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Contents

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

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 34

    2.2.1 Production of x-rays 34

    2.2.2 Interaction of x-rays with matter 37

2.3 Measurement of Line Integrals and Data Conditioning 42

2.4 Sampling Geometry and Sinogram 47

2.5 Problems 49

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 equi-angular 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 scanner's optics and physics 105

    3.6.4 Updating strategy 109

3.7 Problems 112

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

    4.2.2 Surface rendering 136

4.3 Impact of the Visualization Tools 137

4.4 Problems 140

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

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

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

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

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 approach 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

10 Multislice CT 375

10.1 The Need for Multislice 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 414

    10.5.4 Noise-induced multislice artifacts 416

    10.5.5 Tilt artifacts in multislice CT 417

    10.5.6 Distortion in step-and-shoot mode SSP 419

    10.5.7 Artifacts due to geometric alignment 421

    10.5.8 Comparison of multislice and single-slice helical CT 422

10.6 Problems 424

11 X-ray Radiation and Dose-Reduction Techniques 435

11.1 Biological Effects of X-ray Radiation 436

11.2 Measurement of X-ray dose 437

    11.2.1 Terminologies and the measurement Standard 438

    11.2.2 Other measurement units and methods 444

    11.2.3 Issues with the current CTDI 445

11.3 Methodologies for Dose Reduction 446

    11.3.1 Tube-current modulation 448

    11.3.2 Umbra-penumbra and overbeam issues 449

    11.3.3 Physiological gating 452

    11.3.4 Organ-specific dose reduction 455

    11.3.5 Protocol optimization and impact of the operator 458

    11.3.6 Postprocessing techniques 463

    11.3.7 Advanced reconstruction 464

11.4 Problems 465

12 Advanced CT Applications 471

12.1 Introduction 471

12.2 Cardiac Imaging 473

    12.2.1 Coronary artery calcification (CAC) 474

    12.2.2 Coronary artery imaging 478

      12.2.2.1 Data acquisition and reconstruction 480

      12.2.2.2 Temporal resolution improvement 487

      12.2.2.3 Spatial resolution improvement 494

      12.2.2.4 Dose and coverage 494

12.3 CT Fluoroscopy 498

12.4 CT Perfusion 505

12.5 Screening and Quantitative CT 513

    12.5.1 Lung cancer screening 514

    12.5.2 Quantitative CT 518

    12.5.3 CT colonography 520

12.6 Dual-Energy CT 523

12.7 Problems 533

Glossary 545

Index 551

Preface

Since the release of the first edition of this book in 2003, x-ray computed tomography (CT) has experienced tremendous growth thanks to technological advances and new clinical discoveries. Few could have predicted the speed and magnitude of the progress, and even fewer could have predicted the diverse nature of the technological advancement. The second edition of this book attempts to capture these advances and reflect on their clinical impact.

The second edition provides significant changes and additions in several areas. The first major addition is a new chapter on radiation dose. In the last few years, significant attention has been paid to this subject by academic researchers, radiologists, the general public, and the news media. An increased awareness of the impact of radiation dose on human health has led to the gradual adoption of the "as low as reasonably achievable" (ALARA) principle, the implementation of American College of Radiology (ACR) accreditation and other dose reference levels, and the development of many advanced dose-saving features for CT scanners. The new Chapter 11 briefly describes some of the known biological effects of radiation dose, then presents different dose definitions and measurements, and concludes with an illustration of various dose-reduction techniques. At the time the first edition was published, the term "multislice" CT was an accurate description of state-of-the-art scanners. Sixteen-slice scanners had just been introduced commercially, and their clinical utilities and advantages had just begun to be discovered. Since then, the "slice war" has continued, and now 64-, 128-, 256-, and 320-slice scanners are the new state of the art. These scanners can be easily labeled as "cone-beam" CT. They require not only a detector with wider coverage, but also other technologies such as new calibration techniques and reconstruction algorithms. Chapter 10 has been significantly expanded to discuss the technologies associated with these scanners and the new image artifacts created by them.

Since the first edition, CT advancement has not been limited to the technology. Advances also have been made in many areas of clinical applications, including the rapid development of cardiac CT imaging and new applications inspired by the reintroduction of dual-energy CT. Chapter 12 presents these advances and the fundamental physics and technologies behind them.

Image artifacts have accompanied x-ray CT ever since its birth over 30 years ago. Some artifacts are caused by the characteristics of the physics involved, some are caused by technological limitations, some are created by new technologies, some are related to the patient, some result from suboptimal design, and some are introduced by the operator. Chapter 7 has been expanded to reflect the ever-evolving nature of these artifacts and various efforts to overcome them.

Historically, CT advances were driven by the development of new hardware. However, it has become increasingly clear that hardware alone cannot solve all of the technical and clinical problems that CT operators face. The second edition includes significant updates to the section on statistical iterative reconstruction technology and presents some of the exciting new developments in this area.

To enhance readers' understanding of the material and to inspire creative thinking about these subjects, a set of "problems" concludes each chapter. Many problems are open-ended and may not have uniquely correct solutions. Hopefully readers will find these problems useful and will develop new problems of their own.

At the time of this writing, the world is experiencing an unprecedented financial crisis—that some call a financial "tsunami." It is impossible to estimate or predict the impact of this crisis on the market for x-ray CT. However, CT technology is unlikely to remain stagnant. Many new exciting advances will take place in both the technology and its clinical applications.

Jiang Hsieh
May 2009