1 Principles of Computed Tomography 18

1.1 General Considerations on Slice Imaging 18

1.1.1 Computed Tomography – a Digital Modality 18

1.1.2 Why Do Slice Images Offer Higher Contrast? 21

1.2 Basic Principles of CT 23

1.2.1 What Do We Measure in CT? 24

1.2.2 How Do We Measure an Object in CT? 26

1.2.3 How Do We Compute a CT Image? 27

1.2.4 What Is Displayed in CT Images? 31

2 Technical Concepts 37

2.1 Phases of Development and Goals 37

2.1.1 The Seventies – from Head to Whole Body Scanning 37

2.1.2 The Eighties – Fast Scanning of Single Slices 39

2.1.3 The Nineties – Fast Volume Scanning 40

2.1.4 The 2000s – Diversity and Even Faster Volume Scanning 41

2.1.5 The 2010s will be the Decade of Sub-mSv CT! 42

2.2 Standard Scanner Configuration 42

2.2.1 Mechanical Design 42

2.2.2 X-ray Components 47

2.2.3 Collimators and Filtration 51

2.2.4 Detector Systems 53

2.3 Scan Modes and Scan Parameters 64

2.3.1 Survey Radiographs 64

2.3.2 Scanning Single Sections – Sequential CT 65

2.3.3 Scanning Single Sections – "Step and Shoot" Modes 66

2.3.4 Material-Selective Imaging – Dual-Energy CT 67

2.3.5 Serial Scanning – Dynamic CT 67

2.3.6 CT Fluoroscopy – Interventional CT 68

2.3.7 Volume Scanning – Spiral CT 68

2.3.8 Volume Scanning – Cone-beam CT 69

2.4 Special Scanner Concepts 71

2.4.1 Electron Beam CT 72

2.4.2 The "Dynamic Spatial Reconstructor" 73

2.4.3 Flat Detector CT Scanners 74

2.4.4 PET/CT Combination Scanners 79

2.4.5 SPECT/CT Combination Scanners 81

2.4.6 Dual Source CT 83

3 Spiral CT 85

3.1 First Considerations and Efforts 85

3.2 Scanning Principle and Techniques in Spiral CT 87

3.3 Image Reconstruction in Spiral CT 90

3.3.1 Basic Approach to z-Interpolation (360°LI) 91

3.3.2 z-Interpolation Using Data Rebinning (180°LI) 92

3.3.3 Variations of 180° z-Interpolation Algorithms 94

3.4 Considerations for Multi-slice Spiral CT 97

3.4.1 z-Interpolation in Multi-slice Spiral CT (180°MLI) 97

3.4.2 z-Filtering in Multi-slice Spiral CT (180°MFI) 97

3.4.3 ECG-correlated Cardiac Imaging 100

3.5 Considerations for Cone-beam Spiral CT 102

3.5.1 Approaches for up to 64 Slices 102

3.5.2 Approaches for 64 Slices and more 106

3.5.3 High-pitch Dual Source CT Spiral Scanning 108

4 Image Quality 111

4.1 Variables and Procedures for Sequential CT 112

4.1.1 CT Values, Uniformity, Contrast and Linearity 112

4.1.2 Pixel Noise 114

4.1.3 Spatial Resolution – Resolution at High Contrast 116

4.1.4 Contrast Resolution – Resolution at Low Contrast 128

4.1.5 Artifacts 130

4.2 Variables and Procedures for Spiral CT 134

4.2.1 General Considerations 134

4.2.2 Pixel Noise 135

4.2.3 Slice Sensitivity Profiles 137

4.2.4 Resolution in the z-Direction 140

4.2.5 Considerations for Multi-slice Spiral CT 146

4.2.6 Considerations for Cone-beam Spiral CT 148

4.2.7 Artifacts in Spiral CT 151

4.2.8 The Effect of Finer Sampling in the z-Direction 153

4.2.9 Performance of Dual Source CT 156

4.3 Considerations for Flat Detector CT 157

4.3.1 Image quality considerations for C-arm-based FDCT 158

4.3.2 Image quality considerations for FDCT of the facial skull 162

4.3.3 Efforts at artifact reduction in FDCT 164

4.4 Total System Performance 168

4.4.1 The Interdependence of Noise, Dose and Resolution 168

4.4.2 Figures of Merit 171

4.5 Acceptance Test and Constancy Test 172

5 Dose 175

5.1 CT – the High Dose Myth 175

5.2 Technical Parameters for Dose Measurement 178

5.2.1 Dose Distributions in Sequential Single-slice Scans 178

5.2.2 Stray Radiation 186

5.2.3 Additional Considerations for Spiral CT Scans 187

5.2.4 Additional Considerations for Wide Detectors 189

5.2.5 CTDI Concepts for Wide Detectors 190

5.2.6 Dose Reference Levels for CT 192

5.2.7 Issues with CTDI 193

5.3 Patient Dose in CT 194

5.3.1 Influence of Scanning Parameters on the Patient Dose 194

5.3.2 Influence of Spiral CT on Patient Dose 196

5.3.3 Estimation of Organ Dose Values and Effective Dose 197

5.3.4 Estimation of Effective Dose 201

5.3.5 Issues with the determination of patient dose 207

5.4 Possibilities for Reducing the Dose Further 208

5.4.1 Influence by the Examiner  208

5.4.2 Technical Measures and New Approaches 210

5.5 How shall we deal with the discussion of dose? 222

5.5.1 Further Optimization of CT Systems 223

5.5.2 Information about Dose, Benefits and Risks 224

5.5.3 The Author’s Summing up and Recommendations 228

6 Processing and Visualization of Images 230

6.1 Simple Image Processing and Evaluation Procedures 230

6.2 Two-dimensional Displays 231

6.3 Three-dimensional Displays 233

6.3.1 Surface Displays 234

6.3.2 Projection Displays 236

6.3.3 Volume Rendering Techniques 237

6.3.4 Virtual Endoscopy 238

6.3.5 Recommendations on the Choice of 3D Display Methods 239

6.4 How to handle all the Images  242

7 Special Applications 245

7.1 General Considerations  245

7.2 Quantitative CT 246

7.3 Phase-selective Imaging of the Heart 250

7.3.1 Prospective Triggering in Sequential CT 251

7.3.2 Retrospective Gating in Spiral CT 252

7.3.3 High-pitch Spiral Dual Source CT with Prospective Triggering 254

7.3.4 Coronary Calcium Measurements with CT 255

7.4 Dual Energy CT  257

7.4.1 Basic physics of DECT 258

7.4.2 Technical solutions 263

7.4.3 DECT applications 265

7.5 Navigated Image-guided Interventions 268

7.6 Pre-clinical Imaging with CT (Micro-CT) 272

7.6.1 Micro-CT in-vitro imaging 272

7.6.2 Micro-CT in-vivo imaging 275

7.6.3 Quality control and dose assessment 278

7.7 Assessment of Tissue Perfusion with CT 282

7.7.1 Brain perfusion measurements in clinical CT 282

7.7.2 Alternative approaches to perfusion assessment by CT 285

7.7.3 Considerations regarding quality control and dose 287

8 The Future of CT 290

8.1 General considerations 291

8.2 Developments of technologies 292

8.3 Features of a dedicated breast CT scanner 294

8.4 Conclusions 302

9 Mathematical Aspects of Image Reconstruction 305

9.1 2D Image Reconstruction 307

9.1.1 Definition of 2D Parallel Projections 307

9.1.2 Reconstruction of Parallel Data 308

9.1.3 Parallel-Beam FBP 310

9.1.4 Definition of 2D Fan-Beam Projections 311

9.1.5 Fan-Beam FBP 312

9.1.6 Fan-Beam FBP for Equiangular Fans 313

9.1.7 Rebinning 315

9.1.8 Rebinning of Equiangular Fan-Beam Data 316

9.2 3D Image Reconstruction 316

9.2.1 Definition of Cone-Beam Projections 317

9.2.2 The Feldkamp Algorithm 318

9.2.3 EPBP, a Feldkamp-Type Algorithm 319

9.2.4 Single-Slice Rebinning Algorithms 322

9.2.5 Exact 3D Reconstruction from Cone-Beam Projections 324

References 329

Abbreviations and Symbols 346

Glossary 350

Index Terms 370