Table of Contents

Preface

Nomenclature and Abbreviations

1 Introduction

1.1 Conventional X-ray Tomography

1.2 History of Computed Tomography

1.3 Different Generations of CT Scanners

1.4 Problems

References

2 Preliminaries

2.1 Mathematics Fundamentals

     2.1.1 Fourier transform and convolution

     2.1.2 Random variables

     2.1.3 Linear algebra

2.2 Fundamentals of X-ray Physics

     2.2.1 Production of x rays

     2.2.2 Interaction of x rays with matter

2.3 Measurement of Line Integrals and Data Conditioning

2.4 Sampling Geometry and Sinogram

2.5 Artificial Intelligence, Machine Learning, and Deep Learning

     2.5.1 Overview of AI development

     2.5.2 Neural network structure

     2.5.3 Neural network training

     2.5.4 Recent advances in DL

2.6 Problems

References

3 Image Reconstruction

3.1 Introduction

3.2 Intuitive Approach to Image Reconstruction

3.3 The Fourier Slice Theorem

3.4 The Filtered Backprojection Algorithm

     3.4.1 Derivation of the filtered back-projection formula

     3.4.2 Computer implementation

     3.4.3 Targeted reconstruction

3.5 Fan-Beam Reconstruction

     3.5.1 Reconstruction formula for equiangular sampling

     3.5.2 Reconstruction formula for equally spaced sampling

     3.5.3 Fan-beam to parallel-beam rebinning

3.6 Iterative Reconstruction

     3.6.1 Mathematics verses reality

     3.6.2 The general approach to iterative reconstruction

     3.6.3 Algebraic reconstruction

     3.6.4 System modeling process

     3.6.5 Optimization algorithms

     3.6.6 Image quality benefit of model-based iterative reconstruction

     3.6.7 Reconstruction speedup

3.7 Deep Learning–based Reconstruction

     3.7.1 General approach

     3.7.2 Training dataset selection

     3.7.3 Determination of the training dataset size

     3.7.4 Examples of DL-based reconstruction

3.8 Problems

Reference

4 Image Presentation

4.1 CT Image Display

4.2 Volume Visualization

     4.2.1 Multiplanar reformation

     4.2.2 MIP, minMIP, and volume rendering

     4.2.3 Surface rendering

4.3 Impact of Visualization Tools

4.4 Volume Visualization

     4.4.1 Clinical utility

     4.4.2 Hardware technologies

     4.4.3 File format

     4.4.4 Typical 3D printing workflow

4.5 Problems

References

5 Key Performance Parameters of the CT Scanner

5.1 High-Contrast Spatial Resolution

     5.1.1 In-plane resolution

     5.1.2 Slice sensitivity profile

5.2 Low-Contrast Resolution

     5.2.1 Factors impacting low-contrast detectability

     5.2.2 LCD phantoms

     5.2.3 LCD evaluation methodologies

5.3 Temporal Resolution

5.4 CT Number Accuracy and Noise

5.5 Impact of Iterative Reconstruction on Performance Measurement

     5.5.1 Performance-metric-based approach

     5.5.2 Task-based approach

     5.5.3 Surrogate task with clinical data

     5.5.4 Surrogate task with nonclinical data

5.6 Performance of the Scanogram

5.7 Problems

References

6 Major Components of the CT Scanner

6.1 System Overview

6.2 The X-ray Tube and High-Voltage Generator

6.3 The X-ray Detector and Data-Acquisition Electronics

     6.3.1 Direct-conversion gas detector

     6.3.2 Indirect-conversion solid-state detector

     6.3.3 Direct-conversion semiconductor detector

     6.3.4 General performance parameters

     6.3.5 Specific performance parameters

6.4 The Gantry and Slip Ring

6.5 Collimation and Filtration

6.6 The Reconstruction Engine

6.7 The Patient Table

6.8 Problems

References

7 Image Artifacts: Appearances, Causes, and Corrections

7.1 What Is an Image Artifact?

7.2 Different Appearances of Image Artifacts

7.3 Artifacts Related to System Design

     7.3.1 Aliasing

     7.3.2 Partial volume

     7.3.3 Scatter

     7.3.4 Noise-induced streaks

7.4 Artifacts Related to X-ray Tubes

     7.4.1 Off-focal radiation

     7.4.2 Tube arcing

     7.4.3 Tube rotor wobble

7.5 Detector-Induced Artifacts

     7.5.1 Offset, gain, nonlinearity, and radiation damage

     7.5.2 Primary speed and afterglow

     7.5.3 Detector response uniformity

7.6 Patient-Induced Artifacts

     7.6.1 Patient motion

     7.6.2 Beam hardening

     7.6.3 Metal and high-density object artifacts

     7.6.4 Incomplete projections

7.7 Operator-Induced Artifacts

7.8 Problems

References

8 Computer Simulation and Analysis

8.1 What Is Computer Simulation?

8.2 Simulation Overview

8.3 Simulation of Optics

8.4 Simulation of Physics-Related Performance

8.5 Simulation of a Clinical Study

8.6 Problems

References

9 Helical or Spiral CT

9.1 Introduction

     9.1.1 Clinical needs

     9.1.2 Enabling technologies

9.2 Terminology and Reconstruction

     9.2.1 Helical pitch

     9.2.2 Basic reconstruction approaches

9.3 Slice Sensitivity Profile and Noise

9.4 Helically Related Image Artifacts

     9.4.1 High-pitch helical artifacts

     9.4.2 Noise-induced artifacts

     9.4.3 System-misalignment-induced artifacts

     9.4.4 Helical artifacts caused by object slope

9.5 Problems

References

10 Multislice CT

10.1 The Need for Multislice CT

10.2 Detector Configurations of Multislice CT

10.3 Nonhelical Mode of Reconstruction

10.4 Multislice Helical Reconstruction

     10.4.1 2D backprojection algorithm

     10.4.2 Reconstruction algorithms with 3D backprojection

     10.4.3 Over-beaming (or over-scanning) compensation

10.5 Multislice Artifacts

     10.5.1 General description

     10.5.2 Multislice CT cone-beam effects

     10.5.3 Interpolation-related image artifacts

     10.5.4 Noise-induced multislice artifacts

     10.5.5 Tilt artifacts in multislice helical CT

     10.5.6 Distortion in step-and-shoot mode SSP

     10.5.7 Artifacts due to geometric inaccuracy

     10.5.8 Comparison of multislice and single-slice helical CT

10.6 Problems

References

11 X-ray Radiation and Dose-Reduction Techniques

11.1 Biological Effects of X-ray Radiation

11.2 Measurement of X-ray Dose

     11.2.1 Terminology and the measurement standard

     11.2.2 Other measurement units and methods

     11.2.3 Issues with the current CTDI

11.3 Methodologies for Dose Reduction

     11.3.1 Tube-current modulation

     11.3.2 Umbra-penumbra and overbeam issues

     11.3.3 Physiological gating

     11.3.4 Organ-specific dose reduction

     11.3.5 Protocol optimization and impact of the operator

     11.3.6 Postprocessing techniques

     11.3.7 Advanced reconstruction

11.4 Problems

References

12 Dual-Energy and Spectral CT

12.1 Intuitive Explanation

     12.1.1 Material differentiation

     12.1.2 Material representation

12.2 Theory of Basis Material Decomposition

     12.2.1 Basis material

     12.2.2 Projection-space material decomposition (MD)

     12.2.3 Image-space material decomposition

     12.2.4 Multimaterial identification and quantification

     12.2.5 Noise

12.3 Generation of Derivative Images

     12.3.1 Monochromatic image

     12.3.2 Basis material transformation

     12.3.3 Electron density image

     12.3.4 Effective atomic number image

12.4 Data Acquisition

     12.4.1 Energy-integrating systems

     12.4.2 Photon-counting system

12.5 Clinical Applications

12.6 Problems

References

13 Advanced CT Applications

13.1 Introduction

13.2 Cardiac Imaging

     13.2.1 Coronary calcium scan

     13.2.2 Coronary artery imaging

     13.2.3 Cardiac function

13.3 Interventional Procedures

13.4 Stroke: CT Perfusion and Multiphase CTA

     13.4.1 Perfusion

     13.4.2 Multiphase CTA

13.5 Screening and Quantitative CT

     13.5.1 Lung cancer screening

     13.5.2 Quantitative CT

     13.5.3 CT colonography

13.6 Impact of Artificial Intelligence

13.7 Problems

References

Glossary

Preface

The technological innovations experienced by x-ray computed tomography (CT) during the last half century are a phenomenon rarely seen in industry. When the first edition of this book was published in 2003, few could have predicted the speed, magnitude, and extent of the progress made by CT. Even fewer could foresee the tremendous impact of modern x-ray CT on patients, technologists, physicists, and radiologists. This edition of Computed Tomography aims to capture the most recent advances in the technology and clinical applications.

It is safe to state that artificial intelligence (AI) and, more specifically, deep learning (DL) technology, are among the few innovations that have had a profound impact on society. AI is literally transforming the world: the entertainment industry, medical imaging industry, communication industry, security, and even our daily lives. This fourth edition provides an overview of AI technology in CT, presents a detailed description of the neural network structure and training, and offers several examples in which this technology has impacted the way a patient is scanned, images are reconstructed, and diagnoses are made.

Over the past decade, the field of additive manufacturing (AM) or 3D printing has generated many headlines and has changed many aspects of industrial design, parts production, and aftermarket support. AM has experienced significant advancement in the materials used to produce the object, methodologies employed to construct the parts, and even the software used to drive the operation. This fourth edition features a new section dedicated to covering various AM hardware technologies, common file formats to communicate with these machines, and typical 3D printing processes.

Since its invention in the 1970s, the x-ray CT detector has evolved over three generations of technology—from the xenon detector used in the early vintage CT scanner to the solid-state integrating detector currently deployed on all commercial CT scanners, and soon, to the semiconductor photoncounting detector, which shows excellent potential. Given the various approaches and technologies used in photon-counting detectors, a detailed presentation is provided in this new edition on advantages, challenges, and potential issues facing these detectors. Key performance criteria used to evaluate these detectors and potential applications to clinical tasks are also discussed.

New technological advancements have naturally led to new clinical applications that were difficult or impossible to perform in the past. One application area covers the development of cardiac imaging that goes beyond the morphological information and explores the functional aspect of the heart. Another application takes new approaches to stroke management to enable speedy treatment of patients to take full advantage of new clot-removing procedures.

A significant portion of the third edition was devoted to the treatment of iterative reconstruction (IR), a then new reconstruction technology that enables significant dose reduction. Nowadays, IR is gradually being replaced by deep-learning–based image reconstruction (DLIR) to overcome its drawbacks in degraded noise texture. Compared to fully model-based iterative reconstruction (MBIR), the DL-based approach also offers the distinct advantage of reconstruction speed. The fourth edition has a dedicated section on DL-based image reconstruction and its evaluation.

Many modifications and additions have been incorporated into this edition, even on topics that were covered in the third edition. The topic of dual-energy, or spectral, CT is now an independent chapter with added intuitive explanations of the key concepts of multimaterial decomposition and differentiation. To enhance readers' understanding of the material presented in the book and to inspire creative thinking about different topics, additional problems are included at the end of each chapter. Many problems are open-ended and may not have uniquely correct solutions.

During the release of the second edition of this book, the world was experiencing an unprecedented financial crisis often called a "financial tsunami." Despite this crisis, technological advancement in x-ray CT continued. During the release of this edition, the world is experiencing an unprecedented pandemic crisis: COVID-19. Many industries, even some of the medical imaging modalities, have been severely impacted by the crisis. X-ray CT, however, is one of the few modalities that is experiencing a higher demand. CT has been used in many ways to battle the COVID-19 pandemic, ranging from the first line of defense in some countries to monitoring the disease progression in others. Once again, CT has shown its tremendous capability and value. The future of CT is bright.

Jiang Hsieh
June 2022