H.H. Rossi M. Zaider Microdosimetry and Its Applications

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H.H. Rossi M. Zaider

Microdosimetry and Its Applications

With 128 Figures

Springer

H.H. Rossi Professor emeritus Columbia University 105 Larchdale Avenue Upper Nyack, NY 10960 USA

Dr. M. Zaider Columbia University College of Physicians and Surgeons Radiation Oncology 622 West 168th Street New York, NY 10032 USA

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Rossi, H. H.: Microdosirnetry and its applications / H. H. Rossi; M. Zaider. - Berlin; Heidelberg; New York; Barcelona; Budapest; Hong Kong; London; Milan; Paris; Santa Clara; Singapore; Tokyo: Springer, 1996

ISBN-13: 978-3-64233-85186-5 NE: Zaider. M.:

ISBN-13:978-3-642-85186-5 e-ISBN-13:978-3-642-85184-1 DOl: 10.1007/978-3-642-85184-1

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Preface

Microdosimetry originated more than 35 years ago when the senior author studied energy deposition in small irradiated masses and formulated what is now termed Regional Microdosimetry. A.M. Kellerer developed the further concepts of Structural Microdosimetry. Microdosimetry and its applications have been the subject of an extensive literature. This includes several hundred papers which have appeared in the Proceedings of what to date have been eleven Symposia on Microdosimetry. General reviews are contained in chapters of books and in a journal dealing with a broader range of subjects. The International Commission on Radiation Units and Measurements has produced Report 36 on Microdosimetry. The form of these publications limited their scope and in this work it is our aim to provide a more comprehensive account.

Dealing extensively with interdisciplinary matters (from atomic and solid state physics to integral geometry and molecular biology) we were confronted with the standard problem of presenting material in a manner that makes it comprehensible to readers with diverse backgrounds, without providing a superficial treatise. Although some readers may find it too difficult to absorb the entire contents of some chapters, they should be able to gain substantial information from introductory sections and from data presented. Occasional repetitions, including identical formulae, have reduced the need for cross-references between chapters.

With the exception of chapter III it is recommended to read the book sequentially; this appeared to us to be the logical way of learning microdosimetry. The conceptual framework of microdosimetry is introduced in the first two chapters. At this stage of the presentation the details of energy deposition in matter are unimportant. The fourth and fifth chapter are the twin workhorses of microdosimetry. The fourth chapter is about the art of measuring microdosirnetric spectra. It gives details on the construction and operation of microdosimetric detectors. It also makes aware both the experimentalist and the theorist that what one measures may sometimes be different from the actual pattern of energy deposition. The material in Chapter V, the theoretical companion of the preceding chapter, comes as a result of the tremendous progress made during the past 20 years or so in obtaining cross sections for the interaction of charged particles with matter, and of the subsequent effort made to integrate these into sophisticated Monte Carlo transport codes that simulate the passage of particles through structured or unstructured matter. This chapter also brings forth the two

VI Preface

complementary descriptions of microdosimetric events: regional microdosimetry and structural microdosimetry. The applications of microdosimetry are described in the last two chapters. The selection of topics here reflects the research interests of the authors and also the need to provide this information within the limitations of a single volume. As a result the list of topics here should be seen as illustrative rather than comprehensive.

Chapter III is largely self contained (the only exception is section III.6.2 that makes use of material treated in II.2). The general intention in this chapter was to collect known mathematical expressions that describe the interaction of radiation with matter. An unusual and perhaps to some surprising feature is the Appendix to this chapter which contains a rather advanced formal treatment of the scattering formalism. The reasons for adding this Appendix are twofold: Firstly, the material presented here is important for understanding (and perhaps being able to derive) many of the equations used in Chapters III and V. More importantly however, the treatment presented here is phase-independent (in fact it originates in many-body physics) and as such it is relevant to the gradual replacement of the current gas­based microdosimetry with the study of (relevant) energy depositions in realistic targets such as DNA and protein chains of known sequence, or the structured water that surrounds these biomolecules when in cellular environment. Some examples of these newer results are given in the book.

We have adopted various common simplifications of terminology. Thus the proper term "absorbed dose" is frequently abbreviated to "dose", especially in such expressions as "dose rate" or "dose effect curve". We have found it necessary to employ the same symbol for different quantities if only because of general practice. Thus Q has traditionally stood for both the change of rest mass in nuclear reactions and the quality factor in radiation protection. An effort was made to avoid the converse situation where different symbols refer to the same quantity.

Several chapters from this book have been used by one of us (MZ) to teach microdosimetry to engineering students enrolled in a Master's level graduate program in Medical Physics and Health Physics at Columbia University. In particular, material from Chapter IV is used in conjunction with a laboratory course where students are being familiarized, among other things, with experimental microdosimetry. In the following we recommend a syllabus for a one semester (I3-week) course based on material from this book.

Lecture I: Chapters I and II Lecture II: Sections III. I to III.3 Lecture III: Section IlIA Lecture IV: Sections III.S and 1II.6 Lecture V: Sections IV.I to IV.3 Lecture VI: Sections IVA to IV.7 Lecture VII: Section V.2

Lecture VIII: Section V.3 Lecture IX: Section VA Lecture X: Sections V1.1.1 and VI. 1.2 Lecture XI: Section VI. 1.3 Lecture XII: Section VI.1A Lecture XIII: Section VI.2 and VI.3

New York, 1994

VII Preface

Harald H. Rossi and Marco Zaider

Acknowledgments

We are grateful for the help of several fellow scientists. In particular, we wish to acknowledge the importance of many discussions with Prof. A.M. Kellerer who has made numerous and profound contributions to microdosimetry and its applications in radiobiology and radiation protection.

We are much indebted to Dr. D. Srdoc and Prof. A. Wambersie whose expert comments resulted in improvements of the chapters dealing with experimental microdosimetry and microdosimetry in radiotherapy. Help in the preparation of individual sections was also given by Prof. J.F. Dicello, Dr. P. Goldhagen, Dr. G. Luxton and Prof. P.l McNulty. While the design of the proportional counters described here originated with the senior author they were frequently improved and skillfully executed by Mr. Rudolph Gand - later in collaboration with his worthy successor Gary W. Johnson who also provided the photographs of these instruments.

The final text of the book was cross checked in its entirety for possible inconsistencies of notations and/or textual errors by Ian H. Zaider. He is also responsible for patiently and efficiently renumbering all the equations and figures when single chapters were consolidated in one draft. The efficient help of Ms. Emilia Schneider was essential.

Our deep thanks and appreciation go to all those mentioned above.

New York, 1994

Table of Contents

I Introduction ................................................................................................ 1

1.1 The Role of Microdosimetry ........................................................................ 1 1.2 The Transfer of Energy from Ionizing Radiation to Matter ......................... 2 1.3 Stochastic Quantities .................................................................................... 6 104 Spatial Aspects of Micro dosimetry ............................................................. 10 1.5 Temporal Aspects of Microdosimetry ........................................................ 13

II Microdosimetric Quantities and their Moments ..... ............................... 17

11.1 Definitions .................................................................................................. 17 II.2 Microdosimetric Distributions and their Moments ..................................... 18 11.3 Representations of Microdosimetric Distributions ..................................... 23 1104 Experimental versus Calculated Microdosimetric Distributions ................ 26

III Interactions of Particles with Matter ...................................................... 28

III. 1 Overview .................................................................................................... 28 I1I.2 Quantities and Terms Relating to the Interaction Between

Projectiles and Targets ................................................................................ 29 I1I.3 Kinematics of the Scattering Process .......................................................... 34 IliA Sources of Charged Particles ...................................................................... 39

I1I.4.1 Photon-interaction Cross Sections ................................................ 39 111.4.2 Neutron-interaction Cross Sections ............................................. .44 I1I.4.3 Charged Particles as Sources of other Charged Particles ............ .46

111.5 Microscopic Description of the Electromagnetic Interaction of Charged Particles with Matter ................................................................... .48 111.5.1 Theoretical Outline ....................................................................... 49 III.5.2 Experimental Data on the Energy Loss Function ......................... 50

III.6 The Interaction of Charged Particles with Bulk Matter .............................. 52 IIl.6.1 The Stopping Power of the Medium ............................................. 52 III.6.2 Statistical Fluctuations of the Energy Lost by Charged

Particles ........................................................................................ 56 111.6.3 Range and Range Straggling ........................................................ 57

X Table of Contents

IIl.7 Appendix: Fonnal Treatment of the Interaction of Charged Particles with Matter ................................................................................... 59 III.7.1 Scattering Fonnalism .................................................................... 59 III. 7.2 The Dielectric Response Function ................................................ 66 III.7.3 Theoretical Calculations of the Energy Loss Function ................. 70

III.7.3.1 Drude-function Expansions of (q,co) ........................... 70 III.7.3.2 Random-phase Approximation (RPA) for (q,co) ......... 71 III. 7.3.3 Ab initio Calculations of (q,co) .................................... 72

IV Experimental Microdosimetry ................................................................. 73

IV.I The Site Concept ........................................................................................ 73 IV.2 Fluctuations in Regional Microdosimetry .................................................. 78 IV.3 Measurements in Regional Microdosimetry ............................................... 83

IV.3.1 General Considerations ................................................................. 83 IV.3.2 The Proportional Counter ............................................................. 85 IV.3.3 Energy loss versus Ionization ....................................................... 86 IV.3A Gas Multiplication ........................................................................ 89 IV.3.5 The Wall Effect ............................................................................ 96 IV.3.6 Tissue Equivalent Materials ....................................................... 100 IV.3.7 Counter Designs ......................................................................... 103 IV.3.8 Gas Supply .................................................................................. 110 IV.3.9 Electronics .................................................................................. III IV.3.10 Calibration .................................................................................. 114 IV.3.11 Resolution ................................................................................... II 5

IV A Measured Distributions of Lineal Energy ................................................. 117 IVA.I General Comments ..................................................................... 117 IVA.2 Neutrons ..................................................................................... 119 IVA.3 Photons ....................................................................................... 123 IVAA Electrons ..................................................................................... 126 IVA.5 Ions ............................................................................................. 129 IVA.6 Pions ........................................................................................... 133

IV.5 Measurement of Distributions of Specific Energy .................................... 134 IV.5.1 General Comments ..................................................................... 134 IV.5.2 The Variance Method ................................................................. 135

IV.6 Measurement of LET Distributions .......................................................... 139 IV.7 Appendix: The V Effect ........................................................................... 142

V Theoretical Microdosimetry .................................................................. 148

V.I A Diversion in Geometric Probability ...................................................... 148 V.2 Monte Carlo Simulation of Charged-Particle Tracks ............................... 152

Table of Contents XI

V.2.l A Brief Visit to Monte Carlo Sampling ...................................... 152 V.2.2 Geometrical Randomness ........................................................... 157 V.2.3 An Illustration: Monte Carlo Simulation of Electron Tracks ..... 158

V.3 Calculation of Microdosimetric Spectra ................................................... 166 V.3.1 Analytic Methods ....................................................................... 166 V.3.2 Monte Carlo Methods ................................................................. 171 V.3.3 Microdosimetric Spectra for Combined Radiations ................... 173

VA Methods for Obtaining Proximity Functions ............................................ 176 VA.l Proximity Functions for Simple Geometric Objects ................... 176 VA.2 Proximity Functions for Amorphous Tracks .............................. 179 VA.3 Proximity Functions from Experimental Data ............................ 184

VA.3.1 t(x) and YD""""""""""""""""""""""" •••••••••••••••••••• 185 VA.3.2 Proximity Functions for Diffused Charged

Particle Tracks ........................................................... 188 VA.3.3 Proximity Functions obtained from

Cloud-Chamber Data ................................................. 190 V.5 The Informational Content of the Moments of the

Microdosimetric Distributions .................................................................. 198 V.6 Appendix: The Maximum Entropy Principle ........................................... 201

VI Applications of Microdosimetry in Biology .......................................... 205

VI.l Radiobiology ............................................................................................ 205 VI.l.l Introduction ................................................................................ 205 VL1.2 Microdosimetric Constraints on Biophysical Models ................. 206 VL1.3 Empirical Data in Radiation Biology ......................................... 216 VI.IA The Theory of Dual Radiation Action ........................................ 229 VI.l.5 Other Topics in Dual Radiation Action Theory .......................... 241 VL1.6 DNA-lesion Theory of Radiation Action ................................... 247

VI.2 Radiotherapy ............................................................................................. 250 VI .2.1 General Considerations ............................................................... 250 V1.2.2 Microdosimetric Distributions .................................................... 253

VL3 Radiation Protection ................................................................................. 264 VI.3.1 Quantities .................................................................................... 264 VL3.2 General Considerations Regarding Measurements ..................... 269 V1.3.3 Measurements of the "Counter" Dose Equivalent ...................... 272 VI.3A Measurement of Operational Quantities ..................................... 274 VL3.5 Specific Quality Functions ......................................................... 275

VII Other Applications .................................................................................. 279

VILI Microdosimetry and Radiation Chemistry ................................................ 279 VII.2 Radiation Effects on Microelectronics ..................................................... 291

XII Table of Contents

VII.2.1 Appendix: Example .................................................................... 297 VII.3 Microdosimetry and Thermoluminescence .............................................. 298

References ........................................................................................................... 301

Subject Index ................................................................... ................................... 317