Part I Basic Imaging Principles 1 <br> 1 Introduction 5 <br>1.1 History of Medical Imaging 5 <br>1.2 Physical Signals 6 <br>1.3 Imaging Modalities 7 <br>1.4 Projection Radiography 7 <br>1.5 Computed Tomography 9 <br>1.6 Nuclear Medicine 10 <br>1.7 Ultrasound Imaging 11 <br>1.8 Magnetic Resonance Imaging 12 <br>1.9 Multimodality Imaging 13 <br>1.10 Summary and Key Concepts 13 <br> <br> 2 Signals and Systems 15 <br>2.1 Introduction 15 <br>2.2 Signals 16 <br>2.2.1 Point Impulse 16 <br>2.2.2 Line Impulse 19 <br>2.2.3 Comb and Sampling Functions 19 <br>2.2.4 Rect and Sinc Functions 20 <br>2.2.5 Exponential and Sinusoidal Signals 22 <br>2.2.6 Separable Signals 23 <br>2.2.7 Periodic Signals 23 <br>2.3 Systems 24 <br>2.3.1 Linear Systems 24 <br>2.3.2 Impulse Response 25 <br>2.3.3 Shift Invariance 25 <br>2.3.4 Connections of LSI Systems 28 <br>2.3.5 Separable Systems 30 <br>2.3.6 Stable Systems 31 <br>2.4 The Fourier Transform 31 <br>2.5 Properties of the Fourier Transform 36 <br>2.5.1 Linearity 36 <br>2.5.2 Translation 37 <br>2.5.3 Conjugation and Conjugate Symmetry 37 <br>2.5.4 Scaling 37 <br>2.5.5 Rotation 38 <br>2.5.6 Convolution 38 <br>2.5.7 Product 39 <br>2.5.8 Separable Product 40 <br>2.5.9 Parseval’s Theorem 40 <br>2.5.10 Separability 40 <br>2.6 Transfer Function 41 <br>2.7 Circular Symmetry and the Hankel Transform 43 <br>2.8 Summary and Key Concepts 47 <br> <br> 3 Image Quality 54 <br>3.1 Introduction 54 <br>3.2 Contrast 55 <br>3.2.1 Modulation 56 <br>3.2.2 Modulation Transfer Function 56 <br>3.2.3 Local Contrast 60 <br>3.3 Resolution 61 <br>3.3.1 Line Spread Function 61 <br>3.3.2 Full Width at Half Maximum 62 <br>3.3.3 Resolution and Modulation Transfer Function 63 <br>3.3.4 Subsystem Cascade 65 <br>3.3.5 Resolution Tool 68 <br>3.3.6 Temporal and Spectral Resolution 68 <br>3.4 Noise 69 <br>3.4.1 Random Variables 70 <br>3.4.2 Continuous Random Variables 70 <br>3.4.3 Discrete Random Variables 72 <br>3.4.4 Independent Random Variables 75 <br>3.5 Signal-to-Noise Ratio 76 <br>3.5.1 Amplitude SNR 77 <br>3.5.2 Power SNR 77 <br>3.5.3 Differential SNR 79 <br>3.5.4 Decibels 80 <br>3.6 Sampling 80 <br>3.6.1 Signal Model for Sampling 81 <br>3.6.2 Nyquist Sampling Theorem 83 <br>3.6.3 Anti-Aliasing Filters 85 <br>3.7 Other Effects 86 <br>3.7.1 Artifacts 86 <br>3.7.2 Distortion 88 <br>3.8 Accuracy 88 <br>3.8.1 Quantitative Accuracy 89 <br>3.8.2 Diagnostic Accuracy 89 <br>3.9 Summary and Key Concepts 92 <br> <br> Part II Radiographic Imaging 101 <br> 4 Physics of Radiography 106 <br>4.1 Introduction 106 <br>4.2 Ionization 107 <br>4.2.1 Atomic Structure 107 <br>4.2.2 Electron Binding Energy 109 <br>4.2.3 Ionization and Excitation 109 <br>4.3 Forms of Ionizing Radiation 110 <br>4.3.1 Particulate Radiation 110 <br>4.3.2 Electromagnetic Radiation 112 <br>4.4 Nature and Properties of Ionizing Radiation 113 <br>4.4.1 Primary Energetic Electron Interactions 114 <br>4.4.2 Primary Electromagnetic Radiation Interactions 116 <br>4.5 Attenuation of Electromagnetic Radiation 120 <br>4.5.1 Measures of X-Ray Beam Strength 121 <br>4.5.2 Narrow Beam, Monoenergetic Photons 123 <br>4.5.3 Narrow Beam, Polyenergetic Photons 125 <br>4.5.4 Broad Beam Case 127 <br>4.6 Radiation Dosimetry 127 <br>4.6.1 Exposure 127 <br>4.6.2 Dose and Kerma 128 <br>4.6.3 Linear Energy Transfer (LET) 128 <br>4.6.4 The f -Factor 128 <br>4.6.5 Dose Equivalent 129 <br>4.6.6 Effective Dose 130 <br>4.7 Summary and Key Concepts 131 <br> <br> 5 Projection Radiography 135 <br>5.1 Introduction 135 <br>5.2 Instrumentation 136 <br>5.2.1 X-Ray Tubes 136 <br>5.2.2 Filtration and Restriction 139 <br>5.2.3 Compensation Filters and Contrast Agents 141 <br>5.2.4 Grids, Airgaps, and Scanning Slits 143 <br>5.2.5 Film-Screen Detectors 146 <br>5.2.6 X-Ray Image Intensifiers 148 <br>5.2.7 Digital Radiography 149 <br>5.2.8 Mammography 154 <br>5.3 Image Formation 154 <br>5.3.1 Basic Imaging Equation 154 <br>5.3.2 Geometric Effects 155 <br>5.3.3 Blurring Effects 162 <br>5.3.4 Film Characteristics 166 <br>5.4 Noise and Scattering 169 <br>5.4.1 Signal-to-Noise Ratio 169 <br>5.4.2 Quantum Efficiency and Detective Quantum Efficiency 171 <br>5.4.3 Compton Scattering 173 <br>5.5 Summary and Key Concepts 175 <br> <br> 6 Computed Tomography 186 <br>6.1 Introduction 186 <br>6.2 CT Instrumentation 188 <br>6.2.1 CT Generations 188 <br>6.2.2 X-Ray Source and Collimation 194 <br>6.2.3 Dual-Energy CT 194 <br>6.2.4 CT Detectors 195 <br>6.2.5 Gantry, Slip Ring, and Patient Table 196 <br>6.3 Image Formation 197 <br>6.3.1 Line Integrals 197 <br>6.3.2 CT Numbers 198 <br>6.3.3 Parallel-Ray Reconstruction 198 <br>6.3.4 Fan-Beam Reconstruction 208 <br>6.3.5 Helical CT Reconstruction 212 <br>6.3.6 Cone Beam CT 213 <br>6.3.7 Iterative Reconstruction 213 <br>6.4 Image Quality in CT 213 <br>6.4.1 Resolution 214 <br>6.4.2 Noise 216 <br>6.4.3 Artifacts 221 <br>6.5 Summary and Key Points 223 <br> <br> Part III Nuclear Medicine Imaging 235<br>7 The Physics of Nuclear Medicine 239 <br>7.1 Introduction 239 <br>7.2 Nomenclature 240 <br>7.3 Radioactive Decay 240 <br>7.3.1 Mass Defect and Binding Energy 240 <br>7.3.2 Line of Stability 242 <br>7.3.3 Radioactivity 243 <br>7.3.4 Radioactive Decay Law 243 <br>7.4 Modes of Decay 245 <br>7.4.1 Positron Decay and Electron Capture 245 <br>7.4.2 Isomeric Transition 246 <br>7.5 Statistics of Decay 247 <br>7.6 Radiotracers 249 <br>7.7 Summary and Key Concepts 251 <br> <br> 8 Planar Scintigraphy 255 <br>8.1 Introduction 255 <br>8.2 Instrumentation 255 <br>8.2.1 Collimators 256 <br>8.2.2 Scintillation Crystal 258 <br>8.2.3 Photomultiplier Tubes 258 <br>8.2.4 Positioning Logic 260 <br>8.2.5 Pulse Height Analyzer 260 <br>8.2.6 Gating Circuit 262 <br>8.2.7 Image Capture 263 <br>8.2.8 Solid State and Other New Cameras 264 <br>8.3 Image Formation 264 <br>8.3.1 Event Position Estimation 264 <br>8.3.2 Acquisition Modes 266 <br>8.3.3 Anger Camera Imaging Equation 269 <br>8.4 Image Quality 272 <br>8.4.1 Resolution 273 <br>8.4.2 Sensitivity 276 <br>8.4.3 Uniformity 278 <br>8.4.4 Energy Resolution 279 <br>8.4.5 Noise 280 <br>8.4.6 Factors Affecting Count Rate 281 <br>8.5 Summary and Key Concepts 282 <br> <br> 9 Emission Computed Tomography 293 <br>9.1 Instrumentation 294 <br>9.1.1 SPECT Instrumentation 294 <br>9.1.2 PET Instrumentation 298 <br>9.2 Image Formation 304 <br>9.2.1 SPECT Image Formation 304 <br>9.2.2 PET Image Formation 309 <br>9.2.3 Iterative Reconstruction 313 <br>9.3 Image Quality in SPECT and PET 317 <br>9.3.1 Spatial Resolution 318 <br>9.3.2 Attenuation and Scatter 319 <br>9.3.3 Random Coincidences 320 <br>9.3.4 Contrast 320 <br>9.3.5 Noise and Signal-to-Noise Ratio 321 <br>9.4 Summary and Key Concepts 321 <br> <br> Part IV Ultrasound Imaging 331<br>10 The Physics of Ultrasound 335 <br>10.1 Introduction 335 <br>10.2 The Wave Equation 336 <br>10.2.1 Three-Dimensional Acoustic Waves 336 <br>10.2.2 Plane Waves 338 <br>10.2.3 Spherical Waves 340 <br>10.3 Wave Propagation 341 <br>10.3.1 Acoustic Energy and Intensity 341 <br>10.3.2 Reflection and Refraction at Plane Interfaces 342 <br>10.3.3 Transmission and Reflection Coefficients at Plane Interfaces 343 <br>10.3.4 Attenuation 344 <br>10.3.5 Scattering 347 <br>10.3.6 Nonlinear Wave Propagation 347 <br>10.4 Doppler Effect 349 <br>10.5 Beam Pattern Formation and Focusing 353 <br>10.5.1 Simple Field Pattern Model 354 <br>10.5.2 Diffraction Formulation 355 <br>10.5.3 Focusing 361 <br>10.6 Summary and Key Concepts 362 <br> <br> 11 Ultrasound Imaging Systems 367 <br>11.1 Introduction 367 <br>11.2 Instrumentation 367 <br>11.2.1 Ultrasound Transducer 367 <br>11.2.2 Ultrasound Probes 372 <br>11.3 Pulse-Echo Imaging 374 <br>11.3.1 The Pulse-Echo Equation 374 <br>11.4 Transducer Motion 377 <br>11.5 Ultrasound Imaging Modes 380 <br>11.5.1 A-Mode Scan 380 <br>11.5.2 M-Mode Scan 381 <br>11.5.3 B-Mode Scan 381 <br>11.6 Steering and Focusing 386 <br>11.6.1 Transmit Steering and Focusing 386 <br>11.6.2 Beamforming and Dynamic Focusing 388 <br>11.7 Three-Dimensional Ultrasound Imaging 391 <br>11.8 Image Quality 392 <br>11.8.1 Resolution 392 <br>11.8.2 Noise and Speckle 395 <br>11.9 Summary and Key Concepts 396 <br> <br> Part V Magnetic Resonance Imaging 407<br>12 Physics of Magnetic Resonance 410 <br>12.1 Introduction 410 <br>12.2 Microscopic Magnetization 410 <br>12.3 Macroscopic Magnetization 412 <br>12.4 Precession and Larmor Frequency 414 <br>12.5 Transverse and Longitudinal Magnetization 416 <br>12.5.1 NMR Signals 417 <br>12.5.2 Rotating Frame 419 <br>12.6 RF Excitation 419 <br>12.7 Relaxation 422 <br>12.8 The Bloch Equations 425 <br>12.9 Spin Echoes 426 <br>12.10 Basic Contrast Mechanisms 429 <br>12.11 Summary and Key Concepts 433 <br> <br> 13 Magnetic Resonance Imaging 439 <br>13.1 Instrumentation 439 <br>13.1.1 System Components 439 <br>13.1.2 Magnet 441 <br>13.1.3 Gradient Coils 442 <br>13.1.4 Radio Frequency Coils 445 <br>13.1.5 Scanning Console and Computer 446 <br>13.2 MRI Data Acquisition 447 <br>13.2.1 Encoding Spatial Position 447 <br>13.2.2 Slice Selection 449 <br>13.2.3 Frequency Encoding 455 <br>13.2.4 Polar Scanning 460 <br>13.2.5 Gradient Echoes 461 <br>13.2.6 Phase Encoding 462 <br>13.2.7 Spin Echoes 465 <br>13.2.8 Pulse Repetition Interval 467 <br>13.2.9 Realistic Pulse Sequences 467 <br>13.3 Image Reconstruction 469 <br>13.3.1 Rectilinear Data 470 <br>13.3.2 Polar Data 471 <br>13.3.3 Imaging Equations 472 <br>13.4 Image Quality 475 <br>13.4.1 Sampling 475 <br>13.4.2 Resolution 477 <br>13.4.3 Noise 479 <br>13.4.4 Signal-to-Noise Ratio 481 <br>13.4.5 Artifacts 482 <br>13.5 Advanced Contrast Mechanisms 483 <br>13.6 Summary and Key Concepts 487 <br>Index 497 <br>