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Nuclear Medicine Physics
A Handbook for Teachers and Students
D.L. Bailey J.L. Humm
A. Todd-Pokropek A. van Aswegen
Technical Editors
International Atomic Energy Agency Vienna
eachers and Students
1 @
This handbook provides a comprehensive overview of the medical physics knowledge required in the fi eld of nuclear medicine. It is intended for teachers, students and residents involved in medical physics programmes. It will serve as a resource for interested readers from other disciplines, for example, nuclear medicine physicians, radiochemists and medical technologists, who would like to familiarize themselves with the basic concepts and practice of nuclear medicine physics. Physics is a vital aspect of nearly every area of nuclear medicine, including imaging instrumentation, image processing and reconstruction, data analysis, radionuclide production, radionuclide therapy, radiopharmacy, radiation protection and biology. The 20 chapters of this handbook include a broad coverage of topics relevant to nuclear medicine physics. The authors and reviewers were drawn from a variety of regions and were selected because of their knowledge, teaching experience and scientifi c acumen. This book was written to address an urgent need for a comprehensive, contemporary text on the physics of nuclear medicine and has been endorsed by several international and national organizations. It complements similar texts in radiation oncology physics and diagnostic radiology physics published
by the IAEA.
sTudeNTs
aNGola arGeNTiNa arMeNia ausTralia ausTria aZerbaiJaN bahaMas bahraiN baNGladesh belarus belGiuM beliZe beNiN boliVia
bosNia aNd herZeGoViNa boTsWaNa
braZil
bruNei darussalaM bulGaria
burkiNa faso buruNdi caMbodia caMerooN caNada
ceNTral africaN rePublic chadchile chiNa coloMbia coNGo cosTa rica cÔTe d’iVoire croaTia cubacyPrus cZech rePublic deMocraTic rePublic
of The coNGo deNMark doMiNica
doMiNicaN rePublic ecuador
eGyPT el salVador eriTrea esToNia eThioPia fiJifiNlaNd fraNce GaboN GeorGia GerMaNy
haiTi holy see hoNduras huNGary icelaNd iNdia iNdoNesia
iraN, islaMic rePublic of iraQirelaNd
israel iTaly JaMaica JaPaN JordaN kaZakhsTaN keNya
korea, rePublic of kuWaiT
kyrGyZsTaN
lao PeoPle’s deMocraTic rePublic
laTVia lebaNoN lesoTho liberia libya liechTeNsTeiN liThuaNia luXeMbourG MadaGascar MalaWi Malaysia MaliMalTa
Marshall islaNds MauriTaNia, islaMic
rePublic of MauriTius MeXico MoNaco MoNGolia MoNTeNeGro Morocco MoZaMbiQue MyaNMar NaMibia NePal NeTherlaNds NeW ZealaNd NicaraGua NiGer NiGeria NorWay
PaNaMa
PaPua NeW GuiNea ParaGuay PeruPhiliPPiNes PolaNd PorTuGal QaTar
rePublic of MoldoVa roMaNia
russiaN federaTioN rWaNda
saN MariNo saudi arabia seNeGal serbia seychelles sierra leoNe siNGaPore sloVakia sloVeNia souTh africa sPaiN sri laNka sudaN sWaZilaNd sWedeN sWiTZerlaNd syriaN arab rePublic TaJikisTaN
ThailaNd
The forMer yuGoslaV rePublic of MacedoNia ToGoTriNidad aNd TobaGo TuNisia
Turkey uGaNda ukraiNe
uNiTed arab eMiraTes uNiTed kiNGdoM of
GreaT briTaiN aNd NorTherN irelaNd uNiTed rePublic
of TaNZaNia
uNiTed sTaTes of aMerica uruGuay
uZbekisTaN
VeNeZuela, boliVariaN rePublic of
VieT NaM yeMeN ZaMbia 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’’.
Nuclear MediciNe Physics:
a haNdbook for Teachers aNd sTudeNTs
eNdorsed by:
aMericaN associaTioN of PhysicisTs iN MediciNe, asia–oceaNia federaTioN of orGaNiZaTioNs
for Medical Physics,
ausTralasiaN colleGe of Physical scieNTisTs aNd eNGiNeers iN MediciNe,
euroPeaN federaTioN of orGaNisaTioNs for Medical Physics,
federaTioN of africaN Medical Physics orGaNisaTioNs, World federaTioN of Nuclear MediciNe aNd bioloGy
iNTerNaTioNal aToMic eNerGy aGeNcy VieNNa, 2014
aNGola arGeNTiNa arMeNia ausTralia ausTria aZerbaiJaN bahaMas bahraiN baNGladesh belarus belGiuM beliZe beNiN boliVia
bosNia aNd herZeGoViNa boTsWaNa
braZil
bruNei darussalaM bulGaria
burkiNa faso buruNdi caMbodia caMerooN caNada
ceNTral africaN rePublic chadchile chiNa coloMbia coNGo cosTa rica cÔTe d’iVoire croaTia cubacyPrus cZech rePublic deMocraTic rePublic
of The coNGo deNMark doMiNica
doMiNicaN rePublic ecuador
eGyPT el salVador eriTrea esToNia eThioPia fiJifiNlaNd fraNce GaboN GeorGia GerMaNy
haiTi holy see hoNduras huNGary icelaNd iNdia iNdoNesia
iraN, islaMic rePublic of iraQirelaNd
israel iTaly JaMaica JaPaN JordaN kaZakhsTaN keNya
korea, rePublic of kuWaiT
kyrGyZsTaN
lao PeoPle’s deMocraTic rePublic
laTVia lebaNoN lesoTho liberia libya liechTeNsTeiN liThuaNia luXeMbourG MadaGascar MalaWi Malaysia MaliMalTa
Marshall islaNds MauriTaNia, islaMic
rePublic of MauriTius MeXico MoNaco MoNGolia MoNTeNeGro Morocco MoZaMbiQue MyaNMar NaMibia NePal NeTherlaNds NeW ZealaNd NicaraGua NiGer NiGeria NorWay
PaNaMa
PaPua NeW GuiNea ParaGuay PeruPhiliPPiNes PolaNd PorTuGal QaTar
rePublic of MoldoVa roMaNia
russiaN federaTioN rWaNda
saN MariNo saudi arabia seNeGal serbia seychelles sierra leoNe siNGaPore sloVakia sloVeNia souTh africa sPaiN sri laNka sudaN sWaZilaNd sWedeN sWiTZerlaNd syriaN arab rePublic TaJikisTaN
ThailaNd
The forMer yuGoslaV rePublic of MacedoNia ToGoTriNidad aNd TobaGo TuNisia
Turkey uGaNda ukraiNe
uNiTed arab eMiraTes uNiTed kiNGdoM of
GreaT briTaiN aNd NorTherN irelaNd uNiTed rePublic
of TaNZaNia
uNiTed sTaTes of aMerica uruGuay
uZbekisTaN
VeNeZuela, boliVariaN rePublic of
VieT NaM yeMeN ZaMbia 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’’.
IAEA Library Cataloguing in Publication Data
Nuclear medicine physics : a handbook for students and teachers. — Vienna : International Atomic Energy Agency, 2014.
p. ; 24 cm.
STI/PUB/1617
ISBN 978–92–0–143810–2
Includes bibliographical references. 1. Nuclear medicine — Handbooks, manuals, etc.
2. Medical physics handbooks. 3. Medical physics. I. International Atomic Energy Agency.
IAEAL 14–00880
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 considered on a case-by-case basis. Enquiries should be addressed to the IAEA Publishing Section at:
Marketing and Sales Unit, Publishing Section International Atomic Energy Agency
Vienna International Centre PO Box 100
1400 Vienna, Austria fax: +43 1 2600 29302 tel.: +43 1 2600 22417
email: [email protected] http://www.iaea.org/books
© IAEA, 2014 Printed by the IAEA in Austria
December 2014 STI/PUB/1617
staging of disease, therapy and monitoring the response of a disease process.
it is also a powerful translational tool in the basic sciences, such as biology, in drug discovery and in pre-clinical medicine. developments in nuclear medicine are driven by advances in this multidisciplinary science that includes physics, chemistry, computing, mathematics, pharmacology and biology.
This handbook comprehensively covers the physics of nuclear medicine.
it is intended for undergraduate and postgraduate students of medical physics.
it will also serve as a resource for interested readers from other disciplines, for example, clinicians, radiochemists and medical technologists who would like to familiarize themselves with the basic concepts and practice of nuclear medicine physics.
The scope of the book is intentionally broad. Physics is a vital aspect of nearly every area of nuclear medicine, including imaging instrumentation, image processing and reconstruction, data analysis, radionuclide production, radionuclide therapy, radiopharmacy, radiation protection and biology. The authors were drawn from a variety of regions and were selected because of their knowledge, teaching experience and scientific acumen.
This book was written to address an urgent need for a comprehensive, contemporary text on the physics of nuclear medicine. it complements similar texts in radiation oncology physics and diagnostic radiology physics that have been published by the iaea.
endorsement of this handbook has been granted by the following international professional bodies: the american association of Physicists in Medicine (aaPM), the asia–oceania federation of organizations for Medical Physics (afoMP), the australasian college of Physical scientists and engineers in Medicine (acPseM), the european federation of organisations for Medical Physics (efoMP), the federation of african Medical Physics organisations (faMPo), and the World federation of Nuclear Medicine and biology (WfNMb).
The following international experts are gratefully acknowledged for making major contributions to this handbook as technical editors:
d.l. bailey (australia), J.l. humm (united states of america), a. Todd-Pokropek (united kingdom) and a. van aswegen (south africa). The iaea officers responsible for this publication were s. Palm and G.l. Poli of the division of human health.
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 considered on a case-by-case basis. enquiries should be addressed to the iaea Publishing section at:
Marketing and sales unit, Publishing section international atomic energy agency
Vienna international centre Po box 100
1400 Vienna, austria fax: +43 1 2600 29302 tel.: +43 1 2600 22417
email: [email protected] http://www.iaea.org/books
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 IAEA has no responsibility for the persistence or accuracy of URLs for external or third party Internet web sites referred to in this book and does not guarantee that any content on such web sites is, or will remain, accurate or appropriate.
medicine to image and treat human disease. it relies on the ‘tracer principle’ first espoused by Georg karl von hevesy in the early 1920s. The tracer principle is the study of the fate of compounds in vivo using minute amounts of radioactive tracers which do not elicit any pharmacological response by the body to the tracer.
Today, the same principle is used to study many aspects of physiology, such as cellular metabolism, dNa (deoxyribonucleic acid) proliferation, blood flow in organs, organ function, receptor expression and abnormal physiology, externally using sensitive imaging devices. larger amounts of radionuclides are also applied to treat patients with radionuclide therapy, especially in disseminated diseases such as advanced metastatic cancer, as this form of therapy has the ability to target abnormal cells to treat the disease anywhere in the body.
Nuclear medicine relies on function. for this reason, it is referred to as
‘functional imaging’. rather than just imaging a portion of the body believed to have some abnormality, as is done with X ray imaging in radiology, nuclear medicine scans often depict the whole body distribution of the radioactive compound often acquired as a sequence of images over time showing the temporal course of the radiotracer in the body.
There are two main types of radiation of interest for imaging in nuclear medicine: γ ray emission from excited nuclei, and annihilation (or coincidence) radiation (γ±) arising after positron emission from proton-rich nuclei. Gamma photons are detected with a gamma camera as either planar (2-d) images or tomographically in 3-d using single photon emission computed tomography.
The annihilation photons from positron emission are detected using a positron emission tomography (PeT) camera. The most recent major development in this field is the combination of gamma cameras or PeT cameras with high resolution structural imaging devices, either X ray computed tomography (cT) scanners or, increasingly, magnetic resonance imaging (Mri) scanners, in a single image device. The combined PeT/cT (or PeT/Mri) scanner represents one of the most sophisticated and powerful ways to visualize normal and altered physiology in the body.
it is in this complex environment that the medical physicist, along with nuclear medicine physicians and technologists/radiographers, plays a significant role in the multidisciplinary team needed for medical diagnosis. The physicist is responsible for such areas as instrumentation performance, radiation dosimetry for treatment of patients, radiation protection of staff and accuracy of the data analysis. The physicist draws on training in radiation and nuclear science, in addition to scientific rigour and attention to detail in experiments and measurements, to join forces with the other members of the multidisciplinary
This handbook was conceived and written by physicists, and is intended primarily for physicists, although interested readers from medical, paramedical and other science and engineering backgrounds could find it useful. The level of understanding of the material covered will be different depending on the background of the reader. readers are encouraged to visit the iaea human health web site (http://www-naweb.iaea.org/Nahu/index.html) to discover the wealth of resources available.
The technical editors and authors, selected for their experience and in recognition of their contributions to the field, were drawn from around the world and, thus, this book represents a truly international collaboration. The technical editors travelled to the iaea headquarters in Vienna on four occasions over three years to bring this project to fruition. We would like to thank all of the authors for their important contribution.
d.l. bailey, J.l. humm a. Todd-Pokropek, a. van aswegen
1.1. iNTroducTioN . . . 1
1.1.1. fundamental physical constants . . . 1
1.1.2. Physical quantities and units . . . 2
1.1.3. classification of radiation . . . 4
1.1.4. classification of ionizing radiation . . . 4
1.1.5. classification of indirectly ionizing photon radiation . . 5
1.1.6. characteristic X rays . . . 5
1.1.7. bremsstrahlung . . . 5
1.1.8. Gamma rays . . . 6
1.1.9. annihilation quanta . . . 6
1.1.10. radiation quantities and units . . . 7
1.2. basic defiNiTioNs for aToMic sTrucTure . . . 8
1.2.1. rutherford model of the atom . . . 10
1.2.2. bohr model of the hydrogen atom . . . 10
1.3. basic defiNiTioNs for Nuclear sTrucTure . . . 10
1.3.1. Nuclear radius . . . 12
1.3.2. Nuclear binding energy . . . 12
1.3.3. Nuclear fusion and fission . . . 13
1.3.4. Two-particle collisions and nuclear reactions . . . 14
1.4. radioacTiViTy . . . 16
1.4.1. decay of radioactive parent into a stable or unstable daughter . . . 17
1.4.2. radioactive series decay . . . 19
1.4.3. equilibrium in parent–daughter activities . . . 21
1.4.4. Production of radionuclides (nuclear activation) . . . 22
1.4.5. Modes of radioactive decay . . . 23
1.4.6. alpha decay . . . 25
1.4.7. beta minus decay . . . 26
1.4.8. beta plus decay . . . 26
1.4.9. electron capture . . . 27
1.4.10. Gamma decay and internal conversion . . . 27
1.4.11. characteristic (fluorescence) X rays and auger electrons . . . 28
1.5. elecTroN iNTeracTioNs WiTh MaTTer . . . 29
1.5.1. electron–orbital interactions . . . 29
1.5.2. electron–nucleus interactions . . . 29
1.6.3. attenuation coefficients . . . 34
1.6.4. Photon interactions on the microscopic scale . . . 35
1.6.5. Photoelectric effect . . . 38
1.6.6. rayleigh (coherent) scattering . . . 39
1.6.7. compton effect (incoherent scattering) . . . 39
1.6.8. Pair production . . . 44
1.6.9. relative predominance of individual effects . . . 46
1.6.10. Macroscopic attenuation coefficients . . . 47
1.6.11. effects following photon interactions with absorber and summary of photon interactions . . . 48
chaPTer 2. basic radiobioloGy . . . 49
2.1. iNTroducTioN . . . 49
2.2. radiaTioN effecTs aNd TiMescales . . . 49
2.3. bioloGical ProPerTies of ioNiZiNG radiaTioN . . 51
2.3.1. Types of ionizing radiation . . . 51
2.4. Molecular effecTs of radiaTioN aNd Their Modifiers . . . 53
2.4.1. role of oxygen . . . 54
2.4.2. bystander effects . . . 54
2.5. dNa daMaGe aNd rePair . . . 55
2.5.1. dNa damage . . . 55
2.5.2. dNa repair . . . 55
2.6. cellular effecTs of radiaTioN . . . 56
2.6.1. concept of cell death . . . 56
2.6.2. cell survival curves . . . 56
2.6.3. dose deposition characteristics: linear energy transfer . 57 2.6.4. determination of relative biological effectiveness . . . . 58
2.6.5. The dose rate effect and the concept of repeat treatments . . . 62
2.6.6. The basic linear–quadratic model . . . 63
2.6.7. Modification to the linear–quadratic model for radionuclide therapies . . . 64
2.6.8. Quantitative intercomparison of different treatment types . . . 64
2.6.9. cellular recovery processes . . . 65
2.6.10. consequence of radionuclide heterogeneity . . . 66
2.7.2. determinants of tumour response . . . 67
2.7.3. The concept of therapeutic index in radiation therapy and radionuclide therapy . . . 68
2.7.4. long term concerns: stochastic and deterministic effects . . . 68
2.8. sPecial radiobioloGical coNsideraTioNs iN TarGeTed radioNuclide TheraPy . . . 69
2.8.1. radionuclide targeting . . . 69
2.8.2. Whole body irradiation . . . 69
2.8.3. critical normal tissues for radiation and radionuclide therapies . . . 70
2.8.4. imaging the radiobiology of tumours . . . 71
2.8.5. choice of radionuclide to maximize therapeutic index . 71 chaPTer 3. radiaTioN ProTecTioN . . . 73
3.1. iNTroducTioN . . . 73
3.2. basic PriNciPles of radiaTioN ProTecTioN . . . 74
3.2.1. The international commission on radiological Protection system of radiological protection . . . 74
3.2.2. safety standards . . . 76
3.2.3. radiation protection quantities and units . . . 77
3.3. iMPleMeNTaTioN of radiaTioN ProTecTioN iN a Nuclear MediciNe faciliTy . . . 81
3.3.1. General aspects . . . 81
3.3.2. responsibilities . . . 82
3.3.3. radiation protection programme . . . 84
3.3.4. radiation protection committee . . . 84
3.3.5. education and training . . . 84
3.4. faciliTy desiGN . . . 85
3.4.1. location and general layout . . . 85
3.4.2. General building requirements . . . 85
3.4.3. source security and storage . . . 86
3.4.4. structural shielding . . . 87
3.4.5. classification of workplaces . . . 87
3.4.6. Workplace monitoring . . . 88
3.4.7. radioactive waste . . . 88
3.5.3. conditions for pregnant workers and young persons . . 91
3.5.4. Protective clothing . . . 92
3.5.5. safe working procedures . . . 92
3.5.6. Personal monitoring. . . 94
3.5.7. Monitoring of the workplace . . . 95
3.5.8. health surveillance . . . 95
3.5.9. local rules and supervision . . . 96
3.6. Public eXPosure . . . 97
3.6.1. Justification, optimization and dose limitation . . . 97
3.6.2. design considerations . . . 97
3.6.3. exposure from patients . . . 98
3.6.4. Transport of sources . . . 98
3.7. Medical eXPosure . . . 99
3.7.1. Justification of medical exposure . . . 99
3.7.2. optimization of protection . . . 100
3.7.3. helping in the care, support or comfort of patients . . . . 107
3.7.4. biomedical research . . . 107
3.7.5. local rules . . . 108
3.8. PoTeNTial eXPosure. . . 108
3.8.1. safety assessment and accident prevention . . . 108
3.8.2. emergency plans . . . 110
3.8.3. reporting and lessons learned . . . 111
3.9. QualiTy assuraNce . . . 112
3.9.1. General considerations . . . 112
3.9.2. audit . . . 114
chaPTer 4. radioNuclide ProducTioN . . . 117
4.1. The oriGiNs of differeNT Nuclei . . . 117
4.1.1. induced radioactivity . . . 118
4.1.2. Nuclide chart and line of nuclear stability . . . 120
4.1.3. binding energy, Q-value, reaction threshold and nuclear reaction formalism . . . 123
4.1.4. Types of nuclear reaction, reaction channels and cross-section . . . 124
4.2. reacTor ProducTioN . . . 127
4.2.1. Principle of operation and neutron spectrum. . . 128
4.3.1. cyclotron, principle of operation,
negative and positive ions . . . 134
4.3.2. commercial production (low and high energy) . . . 136
4.3.3. in-house low energy production (PeT) . . . 137
4.3.4. Targetry, optimizing the production regarding yield and impurities, yield calculations . . . 140
4.4. radioNuclide GeNeraTors . . . 141
4.4.1. Principles of generators . . . 142
4.5. radiocheMisTry of irradiaTed TarGeTs . . . 143
4.5.1. carrier-free, carrier-added systems . . . 144
4.5.2. separation methods, solvent extraction, ion exchange, thermal diffusion . . . 145
4.5.3. radiation protection considerations and hot-box facilities . . . 147
chaPTer 5. sTaTisTics for radiaTioN MeasureMeNT . . . 149
5.1. sources of error iN Nuclear MediciNe MeasureMeNT . . . 149
5.2. characTeriZaTioN of daTa . . . 153
5.2.1. Measures of central tendency and variability . . . 153
5.3. sTaTisTical Models . . . 157
5.3.1. conditions when binomial, Poisson and normal distributions are applicable . . . 158
5.3.2. binomial distribution . . . 160
5.3.3. Poisson distribution . . . 163
5.3.4. Normal distribution . . . 165
5.4. esTiMaTioN of The PrecisioN of a siNGle MeasureMeNT iN saMPle couNTiNG aNd iMaGiNG . . . 168
5.4.1. assumption . . . 168
5.4.2. The importance of the fractional σf as an indicator of the precision of a single measurement in sample counting and imaging . . . 170
5.4.3. caution on the use of the estimate of the precision of a single measurement in sample counting and imaging . . . 171
5.5.3. Products and ratios . . . 176
5.6. aPPlicaTioNs of sTaTisTical aNalysis . . . 177
5.6.1. Multiple independent counts . . . 177
5.6.2. standard deviation and relative standard deviation for counting rates . . . 178
5.6.3. effects of background counts . . . 179
5.6.4. significance of differences between counting measurements . . . 183
5.6.5. Minimum detectable counts, count rate and activity . . . 184
5.6.6. comparing counting systems . . . 187
5.6.7. estimating required counting times . . . 188
5.6.8. calculating uncertainties in the measurement of plasma volume in patients . . . 189
5.7. aPPlicaTioN of sTaTisTical aNalysis: deTecTor PerforMaNce . . . 191
5.7.1. energy resolution of scintillation detectors . . . 191
5.7.2. intervals between successive events . . . 193
5.7.3. Paralysable dead time . . . 194
chaPTer 6. basic radiaTioN deTecTors . . . 196
6.1. iNTroducTioN . . . 196
6.1.1. radiation detectors — complexity and relevance . . . 196
6.1.2. interaction mechanisms, signal formation and detector type . . . 196
6.1.3. counting, current, integrating mode . . . 197
6.1.4. detector requirements . . . 197
6.2. Gas filled deTecTors . . . 200
6.2.1. basic principles . . . 200
6.3. seMicoNducTor deTecTors . . . 202
6.3.1. basic principles . . . 202
6.3.2. semiconductor detectors . . . 204
6.4. sciNTillaTioN deTecTors aNd sToraGe PhosPhors . . . 205
6.4.1. basic principles . . . 205
6.4.2. light sensors . . . 206
6.4.3. scintillator materials . . . 209
7.1. iNTroducTioN . . . 214
7.2. PriMary radiaTioN deTecTioN Processes . . . 215
7.2.1. scintillation counters . . . 215
7.2.2. Gas filled detection systems . . . 216
7.2.3. semiconductor detectors . . . 216
7.3. iMaGiNG deTecTors . . . 217
7.3.1. The gamma camera . . . 217
7.3.2. The positron camera . . . 218
7.3.3. Multiwire proportional chamber based X ray and γ ray imagers . . . 219
7.3.4. semiconductor imagers . . . 220
7.3.5. The autoradiography imager . . . 221
7.4. siGNal aMPlificaTioN . . . 222
7.4.1. Typical amplifier . . . 222
7.4.2. Properties of amplifiers . . . 224
7.5. siGNal ProcessiNG . . . 226
7.5.1. analogue signal utilization . . . 226
7.5.2. signal digitization . . . 226
7.5.3. Production and use of timing information . . . 228
7.6. oTher elecTroNics reQuired by iMaGiNG sysTeMs . . . 230
7.6.1. Power supplies . . . 230
7.6.2. uninterruptible power supplies . . . 231
7.6.3. oscilloscopes . . . 231
7.7. suMMary . . . 232
chaPTer 8. GeNeric PerforMaNce Measures . . . 234
8.1. iNTriNsic aNd eXTriNsic Measures . . . 234
8.1.1. Generic nuclear medicine imagers . . . 234
8.1.2. intrinsic performance. . . 236
8.1.3. extrinsic performance . . . 236
8.2. eNerGy resoluTioN . . . 237
8.2.1. energy spectrum . . . 237
8.2.2. intrinsic measurement — energy resolution . . . 238
8.2.3. impact of energy resolution on extrinsic imager performance . . . 239
8.3.3. intrinsic measurement — spatial resolution . . . 242
8.3.4. extrinsic measurement — spatial resolution . . . 242
8.4. TeMPoral resoluTioN. . . 244
8.4.1. intrinsic measurement — temporal resolution . . . 244
8.4.2. dead time. . . 244
8.4.3. count rate performance measures . . . 246
8.5. seNsiTiViTy . . . 247
8.5.1. image noise and sensitivity . . . 247
8.5.2. extrinsic measure — sensitivity . . . 248
8.6. iMaGe QualiTy . . . 249
8.6.1. image uniformity . . . 249
8.6.2. resolution/noise trade-off . . . 249
8.7. oTher PerforMaNce Measures . . . 250
chaPTer 9. Physics iN The radioPharMacy . . . 251
9.1. The ModerN radioNuclide calibraTor . . . 251
9.1.1. construction of dose calibrators . . . 251
9.1.2. calibration of dose calibrators. . . 253
9.1.3. uncertainty of activity measurements . . . 254
9.1.4. Measuring pure β emitters . . . 258
9.1.5. Problems arising from radionuclide contaminants . . . . 259
9.2. dose calibraTor accePTaNce TesTiNG aNd QualiTy coNTrol . . . 260
9.2.1. acceptance tests . . . 260
9.2.2. Quality control . . . 262
9.3. sTaNdards aPPlyiNG To dose calibraTors . . . 262
9.4. NaTioNal acTiViTy iNTercoMParisoNs . . . 263
9.5. disPeNsiNG radioPharMaceuTicals for iNdiVidual PaTieNTs . . . 264
9.5.1. adjusting the activity for differences in patient size and weight . . . 264
9.5.2. Paediatric dosage charts . . . 264
9.5.3. diagnostic reference levels in nuclear medicine . . . 266
9.6. radiaTioN safeTy iN The radioPharMacy . . . 269
9.6.1. surface contamination limits . . . 269
9.6.2. Wipe tests and daily surveys . . . 270
9.6.3. Monitoring of staff finger doses during dispensing . . . 270
9.7.3. isolator cabinets . . . 273
9.8. shieldiNG for radioNuclides . . . 274
9.8.1. shielding for γ, β and positron emitters . . . 274
9.8.2. Transmission factors for lead and concrete . . . 278
9.9. desiGNiNG a radioPharMacy . . . 280
9.10. securiTy of The radioPharMacy . . . 282
9.11. record keePiNG . . . 283
9.11.1. Quality control records . . . 283
9.11.2. records of receipt of radioactive materials . . . 283
9.11.3. records of radiopharmaceutical preparation and dispensing . . . 284
9.11.4. radioactive waste records . . . 284
chaPTer 10. NoN-iMaGiNG deTecTors aNd couNTers . . . 287
10.1. iNTroducTioN . . . 287
10.2. oPeraTiNG PriNciPles of radiaTioN deTecTors . 287 10.2.1. ionization detectors . . . 288
10.2.2. scintillation detectors . . . 292
10.3. radiaTioN deTecTor PerforMaNce . . . 294
10.3.1. sensitivity . . . 294
10.3.2. energy resolution . . . 295
10.3.3. count rate performance (‘speed’) . . . 296
10.4. deTecTioN aNd couNTiNG deVices . . . 298
10.4.1. survey meters . . . 298
10.4.2. dose calibrator. . . 299
10.4.3. Well counter . . . 299
10.4.4. intra-operative probes . . . 300
10.4.5. organ uptake probe . . . 302
10.5. QualiTy coNTrol of deTecTioN aNd couNTiNG deVices . . . 305
10.5.1. reference sources . . . 305
10.5.2. survey meter . . . 306
10.5.3. dose calibrator. . . 307
10.5.4. Well counter . . . 310
10.5.5. intra-operative probe . . . 310
10.5.6. organ uptake probe . . . 311
11.2. GaMMa caMera sysTeMs . . . 312
11.2.1. basic principles . . . 312
11.2.2. The anger camera . . . 314
11.2.3. sPecT . . . 341
11.3. PeT sysTeMs . . . 353
11.3.1. Principle of annihilation coincidence detection . . . 353
11.3.2. design considerations for PeT systems . . . 356
11.3.3. detector systems . . . 362
11.3.4. data acquisition . . . 369
11.3.5. data corrections . . . 380
11.4. sPecT/cT aNd PeT/cT sysTeMs . . . 392
11.4.1. cT uses in emission tomography . . . 392
11.4.2. sPecT/cT . . . 393
11.4.3. PeT/cT . . . 394
chaPTer 12. coMPuTers iN Nuclear MediciNe . . . 398
12.1. PheNoMeNal iNcrease iN coMPuTiNG caPabiliTies . . . 398
12.1.1. Moore’s law . . . 398
12.1.2. hardware versus ‘peopleware’ . . . 398
12.1.3. future trends . . . 399
12.2. sToriNG iMaGes oN a coMPuTer . . . 400
12.2.1. Number systems . . . 400
12.2.2. data representation . . . 401
12.2.3. images and volumes . . . 403
12.3. iMaGe ProcessiNG . . . 405
12.3.1. spatial frequencies. . . 406
12.3.2. sampling requirements . . . 412
12.3.3. convolution . . . 412
12.3.4. filtering . . . 414
12.3.5. band-pass filters . . . 416
12.3.6. deconvolution . . . 421
12.3.7. image restoration filters . . . 422
12.3.8. other processing . . . 424
12.4. daTa acQuisiTioN . . . 425
12.4.1. acquisition matrix size and spatial resolution. . . 426
12.4.2. static and dynamic planar acquisition . . . 426
12.4.6. list-mode . . . 431
12.5. file forMaT . . . 431
12.5.1. file format design . . . 432
12.5.2. common image file formats . . . 435
12.5.3. Movie formats . . . 437
12.5.4. Nuclear medicine data requirements . . . 437
12.5.5. common nuclear medicine data storage formats . . . 442
12.6. iNforMaTioN sysTeM . . . 443
12.6.1. database . . . 443
12.6.2. hospital information system . . . 445
12.6.3. radiology information system . . . 445
12.6.4. Picture archiving and communication system . . . 446
12.6.5. scheduling . . . 447
12.6.6. broker . . . 447
12.6.7. security . . . 447
chaPTer 13. iMaGe recoNsTrucTioN. . . 449
13.1. iNTroducTioN . . . 449
13.2. aNalyTical recoNsTrucTioN . . . 450
13.2.1. Two dimensional tomography . . . 451
13.2.2. frequency–distance relation . . . 456
13.2.3. fully 3-d tomography . . . 457
13.2.4. Time of flight PeT . . . 466
13.3. iTeraTiVe recoNsTrucTioN . . . 468
13.3.1. introduction . . . 468
13.3.2. optimization algorithms . . . 473
13.3.3. Maximum-likelihood expectation-maximization . . . 479
13.3.4. acceleration . . . 485
13.3.5. regularization . . . 488
13.3.6. corrections . . . 495
13.4. Noise esTiMaTioN . . . 507
13.4.1. Noise propagation in filtered back projection . . . 507
13.4.2. Noise propagation in maximum-likelihood expectation-maximization . . . 508
14.2. diGiTal iMaGe disPlay aNd Visual PercePTioN . . 513
14.2.1. display resolution . . . 514
14.2.2. contrast resolution. . . 515
14.3. disPlay deVice hardWare . . . 516
14.3.1. display controller . . . 516
14.3.2. cathode ray tube . . . 517
14.3.3. liquid crystal display panel. . . 519
14.3.4. hard copy devices . . . 521
14.4. Grey scale disPlay . . . 521
14.4.1. Grey scale standard display function . . . 522
14.5. colour disPlay . . . 525
14.5.1. colour and colour gamut . . . 528
14.6. iMaGe disPlay MaNiPulaTioN . . . 530
14.6.1. histograms . . . 530
14.6.2. Windowing and thresholding . . . 530
14.6.3. histogram equalization . . . 532
14.7. VisualiZaTioN of VoluMe daTa . . . 533
14.7.1. slice mode . . . 533
14.7.2. Volume mode . . . 534
14.7.3. Polar plots of myocardial perfusion imaging . . . 538
14.8. dual ModaliTy disPlay . . . 540
14.9. disPlay MoNiTor QualiTy assuraNce . . . 541
14.9.1. acceptance testing . . . 542
14.9.2. routine quality control . . . 542
chaPTer 15. deVices for eValuaTiNG iMaGiNG sysTeMs . . . 547
15.1. deVeloPiNG a QualiTy MaNaGeMeNT sysTeM aPProach To iNsTruMeNT QualiTy assuraNce . . 547
15.1.1. Methods for routine quality assurance procedures . . . . 547
15.2. hardWare (Physical) PhaNToMs . . . 550
15.2.1. Gamma camera phantoms . . . 550
15.2.2. sPecT phantoms . . . 558
15.2.3. PeT phantoms . . . 568
15.3. coMPuTaTioNal Models . . . 575
15.3.1. emission tomography simulation toolkits . . . 577
15.4.3. acceptance testing as a baseline for regular quality
assurance . . . 583 15.4.4. What to do if the instrument fails acceptance testing . . 584 15.4.5. Meeting the manufacturer’s specifications . . . 584 chaPTer 16. fuNcTioNal MeasureMeNTs iN Nuclear
MediciNe . . . 587 16.1. iNTroducTioN . . . 587 16.2. NoN-iMaGiNG MeasureMeNTs . . . 588 16.2.1. renal function measurements . . . 588 16.2.2. 14c breath tests . . . 591 16.3. iMaGiNG MeasureMeNTs . . . 591 16.3.1. Thyroid . . . 592 16.3.2. renal function . . . 594 16.3.3. lung function . . . 596 16.3.4. Gastric function . . . 596 16.3.5. cardiac function . . . 599 chaPTer 17. QuaNTiTaTiVe Nuclear MediciNe . . . 608
17.1. PlaNar Whole body biodisTribuTioN
MeasureMeNTs . . . 608 17.2. QuaNTiTaTioN iN eMissioN ToMoGraPhy. . . 609 17.2.1. region of interest . . . 609 17.2.2. use of standard . . . 610 17.2.3. Partial volume effect and the recovery coefficient . . . . 610 17.2.4. Quantitative assessment . . . 612 17.2.5. estimation of activity . . . 616 17.2.6. evaluation of image quality. . . 618 chaPTer 18. iNTerNal dosiMeTry . . . 621
18.1. The Medical iNTerNal radiaTioN dose
forMalisM . . . 621 18.1.1. basic concepts . . . 621 18.1.2. The time-integrated activity in the source region . . . 626
18.2.1. introduction . . . 635 18.2.2. dosimetry on an organ level . . . 636 18.2.3. dosimetry on a voxel level . . . 637 chaPTer 19. radioNuclide TheraPy . . . 641 19.1. iNTroducTioN . . . 641 19.2. Thyroid TheraPies . . . 642 19.2.1. benign thyroid disease . . . 642 19.2.2. Thyroid cancer . . . 643 19.3. PalliaTioN of boNe PaiN . . . 645 19.3.1. Treatment specific issues . . . 646 19.4. hePaTic caNcer . . . 646 19.4.1. Treatment specific issues . . . 647 19.5. NeuroeNdocriNe TuMours . . . 647 19.5.1. Treatment specific issues . . . 648 19.6. NoN-hodGkiN’s lyMPhoMa . . . 649 19.6.1. Treatment specific issues . . . 649 19.7. PaediaTric MaliGNaNcies . . . 650 19.7.1. Thyroid cancer . . . 651 19.7.2. Neuroblastoma . . . 651 19.8. role of The PhysicisT . . . 652 19.9. eMerGiNG TechNoloGy . . . 654 19.10. coNclusioNs . . . 656 chaPTer 20. MaNaGeMeNT of TheraPy PaTieNTs . . . 658 20.1. iNTroducTioN . . . 658 20.2. occuPaTioNal eXPosure . . . 658 20.2.1. Protective equipment and tools . . . 658 20.2.2. individual monitoring . . . 659 20.3. release of The PaTieNT . . . 659 20.3.1. The decision to release the patient. . . 660 20.3.2. specific instructions for releasing the radioactive
patient . . . 662 20.4. Public eXPosure . . . 665 20.4.1. Visitors to patients . . . 665 20.4.2. radioactive waste . . . 665
20.5.2. designing for control of contamination . . . 668 20.6. oPeraTiNG Procedures . . . 668 20.6.1. Transport of therapy doses . . . 669 20.6.2. administration of therapeutic radiopharmaceuticals. . . 669 20.6.3. error prevention. . . 670 20.6.4. exposure rates and postings . . . 670 20.6.5. Patient care in the treating facility . . . 672 20.6.6. contamination control procedures . . . 673 20.7. chaNGes iN Medical sTaTus . . . 674 20.7.1. emergency medical procedures . . . 675 20.7.2. The radioactive patient in the operating theatre . . . 675 20.7.3. radioactive patients on dialysis . . . 676 20.7.4. re-admission of patients to the treating institution . . . . 676 20.7.5. Transfer to another health care facility . . . 677 20.8. deaTh of The PaTieNT . . . 677 20.8.1. death of the patient following radionuclide therapy . . . 678 20.8.2. organ donation . . . 679 20.8.3. Precautions during autopsy . . . 679 20.8.4. Preparation for burial and visitation . . . 680 20.8.5. cremation . . . 681 aPPeNdiX i: arTefacTs aNd TroubleshooTiNG . . . 684 aPPeNdiX ii: radioNuclides of iNTeresT iN diaGNosTic
aNd TheraPeuTic Nuclear MediciNe . . . 719 abbreViaTioNs . . . 723 syMbols . . . 729 coNTribuTors To drafTiNG aNd reVieW . . . 735
e.b. PodGorsak
department of Medical Physics, McGill university,
Montreal, canada a.l. kesNer
division of human health,
international atomic energy agency, Vienna
P.s. soNi
Medical cyclotron facility,
board of radiation and isotope Technology, bhabha atomic research centre,
Mumbai, india
1.1. iNTroducTioN
The technologies used in nuclear medicine for diagnostic imaging have evolved over the last century, starting with röntgen’s discovery of X rays and becquerel’s discovery of natural radioactivity. each decade has brought innovation in the form of new equipment, techniques, radiopharmaceuticals, advances in radionuclide production and, ultimately, better patient care. all such technologies have been developed and can only be practised safely with a clear understanding of the behaviour and principles of radiation sources and radiation detection. These central concepts of basic radiation physics and nuclear physics are described in this chapter and should provide the requisite knowledge for a more in depth understanding of the modern nuclear medicine technology discussed in subsequent chapters.
1.1.1. Fundamental physical constants
The chapter begins with a short list of physical constants of importance to general physics as well as to nuclear and radiation physics. The data listed below were taken from the codaTa set of values issued in 2006 and are available
from a web site supported by the National institute of science and Technology in Washington, dc, united states of america: http://physics.nist.gov/cuu/constants
— avogadro’s number: Na = 6.022 × 1023 mol–1 or 6.022 × 1023 atoms/mol.
— speed of light in vacuum: c = 2.998 × 108 m/s ≈ 3 × 108 m/s.
— electron charge: e = 1.602 × 10–19 c.
— electron and positron rest mass: me = 0.511 MeV/c2.
— Proton rest mass: mp = 938.3 MeV/c2.
— Neutron rest mass: mn = 939.6 MeV/c2.
— atomic mass unit: u = 931.5 MeV/c2.
— Planck’s constant: h = 6.626 × 10–34 J · s.
— electric constant (permittivity of vacuum): ε0 = 8.854 × 10–12 c · V–1 · m–1.
— Magnetic constant (permeability of vacuum): μ0 = 4π × 10–7 V · s · a–1 · m–1.
— Newtonian gravitation constant: G = 6.672 × 10–11 m3 · kg–1 · s–2.
— Proton mass/electron mass: mp/me = 1836.0.
— specific charge of electron: e/me = 1.758 × 1011 c/kg.
1.1.2. Physical quantities and units
a physical quantity is defined as a quantity that can be used in mathematical equations of science and technology. it is characterized by its numerical value (magnitude) and associated unit. The following rules apply to physical quantities and their units in general:
— symbols for physical quantities are set in italics (sloping type), while symbols for units are set in roman (upright) type (e.g. m = 21 kg;
E = 15 MeV; K = 220 Gy).
— superscripts and subscripts used with physical quantities are set in italics if they represent variables, quantities or running numbers; they are in roman type if they are descriptive (e.g. Nx, λm but λmax, Eab, μtr).
— symbols for vector quantities are set in bold italics.
The currently used metric system of units is known as the international system of units (si). The system is founded on base units for seven basic physical quantities. all other quantities and units are derived from the seven base quantities and units. The seven base si quantities and their units are:
(a) length l: metre (m).
(b) Mass m: kilogram (kg).
(c) Time t: second (s).
(d) electric current I: ampere (a).
(e) Temperature T: kelvin (k).
(f) amount of substance: mole (mol).
(g) luminous intensity: candela (cd).
examples of basic and derived physical quantities and their units are given in Table 1.1.
Table 1.1. basic QuaNTiTies aNd seVeral deriVed Physical QuaNTiTies aNd Their uNiTs iN The iNTerNaTioNal sysTeM of uNiTs aNd iN radiaTioN Physics
Physical
quantity symbol si unit units commonly used in radiation
physics conversion
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, μs, ns, ps 1 s = 103 ms = 106 μs = 109 ns = 1012 ps current I a mA, μA, nA, pA 1 a = 103 ma = 106 μA = 109 na
Temperature T k T (in k) = T (in °c) + 273.16
Mass density ρ kg/m3 g/cm3 1 kg/m3 = 10–3 g/cm3 current density j a/m2
Velocity υ m/s
acceleration a m/s2
frequency ν hz 1 hz = 1 s–1
electric charge q c e 1 e = 1.602 × 10–19 c
force F N 1 N = 1 kg · m · s–2
Pressure P Pa 760 torr = 101.3 kPa 1 Pa = 1 N/m2 = 7.5 × 10–3 torr
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
Power P W 1 W = 1 J/s = 1 V · a
1.1.3. Classification of radiation
radiation, the transport of energy by electromagnetic waves or atomic particles, can be classified into two main categories 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 24.6 eV for helium which is in the group of noble gases. ionization potentials for all other atoms are between the two extremes.
— Non-ionizing radiation cannot ionize matter because its energy per quantum is below the ionization potential of atoms. Near ultraviolet radiation, visible light, infrared photons, microwaves and radio waves are examples of non-ionizing radiation.
— ionizing radiation can ionize matter either directly or indirectly because its quantum energy exceeds the ionization potential of atoms. X rays, γ rays, energetic neutrons, electrons, protons and heavier particles are examples of ionizing radiation.
1.1.4. Classification of ionizing radiation
ionizing radiation is radiation that carries enough energy per quantum to remove an electron from an atom or a molecule, thus introducing a reactive and potentially damaging ion into the environment of the irradiated medium. ionizing radiation can be categorized into two types: (i) directly ionizing radiation and (ii) indirectly ionizing radiation. both directly and indirectly ionizing radiation can traverse human tissue, thereby enabling the use of ionizing radiation in medicine for both imaging and therapeutic procedures.
— directly ionizing radiation consists of charged particles, such as electrons, protons, α particles and heavy ions. It deposits energy in the medium through direct coulomb interactions between the charged particle and orbital electrons of atoms in the absorber.
— indirectly ionizing radiation consists of uncharged (neutral) particles which deposit energy in the absorber through a two-step process. in the first step, the neutral particle releases or produces a charged particle in the absorber which, in the second step, deposits at least part of its kinetic energy in the absorber through coulomb interactions with orbital electrons of the absorber in the manner discussed above for directly ionizing charged particles.
1.1.5. Classification of indirectly ionizing photon radiation
indirectly ionizing photon radiation consists of three main categories:
(i) ultraviolet, (ii) X ray and (iii) γ ray. Ultraviolet photons are of limited use in medicine. radiation used in imaging and/or treatment of disease consists mostly of photons of higher energy, such as X rays and γ rays. The commonly accepted difference between the two is based on the radiation’s origin. The term ‘γ ray’
is reserved for photon radiation that is emitted by the nucleus or from other particle decays. The term ‘X ray’, on the other hand, refers to radiation emitted by electrons, either orbital electrons or accelerated electrons (e.g. bremsstrahlung type radiation).
With regard to their origin, the photons of the indirectly ionizing radiation type fall into four categories: characteristic (fluorescence) X rays, bremsstrahlung X rays, photons resulting from nuclear transitions and annihilation quanta.
1.1.6. Characteristic X rays
orbital electrons have a natural tendency to configure themselves in such a manner that they inhabit a minimal energy state for the atom. When a vacancy is opened within an inner shell, as a result of an ionization or excitation process, an outer shell electron will make a transition to fill the vacancy, usually within a nanosecond for solid materials. The energy liberated in this transition may be released in the form of a characteristic (fluorescence) photon of energy equal to the difference between the binding energies of the initial and final vacancies.
since different elements have different binding energies for their electronic shells, the energy of the photon released in this process will be characteristic of the particular atom. rather than being emitted as a characteristic photon, the transition energy may also be transferred to an orbital electron that is then emitted with kinetic energy that is equal to the transition energy less the electron binding energy. The emitted orbital electron is called an auger electron.
1.1.7. Bremsstrahlung
The word ‘bremsstrahlung’ can be translated from its original German term as ‘braking radiation’, and is a name aptly assigned to the phenomenon.
When light charged particles (electrons and positrons) are slowed down or
‘negatively’ accelerated (decelerated) by interactions with other charged particles in matter (e.g. by atomic nuclei), the kinetic energy that they lose is converted to electromagnetic radiation, referred to as bremsstrahlung radiation. The energy spectrum of bremsstrahlung is non-discrete (i.e. continuous) and ranges between zero and the kinetic energy of the initial charged particle. bremsstrahlung plays
a central role in modern imaging and therapeutic equipment, since it can be used to produce X rays on demand from an electrical energy source. The power emitted in the form of bremsstrahlung photons is proportional to the square of the particle’s charge and the square of the particle’s acceleration.
1.1.8. Gamma rays
When a nuclear reaction or spontaneous nuclear decay occurs, the process may leave the product (daughter) nucleus in an excited state. The nucleus can then make a transition to a more stable state by emitting a γ ray photon and the process is referred to as γ decay. The energy of the photon emitted in γ decay is characteristic of the nuclear energy transition, but the recoil of the emitting atom produces a spectrum centred on the characteristic energy. Gamma rays typically have energies above 100 keV and wavelengths less than 0.1 Å.
1.1.9. Annihilation quanta
When a parent nucleus undergoes β plus decay or a high energy photon interacts with the electric field of either the nucleus or the orbital electron, an energetic positron may be produced. in moving through an absorber medium, the positron loses most of its kinetic energy as a result of coulomb interactions with absorber atoms. These interactions result in collision loss when the interaction is with an orbital electron of the absorber atom and in radiation loss (bremsstrahlung) when the interaction is with the nucleus of the absorber atom.
Generally, after the positron loses all of its kinetic energy through collision and radiation losses, it will undergo a final collision with an available orbital electron (due to the coulomb attractive force between the positively charged positron and a local negatively charged electron) in a process called positron annihilation.
during annihilation, the positron and electron disappear and are replaced by two oppositely directed annihilation quanta, each with an energy of 0.511 MeV.
This process satisfies a number of conservation laws: conservation of electric charge, conservation of linear momentum, conservation of angular momentum and conservation of total energy.
a percentage of positron annihilations occur before the positron expends all of its kinetic energy and the process is then referred to as in-flight annihilation.
The two quanta emitted in in-flight annihilation are not of identical energies and do not necessarily move in absolute opposite directions.
1.1.10. Radiation quantities and units
accurate measurement of radiation is very important in all medical uses of radiation, be it for diagnosis or treatment of disease. in diagnostic imaging procedures, image quality must be optimized, so as to obtain the best possible image with the lowest possible radiation dose to the patient to minimize the risk of morbidity. in radiotherapy, the prescribed dose must be delivered accurately and precisely to maximize the tumour control probability (TcP) and to minimize the normal tissue complication probability (NTcP). in both instances, the risk of morbidity includes acute radiation effects (radiation injury) as well as late radiation-induced effects, such as induction of cancer and genetic damage.
several quantities and units were introduced for the purpose of quantifying radiation and the most important of these are listed in Table 1.2. also listed are the definitions for the various quantities and the relationships between the old units and the si units for these quantities. The definitions of radiation related physical quantities are as follows:
—Exposure X is related to the ability of photons to ionize air. its unit, roentgen (r), is defined as a charge of 2.58 × 10–4 coulombs produced per kilogram of air.
—Kerma K (acronym for kinetic energy released in matter) is defined for indirectly ionizing radiation (photons and neutrons) as energy transferred to charged particles per unit mass of the absorber.
—Dose (also referred to as absorbed dose) is defined as energy absorbed per unit mass of medium. its si unit, gray (Gy), is defined as 1 joule of energy absorbed per kilogram of medium.
—Equivalent dose HT is defined as the dose multiplied by a radiation weighting factor wr. When different types of radiation are present, HT is defined as the sum of all of the individual weighted contributions. The si unit of equivalent dose is the sievert (sv).
—Effective dose E of radiation is defined as the equivalent dose HT multiplied by a tissue weighting factor wT. The si unit of effective dose is also the sievert (sv).
—Activity A of a radioactive substance is defined as the number of nuclear decays per time. its si unit, becquerel (bq), corresponds to one decay per second.
1.2. 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. Protons have a positive charge, neutrons are neutral and electrons have a negative charge mirroring that of a proton. in comparison to electrons, protons and neutrons have a relatively large mass exceeding the electron mass by a factor of almost 2000 (note: mp/me = 1836).
The following general definitions apply to atomic structure:
— atomic number Z is the number of protons and number of electrons in an atom.
— atomic mass number A is the number of nucleons in an atom, i.e. the number of protons Z plus the number of neutrons N in an atom: A = Z + N.
— atomic mass ma is the mass of a specific isotope expressed in atomic mass units u, where 1 u is equal to one twelfth of the mass of the 12c atom (unbound, at rest and in the ground state) or 931.5 MeV/c2. The atomic mass is smaller than the sum of the individual masses of the constituent particles because of the intrinsic energy associated with binding the particles (nucleons) within the nucleus. on the other hand, the atomic mass is larger than the nuclear mass M because the atomic mass includes the mass contribution of Z orbital Table 1.2. radiaTioN QuaNTiTies, uNiTs aNd coNVersioN beTWeeN old aNd si uNiTs
Quantity definition si unit old unit conversion
exposure X
air
X Q m
= ∆
∆
10 C4
2.58 kg air
× − 3
STP
1 esu
1 R=cm air 10 C4
1 R 2.58 kg air
= × −
kerma K K Etr m
=∆
∆
1 Gy 1 J
= kg — —
dose D D Eab
m
=∆
∆
1 Gy 1 J
= kg 1 rad 100 erg
= g 1 Gy = 100 rad
equivalent
dose HT HT = Dwr 1 sv 1 rem 1 sv = 100 rem
effective
dose E E=H wT T 1 sv 1 rem 1 sv = 100 rem
activity A A = lN 1 Bq = 1 s−1 1 Ci = 3.7 10 s× 10 1− 1 Bq = 1 Ci10 3.7 10×
electrons while the nuclear mass M does not. The binding energy of orbital electrons to the nucleus is ignored in the definition of the atomic mass.
While for 12c the atomic mass is exactly 12 u, for all other atoms ma does not exactly match the atomic mass number A. however, for all atomic entities, A (an integer) and ma are very similar to one another and often the same symbol (A) is used for the designation of both. The mass in grams equal to the average atomic mass of a chemical element is referred to as the mole (mol) of the element and contains exactly 6.022 × 1023 atoms. This number is referred to as the avogadro constant Na of entities per mole. The atomic mass number of all elements is, thus, defined such that A grams of every element contain exactly Na atoms. for example, the atomic mass of natural cobalt is 58.9332 u. Thus, one mole of natural cobalt has a mass of 58.9332 g and by definition contains 6.022 × 1023 entities (cobalt atoms) per mole of cobalt.
The number of atoms Na per mass of an element is given as:
a A
N N
m = A (1.1)
The number of electrons per volume of an element is:
a a A
N N N
Z Z Z
V = m = A (1.2)
The number of electrons per mass of an element is:
a A
N N
Z Z
m = A (1.3)
it should be noted that Z/A ≈ 0.5 for all elements with 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. for example, Z/A for 4he is 0.5, for 60co is 0.45 and for 235u is 0.39.
if it is assumed 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 mole of the compound where the mole in grams is defined as the sum of the atomic mass numbers of the atoms making up the molecule. for example, 1 mole of water (h2o) is 18 g of water and 1 mole of carbon dioxide (co2) is 44 g of carbon dioxide. Thus, 18 g of water or 44 g of carbon dioxide contain exactly Na molecules (or 3 Na atoms, since each molecule of water and carbon dioxide contains three atoms).
