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