Preface ........................................................ xi
Nomenclature and Abbreviations ............................... xiii
1 Introduction ................................................. 1
1.1 Conventional X-ray Tomography ........................... 2
1.2 History of Computed Tomography .......................... 7
1.3 Different Generations of CT Scanners ................... 14
1.4 Problems ............................................... 19
References ............................................. 19
2 Preliminaries ............................................... 23
2.1 Mathematics Fundamentals ............................... 23
2.1.1 Fourier transform and convolution ............... 23
2.1.2 Random variables ................................ 27
2.1.3 Linear algebra .................................. 30
2.2 Fundamentals of X-ray Physics .......................... 33
2.2.1 Production of x rays ............................ 33
2.2.2 Interaction of x rays with matter ............... 36
2.3 Measurement of Line Integrals and Data Conditioning .... 42
2.4 Sampling Geometry and Sinogram ......................... 46
2.5 Problems ............................................... 48
References ............................................. 52
3 Image Reconstruction ........................................ 55
3.1 Introduction ........................................... 55
3.2 Several Approaches to Image Reconstruction ............. 57
3.3 The Fourier Slice Theorem .............................. 61
3.4 The Filtered Backprojection Algorithm .................. 65
3.4.1 Derivation of the filtered back-projection
formula ......................................... 68
3.4.2 Computer implementation ......................... 71
3.4.3 Targeted reconstruction ......................... 85
3.5 Fan-Beam Reconstruction ................................ 88
3.5.1 Reconstruction formula for equiangular
sampling ........................................ 89
3.5.2 Reconstruction formula for equal-spaced
sampling ........................................ 95
3.5.3 Fan-beam to parallel-beam rebinning ............. 97
3.6 Iterative Reconstruction .............................. 101
3.6.1 Mathematics verses reality ..................... 102
3.6.2 The general approach to iterative
reconstruction ................................. 103
3.6.3 Modeling of the scanner's optics and physics ... 105
3.6.4 Updating strategy .............................. 109
3.7 Problems .............................................. 112
References ................................................. 114
4 Image Presentation ......................................... 119
4.1 CT Image Display ...................................... 119
4.2 Volume Visualization .................................. 123
4.2.1 Multiplanar reformation ........................ 123
4.2.2 MIP, minMIP, and volume rendering .............. 128
4.2.3 Surface rendering .............................. 136
4.3 Impact of Visualization Tools ......................... 137
4.4 Problems .............................................. 140
References ................................................. 142
5 Key Performance Parameters of the CT Scanner ............... 143
5.1 High-Contrast Spatial Resolution ...................... 143
5.1.1 In-plane resolution ............................ 144
5.1.2 Slice sensitivity profile ...................... 150
5.2 Low-Contrast Resolution ............................... 154
5.3 Temporal Resolution ................................... 160
5.4 CT Number Accuracy and Noise .......................... 167
5.5 Performance of the Scanogram .......................... 172
5.6 Problems .............................................. 174
References ................................................. 176
6 Major Components of the CT Scanner ......................... 179
6.1 System Overview ....................................... 179
6.2 The X-ray Tube and High-Voltage Generator ............. 180
6.3 The X-ray Detector and Data-Acquisition Electronics ... 190
6.4 The Gantry and Slip Ring .............................. 197
6.5 Collimation and Filtration ............................ 199
6.6 The Reconstruction Engine ............................. 202
6.7 Problems .............................................. 203
References ................................................. 205
7 Image Artifacts: Appearances, Causes, and Corrections ...... 207
7.1 What Is an Image Artifact? ............................ 207
7.2 Different Appearances of Image Artifacts .............. 209
7.3 Artifacts Related to System Design .................... 214
7.3.1 Aliasing ....................................... 214
7.3.2 Partial volume ................................. 226
7.3.3 Scatter ........................................ 231
7.3.4 Noise-induced streaks .......................... 235
7.4 Artifacts Related to X-ray Tubes ...................... 239
7.4.1 Off-focal radiation ............................ 239
7.4.2 Tube arcing .................................... 242
7.4.3 Tube rotor wobble .............................. 244
7.5 Detector-induced Artifacts ............................ 244
7.5.1 Offset, gain, nonlinearity, and radiation
damage ......................................... 244
7.5.2 Primary speed and afterglow .................... 248
7.5.3 Detector response uniformity ................... 253
7.6 Patient-induced Artifacts ............................. 258
7.6.1 Patient motion ................................. 258
7.6.2 Beam hardening ................................. 270
7.6.3 Metal artifacts ................................ 280
7.6.4 Incomplete projections ......................... 283
7.7 Operator-induced Artifacts ............................ 288
7.8 Problems .............................................. 291
References ............................................ 295
8 Computer Simulation and Analysis ........................... 301
8.1 What Is Computer Simulation? .......................... 301
8.2 Simulation Overview ................................... 303
8.3 Simulation of Optics .................................. 305
8.4 Computer Simulation of Physics-related Performance .... 316
8.5 Problems .............................................. 323
References ............................................ 324
9 Helical or Spiral CT ....................................... 327
9.1 Introduction .......................................... 327
9.1.1 Clinical needs ................................. 327
9.1.2 Enabling technology ............................ 331
9.2 Terminology and Reconstruction ........................ 332
9.2.1 Helical pitch .................................. 332
9.2.2 Basic reconstruction approaches ................ 333
9.2.3 Selection of the interpolation algorithm and
reconstruction plane ........................... 339
9.2.4 Helical fan-to-parallel rebinning .............. 343
9.3 Slice Sensitivity Profile and Noise ................... 348
9.4 Helically Related Image Artifacts ..................... 355
9.4.1 High-pitch helical artifacts ................... 355
9.4.2 Noise-induced artifacts ........................ 360
9.4.3 System-misalignment-induced artifacts .......... 364
9.4.4 Helical artifacts caused by object slope ....... 368
9.5 Problems .............................................. 371
References ................................................. 372
10 Multislice CT .............................................. 375
10.1 The Need for Multislice CT ............................ 375
10.2 Detector Configurations of Multislice CT .............. 378
10.3 Nonhelical Mode of Reconstruction ..................... 385
10.4 Multislice Helical Reconstruction ..................... 396
10.4.1 Selection of interpolation samples ............. 398
10.4.2 Selection of region of reconstruction .......... 402
10.4.3 Reconstruction algorithms with 3D
backprojection ................................. 405
10.5 Multislice Artifacts .................................. 410
10.5.1 General description ............................ 410
10.5.2 Multislice CT cone-beam effects ................ 411
10.5.3 Interpolation-related image artifacts .......... 413
10.5.4 Noise-induced multislice artifacts ............. 416
10.5.5 Tilt artifacts in multislice helical CT ........ 416
10.5.6 Distortion in step-and-shoot mode SSP .......... 419
10.5.7 Artifacts due to geometric alignment ........... 420
10.5.8 Comparison of multislice and single-slice
helical CT ..................................... 422
10.6 Problems .............................................. 422
References ............................................ 425
11 X-ray Radiation and Dose-Reduction Techniques .............. 433
11.1 Biological Effects of X-ray Radiation ................. 434
11.2 Measurement of X-ray dose ............................. 436
11.2.1 Terminology and the measurement standard ....... 436
11.2.2 Other measurement units and methods ............ 442
11.2.3 Issues with the current CTDI ................... 443
11.3 Methodologies for Dose Reduction ...................... 445
11.3.1 Tube-current modulation ........................ 446
11.3.2 Umbra-penumbra and overbeam issues ............. 448
11.3.3 Physiological gating ........................... 451
11.3.4 Organ-specific dose reduction .................. 454
11.3.5 Protocol optimization and impact of the
operator ....................................... 456
11.3.6 Postprocessing techniques ...................... 461
11.3.7 Advanced reconstruction ........................ 462
11.4 Problems .............................................. 463
References ................................................. 465
12 Advanced CT Applications ................................... 469
12.1 Introduction .......................................... 469
12.2 Cardiac Imaging ....................................... 471
12.2.1 Coronary artery calcification (CAC) ............ 472
12.2.2 Coronary artery imaging (CAI) .................. 476
12.2.2.1 Data acquisition and reconstruction ... 478
12.2.2.2 Temporal resolution improvement ....... 485
12.2.2.3 Spatial resolution improvement ........ 492
12.2.2.4 Dose and coverage ..................... 493
12.3 CT Fluoroscopy ........................................ 497
12.4 CT Perfusion .......................................... 503
12.5 Screening and Quantitative CT ......................... 512
12.5.1 Lung cancer screening ......................... 512
12.5.2 Quantitative CT ............................... 516
12.5.3 CT colonography ............................... 519
12.6 Dual-Energy CT ........................................ 522
12.7 Problems .............................................. 532
References ................................................. 534
Glossary ...................................................... 545
Index ......................................................... 551
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