New
Physical Principles of Imaging in Medicine,
Edition 1Editors: By Adam W. Anderson, Charles F. Caskey, John C. Gore and Todd E. Peterson
Publication Date:
21 Dec 2026
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Description
Physical Principles of Imaging in Medicine gives an introduction to the mathematical and physical concepts and principles that underlie modern radiological imaging techniques. It explains the basic phenomena and mathematical concepts that are central to the use of physical methods for image formation in biomedicine. By focusing on the physical and mathematical principles, it provides knowledge that will continue to hold true even as technological and other advances change the nature and detail of future medical imaging applications. Written as a pedagogic textbook explaining the principles rather than a technical manual describing imaging methods, Physical Principles of Imaging in Medicine is suitable as a foundational reference for senior undergraduates, graduate students and researchers with a background in either biomedical engineering, engineering, applied physics, computer science, or mathematics. It will be a well-thumbed resource throughout a researcher’s career.Key Features
- Written by a top team of highly respected researchers who between them have taught medical imaging for over a hundred years!
- Focuses on the physical and mathematical principles to provide everlasting foundational knowledge
- Balanced coverage between the modalities reflecting the authors’ areas of expertise
- Provides a motivational historical overview of the field
- Closely ties the physical principles to biology
- Includes instructors support such as solutions and slides of the figures
- Provides computational exercises
About the author
By Adam W. Anderson, Professor of Biomedical Engineering and Radiology and Radiological Sciences, Vanderbilt University, USA; Charles F. Caskey, Associate Professor of Radiology and Radiological Sciences and Biomedical Engineering, Vanderbilt University, USA; John C. Gore, University Professor of Radiology and Radiological Sciences, Biomedical Engineering, Physics and Astronomy, and Molecular Physiology and Biophysics, Vanderbilt University, USA and Todd E. Peterson, Associate Professor of Radiology & Radiological Sciences, Vanderbilt University, USA
1 Information from Medical Imaging
1.1 Introduction to Imaging Science
1.2 Types of Information
1.3 Imaging Biomarkers
1.4 Connections Between Physical Measurements and Biological Changes
1.5 History of Development of Medical Imaging
1.6 Cost and Economics
1.7 Problems
References
2 Mathematics for Imaging
2.1 Introduction
2.2 The Fourier Transform
2.2.1 The Gaussian Function
2.2.2 The Dirac Delta Function
2.3 Inverse Fourier Transforms
2.4 Symmetry Properties of the Fourier Transform
2.4.1 Case 1: Even Functions
2.4.2 Case 2: Odd Functions
2.4.3 Case 3: Arbitrary Functions
2.5 Other Useful Transform Pairs
2.5.1 The Square Function
2.5.2 The Sampling Function
2.6 Summary of Fourier Transform Pairs
2.7 Theorems Concerning the Fourier Transform
2.7.1 The Similarity Theorem
2.7.2 The Shift Theorem
2.7.3 The Derivative Theorem
2.7.4 Convolution and the Convolution Theorem
2.7.5 The Rayleigh (Parseval) Theorem
2.7.6 Autocorrelation and the Autocorrelation Theorem
2.8 Two-Dimensional Transforms
2.9 Hankel Transforms
2.10 The Laplace Transform
2.10.1 Linearity
2.10.2 Time Shifts
2.10.3 Convolution
2.10.4 Time Derivatives
2.10.5 Initial Value Problems
2.11 The Discrete Fourier Transform
2.12 Sampling
2.12.1 Case 1: k0 < kc (i.e., ¿x > ¿xs)
2.12.2 Case 2: k0 > kc (i.e., ¿x < ¿xs)
2.13 Introduction to Linear, Shift Invariant Systems
2.13.1 The Point Spread Function
2.13.2 The Optical Transfer Function
2.14 Random Variables and Fields
2.14.1 Random Fields
2.14.2 Effects of the Point Spread Function on Random Fields
2.15 Propagation of Errors
Appendix 2A: Bessel Functions
Series Expansion
An Integral Representation
Recursion Relations
Derivatives
An Integral Relation
Connection to Differential Equations
Orthogonality
References
Appendix 2B: Linear Least Squares Estimation
Ordinary Least Squares Fitting of Complex Data
Weighted Least Squares Estimation
Weighted Least Squares Fitting of Complex Data
Generalized Least Squares Estimation
Generalized Least Squares of Complex Data
Problems
References
3 Image Quality and the Evaluation of Images
3.1 What Is Image Quality?
3.2 The Ideal Image
3.3 Image Properties: Contrast, Resolution, and Noise
3.3.1 Contrast
3.3.2 Spatial Resolution and Transfer Functions
3.3.3 Image Noise
3.3.4 Contrast-Detail Test Objects
3.4 Statistical Decision Theory Model of Imaging
3.5 Signal Detection Theory and ROC Curves
3.6 Problems
References
4 The Reconstruction of Objects from Projections
4.1 Introduction¿The Formation of Projections
4.1.1 X-ray Computed Tomography
4.1.2 Nuclear Medicine
4.1.3 Magnetic Resonance Imaging
4.1.4 Ultrasonic Computed Tomography
4.2 Exact Reconstruction from Projections
4.3 The Central Slice Theorem
4.4 Conventional Tomography
4.5 Backprojection
4.6 Filtered Backprojection
4.6.1 Exact Case for Finite Objects¿The Inverse Radon Transform
4.6.2 Bandwidth Limited Objects
4.6.3 Discrete (Digital) Version
4.6.4 Physical Interpretation of Filtered Backprojection
4.6.5 Advanced Topic: An Alternative Derivation of the Inverse Radon Transform
4.6.5 Summary of Exact Methods
4.7 Limitations in Reconstruction from Projections
4.7.1 Incomplete Projection Data
4.7.2 Statistical Limitations and the Propagation of Noise
4.7.3 Effects of the Finite Number of Projections on Spatial Resolution
4.8 Iterative Reconstruction Methods
4.8.1 Algebraic Reconstruction Technique (ART)
4.8.2 Maximum-Likelihood Expectation-Maximization (MLEM)
4.9 Problems
References
5 Imaging With X-rays
5.1 Introduction
5.1.1 Historical Note
5.2 X-ray Physics
5.3 X-ray Production
5.3.1 Theory of EM Production
5.4 X-ray Beams and Spectra
5.4.1 The Continuous Spectrum
5.4.2 X-ray Controls
5.4.3 Characteristic Line Spectra
5.5 Image Formation
5.6 X-ray Interactions
5.6.1 X-ray Units of Measurement
5.6.2 Photoelectric Absorption
5.6.3 X-ray Contrast Media
5.6.4 Compton Inelastic Scattering
5.6.5 Cross Sections and Attenuation Coefficients
5.7 X-ray Detection
5.7.1 X-ray Films
5.7.2 Film Screen Combinations
5.7.3 Image Intensifiers for Fluoroscopy
5.7.4 Digital Radiography and Solid-State Detectors
5.8 Image Quality of Radiographic Images
5.8.1 Spatial resolution
5.8.2 Contrast¿Attenuation and Scattering of Real X-ray Beams
5.8.3 Noise in X-ray Images
5.8.4 Detection Limits in X-radiography
5.8.5 Special Techniques in Radiography
5.9 Problems
References
6 X-ray Computed Tomography
6.1 Introduction
6.2 Hounsfield Units
6.3 Scanner Evolution
6.4 CT Hardware
6.5 Fan-Beam Reconstruction
6.6 Helical Acquisition
6.7 Multislice CT
6.8 Cone-beam CT
6.9 Spectral CT
6.10 Image Quality
6.11 Problems
References
7 Nuclear Imaging
7.1 Introduction
7.2 Radioactive Decay
7.2.1 Modes of Decay
7.2.2 Half Life
7.2.3 Radionuclides Relevant for Imaging
7.2.4 Radionuclide Production
7.3 Radiopharmaceuticals
7.3.1 Tracer Principle
7.3.2 Components and Synthesis
7.3.3 Specific Activity and Mass Effects
7.3.4 Some PET Radiotracers
7.4 Radiation Detectors
7.4.1 Scintillators
7.4.2 Photodetectors
7.4.3 Semiconductors
7.4.4 Position Estimation
7.5 Collimators
7.5.1 Pinhole
7.5.2 Parallel Hole
7.5.3 Diverging/Converging
7.5.4 Alternative Collimation Schemes
7.6 Single-Photon Imaging
7.6.1 Planar Scintigraphy
7.6.2 SPECT Data Acquisition
7.6.3 Data Corrections
7.7 Positron Emission Tomography (PET)
7.7.1 Lines of Response/Recording of an Event
7.7.2 Spatial Resolution Considerations
7.7.3 Event Types: Trues, Scatters, Accidentals
7.7.4 2D and 3D PET
7.7.5 3D PET Data and Fourier Rebinning
7.7.6 Data Corrections
7.7.7 NECR
7.7.8 Time-of-Flight PET
7.8 Hybrid Imaging
7.8.1 SPECT/CT
7.8.2 PET/CT
7.8.3 PET/MR
7.9 Problems
References
8 Magnetic Resonance Image Formation
8.1 Introduction
8.2 Overview of NMR
8.3 Nuclearm Magnetization
8.3(a). Equilibrium Magnetization
8.3(b). The Equation of Motion
8.3(c). The Rotating Frame of Reference
8.3(d). Effects of Radio Frequency Pulses
8.3(e). Effects of a Field Gradient
8.4 Image Formation
8.4(a). Slice Selection in MRI
8.4(b). The NMR Signal
8.4(c). Spatial Encoding of Transverse Magnetization
8.4(d). Multislice Imaging
8.4(e). 3D Volume Imaging
8.4(f). Effects of k-space Sampling on Image SNR
8.4(g). Parallel Imaging
8.5 MRI System Design
8.5(a). The Main Magnet
8.5(b). Shim Coils
8.5(c). Gradient Coils
8.5(d). Radio Frequency Coils
8.5(e). The Receiver
Appendix 8A: Physical rinciples of agnetic field Generation
8A.1. Static Magnetic Fields
8A.2. Solutions to the Laplace Equation in Spherical Coordinates
8A.3. Solutions to the Laplace Equation in Cylindrical Coordinates
8A.4. The Magnetic Vector Potential
8A.5. The Green Function for the Laplacian Operator
8A.6. The Biot-Savart Law
8A.7. Time-varying Magnetic Fields
8A.8. Magnetic Fields Produced by Current on a Cylindrical Surface
8.6 Problems
References
9 Magnetic Resonance Image Characteristics
9.1 Introduction
9.2 Effects of Relaxation
9.2.1 A First Look at NMR Relaxation
9.2.2 The Hahn Spin Echo
9.2.3 Effects of Relaxation on the PSF
9.2.4 Effects of Relaxation on Signal Intensity
9.2.5 Inversion Recovery
9.3 Optimizing Contrast
9.3.1 T1 Contrast
9.3.2 T2 Contrast
9.4 Nuclear Magnetic Resonance of Nonaqueous Hydrogen
9.4.1 Fat-Water Imaging
9.4.2 MR Spectroscopy and Spectroscopic Imaging
9.5 Signal and Noise in MRI
9.5.1 Signal Amplitude in NMR
9.5.2 Field due to a Magnetic Dipole
9.5.3 The Reciprocity Principle
9.5.4 Signal Voltage Across an NMR Coil
9.5.5 Noise Power in NMR
9.5.6 The Nyquist Theorem
9.5.7 Coil Noise
9.5.8 Sample (Body) Noise
9.5.9 The Signal-to-Noise Ratio in MRI
9.5.10 Further Reading
9.6 Exercises
11 Imaging Motion With MRI
11.1 Introduction
11.2 Imaging Coherent Motion
11.2.1 Spin Tagging
11.2.2 Phase Contrast
11.3 Incoherent Motion: Molecular Diffusion
11.3.1 Anisotropic Diffusion
11.3.2 Non-Gaussian Diffusion
11.3.3 Fiber Orientation Distributions from Spherical Deconvolution
11.4 Intra-Voxel Incoherent Motion (IVIM)
11.5 Elastography
11.6 Problems
References
12 Ultrasound Physics
12.1 Introduction
12.1.2 Sound Waves in Homogeneous Media
12.2 Wave Motion in a Homogeneous Media
12.2.1 General Wave Motion
12.2.2 Acoustic Wave Equation for Homogeneous Fluids
12.3 Sound Waves in Layered Media
12.3.1 Reflection and Transmission at Oblique Incidence
12.3.2 Transmission through a Layer
12.4 Attenuation of Sound
12.4.1 Attenuation of Plane Sound Waves
12.4.2 Absorption in Tissue
12.4.3 Plane Wave Absorption
12.4.4 Viscous Absorption
12.4.5 Other Forms of the Equation of State
12.4.6 Heat Generation from Ultrasonic Absorption
References
13 Ultrasonic Imaging
13.1 Pulse-Echo Imaging
13.1.1 Scanning Methods with Ultrasound
13.2 Generating Ultrasound and Transmitting It into the Body
13.2.1 Transducers
13.2.2 Impulse Response of a Transducer
13.2.3 Receiver Transfer Function
13.3 Sound Fields from Ultrasound Transducers
13.3.1 The Sound Field from a Single Circular Transducer
13.3.2 Spatial Fourier Relations Between Apertures and Sound Fields with Continuous Excitation
13.3.3 Analytic Description of an Ultrasound Pulse
13.3.4 A Linear Model of Image Generation with Ultrasound
13.4 Ultrasound Arrays and Electronic Beam Formation
13.4.1 Transmit Steering and Focusing
13.4.2 Receive Beamforming
13.5 Image Quality and Artifacts in Ultrasound Imaging
13.5.1 Spatial Resolution
13.5.2 Reverberation and Other Sound Path Artifacts
13.5.3 Shadowing
13.5.4 Artifacts from Nonuniform Sound Speed
13.6 Problems
14 Physical Information From Ultrasound Imaging
14.1 Interactions of Ultrasound With Tissues
14.1.1 Inhomogeneous Wave Equation
14.1.2 Scattering in Inhomogeneous Media
14.1.3 Speckle From Discrete Scatterers
14.1.4 Radiation Force
14.1.5 Non-linear Propagation of Sound
14.1.6 Ultrasound Contrast Agents
14.2 Engineering Principles Underlying Image Formation
14.2.1 A Typical Signal Chain for Ultrasound Imaging
14.2.2 Harmonic Imaging of Non-linear Propagation
14.3 Blood Flow: Doppler Ultrasound, Color Flow Mapping
14.3.1 The Doppler Effect
14.3.2 Transducer and Receive Signal Chain
14.3.3 Pulsed Wave Flow Estimation
14.3.4 Non-linear Imaging of Microbubbles
14.4 Ultrasound Safety and System Characterization
14.4.1 Mechanical Effects and the Mechanical Index
14.4.2 Thermal Effects and Thermal Index
14.5 Problems
References
15 Multimodal Imaging
15.1 Imaging the Heart
15.1.1 Coronary Artery Imaging
15.1.2 Cardiac Functional Imaging
15.1.3 Valvular Imaging
15.1.4 Changes in Tissue Composition
15.1.5 Perfusion and Metabolism
15.2 Imaging the Brain
15.2.1 Measurements of Brain Structure
15.2.2 Vascular Disorders
15.2.3 Changes in Composition
15.2.4 Neurochemistry and Metabolism
15.2.5 Neural Function
15.3 Imaging Biomarkers in Cancer
15.3.1 Tumor Detection
15.3.2 Treatment Selection
15.3.3 Treatment Response
15.4 Problems
Index
1.1 Introduction to Imaging Science
1.2 Types of Information
1.3 Imaging Biomarkers
1.4 Connections Between Physical Measurements and Biological Changes
1.5 History of Development of Medical Imaging
1.6 Cost and Economics
1.7 Problems
References
2 Mathematics for Imaging
2.1 Introduction
2.2 The Fourier Transform
2.2.1 The Gaussian Function
2.2.2 The Dirac Delta Function
2.3 Inverse Fourier Transforms
2.4 Symmetry Properties of the Fourier Transform
2.4.1 Case 1: Even Functions
2.4.2 Case 2: Odd Functions
2.4.3 Case 3: Arbitrary Functions
2.5 Other Useful Transform Pairs
2.5.1 The Square Function
2.5.2 The Sampling Function
2.6 Summary of Fourier Transform Pairs
2.7 Theorems Concerning the Fourier Transform
2.7.1 The Similarity Theorem
2.7.2 The Shift Theorem
2.7.3 The Derivative Theorem
2.7.4 Convolution and the Convolution Theorem
2.7.5 The Rayleigh (Parseval) Theorem
2.7.6 Autocorrelation and the Autocorrelation Theorem
2.8 Two-Dimensional Transforms
2.9 Hankel Transforms
2.10 The Laplace Transform
2.10.1 Linearity
2.10.2 Time Shifts
2.10.3 Convolution
2.10.4 Time Derivatives
2.10.5 Initial Value Problems
2.11 The Discrete Fourier Transform
2.12 Sampling
2.12.1 Case 1: k0 < kc (i.e., ¿x > ¿xs)
2.12.2 Case 2: k0 > kc (i.e., ¿x < ¿xs)
2.13 Introduction to Linear, Shift Invariant Systems
2.13.1 The Point Spread Function
2.13.2 The Optical Transfer Function
2.14 Random Variables and Fields
2.14.1 Random Fields
2.14.2 Effects of the Point Spread Function on Random Fields
2.15 Propagation of Errors
Appendix 2A: Bessel Functions
Series Expansion
An Integral Representation
Recursion Relations
Derivatives
An Integral Relation
Connection to Differential Equations
Orthogonality
References
Appendix 2B: Linear Least Squares Estimation
Ordinary Least Squares Fitting of Complex Data
Weighted Least Squares Estimation
Weighted Least Squares Fitting of Complex Data
Generalized Least Squares Estimation
Generalized Least Squares of Complex Data
Problems
References
3 Image Quality and the Evaluation of Images
3.1 What Is Image Quality?
3.2 The Ideal Image
3.3 Image Properties: Contrast, Resolution, and Noise
3.3.1 Contrast
3.3.2 Spatial Resolution and Transfer Functions
3.3.3 Image Noise
3.3.4 Contrast-Detail Test Objects
3.4 Statistical Decision Theory Model of Imaging
3.5 Signal Detection Theory and ROC Curves
3.6 Problems
References
4 The Reconstruction of Objects from Projections
4.1 Introduction¿The Formation of Projections
4.1.1 X-ray Computed Tomography
4.1.2 Nuclear Medicine
4.1.3 Magnetic Resonance Imaging
4.1.4 Ultrasonic Computed Tomography
4.2 Exact Reconstruction from Projections
4.3 The Central Slice Theorem
4.4 Conventional Tomography
4.5 Backprojection
4.6 Filtered Backprojection
4.6.1 Exact Case for Finite Objects¿The Inverse Radon Transform
4.6.2 Bandwidth Limited Objects
4.6.3 Discrete (Digital) Version
4.6.4 Physical Interpretation of Filtered Backprojection
4.6.5 Advanced Topic: An Alternative Derivation of the Inverse Radon Transform
4.6.5 Summary of Exact Methods
4.7 Limitations in Reconstruction from Projections
4.7.1 Incomplete Projection Data
4.7.2 Statistical Limitations and the Propagation of Noise
4.7.3 Effects of the Finite Number of Projections on Spatial Resolution
4.8 Iterative Reconstruction Methods
4.8.1 Algebraic Reconstruction Technique (ART)
4.8.2 Maximum-Likelihood Expectation-Maximization (MLEM)
4.9 Problems
References
5 Imaging With X-rays
5.1 Introduction
5.1.1 Historical Note
5.2 X-ray Physics
5.3 X-ray Production
5.3.1 Theory of EM Production
5.4 X-ray Beams and Spectra
5.4.1 The Continuous Spectrum
5.4.2 X-ray Controls
5.4.3 Characteristic Line Spectra
5.5 Image Formation
5.6 X-ray Interactions
5.6.1 X-ray Units of Measurement
5.6.2 Photoelectric Absorption
5.6.3 X-ray Contrast Media
5.6.4 Compton Inelastic Scattering
5.6.5 Cross Sections and Attenuation Coefficients
5.7 X-ray Detection
5.7.1 X-ray Films
5.7.2 Film Screen Combinations
5.7.3 Image Intensifiers for Fluoroscopy
5.7.4 Digital Radiography and Solid-State Detectors
5.8 Image Quality of Radiographic Images
5.8.1 Spatial resolution
5.8.2 Contrast¿Attenuation and Scattering of Real X-ray Beams
5.8.3 Noise in X-ray Images
5.8.4 Detection Limits in X-radiography
5.8.5 Special Techniques in Radiography
5.9 Problems
References
6 X-ray Computed Tomography
6.1 Introduction
6.2 Hounsfield Units
6.3 Scanner Evolution
6.4 CT Hardware
6.5 Fan-Beam Reconstruction
6.6 Helical Acquisition
6.7 Multislice CT
6.8 Cone-beam CT
6.9 Spectral CT
6.10 Image Quality
6.11 Problems
References
7 Nuclear Imaging
7.1 Introduction
7.2 Radioactive Decay
7.2.1 Modes of Decay
7.2.2 Half Life
7.2.3 Radionuclides Relevant for Imaging
7.2.4 Radionuclide Production
7.3 Radiopharmaceuticals
7.3.1 Tracer Principle
7.3.2 Components and Synthesis
7.3.3 Specific Activity and Mass Effects
7.3.4 Some PET Radiotracers
7.4 Radiation Detectors
7.4.1 Scintillators
7.4.2 Photodetectors
7.4.3 Semiconductors
7.4.4 Position Estimation
7.5 Collimators
7.5.1 Pinhole
7.5.2 Parallel Hole
7.5.3 Diverging/Converging
7.5.4 Alternative Collimation Schemes
7.6 Single-Photon Imaging
7.6.1 Planar Scintigraphy
7.6.2 SPECT Data Acquisition
7.6.3 Data Corrections
7.7 Positron Emission Tomography (PET)
7.7.1 Lines of Response/Recording of an Event
7.7.2 Spatial Resolution Considerations
7.7.3 Event Types: Trues, Scatters, Accidentals
7.7.4 2D and 3D PET
7.7.5 3D PET Data and Fourier Rebinning
7.7.6 Data Corrections
7.7.7 NECR
7.7.8 Time-of-Flight PET
7.8 Hybrid Imaging
7.8.1 SPECT/CT
7.8.2 PET/CT
7.8.3 PET/MR
7.9 Problems
References
8 Magnetic Resonance Image Formation
8.1 Introduction
8.2 Overview of NMR
8.3 Nuclearm Magnetization
8.3(a). Equilibrium Magnetization
8.3(b). The Equation of Motion
8.3(c). The Rotating Frame of Reference
8.3(d). Effects of Radio Frequency Pulses
8.3(e). Effects of a Field Gradient
8.4 Image Formation
8.4(a). Slice Selection in MRI
8.4(b). The NMR Signal
8.4(c). Spatial Encoding of Transverse Magnetization
8.4(d). Multislice Imaging
8.4(e). 3D Volume Imaging
8.4(f). Effects of k-space Sampling on Image SNR
8.4(g). Parallel Imaging
8.5 MRI System Design
8.5(a). The Main Magnet
8.5(b). Shim Coils
8.5(c). Gradient Coils
8.5(d). Radio Frequency Coils
8.5(e). The Receiver
Appendix 8A: Physical rinciples of agnetic field Generation
8A.1. Static Magnetic Fields
8A.2. Solutions to the Laplace Equation in Spherical Coordinates
8A.3. Solutions to the Laplace Equation in Cylindrical Coordinates
8A.4. The Magnetic Vector Potential
8A.5. The Green Function for the Laplacian Operator
8A.6. The Biot-Savart Law
8A.7. Time-varying Magnetic Fields
8A.8. Magnetic Fields Produced by Current on a Cylindrical Surface
8.6 Problems
References
9 Magnetic Resonance Image Characteristics
9.1 Introduction
9.2 Effects of Relaxation
9.2.1 A First Look at NMR Relaxation
9.2.2 The Hahn Spin Echo
9.2.3 Effects of Relaxation on the PSF
9.2.4 Effects of Relaxation on Signal Intensity
9.2.5 Inversion Recovery
9.3 Optimizing Contrast
9.3.1 T1 Contrast
9.3.2 T2 Contrast
9.4 Nuclear Magnetic Resonance of Nonaqueous Hydrogen
9.4.1 Fat-Water Imaging
9.4.2 MR Spectroscopy and Spectroscopic Imaging
9.5 Signal and Noise in MRI
9.5.1 Signal Amplitude in NMR
9.5.2 Field due to a Magnetic Dipole
9.5.3 The Reciprocity Principle
9.5.4 Signal Voltage Across an NMR Coil
9.5.5 Noise Power in NMR
9.5.6 The Nyquist Theorem
9.5.7 Coil Noise
9.5.8 Sample (Body) Noise
9.5.9 The Signal-to-Noise Ratio in MRI
9.5.10 Further Reading
9.6 Exercises
11 Imaging Motion With MRI
11.1 Introduction
11.2 Imaging Coherent Motion
11.2.1 Spin Tagging
11.2.2 Phase Contrast
11.3 Incoherent Motion: Molecular Diffusion
11.3.1 Anisotropic Diffusion
11.3.2 Non-Gaussian Diffusion
11.3.3 Fiber Orientation Distributions from Spherical Deconvolution
11.4 Intra-Voxel Incoherent Motion (IVIM)
11.5 Elastography
11.6 Problems
References
12 Ultrasound Physics
12.1 Introduction
12.1.2 Sound Waves in Homogeneous Media
12.2 Wave Motion in a Homogeneous Media
12.2.1 General Wave Motion
12.2.2 Acoustic Wave Equation for Homogeneous Fluids
12.3 Sound Waves in Layered Media
12.3.1 Reflection and Transmission at Oblique Incidence
12.3.2 Transmission through a Layer
12.4 Attenuation of Sound
12.4.1 Attenuation of Plane Sound Waves
12.4.2 Absorption in Tissue
12.4.3 Plane Wave Absorption
12.4.4 Viscous Absorption
12.4.5 Other Forms of the Equation of State
12.4.6 Heat Generation from Ultrasonic Absorption
References
13 Ultrasonic Imaging
13.1 Pulse-Echo Imaging
13.1.1 Scanning Methods with Ultrasound
13.2 Generating Ultrasound and Transmitting It into the Body
13.2.1 Transducers
13.2.2 Impulse Response of a Transducer
13.2.3 Receiver Transfer Function
13.3 Sound Fields from Ultrasound Transducers
13.3.1 The Sound Field from a Single Circular Transducer
13.3.2 Spatial Fourier Relations Between Apertures and Sound Fields with Continuous Excitation
13.3.3 Analytic Description of an Ultrasound Pulse
13.3.4 A Linear Model of Image Generation with Ultrasound
13.4 Ultrasound Arrays and Electronic Beam Formation
13.4.1 Transmit Steering and Focusing
13.4.2 Receive Beamforming
13.5 Image Quality and Artifacts in Ultrasound Imaging
13.5.1 Spatial Resolution
13.5.2 Reverberation and Other Sound Path Artifacts
13.5.3 Shadowing
13.5.4 Artifacts from Nonuniform Sound Speed
13.6 Problems
14 Physical Information From Ultrasound Imaging
14.1 Interactions of Ultrasound With Tissues
14.1.1 Inhomogeneous Wave Equation
14.1.2 Scattering in Inhomogeneous Media
14.1.3 Speckle From Discrete Scatterers
14.1.4 Radiation Force
14.1.5 Non-linear Propagation of Sound
14.1.6 Ultrasound Contrast Agents
14.2 Engineering Principles Underlying Image Formation
14.2.1 A Typical Signal Chain for Ultrasound Imaging
14.2.2 Harmonic Imaging of Non-linear Propagation
14.3 Blood Flow: Doppler Ultrasound, Color Flow Mapping
14.3.1 The Doppler Effect
14.3.2 Transducer and Receive Signal Chain
14.3.3 Pulsed Wave Flow Estimation
14.3.4 Non-linear Imaging of Microbubbles
14.4 Ultrasound Safety and System Characterization
14.4.1 Mechanical Effects and the Mechanical Index
14.4.2 Thermal Effects and Thermal Index
14.5 Problems
References
15 Multimodal Imaging
15.1 Imaging the Heart
15.1.1 Coronary Artery Imaging
15.1.2 Cardiac Functional Imaging
15.1.3 Valvular Imaging
15.1.4 Changes in Tissue Composition
15.1.5 Perfusion and Metabolism
15.2 Imaging the Brain
15.2.1 Measurements of Brain Structure
15.2.2 Vascular Disorders
15.2.3 Changes in Composition
15.2.4 Neurochemistry and Metabolism
15.2.5 Neural Function
15.3 Imaging Biomarkers in Cancer
15.3.1 Tumor Detection
15.3.2 Treatment Selection
15.3.3 Treatment Response
15.4 Problems
Index
ISBN:
9780323916233
Page Count:
576
Retail Price
:
9780123964878
Biomedical engineering, engineering, computer science and math students at the senior undergraduate and postgraduate levels and researchers wanting to learn the underlying mathematical and physical principles of medical imaging
