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IPEM–IOP Series in Physics and Engineering in Medicine and Biology
Quantitative
Radiobiology for
Proton Therapy
Bleddyn Jones
With contribution from Joshua Moore
Quantitative Radiobiology
for Proton Therapy
Online at: https://doi.org/10.1088/978-0-7503-6209-2
IPEM–IOP Series in Physics and Engineering in Medicine and Biology
Editorial Advisory Board Members
Frank Verhaegen
Maastro Clinic, The Netherlands
Kwan Hoong Ng
University of Malaya, Malaysia
Carmel Caruana
University of Malta, Malta
Penelope Allisy-Roberts
formerly of BIPM, Sèvres, France
Rory Cooper
University of Pittsburgh, PA, USA
Alicia El Haj
University of Birmingham, UK
John Hossack
University of Virginia, USA
Tingting Zhu
University of Oxford, UK
Dennis Schaart
TU Delft, The Netherlands
Indra J Das
Northwestern University Feinberg School
of Medicine, USA
About the Series
The series in Physics and Engineering in Medicine and Biology will allow the Institute
of Physics and Engineering in Medicine (IPEM) to enhance its mission to ‘advance
physics and engineering applied to medicine and biology for the public good’.
It is focused on key areas including, but not limited to:
• clinical engineering
• diagnostic radiology
• informatics and computing
• magnetic resonance imaging
• nuclear medicine
• physiological measurement
• radiation protection
• radiotherapy
• rehabilitation engineering
• ultrasound and non-ionising radiation.
A number of IPEM–IOP titles are being published as part of the EUTEMPE
Network Series for Medical Physics Experts.
A full list of titles published in this series can be found here: https://iopscience.iop.
org/bookListInfo/physics-engineering-medicine-biology-series.
Quantitative Radiobiology
for Proton Therapy
Bleddyn Jones
Gray Institute, University of Oxford Department of Oncology, Old Road Campus,
Roosevelt Drive, Oxford OX37DQ
With contribution from
Joshua Moore
University of Oxford Mathematical Institute, Woodstock Road, Oxford OX2 6 GG
IOP Publishing, Bristol, UK
ª IOP Publishing Ltd 2024
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system
or transmitted in any form or by any means, electronic, mechanical, photocopying, recording
or otherwise, without the prior permission of the publisher, or as expressly permitted by law or
under terms agreed with the appropriate rights organization. Multiple copying is permitted in
accordance with the terms of licences issued by the Copyright Licensing Agency, the Copyright
Clearance Centre and other reproduction rights organizations.
Permission to make use of IOP Publishing content other than as set out above may be sought
at permissions@ioppublishing.org.
Bleddyn Jones and Joshua Moore have asserted their right to be identified as the authors of this
work in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988.
ISBN 978-0-7503-6209-2 (ebook)
ISBN 978-0-7503-6207-8 (print)
ISBN 978-0-7503-6210-8 (myPrint)
ISBN 978-0-7503-6208-5 (mobi)
DOI 10.1088/978-0-7503-6209-2
Version: 20240701
IOP ebooks
British Library Cataloguing-in-Publication Data: A catalogue record for this book is available
from the British Library.
Published by IOP Publishing, wholly owned by The Institute of Physics, London
IOP Publishing, No.2 The Distillery, Glassfields, Avon Street, Bristol, BS2 0GR, UK
US Office: IOP Publishing, Inc., 190 North Independence Mall West, Suite 601, Philadelphia,
PA 19106, USA
To the late Dr OCA Scott MD (Cantab) FRCR1, who inspired so many scientists and
clinicians, gave freely of his ideas and was such a generous benefactor. Also to my
mother, Mary Margaret Jones, for her patient care over many years and to my late
father, Emlyn John Jones BSc (Wales), CEng for his personalised teaching.
1
The interesting scientific career of Dr OCA Scott is summarised in two obituaries:
1. Jones B and Hendry J 2017 Professor Jack Fowler and Sir Oliver Scott Br. J Radiol. 90 20160904.
2. Trott K-R 2016 Radiother. Oncol. 121 480–481.
Contents
Preface xiv
Acknowledgements xviii
Author biographies xix
Glossary of the main terms and symbols used (some others are
given in specific chapters)
xx
1 Particle physics for biological interactions 1-1
1.1 Physical beam parameters, essential dosimetry and reference
(or control) radiation requirements for RBE studies
1.1.1 Straggling and fragmentation 1-6
1.1.2 Separation of charged particles with increasing tissue depth 1-6
1.1.3 Particle accelerators 1-7
1.1.4 Proton range uncertainties 1-9
1.2 Physics interacting with biology 1-10
1.2.1 Relative biological effect 1-10
1.2.2 Choice of the control (or reference) radiation source 1-12
1.2.3 Can RBE reduce with the depth of the SOBP placement
in the case of passively scattered but not pencil
scanned beams?
References 1-21
1-1
1-15
2 The essential radiobiology background 2-1
2.1 Introduction 2-1
2.2 Background and models 2-1
2.2.1 The linear quadratic model 2-1
2.2.2 Model variants 2-5
2.2.3 Biological effective dose 2-6
2.2.4 Repopulation allowances 2-7
2.2.5 Biological effective dose and repopulation 2-8
2.2.6 BED expression of high-LET radiation 2-9
2.2.7 Dose rate, total fraction treatment time and incomplete repair
between treatment fields
2.2.8 Closely spaced fractions 2-18
2.2.9 Hypoxia 2-18
2-11
vii
Quantitative Radiobiology for Proton Therapy
2.2.10 Very low doses 2-20
2.2.11 Higher doses per fraction 2-22
2.3 The α/β ratio and its choice for modelling particle therapies 2-26
2.3.1 The α/β ratio 2-28
2.3.2 Applications of BED equations 2-28
2.3.3 Special considerations for particle therapy 2-29
2.4 The design of experiments for RBE determination and other
purposes
References 2-42
2-40
3 Medical and surgical considerations that influence radiation
3-1
tolerances, including interpretation of clinical trials
3.1 Introduction 3-1
3.2 Surgery 3-1
3.3 Cytotoxic chemotherapies 3-3
3.4 Age and other medical conditions 3-3
3.5 Reductions in prescribed dose 3-4
3.6 Interpretation of the case histories and literature 3-5
3.7 Clinical trials 3-5
3.8 Ethical issues 3-6
3.9 Mixed end points 3-7
3.10 The importance of follow-up 3-7
3.11 Publication bias 3-7
References 3-9
4 Treatment planning and further medical perspectives 4-1
4.1 Introduction 4-1
4.1.1 Treatment-planning processes 4-2
4.1.2 The important interaction of RBE issues with the marginal
target volumes
4.1.3 Comparative planning studies 4-6
4.1.4 Trade-off situations in comparative treatment planning 4-8
4.1.5 How to accommodate assumed errors in RBE 4-9
4.1.6 The product of LET and dose 4-11
4.1.7 Some final caveats and suggestions 4-12
References 4-14
4-6
viii
Quantitative Radiobiology for Proton Therapy
5 Historical development of radiotherapy: what was learned
5-1
from fast neutrons including their linkage with proton
relative biological effect
5.1 Introduction 5-2
5.2 A brief synopsis 5-2
5.3 Neutron therapy 5-4
5.4 More recent developments based on neutron studies 5-8
5.5 Estimation of neutron RBE from neutron energy 5-14
5.6 Some important conclusions 5-20
Appendix A 5-21
Appendix B 5-22
References 5-22
6 Fractionation modelling 6-1
6.1 Introduction and background radiobiology 6-1
6.2 A brief history of fractionation 6-3
6.2.1 Radiobiology 6-3
6.2.2 A synopsis of clinical fractionation 6-4
6.3 Modelling of fractionation 6-7
6.3.1 LQ modelling of fractionation in high-LET radiations with
inclusion of RBE
6.3.2 BED equations 6-8
6.3.3 Converting a specific low-LET BED fractionation to that for
high LET, when the low-LET α/β ratio is known, but with
no change in overall treatment time
6.3.4 Overall fractionation differences between low- and high-LET
radiations
6.3.5 Boost doses 6-11
6.3.6 Converting a specific low-LET BED fractionation to that for
high LET, when the low-LET α/β ratio is known, but with a
change in overall treatment time
6.3.7 Alternative approach for isoeffect calculations in the case of
two high-LET schedules
6.3.8 Differences in exposure times 6-15
6.3.9 RBE and dose per fraction: clinical implications 6-16
6.3.10 Effects of regions of higher and lower dose per fraction
relative to the prescribed dose for different fractionation
patterns
6-7
6-9
6-10
6-13
6-13
6-18
ix