air,Q surface (9.49) where, for the HVL of the user’s beam (Q): Mfree air,Q is the instrument reading corrected for influence quantities; NK is the air kerma in air chamber calibration coefficient; BSF is the backscatter factor for the field size, HVL and SSD; [(men/r)w,air]free air,Q is the mass–energy absorption coefficient ratio water to air for the free in air (primary) spectrum. Note that, in principle, the type of ionization chamber has no significance when using the backscatter method to determine the surface dose; one is merely using the chamber as a means of transferring the air kerma in air from the standards laboratory to the user’s beam. In practice, however, the chamber is required to exhibit a small variation in NK with the HVL over the full quality range. The IAEA TRS 277 protocol recommends a thin window parallel-plate ionization chamber for this low energy range. In the IPEMB protocol a secondary standard graphite cylindrical chamber, 0.3 cm3, of the type NE 2561 or NE 2611 is to be used over the complete medium and low energy range. The AAPM TG 61 protocol explicitly incorporates in an equation of the Eq. (9.49) type a chamber stem correction termed Pstem,air, which accounts for the change in the chamber calibration coefficient for the difference in field size between the standards laboratory beam and the clinical beam. For an ideal stem free ionization chamber this correction is unity. For a cylindrical Farmer type chamber the correction is less than 1%, but it can be very significant for certain types of thin window chamber, due to their significant chamber bodies. 350

CALIBRATION OF PHOTON AND ELECTRON BEAMS 9.10.4. Air kerma in air based calibration method for very low energies In German and UK protocols there is a third method at the lowest energies, the Bucky therapy range, which corresponds approximately to 8– 50 kV. In this energy range a thin window parallel-plate chamber is recommended for calibration purposes. The backscatter method may be invalid for the very small field sizes sometimes employed clinically in such low energy beams (i.e. the field size can be insufficient to completely cover the chamber and hence the value of the product MNK will no longer yield the correct value for air kerma in air in the user’s beam). For these beams the parallel-plate chamber is placed at the surface of a phantom and the dose at the surface is determined. The relevant expression is identical to that for the in-phantom medium energy method, except that now the factor pQ (denoted as kch) refers to the specific parallel-plate chamber employed and pertains to the surface dose rather than to the dose at 2 cm depth. The lack of data available for the kch factor led to the assumption that it is equal to unity. However, this assumption cannot be correct, since it assumes that the scatter from the body of the chamber is negligible. Recent experiments have found that it varies from about 1.01 to 1.08 for a field diameter of 5.4 cm (at a focal distance of 50 cm), depending on the chamber, beam quality and phantom. An update to the IPEMB protocol will recommend specific values for these significant correction factors. 9.10.5. Absorbed dose to water based calibration method Standards of absorbed dose to water in the kilovoltage X ray range are not generally available. However, it is possible to derive calibration coefficients in terms of absorbed dose to water from air kerma in air calibration coefficients using one of the accepted dosimetry protocols (e.g. IAEA TRS 398). Thus any calibration laboratory with standards of air kerma in air can in this way provide (derived) calibration coefficients in terms of absorbed dose to water. Even though this is formally equivalent to the user obtaining an air kerma in air calibration and individually applying the same air kerma protocol, it has the advantage of permitting the widespread use of the unified methodology of absorbed dose to water standards in an area of dosimetry in which standard methods are notably lacking. 351

CHAPTER 9 9.11. ERROR AND UNCERTAINTY ANALYSIS FOR IONIZATION CHAMBER MEASUREMENTS 9.11.1. Errors and uncertainties An error is defined as the difference between the measured value of a measurand and the true value. An error has a sign, and a correction factor can be associated with it. When the error is known, the true value of the measurand can be calculated from the measured value. An uncertainty associated with a measurement is a parameter that characterizes the dispersion of the values that can be attributed to the measurand. The value of the uncertainty is usually an estimated standard deviation, has no sign and is assumed to be symmetrical with respect to the estimated value of the quantity. It is a measure of our lack of exact knowledge after all recognized systematic effects have been eliminated by applying appropriate corrections. 9.11.2. Classification of uncertainties Uncertainties of measurements are expressed as relative standard uncer- tainties, and the evaluation of standard uncertainties is classified into two types: type A and type B. ● Type A uncertainties are inherently random and are obtained by a statistical analysis of a series of observations. A 1s type A uncertainty corresponds to the standard error on the mean of a set of observations at the 68% confidence level. ● Type B uncertainties are determined through other than statistical, but often subjective, methods and account for systematic effects in the deter- mination of a quantity. Although of a totally different nature, type A and type B uncertainties are often combined assuming they are independent, using the propagation law of uncertainties without cross-correlation (i.e. relative standard uncertainties are quadratically summed). 9.11.3. Uncertainties in the calibration chain The IAEA TRS 398 dosimetry code of practice describes an extensive uncertainty analysis on the calculated values of the beam quality conversion factors kQ for photon and electron beams. For photon beams the estimated relative standard uncertainty for the calculated beam quality conversion factors 352

CALIBRATION OF PHOTON AND ELECTRON BEAMS is 1.0%. For electron beams the value amounts to 1.2% for cylindrical chambers and 1.7% for parallel-plate chambers when based on a 60Co calibration technique and to 0.9% for cylindrical chambers and 0.6% for plane- parallel chambers when based on a cross-calibration technique in an electron beam. In order to obtain the uncertainty on a beam calibration, the above mentioned uncertainties need to be combined with the uncertainties on: ● The absorbed dose calibration coefficient at 60Co or in a high energy electron beam, if a cross-calibration technique is used. ● Issues related to the in-phantom measurement of absorbed dose in the clinic. These comprise type A and type B uncertainties on the positioning of the chamber in the water phantom, the temperature and pressure measurement, the ion recombination, polarity and electrometer correction factor (if present), and the linac stability during the measure- ments of absorbed dose. For a detailed analysis we refer to the IAEA TRS 398 protocol. BIBLIOGRAPHY AMERICAN ASSOCIATION OF PHYSICISTS IN MEDICINE, A protocol for the determination of absorbed dose from high-energy photon and electron beams, Task Group 21, Radiation Therapy Committee, Med. Phys. 10 (1983) 741–771. — AAPM’s TG-51 protocol for clinical reference dosimetry of high energy photon and electron beams, Task Group 51, Med. Phys. 26 (1999) 1847–1870. — AAPM protocol for 40–300 kV x-ray beam dosimetry in radiotherapy and radiobiology, Task Group 61, Med. Phys. 28 (2001) 868–892. BRITISH JOURNAL OF RADIOLOGY, Central Axis Depth Dose Data for Use in Radiotherapy, Supplement 17 (1983). — Central Axis Depth Dose Data for Use in Radiotherapy, Supplement 25 (1996). INSTITUTE OF PHYSICAL SCIENCES IN MEDICINE, Code of practice for high- energy photon therapy dosimetry based on the NPL absorbed dose calibration service, Phys. Med. Biol. 35 (1990) 1355–1360. 353

CHAPTER 9 INSTITUTION OF PHYSICS AND ENGINEERING IN MEDICINE AND BIOLOGY, The IPEMB code of practice for electron dosimetry for radiotherapy beams of initial energy from 2 to 50 MeV based on air-kerma calibration, Phys. Med. Biol. 41 (1996) 2557–2603. — The IPEMB code of practice for the determination of absorbed dose for x-rays below 300 kV generating potential (0.035 mm Al–4 mm Cu HVL; 10–300 kV generating potential), Phys. Med. Biol. 41 (1996) 2605–2625. INTERNATIONAL ATOMIC ENERGY AGENCY, Absorbed Dose Determination in Photon and Electron Beams, Technical Reports Series No. 277, IAEA, Vienna (1987). — Absorbed Dose Determination in Photon and Electron Beams, 2nd edn, Technical Reports Series No. 277, IAEA, Vienna (1997). — Calibration of Dosimeters Used in Radiotherapy, Technical Reports Series No. 374, IAEA, Vienna (1994). — The Use of Plane Parallel Ionization Chambers in High Energy Electron and Photon Beams, Technical Reports Series No. 381, IAEA, Vienna (1997). — Absorbed Dose Determination in External Beam Radiotherapy, Technical Reports Series No. 398, IAEA, Vienna (2000). INTERNATIONAL ELECTROTECHNICAL COMMISSION, Medical Electrical Equipment — Dosimeters with Ionization Chambers as Used in Radiotherapy, IEC 60731, IEC, Geneva (1997). INTERNATIONAL ORGANIZATION FOR STANDARDIZATION, Quantities and Units — Part 0: General Principles, ISO 31-0, ISO, Geneva (1992). 354

Chapter 10 ACCEPTANCE TESTS AND COMMISSIONING MEASUREMENTS J.L. HORTON Department of Radiation Physics, University of Texas MD Anderson Cancer Center, Houston, Texas, United States of America 10.1. INTRODUCTION Following the installation of a therapy machine, be it an orthovoltage X ray unit, cobalt unit, linac or brachytherapy machine, in a radiotherapy clinic, the medical physicist must perform a series of measurements and tasks prior to placing the unit into clinical operation. These duties include acceptance testing and commissioning. Although calibration of the treatment beams is a part of the acceptance tests and commissioning, calibration is not discussed in this chapter, as it is fully covered in Chapter 9. 10.2. MEASUREMENT EQUIPMENT 10.2.1. Radiation survey equipment A Geiger counter and a large volume ionization chamber survey meter are required to carry out a radiation survey of all treatment rooms. For facilities with a treatment unit operated above 10 MeV, neutron survey equipment such as Bonner spheres, long counters and BF3 counters are necessary. However, it may be appropriate to contract neutron measurements to a medical physics consulting service, since this may be a less expensive option than developing the specialized skills and knowledge required for most neutron measurements and acquiring the expensive neutron detection equipment that is typically required only during acceptance testing. 355

CHAPTER 10 10.2.2. Ionometric dosimetry equipment A variety of ionization chambers are required to compile the radiation beam properties measured during the acceptance testing and commissioning of a radiation treatment unit. Thimble ionization chambers with volumes of the order of 0.1–0.2 cm3 are used to measure a number of relative quantities and factors. These relative factors, including central axis percentage depth doses (PDDs), output factors and penumbra, may exhibit a rapidly changing dose gradient. In this situation small volume ionization chambers are preferred to reduce the uncertainty in the effective point of measurement. For measure- ments in the buildup region, which exhibits the greatest change in dose gradient, a parallel-plate or extrapolation chamber is required. Calibration measurements are typically performed with a thimble ionization chamber with a volume of the order of 0.5 cm3 to increase the signal to noise ratio. A single electrometer that can be used with all these ionization chambers is a wise choice. 10.2.3. Film Radiographic film has a long history of use in radiotherapy physics measurements. It has been used most successfully for quality control and electron beam measurements. However, the composition of radiographic film is very different from that of tissue, which makes it difficult for use in photon beam dosimetry. In the past decade radiochromic film has been introduced into radio- therapy physics practice. This film is more tissue equivalent than radiographic film and is becoming more widely used for photon beam dosimetry. Film dosimetry also requires a densitometer to evaluate the darkening of the film and to relate the darkening to the radiation received. It should be noted that different densitometers are suggested for radiochromic film than for conventional radiographic film, as the absorption peaks occur at different wavelengths for these different films. 10.2.4. Diodes Owing to their small size, silicon diodes are convenient for measurements in small photon radiation fields. Diodes are also used for electron beam measurements because the stopping power ratio of silicon to water is almost constant over the energies measured in radiotherapy. The response of diodes should be checked against ionometric measurements before routine use. 356

ACCEPTANCE TESTS AND COMMISSIONING MEASUREMENTS 10.2.5. Phantoms 10.2.5.1. Radiation field analyser and water phantom A water phantom that scans ionization chambers or diodes in the radiation field is required for acceptance testing and commissioning. This type of water phantom is frequently referred to as a radiation field analyser (RFA) or an isodose plotter. Although a 2-D RFA is adequate, a 3-D RFA is preferable, as it allows the scanning of the radiation field in orthogonal directions without changing the phantom set-up. The traversing mechanism for the ionization chambers or diodes may also be used to move the film densitometer. The traversing mechanism should have an accuracy of movement of 1 mm and a precision of 0.5 mm. A 3-D scanner of an RFA should be able to scan 50 cm in both horizontal dimensions and 40 cm in the vertical dimension. The water tank should be at least 10 cm larger than the scan in each dimension. The RFA should be filled with water and then positioned with the radiation detector centred on the central axis of the radiation beam. The traversing mechanism should move the radiation detector along the principal axes of the radiation beam. After the gantry has been levelled with the beam directed vertically downwards, levelling of the traversing mechanism can be accomplished by scanning the radiation detector along the central axis of the radiation beam, indicated by the image of the cross-hair. Any deviation of the radiation detector from the central axis, as the detector is moved away from the water surface, indicates that the traversing mechanism is not levelled. 10.2.5.2. Plastic phantoms For ionometric measurements in the buildup region a polystyrene or water equivalent plastic phantom is convenient. A useful configuration for this phantom consists of ten blocks of 25 × 25 × 5 cm3. One block should be drilled to accommodate a Farmer type ionization chamber with the centre of the hole 1 cm from one surface. A second block should be machined to place the entrance window of a parallel-plate chamber at the level of one surface of the block. This arrangement allows measurements with the parallel-plate chamber with no material between the window and the radiation beam. An additional seven blocks of the same material as the rest of the phantom should be 25 × 25 cm2. These blocks should be 0.5, 1, 2, 4, 8, 16 and 32 mm thick. These seven blocks combined with the 5 cm thick blocks allow measurement of depth ionization curves in 0.5 mm increments to any depth from the surface to 40 cm with the parallel-plate chamber and from 1 to 40 cm with the Farmer chamber. 357

CHAPTER 10 The depth of 40 cm is the limit, because 10 cm of backscatter should be maintained downstream from the measurement point. A plastic phantom for film dosimetry is also required. It is convenient to design one section of the phantom to serve as a film cassette. Other phantom sections can be placed adjacent to the cassette holder to provide full scattering conditions. Use of ready pack film irradiated parallel to the central axis of the beam requires that the edge of the film be placed at the surface of the phantom and that the excess paper be folded down and secured to the entrance surface of the phantom. Pinholes should be placed in a corner of the downstream edge of the paper package so that air can be squeezed out before placing the ready pack in the phantom, otherwise air bubbles will be trapped between the film and the paper. Radiation will be transmitted unattenuated through these air bubbles, producing incorrect data. Plastic phantoms are also commonly used for routine quality control measurements. The design of these phantoms will depend on the requirements of the quality control programme. 10.3. ACCEPTANCE TESTS Acceptance tests assure that the specifications contained in the purchase order are fulfilled and that the environment is free of radiation and electrical hazards to staff and patients. The tests are performed in the presence of a manufacturer’s representative. Upon satisfactory completion of the acceptance tests, the physicist signs a document certifying that these conditions are met. When the physicist accepts the unit, the final payment is made for the unit, ownership of the unit is transferred to the institution and the warranty period begins. These conditions place a heavy responsibility on the physicist for the correct performance of these tests. Acceptance tests may be divided into three groups: ● Safety checks; ● Mechanical checks; ● Dosimetry measurements. A number of national and international protocols exist to guide the physicist in the performance of these tests. 358

ACCEPTANCE TESTS AND COMMISSIONING MEASUREMENTS 10.3.1. Safety checks Acceptance tests begin with safety checks to assure a safe environment for the staff and public. 10.3.1.1. Interlocks, warning lights and patient monitoring equipment The initial safety checks should verify that all interlocks are functioning properly. These interlock checks should include the door interlock, all radiation beam-off interlocks, all motion disable interlocks and all emergency-off interlocks. The door interlock prevents irradiation from occurring when the door to the treatment room is open. The radiation beam-off interlocks halt irradiation but they do not halt the motion of the treatment unit or patient treatment table. The motion disable interlocks halt motion of the treatment unit and patient treatment table but they do not stop machine irradiation. Emergency-off interlocks typically disable power to the motors that drive the treatment unit and treatment table motions and disable power to some of the radiation producing elements of the treatment unit. The idea is both to prevent collisions between the treatment unit and personnel, patients or other equipment and to halt undesirable irradiation. The medical physicist must verify the proper functioning of all these interlocks and ensure that all personnel operating the equipment have a clear understanding of each. After verifying that all interlocks and emergency-off switches are operational, all warning lights should be checked. Next, the proper functioning of the patient monitoring audiovideo equipment can be verified. The audiovideo equipment is normally used for patient monitoring but is often also useful for monitoring equipment or gauges during acceptance testing and commissioning involving radiation measurements. 10.3.1.2. Radiation survey After completion of the interlock checks, the medical physicist should perform a radiation survey in all areas outside the treatment room. For cobalt units and linacs operated below 10 MeV a photon survey is required; for linacs operated above 10 MeV the physicist must survey for neutrons in addition to photons. The survey should be conducted using the highest energy photon beam. To ensure meaningful results the physicist should perform a preliminary calibration of the highest energy photon beam before conducting the radiation survey. Photon measurements will require both a Geiger counter and an ionization chamber survey meter. Neutron measurements will require a 359

CHAPTER 10 neutron survey meter. Several types are available, including Bonner spheres, long counters and BF3 counters. The fast response of the Geiger counter is advantageous in performing a quick initial survey to locate the areas of highest radiation leakage through the walls. After the location of these hot spots is determined, the ionization chamber type survey meter may be used to quantify leakage currents. ● All primary barriers should be surveyed with the largest field size, with the collimator rotated to 45º and with no phantom in the beam; ● All secondary barriers should be surveyed with the largest field size, with a phantom in the beam; ● The first area surveyed should be the control console area, where an operator will be located to operate the unit for all subsequent measurements. 10.3.1.3. Collimator and head leakage Shielding surrounds the target on a linac or the source on a 60Co unit. Most regulations require this shielding to limit the leakage radiation to 0.1% of the useful beam at 1 m from the source. The adequacy of this shielding must be verified during acceptance testing. This verification may be accomplished by closing the collimator jaws and covering the head of the treatment unit with film. The films should be marked to permit the determination of their position on the machine after they are exposed and processed. The exposure should be long enough to yield an optical density (OD) of 1 on the films. For example, assume that an exposure of 10 cGy yields an OD of 1 on the film and the films are secured to the head of the treatment unit at a distance of 25 cm from the source. Then the expected radiation level at the position of the films is 1.6% of the useful beam (0.1% of the useful beam at 1 m inverse squared to 25 cm). An exposure of 625 cGy at the isocentre (10 cGy divided by 1.6%) should yield an OD of 1 on the film. Any hot spots revealed by the film can be quantified by using an ionization chamber style survey meter. The survey meter can be positioned 1 m from the hot spot with a ring stand and clamps. The reading may be viewed remotely with the closed circuit television camera to be used for patient monitoring. 360

ACCEPTANCE TESTS AND COMMISSIONING MEASUREMENTS 10.3.2. Mechanical checks The mechanical checks establish the precision and accuracy of the mechanical motions of the treatment unit and patient treatment table. 10.3.2.1. Collimator axis of rotation The photon collimator jaws rotate on a circular bearing attached to the gantry. The central axis of the photon, electron and light fields should be aligned with the axis of rotation of this bearing and the photon collimator jaws should open symmetrically about this axis. This axis is an important aspect of any treatment unit and must be carefully determined. The collimator rotation axis can be found with a rigid rod attached to the collimator housing. This rod should terminate in a sharp point and be long enough to reach from where it will be attached to the collimator housing to the approximate position of the isocentre. The gantry should be positioned to point the collimator axis vertically downwards and then the rod is attached to the collimator housing. Millimetre graph paper is attached to the patient treatment table and the treatment table is raised to contact the point of the rod. With the rod rigidly mounted, the collimator is rotated through its range of motion. The point of the rod will trace out an arc as the collimator is rotated. The point of the rod is adjusted to be near the centre of this arc. This point should be the collimator axis of rotation. This process is continued until the minimum radius of the arc is obtained. This minimum radius provides an indication of the precision of the collimator axis of rotation. In most cases this arc will reduce to a point, but should not exceed 1 mm in radius in any event. 10.3.2.2. Photon collimator jaw motion The photon collimator jaws should open symmetrically about the collimator axis of rotation. A dial indicator can be used to verify this. The indicator is attached to a point on the collimator housing that remains stationary during rotation of the collimator jaws. The feeler of the indicator is brought into contact with one set of jaws and the reading is recorded. The collimator is then rotated through 180º and again the indicator is brought into contact with the jaws and the reading is recorded. The collimator jaw symmetry about the rotation axis is one half of the difference in the two readings. This value projected to the isocentre should be less than 1 mm. This procedure is repeated for the other set of collimator jaws. 361

CHAPTER 10 The two sets of collimator jaws should be perpendicular to each other. To check this, the gantry is rotated to orientate the collimator axis of rotation horizontally. Then the collimator is rotated to place one set of jaws horizontally. A spirit level is placed on the jaws to verify that they are horizontal. Then the spirit level is used to verify that the vertically positioned jaws are vertical. With the jaws in this position the collimator angle indicators are verified. These indicators should be reading a cardinal angle at this point, either 0º, 90º, 180º or 270º, depending on the collimator position. This test is repeated with the spirit level at all cardinal angles by rotating the collimator to verify the collimator angle indicators. 10.3.2.3. Congruence of light and radiation field At this point the alignment of the light field is to be verified. With millimetre graph paper attached to the patient treatment table, the table is raised to the nominal isocentre distance. The gantry is orientated to point the collimator axis of rotation vertically downwards. The position of the collimator axis of rotation is indicated on this graph paper. The projected image of the cross-hair should be coincident with the collimator axis of rotation and should not deviate more than 1 mm from this point as the collimator is rotated through its full range of motion. The projected images of the jaws should open and close symmetrically about this point. The symmetry of the collimator jaw images about this point should be better than 1 mm at all cardinal angles of the collimator. The congruence of the light and radiation field can now be verified. A ready pack of radiographic film is placed perpendicularly to the collimator axis of rotation. The edges of the light field are marked with radio-opaque objects or by pricking holes with a pin through the ready pack film at the corners of the light field. The film is positioned near zmax by placing plastic on top of it and is irradiated to yield an OD of between 1 and 2. The light field edge should correspond to the radiation field edge within 2 mm. This test should be repeated over the range of field sizes and at two different distances to verify that the virtual light and photon sources are the same distance from the isocentre. At this point the light field has been aligned to the collimator axis of rotation. Any misalignment between the light and radiation field may indicate that the central axis of the radiation field is not aligned to the collimator axis of rotation. The alignment of the photon field is a complex procedure that should only be performed by factory personnel. Any misalignment must be evaluated for its magnitude, effect on treatment and whether factory personnel should be called in to verify and correct the problem. 362

ACCEPTANCE TESTS AND COMMISSIONING MEASUREMENTS 10.3.2.4. Gantry axis of rotation The gantry axis of rotation can be found with any rigid rod that has a telescoping capability. Many treatment machines are supplied with a mechanical front pointer that may be used for this purpose. The axis of the front pointer should be aligned along the collimator axis of rotation and its tip should be at the nominal isocentre distance. The gantry is positioned to point the central axis of the beam vertically downwards; a second rigid rod that terminates in a small diameter tip off the end of the patient treatment table is then affixed and the treatment table is adjusted to bring the rod affixed to the treatment table to contact the point of the rod fixed to the gantry. The treatment table is then shifted along its longitudinal axis to move the point of the rod out of contact with the rod affixed to the gantry. Care should be taken not to change the vertical or lateral positions of the rod. The gantry is rotated through 180º and the treatment table is moved back to a position where the two rods contact. If the front pointer correctly indicates the isocentre distance, the points on the two rods should contact in the same relative position at both angles. If not, the treatment table height and the length of the front pointer are adjusted until this condition is achieved as closely as possible. Owing to flexing of the gantry, it may not be possible to achieve the same position at both gantry angles. If so, the treatment table height is positioned to minimize the overlap at both gantry angles. This overlap is a ‘zone of uncertainty’ of the gantry axis of rotation. This zone of uncertainty should not be more than 1 mm in radius. The tip of the rod affixed to the treatment table now indicates the height of the gantry axis of rotation. This procedure is repeated with the gantry at parallel opposed horizontal angles to establish the right/left position of the gantry axis of rotation. The collimator axis of rotation indicated by the cross-hair image, aligned before, should pass through this point. Patient positioning lasers are then aligned to pass through this point. 10.3.2.5. Patient treatment table axis of rotation The patient treatment table axis of rotation can be found by positioning the gantry with the collimator axis of rotation pointed vertically downwards. Millimetre graph paper is attached to the treatment table and the image of the cross-hair marked on this graph paper. As the treatment table is rotated, the movement of the cross-hair image on the graph paper is noted. The cross-hair image should trace an arc with a radius of less than 1 mm. The collimator axis of rotation, the gantry axis of rotation and the treatment table axis of rotation should all intersect in a sphere. The radius of 363

CHAPTER 10 this sphere determines the isocentre uncertainty. This radius should be no greater than 1 mm, and for machines used in radiosurgery should not exceed 0.5 mm. 10.3.2.6. Radiation isocentre The radiation isocentre should be determined for all photon energies. To locate the radiation isocentre a ready pack film is taped to one of the plastic blocks that comprise a plastic phantom. The plane of the film should be placed in the plane traced out by the central axis of the X ray beam as the gantry is rotated. The film should be perpendicular to and approximately centred on the gantry axis of rotation. A pin prick is made in the film to indicate the gantry axis of rotation. A second block is then placed against the film, sandwiching it between the two blocks, and the collimator jaws are closed to approximately 1 mm × 1 mm. The film is then exposed to produce an OD of 0.3–0.5. Without touching the film, the film is exposed again at a number of different gantry angles in all four quadrants. Gantry angles that are not 180º apart should be chosen to avoid having the entrance of one beam overlap the exit of another. The processed film should show a multiarmed cross, referred to as a ‘star shot’. The point where all central axes intersect is the radiation isocentre. Owing to gantry flex, it may be a few millimetres wide but should not exceed 4 mm. This point should be within 1–2 mm of the mechanical isocentre indicated by the pin prick on the film. Verification of the radiation isocentre can be accomplished by centring an ionization chamber with an appropriate buildup cap on this point. The ionization collected for a fixed number of monitor units (MUs) on a linac or for time on a 60Co unit should be independent of the gantry angle. 10.3.2.7. Optical distance indicator A convenient method to verify the accuracy of the optical distance indicator (ODI) over the range of its readout uses the plastic phantom discussed in Section 10.2.5. With the gantry positioned with the collimator axis of rotation pointing vertically downwards, five of the 5 cm thick blocks are placed on the treatment table, with the top of the top block at the isocentre. The ODI should read the isocentre distance. By adding and removing 5 cm blocks the ODI can be easily verified at other distances in 5 cm increments. 364

ACCEPTANCE TESTS AND COMMISSIONING MEASUREMENTS 10.3.2.8. Gantry angle indicators The accuracy of the gantry angle indicators can be determined by placing a spirit level across the rails that hold the blocking tray. At each of the cardinal angles the level should indicate level. Some spirit levels also have an indicator for 45º angles that can be used to check angles of 45º, 135º, 225º and 315º. The gantry angle indicators should be accurate to within 0.5º. 10.3.2.9. Collimator field size indicators The collimator field size indicators can be checked by comparing the indicated field sizes with values measured on a piece of graph paper fixed to the treatment table with the top of the table raised to the isocentre height. The range of field size should be checked for both symmetric and asymmetric field settings. 10.3.2.10. Patient treatment table motions The patient treatment table should move in the vertical and horizontal planes. The vertical motion can be checked by attaching a piece of millimetre graph paper to the treatment table and, with the gantry positioned with the collimator axis of rotation pointing vertically downwards, marking the position of the image of the cross-hair on the paper. As the treatment table is moved through its vertical range, the cross-hair image should not deviate from this mark. The horizontal motion can be checked in a similar fashion, with the gantry positioned with the collimator axis in a horizontal plane. A piece of graph paper is affixed to the treatment table, the position of the cross-hair is marked and the treatment table is moved through its range of lateral motion. By rotating the treatment table 90º from its ‘neutral’ position, the longitudinal motion can be verified with the collimator axis orientated in a horizontal plane. 10.3.3. Dosimetry measurements Dosimetry measurements establish that the central axis PDDs and off- axis characteristics of clinical beams meet the specifications. The characteristics of the monitor ionization chamber of a linac or the timer of a 60Co unit are also determined. 365

CHAPTER 10 10.3.3.1. Photon energy The energy specification of an X ray beam is usually stated in terms of the central axis PDD. Typical specifications are in terms of the value of the 100 cm source to surface depth (SSD) central axis PDD for a 10 × 10 cm2 field at a depth of 10 cm in a water phantom. This value is compared with values given in the British Journal of Radiology Supplement 25 to determine the nominal energy of the photon beam. During acceptance testing this value will be determined with a small volume ionization chamber in a water phantom in accordance with the acceptance test protocol. 10.3.3.2. Photon beam uniformity The uniformity of a photon beam is typically specified in terms of either transverse beam profiles or the uniformity index. For the case in which transverse beam profiles are used, the flatness and symmetry of the beam are specified over the central 80% of the beam profile at a depth of 10 cm in a water phantom. The beam uniformity should also be specified at the depth of maximum dose zmax in a water phantom. Specification at zmax prevents the off- axis peaking of the beam profile becoming too large at this depth. The off-axis peaking is a product of the design of the flattening filter to produce a flat profile at a depth of 10 cm. The flattening filter also produces a differential hardening across the transverse direction of the beam that results in off-axis peaking at a depth shallower than 10 cm. Beam profiles are measured along the principal planes as well as along a diagonal of the beam. The uniformity index is a measure of the beam uniformity over the entire area of the beam, not just the principal planes. The uniformity index is measured in a plane perpendicular to the central axis. It is defined to be the area enclosed by the 90% isodose curve divided by the area enclosed by the 50% isodose curve. The IEC definition of the flattened area of the beam depends on the field size. According to the IEC, the flattened area is defined by straight lines joining points on the major axes and diagonals of the square fields given in Table 10.1. 10.3.3.3. Photon penumbra The photon penumbra is typically defined as the distance between the 80% and 20% dose points on a transverse beam profile measured 10 cm deep in a water phantom. However, there are also other definitions of the penumbra, 366

ACCEPTANCE TESTS AND COMMISSIONING MEASUREMENTS TABLE 10.1. INTERNATIONAL ELECTROTECHNICAL COMMIS- SION’S DEFINITION OF THE FLATTENED AREA OF THE BEAM Side of square field a (cm) dma ddb 5 £ a £ 10 1 cm 2 cm 10 < a £ 30 0.1a 0.2a 30 < a 3 cm 6 cm a The distance from the contour of the 50% of the absorbed dose on the beam central axis to the flattened area of the beam. It is on a major axis of the beam. b Defined on a beam diagonal. such as the distance between the 90% and 10% dose points on the beam profile at a given depth in a phantom. Whenever penumbra values are quoted, the depth of the profile and the spread in the percentage dose should be stated. 10.3.3.4. Electron energy The electron energy is typically determined from measurements of the practical range in a water phantom. The most probable electron energy at the phantom surface Ep,0 can be determined from the practical range with the following equation: E p,0 = 0.0025R p + 1.98 R p + 0.22 2 (10.1) where Rp is the practical range. Another energy of interest for calibration purposes is the average energy on the phantom surface. Further discussion of the determination of the average energy is found in Chapters 8 and 9. Although the manufacturers state nominal electron energies, the central axis PDD characteristics of electron beams are really the values of clinical interest. 10.3.3.5. Electron beam bremsstrahlung contamination The radiation measured beyond the practical range of the electrons in the phantom material is the bremsstrahlung contamination of the electron beam. All electron beams have bremsstrahlung contamination that results from inter- actions between electrons and materials in the scattering foils, collimators, air and patients. The bremsstrahlung contamination increases with electron energy, as discussed in Section 1.3.2. 367

CHAPTER 10 10.3.3.6. Electron beam uniformity The beam uniformity of an electron beam is typically specified in terms of either transverse beam profiles or the uniformity index. Beam profiles are measured along the principal planes and along a diagonal of the beam. For the case in which beam profiles are used, the flatness and symmetry of the beam are typically specified over the central 80% of the beam profile at a stated depth in a water phantom. The depth of measurement will depend on the machine specifications. If the vendor supplied specifications are inadequate, the physicist should propose an alternative set. The IEC definition of electron field uniformity includes measuring beam profiles at depths of 1 mm, the depth of the 90% dose and one half of the depth of the 80% dose. 10.3.3.7. Electron penumbra The electron penumbra is usually defined as the distance between the 80% and 20% dose points along a major axis at a given depth. The IEC defines this depth as one half of the depth of the 80% dose on the central axis. Machine vendors specify other depths, such as depth of zmax or depth of the 90%, for the definition of electron penumbra. 10.3.3.8. Monitor characteristics The amount of radiation delivered by a treatment unit is determined by the setting of an MU device on the treatment unit. A timer serves this purpose on a cobalt unit and an ionization chamber that intercepts the entire treatment beam is used on a linac. This MU device should be calibrated according to an appropriate national or international protocol for all energies, dose rates and modalities that will be used clinically. The linearity of the MU device should be verified by placing an ionization chamber at a fixed depth in a phantom and recording the ionization collected during irradiations with different time or MU settings over the range of the monitor. The collected ionization can be plotted on the y axis and the monitor or time setting on the x axis. These data should produce a straight line indicating a linear response of the MU device or timer. If these data produce a straight line that does not pass through the origin, then the monitor is linear but has an end effect. A negative x intercept indicates that more radiation is delivered than indicated by the MU setting. Similarly a positive x intercept indicates that less radiation is delivered than indicated by the MU setting. The end effect should be determined for each energy and 368

ACCEPTANCE TESTS AND COMMISSIONING MEASUREMENTS modality on the treatment unit. For teletherapy units and orthovoltage X ray units this effect is referred to as the shutter error. An alternative means of determining the end effect is the multiple start– stop method. With this technique an ionization chamber is placed in the beam and irradiated for a given time or number of MUs. The irradiation is repeated for the same time or number of MUs, but with the irradiation interrupted a fixed number of times. If there is no end effect, the collected ionization should be the same for both irradiations. If the collected ionization is less for the irradiation that was interrupted, less radiation is delivered than indicated by the monitor setting. The end effect can be calculated from the following relationship: Ê I - I1 ˆ a = Á n ˜ T (10.2) Ë nI 1 - I n ¯ where a is the end effect; In is the ionization collected after (n – 1) interruptions; I1 is the ionization collected after no interruptions; T is the total MUs or timer setting. Note that a negative end effect determined with the multiple start–stop method corresponds to a positive x intercept determined from plotting the data for different monitor settings. In both instances less radiation is delivered than indicated by the monitor setting. Most linac manufacturers design the monitor chamber to be either sealed so that the monitor chamber calibration is independent of temperature– pressure fluctuations or with a temperature–pressure compensation circuit. The effectiveness of either method should be evaluated by determining the long term stability of the monitor chamber calibration. This evaluation can be performed during commissioning by measuring the output each morning in a plastic phantom in a set-up designed to reduce set-up variations and increase precision of the measurement. Linacs usually provide the capability of irradiating at several different dose rates. Different dose rates may change the collection efficiency of the monitor ionization chamber, which would change the calibration (cGy/MU) of the monitor ionization chamber. The calibration of the monitor ionization chamber should be determined at all available dose rates of the treatment unit. The constancy of output with the gantry angle should also be verified. 369

CHAPTER 10 10.3.3.9. Arc therapy The verification of the arc or rotational therapy specification is accom- plished by setting a number of MUs on a linac or time on a 60Co unit and a number of degrees for the desired arc. Radiation is then initiated. Termination of radiation and treatment unit motion should agree with the specification. Typical values are within 1 MU and 3º of the set values. This test should be performed for all energies and modalities of treatment and over the range of arc therapy geometry for which arc therapy will be used. 10.4. COMMISSIONING Commissioning of an external beam radiotherapy or brachytherapy device includes a series of tasks that generally should consist of the following: ● Acquiring all radiation beam data (including beam output) required for treatment; ● Organizing these data into a dosimetry data book; ● Entering these data into a computerized treatment planning system (TPS); ● Developing all dosimetry, treatment planning and treatment procedures; ● Verifying the accuracy of these procedures; ● Establishing quality control tests and procedures; ● Training all personnel. An abbreviated commissioning process will be required following any major repair of the unit. 10.4.1. Photon beam measurements 10.4.1.1. Central axis percentage depth doses Typically the first commissioning measurements are of the central axis PDDs. To measure these, the surface of the water phantom is placed at the nominal SSD or at the isocentre. The vertical depth of the ionization chamber in the water phantom is determined by measuring from the bottom of the meniscus of the water to the centre of the chamber. Central axis PDD values should be measured over the range of field sizes from 4 × 4 cm2 to 40 × 40 cm2. Increments between field sizes should be no greater than 5 cm, but are typically 2 cm. Measurements should be made to a 370

ACCEPTANCE TESTS AND COMMISSIONING MEASUREMENTS depth of 35 or 40 cm. Field sizes smaller than 4 × 4 cm2 require special attention. Although 0.1 cm3 chambers typically have diameters of 3–4 mm, the length is of the order of 1.5 cm. Owing to a lack of lateral electronic equilibrium and penumbral effects for ionization field sizes smaller than 4 × 4 cm2, the dose varies significantly across the length of the chamber. Detectors of small dimensions are required for these measurements; several solutions are possible. A 0.1 cm3 chamber orientated with its central electrode parallel to the central axis of the beam or a diode may be used in a water phantom. Alterna- tively, it may be possible to use a polystyrene phantom with a parallel-plate chamber that has a small collecting electrode. These techniques should be validated by first measuring a central axis PDD of a 10 × 10 cm2 field and then comparing these results with the results determined with conventional measurement techniques. By comparing the 10 × 10 cm2 depth dose curves obtained with the two methods one can ascertain the validity of the method and the effective point of measurement of the diode or the ionization chamber. Many photon central axis PDDs reveal a shift in zmax towards the surface as the field size increases. This shift results from an increasing number of secondary electrons and photons generated from the increasing surface area of the collimator jaws and the flattening filter. Some of these electrons and photons strike the detector and, since they have a lower energy than the primary photons, they cause a zmax degradation for large field sizes. 10.4.1.2. Output factors The radiation output at zmax, in cGy/MU for a linac and cGy/min for a cobalt unit, increases with an increase in collimator opening or field size. This increase in output can be measured at zmax of each field size. Alternatively, the increase in output can be measured at a fixed depth for each field size and the output at zmax determined by using the appropriate central axis PDD values. Regardless of which measurement technique is used, the increasing output is normalized to the radiation output of the calibration field size, typically a 10 × 10 cm2 field. The resulting ratios are referred to as output factors (or relative dose factors (RDFs) or total scatter factors). Output factors are usually presented graphically as a function of equivalent square fields. This approach assumes that the output for rectangular fields is equal to the output for the equivalent square field. This assumption must be verified by measuring the output for a number of rectangular fields at their zmax. Outputs for rectangular fields with high and low aspect ratios should be measured. If the outputs for rectangular fields vary from the output for their 371

CHAPTER 10 equivalent square fields by more than 2%, it may be necessary to have a table or graph of output factors for each rectangular field. This matter can be further complicated, as linacs may exhibit a dependence on jaw orientation. For example, the output for a rectangular field may depend on whether the upper or lower jaw forms the long side of the field. This effect is sometimes referred to as the collimator exchange effect and should be investigated as part of the commissioning process. Most modern linacs have collimators that open asymmetrically about the central axis of the X ray beam. Treatment with asymmetric fields requires knowledge of the output factors for these fields, if this effect is not accounted for in the TPS. The output factors for asymmetric fields can usually be approx- imated by: [OF(r)]a,y = [OF(r)]sOAR(zmax, y) (10.3) where [OF(r)]a,y is the output factor for an r × r field formed with an asymmetric collimator opening. The central ray of this field is y centimetres from the central axis of the symmetric field. [OF(r)]s is the output factor for an r × r field formed with a symmetric collimator opening and OAR(zmax, y) is the off-axis ratio (OAR) measured at zmax and y centimetres from the central axis of the symmetric field. The collimator scatter factor is measured in air with a buildup cap large enough to provide electronic equilibrium. Typically, these values are normalized to a 10 × 10 cm2 field. A problem arises for small high energy photon field sizes, as the size of the buildup cap approaches or exceeds the size of the field. A significant portion of the measured signal represents scatter occurring in the buildup cap. This scatter has been estimated to be in the range of 1% to 10% of X ray energies between 2 and 30 MV. Using a buildup cap constructed of higher density material such as aluminium or copper may solve the problem. This stratagem reduces the size of the cap, permitting measurement of fields down to 4 × 4 cm2. Alternatively the collimator scatter correction factor may be determined by placing the ionization chamber at an extended SSD but with the field defined at the nominal SSD. With the chamber at 200 cm the collimator scatter correction factor can be measured for fields with dimensions down to 4 × 4 cm2 at 100 cm. These relative measurements should all be performed under the same conditions. In other words, if one chooses to measure with a high density buildup cap, measurements for all field sizes should be performed with the same buildup cap. As the output factor is the product of the collimator scatter correction factor and the phantom scatter correction factor, the phantom scatter 372

ACCEPTANCE TESTS AND COMMISSIONING MEASUREMENTS correction factor may be found by dividing the output factor by the collimator scatter correction factor. 10.4.1.3. Blocking tray factors Most treatment units have collimators that form rectangular fields. Since treatment volumes are rarely rectangular, high density shielding blocks are used to protect normal critical structures within the irradiated area. The blocks are either individually designed blocks fabricated from a low melting point alloy, such as Lipowitz’s alloy, or standard ‘library’ blocks that may be purchased from the vendor of the treatment machine. In either case these blocks are supported on a plastic tray to correctly position them within the radiation field. This tray attenuates the radiation beam. The amount of beam attenuation provided by the tray must be known to calculate the dose received by the patient. The attenuation for solid trays is easily measured by placing an ionization chamber on the central axis of the beam at 5 cm depth in a phantom in a 10 × 10 cm2 field. The ratio of the ionization chamber signal with the tray in the beam to the signal without the tray is the blocking tray transmission factor. Although the tray transmission factor should be measured for several depths and field sizes, this factor usually has only a weak dependence on these variables and typically one may use one value for all depths and field sizes. 10.4.1.4. Multileaf collimators On most current treatment machines multileaf collimators (MLCs) are finding widespread application for conventional field shaping as a replacement for shielding blocks. The advantages of an MLC include a reduction in the amount of storage space needed in the treatment room, elimination of the need for the treatment technologists to lift heavy blocks and the ability to treat multiple fields without re-entering the treatment room. Disadvantages include the discrete step size of the leaves and additional quality assurance require- ments. Additional data are also required to characterize the output factors, central axis PDDs and penumbra of the MLC fields and the leakage through and between the leaves. Typically the central axis PDDs of MLC defined fields are not signifi- cantly different from fields defined with collimator jaws. The penumbra of MLC defined fields should be measured for both the leaf ends and edges. The penumbra will depend on the leaf design and on whether the leaves are singly or doubly focused. Generally, the MLC penumbra is within 2 mm of the penumbra of fields defined with collimator jaws, with the greatest difference 373

CHAPTER 10 being for singly focused MLC fields not centred on the collimator axis of rotation. The output factor for fields shaped by MLC systems added downstream from the conventional four jaw collimator system are closely approximated by the product of the collimator scatter factor for the collimator setting and the phantom scatter factor for the irradiated area. This relation is the same as for fields formed with conventional blocks. Some MLC systems replace at least one set of conventional jaws. For these MLC systems the product of the collimator scatter factor and phantom scatter factor for the irradiated area approximates the output factor. Of course, the physicist should verify these relationships for central axis PDDs, penumbra and output factors on each machine. Leakage through the MLC consists of transmission through the leaves and leakage between the leaves. Leakage between the leaves is easily demon- strated by exposing a film placed perpendicularly to the collimator axis of rotation with the leaves fully closed. Leakage through the leaves can be determined by comparing the umbra region of transverse beam profiles for fields defined by the MLC with fields defined by the collimator jaws. Typical values of MLC leakage through the leaves are in the range of 3% to 5% of the isocentre dose. 10.4.1.5. Central axis wedge transmission factors Wedges are used to shape the dose distribution of radiation treatment fields. The central axis wedge transmission factor is the ratio of the dose at a specified depth on the central axis of a specified field size with the wedge in the beam to the dose for the same conditions without the wedge in the beam. Central axis wedge transmission factors determined for one field size at one depth are frequently used to calculate beam-on times or MU settings for all wedged fields and depths. However, central axis wedge transmission factors may be a function of both depth and field size. The field size variation may depend not only on the width of the field along the gradient of the wedge but also on the length of the field. In other words, the central axis wedge transmission factor for a given wedge for a 10 × 10 cm2 field may differ from the central axis wedge transmission factor for a 10 × 20 cm2 field even when the 10 cm is along the wedge gradient in both cases. These dependencies require measuring central axis PDDs with the wedge in the beam for a range of field sizes. The dose with the wedge in the beam can then be related to the calibrated dose rate by measuring the central axis wedge transmission factor at one depth for each field size. 374

ACCEPTANCE TESTS AND COMMISSIONING MEASUREMENTS To measure the central axis wedge transmission factor for a given field size at one depth the ionization chamber should be placed on the central axis of the beam with its axis aligned parallel to a constant thickness of the wedge. Measurements should be performed with the wedge in its original position and with the wedge rotated through 180º. This set of measurements verifies that the wedge and the ionization chamber are correctly positioned. The wedge position may be rotated through 180º by rotating the collimator or by rotating the wedge itself. Rotation of the wedge itself reveals whether the side rails are symmetri- cally positioned about the collimator axis of rotation. Rotation of the collimator verifies that the ionization chamber is positioned on the collimator axis of rotation. The measured values should be the same for the two wedge orientations. If the values differ by more than 5% for a 60º wedge or 2% for a 30º wedge, then the wedge or ionization chamber is not positioned correctly and the situation should be corrected. Otherwise it is usually adequate to take the average value of the two wedge orientations as the correct value. 10.4.1.6. Dynamic wedge Linacs are available with an option allowing independent movement of the collimator jaws. This option may be used to create wedged shaped dose distributions by moving one of the independent collimator jaws while the opposite jaw remains stationary during irradiation. This technique is referred to as a dynamic wedge. Clinical implementation of dynamic wedges requires measurement of central axis PDDs, central axis wedge transmission factors and transverse beam profiles of the dynamic wedges. These measurements are complicated by the modulation of the photon fluence during the delivery of the radiation field. The central axis PDD may be measured by integrating the dose at each point during the entire irradiation of the dynamic wedge field. The central axis wedge transmission factors are determined by taking the ratio of the collected ionization at a specified depth for the dynamic wedge field to the collected ionization at the same specified depth for the open field with the same collimator and MU settings. It is important to note that the central axis wedge transmission factors for dynamic wedges may have much larger field size dependence than physical wedges and the field size dependence for dynamic wedges may not be asymptotic. Some manufacturers’ implementations of the dynamic wedge technique show a significant change in the trend of the central axis wedge transmission factor as the field width changes between 9.5 and 10 cm. This change in the central axis wedge transmission ratio has been demonstrated to 375

CHAPTER 10 approach 20%. This characteristic should be carefully investigated on each machine. Dynamic wedge transverse beam profiles can be measured with a detector array or an integrating dosimeter such as radiochromic film. When a detector array is used, the sensitivity of each detector must be determined. 10.4.1.7. Transverse beam profiles/off-axis energy changes The distribution of dose at any point within a radiation beam is required to be known for treatment planning. Transverse beam profiles are measured to characterize the dose at points off the central axis. Frequently off-axis data are normalized to the dose on the central axis at the same depth. These data are referred to as OARs, which are combined with central axis data to generate isodose curves. The number of profiles and the depths at which these profiles are measured will depend on the requirements of the TPS. Some systems require these profiles at a few equally spaced depths, others require several profiles at specified depths and some require only one off-axis profile for the largest field size measured in air with a buildup cap. Transverse beam profiles should be measured in addition to those on which the beam model was determined to verify the accuracy of the TPS algorithms. Of course, these profiles should be measured for both open and wedged fields. The profiles of the wedged field can then be combined with the central axis PDD values for wedged fields to generate wedged isodose curves. Any change in wedge factor (WF) with depth is then included in the isodose curves. 10.4.1.8. Entrance dose and interface dosimetry Knowledge of interface dosimetry, such as the entrance dose between the patient surface and zmax, is important in a variety of clinical situations. Other areas of interface dosimetry that may be important are interfaces at small air cavities such as the nasopharynx, at the exit surface of the patient, at bone– tissue interfaces and between a metallic prosthesis and tissue. These measurements are usually time consuming because they are not easily automated with a water phantom and scanner. The rapidly changing dose gradient demands measurement with a thin window parallel-plate chamber. The requirement for a thin window makes water phantom measurements difficult because of the need to waterproof the chamber and to avoid deformation of the window by hydrostatic pressure. Measurements are typically carried out in a polystyrene phantom in a constant SSD geometry. They begin with the block containing the chamber upstream, backed by two 5 cm blocks of backscattering material with all the 376

ACCEPTANCE TESTS AND COMMISSIONING MEASUREMENTS buildup sheets placed downstream from these blocks. The first measurement is made with no buildup material upstream from the chamber. The next depth is measured by moving the appropriate sheet of buildup material from the bottom to the top of the phantom. This scheme maintains a constant SSD as buildup material is added. Interface dosimetry measurements should always be performed with both polarities on the entrance window of the ionization chamber. Large differences in the signal at the interface will be observed when the polarity is reversed. Measurements further from the interface exhibit smaller differences than measurements nearer the interface. For depths beyond the transition zone readings with either polarity should be the same. The true value QT of the measured ionization at each depth is: QT = (Q+ – Q–)/2 (10.4) The positive or negative signs refer to the polarity of the signal, and the sign of the signal is maintained in this operation. The value computed with Eq. (10.4) is the same as the average of the absolute magnitudes of Q+ and Q–, unless they have the same sign. This will occur in low signal to noise situations in which the cable or stem contributes a significant spurious current that does not change sign with a change in polarity, while the true signal from the sensitive volume of the chamber does change sign with a change in polarity. 10.4.1.9. Virtual source position Knowledge of the virtual source position is required for treatment at extended SSDs. A common technique to determine the virtual source position is to make in-air ionization measurements at several distances from the nominal source position to the chamber. The data are plotted with the distance to the nominal source position on the x axis and the reciprocal of the square root of the ionization on the y axis. These data should follow a straight line; if not, the radiation output does not follow the inverse square law. If the straight line passes through the origin, the virtual and nominal source positions are the same. If the straight line has a positive x intercept, the virtual source position is downstream from the nominal source position, while a negative x intercept indicates an upstream virtual source position. For example, consider a machine with a nominal source to axis distance (SAD) of 100 cm. Assume for this machine that these measurements demon- strated that the reciprocal of the square root of the measured ionization followed a straight line but that the x intercept was +1 cm. This situation reveals 377

CHAPTER 10 that the inverse square law applies but that the virtual source is 99 cm from the isocentre. In this case the inverse square calculation should be from 99 cm rather than 100 cm. This analysis should be performed for the range of field sizes, as collimator scatter may change the virtual source position. Of course, if the data do not follow a straight line, the inverse square law is not applicable and special calibrations will be required at each distance. Measurement of the beam divergence at various distances from the source is a less commonly used technique to determine the virtual source position. This measurement is performed by exposing films orientated perpen- dicularly to the central axis of the beam at a depth of zmax. The full width at half maximum (FWHM) of the beam is determined at each distance. The FWHM at each distance can be plotted and will form a straight line if the inverse square law is valid. The x intercept indicates the virtual source position. This measurement should be performed for a range of field sizes. One problem is that the range of field sizes and distances for which this technique may be used is limited by the size of the film. 10.4.2. Electron beam measurements 10.4.2.1. Central axis percentage depth dose Electron central axis PDD values have been measured with cylindrical and parallel-plate ionization chambers, diodes and film; however, the ionometric method remains the gold standard. The effective point of measurement for parallel-plate chambers is the inside surface of the entrance window. The effective point of measurement with cylindrical chambers, on the other hand, is shifted from the centre of the chamber, and the shift is one half the inside radius of the cavity towards the source. Cylindrical chambers perturb the electron fluence more than parallel- plate chambers. This perturbation is corrected with a replacement correction. This factor is less than 1 for cylindrical chambers, and the value of the factor decreases (further from unity) as the energy of the electron beam decreases and the depth in the phantom increases. Most thin window parallel-plate chambers with a plate separation of 2 mm or less have a replacement correction of unity. However, some of these chambers have a replacement correction different from unity. The replacement factor is dependent on the guard ring design, as well as on the plate separation distance. Chambers with narrow guard rings tend to have replacement factors further removed from unity than those with wider guard rings. 378

ACCEPTANCE TESTS AND COMMISSIONING MEASUREMENTS Parallel-plate chambers can be difficult to waterproof if used in a water phantom. Hydrostatic pressure in a water phantom can also deform a thin entrance window of a parallel-plate chamber if a thin waterproof sheath is used. This deformation changes the chamber’s sensitivity. Use of a parallel-plate chamber in a phantom can lead to a dosimetric mismatch if the phantom material differs from the material of the chamber. This mismatch can result in a change in the number of backscattered electrons with the chamber in place from what would occur in a homogeneous phantom. Depending on the materials involved this change may be either an increase or a decrease. Medical physics societies recommend calibration of low energy electrons with specially designed parallel-plate chambers, because the replacement correction factor is much more significant for cylindrical chambers for electrons less than 10 MeV. Higher energy electrons can be measured with cylindrical chambers. Water is the phantom material generally recommended for high energy electrons, because it is nearly tissue equivalent and has uniform composition regardless of its origin. Plastic phantoms are recommended for low energy electron measure- ments with a thin window parallel-plate chamber that cannot be readily water- proofed, in order to prevent hydrostatic deformation of the window. Plastic phantoms are also useful for film dosimetry measurements. Several plastic materials are acceptable for phantoms. However, these plastics are not exactly water equivalent (i.e. they do not necessarily have the same linear collision and radiative stopping powers and the same linear angular scattering power as water). This lack of exact water equivalence requires that depths of measurements made in plastic phantoms be corrected to water equivalent depths by scaling. The AAPM TG 25 dosimetry protocol recommends a scaling factor based on the ratios of the depth of the 50% ionization measured in the two materials: z water = zmed (R 50 /R 50 ) water med (10.5) where zwater is the depth in water that is equivalent to the measurement depth zmed; water R50 is the depth of the 50% ionization in water; med R50 is the depth of the 50% ionization in a phantom medium. In reference to plastic phantoms, it must be noted that polystyrene is an ambiguous term. Some medical physicists refer to clear polystyrene as 379

CHAPTER 10 polystyrene and to white polystyrene with a 3% loading of TiO2 as ‘high impact’ polystyrene. Other physicists refer to white polystyrene as polystyrene and to the clear version as clear polystyrene. When using tables for depth scaling factors one should ascertain which polystyrene is listed. Also, the density of any plastic should be verified, as it can vary between production batches. Additionally, unlike photons, electron percentage depth ionization curves are not equivalent to PDD curves. Electron ionization measurements must be multiplied by the replacement factor and the restricted mass stopping power ratio to determine dose. These factors are energy dependent, and thus depth dependent, because the electron beam loses energy as it penetrates the phantom. The therapeutic dose is frequently chosen to be the 90% dose at a depth beyond the depth of dose maximum zmax. For fields with dimensions similar to or smaller than the range of the electrons, loss of side scatter equilibrium will result in a shift of the depth of zmax towards the surface and a decrease in the depth of the 90% dose. The range will remain approximately the same as for larger fields. For field sizes larger than the range, the depth of the therapeutic dose remains constant. The electron PDD should be measured in field size increments small enough to permit accurate interpolation to intermediate field sizes. Although skin sparing is much less than for photon beams, skin dose remains an important consideration in many electron treatments. Surface dose is best measured with a thin window parallel-plate ionization chamber. The central axis PDD should be measured to depths large enough to determine the bremsstrahlung contamination in the beam. 10.4.2.2. Output factors The radiation output (cGy/MU) is a function of field size and is determined at zmax at the standard SSD. The output is measured with a small volume ionization chamber at zmax on the central axis of the field. The output depends on the method used to define the field. Three types of collimation are used to define an electron field: secondary collimators (cones) in combination with the X ray jaws; irregularly shaped lead or low melting point alloy metal cut-outs placed in the secondary collimators; and skin collimation. (a) Secondary collimators Cones, or electron collimators, are available for a limited number of square fields, typically 5 × 5 cm2 to 25 × 25 cm2 in 5 cm increments. Circular and rectangular cones are available, but they are not as common as square cones. 380

ACCEPTANCE TESTS AND COMMISSIONING MEASUREMENTS The purpose of the cone depends on the manufacturer. Some use cones only to reduce the penumbra, while others use the cone to scatter electrons off the side of the cone to improve field flatness. The output for each cone must be determined for all electron energies. These values are frequently referred to as cone ratios rather than output factors. (b) Metal cut-outs Irregularly shaped electron fields are formed by placing metal cut-outs of lead or low melting point alloy in the end of the cone nearest the patient. The penumbra produced by these cut-outs is essentially the same as the penumbra produced by the cones themselves. A thickness of 12 mm of a low melting point alloy, such as Lipowitz’s metal, is adequate for electrons up to 20 MeV. The output factors for fields defined with these cut-outs depend on the electron energy, the cone and the area of the cut-out. The dependence of output should be determined for square field inserts down to 4 × 4 cm2 for all energies and cones. As with photons, fields smaller than 4 × 4 cm2 require special precautions because the size of the ionization chamber may approach the size of the field, and smaller detectors are required. A parallel-plate chamber with a small collecting electrode may be used in a polystyrene phantom or a diode used in a water phantom. In either case the same set-up should be used to measure both the small field and the 10 × 10 cm2 field. Since zmax shifts towards the surface in electron fields with dimensions smaller than the range of the electrons, it must be determined for each small field size when measuring output factors. The output factor is the ratio of the dose at zmax for the small field to the dose at zmax for the 10 × 10 cm2 field. For ionometric data this requires converting the ionization to the dose at each zmax before determining the output factor, rather than simply taking the ratio of the ionizations. If central axis PDD data measured with diodes agree with the central axis PDD data determined from ionometric data, the diode data can be used directly to determine the depth of zmax. Use of film is an alternative solution. It can be exposed in a polystyrene or water equivalent plastic phantom in an orientation parallel to the central axis of the beam. One film should be exposed to a 10 × 10 cm2 field, the other film to the smaller field. The films should be scanned to find the central axis zmax for each field. The ratio of the dose at zmax of the small field to the dose at zmax of the large field is the output factor. This requires that the dose has been determined from the net OD with a characteristic curve and that good agreement has been demonstrated between the PDD measured with film to that determined from ionization chamber data for a 15 × 15 cm2 field. 381

CHAPTER 10 The output factor (or cone ratio) is a function of energy, cone size and insert size. Typically, all values are normalized to an open 10 × 10 cm2 cone. For rectangular fields formed by placing inserts in cones the equivalent square can be approximated with a square root method. The validity of this method should be checked on each machine for which the approximation is used. OF(E, x, y, f) = [OF(E, x, x, f) × OF(E, y, y, f)]1/2 (10.6) where f is the SSD; OF(E, x, y, f) is the output factor for an x cm × y cm rectangular field of energy E; OF(E, x, x, f) is the output factor for an x cm × x cm rectangular field of energy E; OF(E, y, y, f) is the output factor for a y cm × y cm rectangular field of energy E. (c) Skin collimation Skin collimation is used to minimize the penumbra for very small electron fields, to protect critical structures near the treatment area and to restore the penumbra when treatment at an extended distance is required. When designing skin collimation the cone insert chosen should be larger than the area to be treated. The skin collimation then collimates this larger field to the treatment area. The skin collimation should also extend a distance beyond the area collimated by the cone insert, to protect the patient from scattered electrons. The thickness required for any electron shielding can be estimated by: tpb (mm) = 0.5Ep,0 (MeV) + 1 for lead and tLm (mm) = 1.2tpb (mm) for Lipowitz’s metal (10.7) where Ep,0 (MeV) is the most probable electron energy at the surface of the patient; tpb (mm) is the thickness of the lead; tLm (mm) is thickness of Lipowitz’s metal. Some clinical situations may require minimizing the weight of the skin collimation on the patient, resulting in somewhat thinner masks. In these situations it is recommended that the degree of shielding be assessed. This 382

ACCEPTANCE TESTS AND COMMISSIONING MEASUREMENTS assessment can be performed with a thin window parallel-plate chamber in a polystyrene phantom at a depth of 1 mm. As for any small field, skin collimation may affect the PDD as well as the penumbra if the dimensions of the treatment field are smaller than the electron range. The field size dependence of the PDD is principally a result of scattering in the patient. The PDD for a field defined by skin collimation can be approximated as the PDD of the field determined by secondary collimation, such as a cone. The field size dependence of the output results from electron scattering from the X ray jaws and in air. In most cases for cones that are 5 cm or more from the skin, the output for a field defined with skin collimation is the same as the output defined by the secondary collimator for that treatment. However, if the skin collimation defines a field so small that the PDD changes, then the output may be affected and a measurement may be required. 10.4.2.3. Transverse beam profiles As for photon beams, transverse electron beam profiles are measured to determine the off-axis dose distribution of electron beams. This information is combined with the central axis PDD to yield the isodose distribution. The number of transverse profiles and the depths at which they must be measured depend on the requirements set by the treatment planning computer. These profiles are measured in a water phantom with a small volume ionization chamber. The surface of the phantom is placed at 100 cm or the nominal SSD and the ionization chamber is scanned perpendicularly to the central axis. An alternative film dosimetry technique is to measure isodose curves rather than beam profiles. The film is exposed parallel to the central axis of the beam. Optical isodensity is converted to isodose. However, the PDD determined with film is typically 1 mm shallower than ionometric determi- nation for depths greater than 10 mm, and for depths shallower than 10 mm the differences may be as great as 5 mm. Isodose curves may also be measured with small volume ionization chambers or diodes. 10.4.2.4. Virtual source position Frequently, electron fields must be treated at extended distances because the surface of the patient prevents positioning of the electron applicator at the normal treatment distance. A common example of this occurs during the treatment of posterior neck fields for head and neck carcinoma. The shoulder typically interferes with positioning of the electron applicator at the normal 383

CHAPTER 10 treatment distance to the neck. Additional scattering in the extended air path increases the penumbral width and decreases the output (cGy/MU). Knowledge of the virtual electron source is required to predict these changes. The virtual source position is the point from which the electrons appear to emanate. Determination of the virtual source position is similar to the verification of the inverse square law for photons. Treatment planning computers use the virtual source position to calculate the divergence of electron beams at extended SSDs. Correction of the output at an extended SSD requires an air gap correction factor in addition to the inverse square factor. The air gap factor corrects the deviations from the inverse square law resulting from the collimator and air scatter of the electrons. The air gap correction factor may be either greater or less than unity, as the output may either increase or decrease at extended distances, depending on the collimator design, electron energy, field size and air gap. However, for SSDs up to 110 cm and energies up to 25 MeV this correction is typically less than 2%. There can be significant changes in the PDD at extended SSDs if the electron cone scatters electrons to improve the field flatness. For these machines it may be necessary to measure isodose curves over a range of SSDs. Treatment at an extended SSD will also increase the penumbra width. At lower energies the width of the penumbra (the distance between the 80% and 20% dose values on a beam profile normalized to 100% on the central axis) increases approximately proportionally with the air gap. As electron energy increases the increase in the penumbra width is less dramatic at depth than for lower energies, but at the surface the increase in penumbra remains approxi- mately proportional to the air gap. Since a large number of clinical situations demand treatment at an extended SSD, it is advisable to measure a sample of isodose curves at extended SSDs to evaluate the algorithms in the TPS in use. The penumbra can be restored when treating at extended distances by the use of skin collimation, as discussed in Chapter 9. 10.5. TIME REQUIRED FOR COMMISSIONING Acceptance testing and commissioning of megavoltage treatment units has been discussed in this chapter. The completion of all the tasks associated with placing a treatment unit in clinical service can be estimated to require from 1.5 weeks to 3 weeks per energy following completion of the acceptance tests. The time will depend on machine reliability, amount of data measurement, sophistication of the treatments planned and experience of the physicist. Highly specialized techniques, such as stereotactic radiosurgery, 384

ACCEPTANCE TESTS AND COMMISSIONING MEASUREMENTS intraoperative treatment, intensity modulated radiotherapy (IMRT) and total skin electron treatment, have not been discussed and are not included in these time estimates. Commonly used methods to estimate data that have not been measured from measured data have been discussed. The accuracy of all these techniques must be verified on each machine, as variations exist between machines. BIBLIOGRAPHY FOOD AND AGRICULTURE ORGANIZATION OF THE UNITED NATIONS, INTERNATIONAL ATOMIC ENERGY AGENCY, INTERNATIONAL LABOUR ORGANISATION, OECD NUCLEAR ENERGY AGENCY, PAN AMERICAN HEALTH ORGANIZATION, WORLD HEALTH ORGANIZATION, International Basic Safety Standards for Protection against Ionizing Radiation and for the Safety of Radiation Sources, Safety Series No. 115, IAEA, Vienna (1996). INTERNATIONAL ELECTROTECHNICAL COMMISSION, Safety of Medical Electrical Equipment, Part 2: Particular Requirements for Medical Electron Accelerators in the Range 1 MeV to 50 MeV, Section 1: General, Section 2: Radiation Safety for Equipment, IEC 601-2-1, IEC, Geneva (1996). PODGORSAK, E.B., METCALFE, P., VAN DYK, J., “Medical accelerators”, Modern Technology of Radiation Oncology: A Compendium for Medical Physicists and Radiation Oncologists (VAN DYK, J., Ed.), Medical Physics Publishing, Madison, WI (1999). 385

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Chapter 11 COMPUTERIZED TREATMENT PLANNING SYSTEMS FOR EXTERNAL PHOTON BEAM RADIOTHERAPY M.D.C. EVANS Department of Medical Physics, McGill University Health Centre, Montreal, Quebec, Canada 11.1. INTRODUCTION Computerized treatment planning systems (TPSs) are used in external beam radiotherapy to generate beam shapes and dose distributions with the intent to maximize tumour control and minimize normal tissue complications. Patient anatomy and tumour targets can be represented as 3-D models. The entire process of treatment planning involves many steps and the medical physicist is responsible for the overall integrity of the computerized TPS to accurately and reliably produce dose distributions and associated calculations for external beam radiotherapy. The planning itself is most commonly carried out by a dosimetrist, and the plan must be approved by a radiation oncologist before implementation in actual patient treatments. Treatment planning prior to the 1970s was generally carried out through the manual manipulation of standard isodose charts on to patient body contours that were generated by direct tracing or lead wire representation, and relied heavily on the judicious choice of beam weight and wedging by an experienced dosimetrist. The simultaneous development of computed tomography (CT), along with the advent of readily accessible computing power from the 1970s on, led to the development of CT based computerized treatment planning, providing the ability to view dose distributions directly superimposed upon a patient’s axial anatomy. The entire treatment planning process involves many steps, beginning from beam data acquisition and entry into the computerized TPS, through patient data acquisition, to treatment plan generation and the final transfer of data to the treatment machine. Successive improvements in treatment planning hardware and software have been most notable in the graphics, calculation and optimization aspects of current systems. Systems encompassing the ‘Virtual Patient’ are able to display 387

CHAPTER 11 beam’s eye views (BEVs) of radiation beams and digitally reconstructed radiographs (DRRs) for arbitrary dose distributions. Dose calculations have evolved from simple 2-D models through 3-D models to 3-D Monte Carlo techniques, and increased computing power continues to increase calculation speed. Traditional forward based treatment planning, which is based on a trial and error approach by experienced professionals, is giving way to inverse planning, which makes use of dose optimization techniques to satisfy the user specified criteria for the dose to the target and critical structures. Dose optimi- zation is possible by making use of dose–volume histograms (DVHs) based on CT, magnetic resonance imaging (MRI) or other digital imaging techniques. These optimized plans make use of intensity modulated radiotherapy (IMRT) to deliver the required dose to the target organ while respecting dose constraint criteria for critical organs. Computerized treatment planning is a rapidly evolving modality, relying heavily on both hardware and software. Thus it is necessary for related profes- sionals to develop a workable quality assurance programme that reflects the use of the TPS in the clinic and that is sufficiently broad in scope to ensure proper treatment delivery. 11.2. SYSTEM HARDWARE 11.2.1. Treatment planning system hardware The principal hardware components of a TPS include a central processing unit (CPU), a graphics display, memory, digitizing devices, output devices, and archiving and network communication devices. As hardware capabilities tend to change quickly, the general approach is to acquire equipment having the highest current specifications while allowing for future upgrades. The CPU must have at least the memory and processor speed required by the operating system and treatment planning software. In particular, the speci- fications for the system speed, random access memory (RAM) and free memory, as well as networking capabilities, must be considered. The graphics display is normally sufficient for accommodating the patient transverse anatomy on a 1:1 scale, typically 17–21 in. (43–53 cm) or larger. The resolution is submillimetre or better so as not to distort the input. Graphics speed can be enhanced with video cards and hardware drivers. Memory and archiving functions are carried out through either removable media or networking. Removable media may include floppy disks, rewritable hard disks, optical disks or digital video disks (DVDs). Mass 388