Nuclear Medicine Physics: A Handbook for Teachers and Students

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.
Contents
CHAPTER 1. BASIC PHYSICS FOR NUCLEAR MEDICINE . 1
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. PHOTON INTERACTIONS WITH MATTER 30
1.6.1. Exponential absorption of photon beam in absorber 30
1.6.2. Characteristic absorber thicknesses 31
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. GROSS RADIATION EFFECTS ON TUMOURS AND TISSUES/ORGANS . 66
2.7.1. Classification of radiation damage (early versus late) 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 FACILI TY 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. FACILI TY 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. OCCUPATIONAL EXPOSURE . 89
3.5.1. Sources of exposure . 90
3.5.2. Justification, optimization and dose limitation 91
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
4.2.2. Thermal and fast neutron reactions 128
4.2.3. Nuclear fission, fission products 131
4.3. ACCELERATOR PRODUCTION 132
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. PROPAGATION OF ERROR . 172
5.5.1. Sums and differences 173
5.5.2. Multiplication and division by a constant 174
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
CHAPTER 7. ELECTRONICS RELATED TO NUCLEAR MEDICINE IMAGING DEVICES 214
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. SPATIAL RESOLUTION 240
8.3.1. Spatial resolution blurring 240
8.3.2. General measures of spatial resolution 241
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 APPLYI NG 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. PRODUCT CONTAINMENT ENCLOSURES 271
9.7.1. Fume cupboards . 271
9.7.2. Laminar flow cabinets . 272
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
CHAPTER 11. NUCLEAR MEDICINE IMAGING DEVICES 312
11.1. INTRODUCTION 312
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
12.4.3. SPECT . 427
12.4.4. PET acquisition 428
12.4.5. Gated acquisition . 430
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. ANALY TICAL 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
CHAPTER 14. NUCLEAR MEDICINE IMAGE DISPLAY . 512
14.1. INTRODUCTION 512
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. ACCEPTANCE TESTING . 578
15.4.1. Introduction . 578
15.4.2. Procurement and pre-purchase evaluations . 580
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
18.1.3. Absorbed dose rate per unit activity (S value) 628
18.1.4. Strengths and limitations inherent in the formalism 631
18.2. INTERNAL DOSIMETRY IN CLINICAL PRACTICE . 635
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 LY MPHOMA . 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. RADIONUCLIDE THERAPY TREATMENT ROOMS AND WARDS . 666
20.5.1. Shielding for control of external dose . 666
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: ARTEFAC TS 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

Fundamentals of Radiation Dosimetry and Radiological Physics

This book arises out of a course I am teaching for a three-credit (42 hour) graduate-level course Dosimetry Fundamentals being taught at the Department of Nuclear Engineering and Radiological Sciences at the University of Michigan. It is far from complete.
1 Photon Monte Carlo Simulation 1
1.1 Basic photon interaction processes 1
1.1.1 Pair production in the nuclear field 2
1.1.2 The Compton interaction (incoherent scattering) 5
1.1.3 Photoelectric interaction 6
1.1.4 R ayleigh (coherent) interaction 9
1.1.5 R elative importance of various processes 10
1.2 Photon transport logic 10
2 Electron Monte Carlo Simulation 21
2.1 Catastrophic interactions 22
2.1.1 Hard bremsstrahlung production 22
2.1.2 Møller (Bhabha) scattering 22
2.1.3 Positron annihilation 23
2.2 Statistically grouped interactions 23
2.2.1 "Continuous" energy loss 23
2.2.2 Multiple scattering 24
2.3 Electron transport "mechanics" 25
2.3.1 Typical electron tracks 25
2.3.2 Typical multiple scattering substeps 25
2.4 Examples of electron transport 26
2.4.1 Effect of physical modeling on a 20 MeV e− depth-dose curve 26
2.5 Electron transport logic 38
3 Transport in media, interaction models 45
3.1 Interaction probability in an infinite medium 45
3.1.1 Uniform, infinite, homogeneous media 46
3.2 Finitemedia 47
3.3 R egions of different scattering characteristics 47
3.4 Obtaining μ frommicroscopic cross sections 50
3.5 Compounds and mixtures 53
3.6 Branching ratios 54
3.7 Other pathlength schemes 54
3.8 Model interactions 55
3.8.1 Isotropic scattering 55
3.8.2 Semi-isotropic or P1 scattering 55
3.8.3 Rutherfordian scattering 56
3.8.4 Rutherfordian scattering—small angle form 56
4 Macroscopic Radiation Physics 59
4.1 Fluence 59
4.2 Radiation equilibrium 62
4.2.1 Planar fluence 63
4.3 Fluence-related radiometric quantities 65
4.3.1 Energy fluence 65
4.4 Attenuation, radiological pathlength 66
4.4.1 Solid angle subtended by a surface 67
4.4.2 Primary fluence determinations 68
4.4.3 Volumetric symmetry 68
4.5 Fano's theorem 69
5 Photon dose calculation models 77
5.1 Kerma, collision kerma, and dose for photo irradiation 77
5.1.1 Kerma 77
5.1.2 Collision Kerma 80
5.1.3 Dose 83
5.1.4 Comparison of dose depositionmodels 85
5.1.5 Transient charged particle equilibrium 87
5.1.6 Dose due to scattered photons 89
6 Electron dose calculation models 93
6.1 Themicroscopic picture of dose deposition 93
6.2 Stopping power 94
6.2.1 Totalmass stopping power 94
6.2.2 R estricted mass stopping power 98
6.3 Electron angular scattering 99
6.4 Dose due to electrons fromprimary photon interaction 100
6.4.1 A practical semi-analytic dose depositionmodel 101
6.5 The convolution method 105
6.6 Monte Carlo methods 105
7 Ionization chamber-based air kerma standards 111
7.1 Bragg-Gray cavity theory 111
7.1.1 Exposure measurements 112
7.2 Spencer-Attix cavity theory 114
7.3 Modern cavity theory 115
7.4 Interface effects 117
7.5 Saturation corrections 117
7.6 Burlin cavity theory 118
7.7 The dosimetry chain 118

Ionizing Radiation Detectors for Medical Imaging

This book is the outcome of this conviction. It took quite a while to become a reality due to the many sub-specialities in Medical Imaging I wanted to be addressed. Intentionally, this book's coverage is limited to Ionizing Radiation Detectors; thus Ultrasound, Magnetic Resonance Imaging and Spectroscopy and other non-Ionizing Radiation Detectors have not been considered
Chapter 1. INTRODUCTION
1.1 Medical Imaging
1.2 Ionizing Radiation Detectors Development: High Energy Physics
1.3 Ionizing Radiation Detectors for Medical Imaging
1.4 Conclusion
versus Medical Physics
Chapter 2. CONVENTIONAL RADIOLOGY
2.1 Introduction
2.2 Physical Properties of X-Ray Screens
2.2.1 Screen Eficiency
2.2.2 Swank Noise
2.3 Physical Properties of Radiographic Films
2.3.1 Film Characteristic Curve
2.3.2 Film Contrast
2.3.3 Contrast vs Latitude
2.3.4 Film Speed
2.3.5 Reciprocity-Law Failure
2.4 Radiographic Noise
2.5 Definition of Image-Quality
2.5.1 MTF
2.5.2 NPS
2.5.3 DQE
2.6 Image Contrast
2.6.1 The Concept of Sampling Aperture
2.6.2 Noise Contrast
2.6.3 Contrast-Detail Analysis
2.7 Image-Quality of Screen-Film Combinations
2.7.1 MTF, NPS and DQE Measurement
2.7.2 Quality Indices
References
Chapter 3. DETECTORS FOR DIGITAL RADIOGRAPHY
3.1 Introduction
3.2 Characteristics of X-Ray Imaging Systems
3.2.1 Figure of Merit for Image Quality: Detective Quantum
3.2.2 Integrating vs Photon Counting Systems Eficiency
3.3 Semiconductor materials for X-Ray Digital Detectors
3.4 X-Ray Imaging Technologies
3.4.1 Photo-Stimulable Storage Phosphor Imaging Plate
3.4.2 Scintillators/Phosphor + Semiconductor Material
3.4.3 Semiconductor Material (e.g. a-Se) + Readout Matrix Array
3.4.4 Scintillation Material (e.g. Csl) + CCD
3.4.5 20 microstrip Array on Semiconductor Crystal + Integrated
3.4.6 Matrix Array of Pixels on Crystals + VLSI Integrated
3.4.7 X-Ray-to-Light Converter Plates (AlGaAs) (e.g. a-Si:H) + TFT Flat Panels of Thin Film Transistors (TFT) Front-End and Readout Front-End and Readout
3.5 Conclusions
Acknowledgments
References
Chapter 4. DETECTORS FOR CT SCANNERS
4.1 Introduction
4.2 Basic Principle of CT Measurement and Standard Scanner
Configuration
4.3 Mechanical Design
4.4 X-Ray Components
4.5 Collimators and Filtration
4.6 Detector Systems
4.7 Concepts for Multi-Row Detectors
4.8 Outlook
Acknowledgment
References
Chapter 5. SPECIAL APPLICATIONS IN RADIOLOGY
5.1 Introduction
5.2 Special Applications
5.2.1. Mammography
5.2.2 Digital Mammography with Synchrotron Radiation
5.2.3. Subtraction Techniques at the k-Edge of Contrast Agents
5.2.3.1. Detectors and Detector Requirements for Dichromography
5.2.4. Phase Effects
5.3 Conclusion and Outlook
Acknowledgment
Appendix
5.2.4.1. Detectors for Phase Imaging
A. Image formation and Detector Characterization
B. Digital Subtraction Technique
References
Chapter 6. AUTORADIOGRAPHY
6.1 Autoradiographic Methods
6.1.1 Traditional Autoradiography: Methods
6.1.2 Traditional Autoradiography: Limits
6.1.3 New Detectors for Autoradiography
6.2.1 Principles
6.2.2 Commercial Systems and Pe$ormance
6.3.1 Principles
6.3.2 Research Fields
6.3.3 Commercial Systems
6.4.1 Principles
6.2 Imaging Plates
6.3 Gaseous Detectors
6.4 Semiconductor Detectors
6.4.2 Silicon Strip Detectors
6.4.2.1 Strip Architecture
6.4.2.2 Research Fields
6.4.2.3 Commercial Systems
6.4.3.1 Pixel Architecture
6.4.3.2 Research Systems
6.4.3 Pixel Detectors
6.5 Amorphous Materials
6.5.1 Principles
6.5.2 Research and Commercial Systems
6.6 CCD Based Systems
6.6.1 Principles
6.6.2 System Description and Pegormance
6.7.1 Principles
6.7.2 System Description and Performance
6.8 Microchannel Plates
6.8.1 Principles
6.8.2 System Description and Pegormance
6.7 Avalanche Photodiodes
References
Chapter 7. SPECT AND PLANAR IMAGING IN NUCLEAR MEDICINE
7.1 Introduction
7.2 Collimators
7.2.1 Multi-Hole Theory
7.2.2 Single-Hole Theory
7.2.3 Penetration Effects
7.3.1 Scintillators
7.3 Detectors
7.3.1.1 Ya103: Ce
7.3.1.2 Gd2SiOs:Ce
7.3.1.3 Lu2SiOs:Ce
7.3.2.1 Materials
7.3.2.2 Nuclear Medicine Applications
7.3.2 Semiconductors
1.4 Reconstruction Algorithms
1.4.1 Inverse Problems
1.4.2 Ill-Posed Problems
1.4.3 Ill-Conditioning and Regularization
1.4.4 The Radon Transfom
1.4.5 Analytical Methods: Filtered Back-Projection
7.4.6 Iterative Algorithms
1.5.1 High-Resolution SPECT Imaging
I S.2 Planar Imaging from Semiconductor Detectors
1.5.3 Attenuation Corrected Imaging
7.5 Clinical Imaging
References
Chapter 8. POSITRON EMISSION TOMOGRAPHY 281
8.1.1 Tomography Procedures and Terminologies 289
8.2.1 Positron Emission and Radionuclides 292
8.2.2 Annihilation of Positron 296
8.2.3 Interaction of Gamma Rays in Biological Tissue 302
8.3.1 Photon Detection with Inorganic Scintillator Crystals 304
8.3.2 Inorganic Scintillator Readout 311
8.3.3 Parallax Error, Radial Distortion and Depth of Interaction 316
8.4.1 The Filtered Backprojection 320
8.4.2 The Expectation Maximisation Algorithm 330
8.4.3 The OSEM Algorithm 336
8.5 Correction and Normalization Procedures 331
8.5.1 Attenuation 337
8.5.2 Scattering 34 1
8.5.3 Random Coincidences 348
8.5.4 Partial Volume Effect 350
8.5.5 Normalization 35 1
8.6 Commercial Camera Overview 353
References 355
8.1 Introduction to Emission Imaging
8.2 Physics of Positron Emission Tomography
8.3 Detection of Annihilation Photon
8.4 Image Reconstruction 318
Chapter 9. NUCLEAR MEDICINE: SPECIAL APPLICATIONS
IN FUNCTIONAL IMAGING
9.1 Introduction
9.2 Position Sensitive Photo Multiplier Tube
9.2.1 Hamamatsu First PSPMT Generation
9.2.2 Hamamatsu Second PSPMT Generation
9.2.3 Hamamatsu 3rd Generation PSPMT
9.3 Signal Read Out Methods and Scintillation Crystals
9.4 The Role of Compact Imagers in Clinical Application
References
Chapter 10. SMALL ANIMAL SCANNERS
10.1 Introduction
10.2 Position Sensitive Detectors
10.2.1 Gamma-Ray Detection
10.2.2 Scintillator Based Position Sensitive Detectors
10.2.2.1 Continuous Scintillators
10.2.2.2 Matrix Crystals
10.3 Single Photon Emission Computerized Tomography (SPECT)
10.3.1 The Detector
10.3.1.1 Intrinsic Spatial Resolution in SPECT
10.3.1.2 Energy Resolution
10.3.1.3. Rate of Acquisition and Detector Speed
10.3.2.1 Pinhole Collimator
10.3.2.2 Parallel Hole Collimator
10.3.3 Small Animal SPECT Scanners Examples
10.3.2 Collimator Geometries
10.3.3.1 Pinhole Collimator Scanners
10.3.3.2 Parallel Hole Collimator Scanners
10.3.3.3 Converging Hole Collimator Scanner
10.4 Positron Emission Tomography (PET)
10.4.1 Physical Limitations to Spatial Resolution
10.4.1.1 Electron Fermi Motion
10.4.1.2 Scattering in the Source
10.4.1.3 Positron Range
10.4.2 ESficiency and Coincidence Detection of 511 keV gamma rays
10.4.2.1 Intrinsic Detector ESficiency
10.4.2.2 Detector Scatter Fraction
10.4.2.3 Intrinsic Spatial Resolution
10.4.2.3.1 Detector intrinsic spatial resolution
10.4.2.3.2 System intrinsic spatial resolution
10.4.2.4 Random Coincidences and Pile Up Events
10.4.2.5 Energy Resolution
10.4.3 Small Animal PET Scanner Geometries
10.4.3.1 Planar Geometry
10.4.3.2 Ring Geometry
10.5 Small Animal PET Scanner Examples
10.5.1 First Generation Animal Scanners
10.5.1.1 Hamamatsu SHR-2000 and SHR-7700 Scanners
10.5.1.2 CTI-PET Systems ECAT-713
10.5.2.1 Hammersmith RatPET
10.5.2.2 MicroPET
10.5.2.3 Sherbrooke PET and the Munich MADPET
10.5.2.4 The NIH Atlas Scanner
10.5.2.5 Scanner of the Brussels Group: The VUB-PET
10.5.3 Dedicated Rodent Rotating Planar Scanners
10.5.3.1 YAP-(S)PET and TierPET
10.5.3.2 HIDAC
10.5.2 Dedicated Rodent Ring Scanners
10.6 Conclusions
References
Chapter 11. DETECTORS FOR RADIOTHERAPY
1 1.1 Introduction
11.2 Introduction to Radiotherapy
1 1.2.1 External Beam Radiation Delivery
11.2.2 Requirements for Standards and Reporting
11.3 The Physics of Detection for Radiotherapy
1 1.3.1 Photon Interaction Mechanisms
1 1.3.2 Electron Interaction Mechanisms
11.3.3 Units
11.3.4 Charged Particle Equilibrium and Cavity Theory
11.3.5 Effects of Measurement Depth
11.3.6 Quality Assurance and Verijkation Measurements
1 1.4.1 Ionisation Chambers
1 1.4.2 Themzoluminiscent Detectors
1 1.4.3 Diode Detectors
1 1.4.4 Diamond Detectors
11.4 Point Detectors
11.5 Film
1 1.6 Electronic Portal Imaging
11.6.1 Camera-Based Systems
11.6.2 Liquid Ionisation Chamber Based Systems
11.6.3 Amorphous Silicon Flat-Panel Systems
1 1.7.1 Fricke Dosimetry
11.7.2 Polymer Gels
11.7 Radio-Sensitive Chemical Detectors
References

Computer Tomography - From Photon Statistics to Modern Cone-Beam CT

This book provides an overview of X-ray technology, the historic developmental milestones ofmodern CT systems, and gives a comprehensive insight into themain reconstruction methods used in computed tomography. The basis of reconstruction is, undoubtedly, mathematics. However, the beauty of computed tomography cannot be understood without a detailed knowledge of X-ray generation, photon– matter interaction, X-ray detection, photon statistics, as well as fundamental signal processing concepts and dedicated measurement systems.Therefore, the reader will find a number of references to these basic disciplines together with a brief introduction to the underlying principles of CT.
1 Introduction 1
Computed Tomography – State of the Art 1
Inverse Problems 2
Historical Perspective 4
Some Examples 7
Structure of the Book 11
2 Fundamentals of X-ray Physics 15
Introduction 15
X-ray Generation 15
X-ray Cathode 16
Electron–Matter Interaction 19
Temperature Load 23
X-ray Focus and Beam Quality 24
Beam Filtering 28
Special Tube Designs 30
Photon–Matter Interaction 31
Lambert–Beer's Law 32
Mechanisms of Attenuation 34
Problems with Lambert–Beer's Law 46
X-ray Detection 48
Gas Detectors 48
Solid-State Scintillator Detectors 50
Solid-State Flat-Panel Detectors 52
X-ray Photon Statistics 59
Statistical Properties of the X-ray Source 60
Statistical Properties of the X-ray Detector 64
Statistical Law of Attenuation 66
Moments of the Poisson Distribution 68
Distribution for a High Number of X-ray Quanta 70
Non-Poisson Statistics 72
X Contents
3 Milestones of Computed Tomography 75
Introduction 75
Tomosynthesis 76
Rotation–Translation of a Pencil Beam (First Generation) 79
Rotation–Translation of a Narrow Fan Beam (Second Generation) 83
Rotation of aWide Aperture Fan Beam (Third Generation) 84
Rotation–Fix with Closed Detector Ring (Fourth Generation) 87
Electron Beam Computerized Tomography 89
Rotation in Spiral Path 90
Rotation in Cone-Beam Geometry 91
Micro-CT 93
PET-CT Combined Scanners 96
Optical Reconstruction Techniques 98
4 Fundamentals of Signal Processing 101
Introduction 102
Signals 102
Fundamental Signals 102
Systems 104
Linearity 104
Position or Translation Invariance 105
Isotropy and Rotation Invariance 105
Causality 106
Stability 106
Signal Transmission 106
Dirac's Delta Distribution 109
Dirac Comb 112
Impulse Response 115
Transfer Function 116
Fourier Transform 118
ConvolutionTheorem 124
Rayleigh'sTheorem125
PowerTheorem 125
Filtering in the Frequency Domain 126
Hankel Transform 128
Abel Transform 132
Hilbert Transform 133
SamplingTheorem and Nyquist Criterion 135
Wiener–KhintchineTheorem141
Fourier Transform of Discrete Signals 144
Finite Discrete Fourier Transform 145
z-Transform 147
Chirp z-Transform 148
Contents XI
5 Two-Dimensional Fourier-Based Reconstruction Methods 151
Introduction 151
Radon Transformation 153
Inverse Radon Transformation and Fourier SliceTheorem 163
Implementation of the Direct Inverse Radon Transform 167
Linogram Method 170
Simple Backprojection 175
Filtered Backprojection 179
Comparison Between Backprojection and Filtered Backprojection 183
Filtered Layergram: Deconvolution of the Simple Backprojection 187
Filtered Backprojection and Radon's Solution 191
Cormack Transform 194
6 Algebraic and Statistical Reconstruction Methods 201
Introduction 201
Solution with Singular Value Decomposition 207
Iterative Reconstruction with ART 211
Pixel Basis Functions and Calculation of the SystemMatrix 218
Discretization of the Image: Pixels and Blobs 219
Approximation of the SystemMatrix in the Case of Pixels 221
Approximation of the SystemMatrix in the Case of Blobs 222
Maximum Likelihood Method 223
Maximum Likelihood Method for Emission Tomography 224
Maximum Likelihood Method for Transmission CT 230
Regularization of the Inverse Problem 235
ApproximationThroughWeighted Least Squares 238
7 Technical Implementation 241
Introduction 241
Reconstruction with Real Signals 242
Frequency DomainWindowing 244
Convolution in the Spatial Domain 247
Discretization of the Kernels 252
Practical Implementation of the Filtered Backprojection 255
Filtering of the Projection Signal 255
Implementation of the Backprojection 258
Minimum Number of Detector Elements 258
Minimum Number of Projections 259
Geometry of the Fan-Beam System261
Image Reconstruction for Fan-Beam Geometry 262
Rebinning of the Fan Beams 265
Complementary Rebinning 270
XII Contents
Filtered Backprojection for Curved Detector Arrays 272
Filtered Backprojection for Linear Detector Arrays 280
Discretization of Backprojection for Fan-Beam Geometry 286
Quarter-Detector Offset and SamplingTheorem 293
8 Three-Dimensional Fourier-Based Reconstruction Methods 303
Introduction 303
Secondary Reconstruction Based on 2D Stacks of Tomographic Slices 304
Spiral CT 309
Exact 3D Reconstruction in Parallel-Beam Geometry 321
3D Radon Transform and the Fourier Slice Theorem321
Three-Dimensional Filtered Backprojection 326
Filtered Backprojection and Radon's Solution 327
Central SectionTheorem 329
Orlov's Sufficiency Condition 335
Exact 3D Reconstruction in Cone-Beam Geometry 336
Key Problem of Cone-Beam Geometry 339
Method of Grangeat 341
Computation of the First Derivative on the Detector 347
Reconstruction with the Derivative of the Radon Transform 348
Central SectionTheorem and Grangeat's Solution 350
Direct 3D Fourier Reconstruction with the Cone-Beam Geometry 354
Exact Reconstruction using Filtered Backprojection 357
Approximate 3D Reconstructions in Cone-Beam Geometry 366
Missing Data in the 3D Radon Space 366
FDK Cone-Beam Reconstruction for Planar Detectors 371
FDK Cone-Beam Reconstruction for Cylindrical Detectors 388
Variations of the FDK Cone-Beam Reconstruction 390
Helical Cone-Beam Reconstruction Methods 394
9 Image Quality and Artifacts 403
Introduction 403
Modulation Transfer Function of the Imaging Process 404
Modulation Transfer Function and Point Spread Function 410
Modulation Transfer Function in Computed Tomography 412
SNR, DQE, and ROC421
2D Artifacts 423
Partial Volume Artifacts 423
Beam-Hardening Artifacts 425
Motion Artifacts 432
Sampling Artifacts 435
Electronic Artifacts 435
Detector Afterglow 437
Metal Artifacts 438
Contents XIII
Scattered Radiation Artifacts 443
3D Artifacts 445
Partial Volume Artifacts 446
Staircasing in Slice Stacks 448
Motion Artifacts 450
Shearing in Slice Stacks Due to Gantry Tilt 451
Sampling Artifacts in Secondary Reconstruction 454
Metal Artifacts in Slice Stacks 455
Spiral CT Artifacts 456
Cone-Beam Artifacts 458
Segmentation and Triangulation Inaccuracies 459
Noise in Reconstructed Images 462
Variance of the Radon Transform 462
Variance of the Reconstruction 464
Dose, Contrast, and Variance 467
10 Practical Aspects of Computed Tomography 471
Introduction 471
Scan Planning 471
Data Representation 475
Hounsfield Units 475
Window Width and Window Level 476
Three-Dimensional Representation 479
Some Applications in Medicine 482
11 Dose 485
Introduction 485
Energy Dose, Equivalent Dose, and Effective Dose 486
Definition of Specific CT Dose Measures 487
Device-RelatedMeasures for Dose Reduction 493
User-RelatedMeasures for Dose Reduction 499