Physical Principles of Imaging in Medicine
- 1 Edición - 24 de septiembre de 2026
- Última edición
- Autores: Adam W. Anderson, Charles F. Caskey, John C. Gore, Todd E. Peterson
- Idioma: Inglés
Medical Imaging: Mathematical and Physical Principles gives an introduction to the mathematical and physical concepts and principles that underlie modern radiological imagin… Leer más
Descripción
Descripción
Medical Imaging: Mathematical and Physical Principles 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, Medical Imaging: Mathematical and Physical Principles is very suitable as a foundational reference for senior undergraduates, graduate students and researchers with a background in either biomedical engineering, engineering, applied physics, computer science, and mathematics. It will be a well-thumbed resource throughout a researcher’s career.
Puntos claves
Puntos claves
- 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
De interès para
De interès para
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
Índice
Índice
1. Introduction to Medical Imaging
1.1 Overview of medical imaging: historical development
1.2 Types of information in imaging
1.3 Examples of relationships between physical and biological changes
1.4 Overview of energy forms used for imaging: X-ray, CT, ultrasound, MRI, nuclear, other imaging
1.5 Problems
2. Mathematics for Imaging
2.1 The Fourier Transform: introduction; inverse Fourier Transforms; symmetry properties; examples of useful transforms; theorems concerning Fourier Transforms; two dimensional transforms; relations to other integral transforms; the discrete Fourier Transform
2.2 Sampling: band limited functions; the sampling theorem; aliasing and the Nyquist rate
2.3 Linear systems: introduction; transfer functions; point spread function; modulation transfer function
2.4 Random variables: introduction; examples - Poisson statistics; random fields
2.5 Problems
2.6 Appendix: Bessel functions: integral representations; recursion relations; relation to Bessels equation; simple integrals of Bessel functions
3. Image Quality
3.1 What is image quality?
3.2 Physical measures of quality - resolution, contrast, noise
3.3 Effects of Point Spread Function and Modulation Transfer Function on image quality
3.4 Figures of merit of image quality
3.5 Signal Detection Theory model of imaging
3.6 ROC analysis
3.7 Elementary digital image processing
3.8 Summary of factors affecting image quality
3.9 Human visual psychophysics + image perception
3.10 Problems
4. Reconstruction of Objects from Projections
4.1 Formation of projections
4.2 Reconstruction from projections
4.3 Central Slice Theorem
4.4 Conventional tomography
4.5 Back projection
4.6 Filtered back projection: the Radon Transform; band limited objects; discrete filters; physical interpretation, summary
4.7 Limitations in reconstruction from projections: incomplete data, statistical limitations and propagation of noise, effects of finite number of projections, artifacts
4.8 Radial projections and reconstructions
4.9 Algebraic and model based reconstructions
4.10 Problems
5. X-Radiographic Imaging; Image Formation
5.1 Overview of X-ray imaging: radiography, fluoroscopy, CT, digital radiography
5.2 Production and characteristics of X-rays
5.3 X-radiographic imaging: physical properties relevant for imaging
5.4 X-ray interactions with tissues: classical scattering, photoelectric effect, Compton effect
5.5 Origins of contrast in X-ray imaging; relation to tissue composition
5.6 Effects of scatter; spectral effects
5.7 X-ray contrast materials
5.8 Image formation in radiography: transfer functions for projection imaging, magnification, effect of focal spot, motion blurring
5.9 Image recording: PSF of films and screens; detector quantum efficiency and noise in X-ray images; model of array of photon counters, derivation of characteristic curve and effects; propagation of signal and noise in and image quality in digital radiography
5.10 Problems
6. Nuclear Imaging: Image Formation
6.1 Overview of nuclear medicine: radioactivity, radioisotopes, radiopharmaceuticals, detectors
6.2 Image formation in projection imaging; effects of collimators, countrate
6.3 Design of cameras
6.4 Image formation in SPECT and PET; effects of attenuation, scatter
6.5 Reconstruction theory
6.6 Sensitivity and resolution considerations in nuclear imaging
6.7 Problems
7. Nuclear Magnetic Resonance Imaging: Image Formation
7.1 Overview
7.2 Equilibrium and dynamics of spin systems
7.3 Image formation
7.4 Effects of relaxation
7.5 Classes of pulse sequences
7.6 Signal and noise ratio in MR imaging
7.7 Problems
8. Nuclear Magnetic Resonance Imaging: Design of Systems
8.1 The Bo magnet
8.2 Bo shims
8.3 Gradient coils
8.4 The radiofrequency coil
8.5 The NMR receiver and signal processing
8.6 Problems
9. Nuclear Magnetic Resonance Imaging: Physical Properties Relevant for Imaging [1] Relaxation
9.1 Classical description of relaxation in solutions
9.2 Relaxation by dipole-dipole interactions
9.3 Relaxation mechanisms in biological tissues
9.4 Anderson-Weiss theory
9.5 MRI contrast agents: paramagnetic relaxation effects, susceptibility effects
9.6 Chemical shift and J-coupling effects
9.7 Problems
9.8 Appendix: Simple quantum theory of spin 1/2 nuclei
9.8.1 States of a system of spins
9.8.2 Transitions between states
9.8.3 Quantum form of the Bloch equations
9.8.4 Quantum description of a spin echo
9.8.5 Quantum description of relaxation
10. Nuclear Magnetic Resonance Imaging: Physical Properties Relevant for Imaging [2] Motion and Flow
10.1 Effects of gradients, phase dispersion, q space
10.2 Effects of incoherent motion; diffusion, IVIM, turbulent flow
10.3 Spin tagging and tissue deformation
10.4 Time of flight effects, ASL, perfusion
10.5 Phase contrast effects
10.6 Problems
11. Ultrasound Imaging: Image Formation
11.1 Introduction
11.2 Overview of ultrasonic imaging
11.3 Physics of sound waves and vibrations
11.4 Image formation with ultrasound: transducers as sound radiators; sound fields from transducers; equivalent circuits of transducers; the impulse responses of a transducer
11.5 Sound propagation in uniform layers of tissue: homogeneous wave equation, reflection, refraction, behavior of pulses at smooth interfaces
11.6 Design of ultrasonic pulse echo imaging systems; limits on resolution
11.7 Image artifacts
11.8 Problems
12. Ultrasound Imaging: Physical Properties Relevant for Imaging
12.1 Characteristic Impedance, sound velocity, elastic properties of tissues
12.2 Inhomogeneous wave equation
12.3 Scattering of sound pulses: continuum description of backscattering; scattering from discrete scatterers, approaches to tissue characterization
12.4 Absorption: factors affecting absorption; wave equation with absorption
12.5 Non-linear waves; cavitation
12.6 Doppler effect: scattering from blood, signal processing and physics of flow measurements
12.7 Problems
14. Physiological Function from Imaging
14.1 Compartmental modeling and simple tracer kinetics
14.2 Measurement of blood flow and organ function using imaging:
14.2.1 Assessment of brain function
14.2.2 Assessment of cardiac function
14.3 Problem
1.1 Overview of medical imaging: historical development
1.2 Types of information in imaging
1.3 Examples of relationships between physical and biological changes
1.4 Overview of energy forms used for imaging: X-ray, CT, ultrasound, MRI, nuclear, other imaging
1.5 Problems
2. Mathematics for Imaging
2.1 The Fourier Transform: introduction; inverse Fourier Transforms; symmetry properties; examples of useful transforms; theorems concerning Fourier Transforms; two dimensional transforms; relations to other integral transforms; the discrete Fourier Transform
2.2 Sampling: band limited functions; the sampling theorem; aliasing and the Nyquist rate
2.3 Linear systems: introduction; transfer functions; point spread function; modulation transfer function
2.4 Random variables: introduction; examples - Poisson statistics; random fields
2.5 Problems
2.6 Appendix: Bessel functions: integral representations; recursion relations; relation to Bessels equation; simple integrals of Bessel functions
3. Image Quality
3.1 What is image quality?
3.2 Physical measures of quality - resolution, contrast, noise
3.3 Effects of Point Spread Function and Modulation Transfer Function on image quality
3.4 Figures of merit of image quality
3.5 Signal Detection Theory model of imaging
3.6 ROC analysis
3.7 Elementary digital image processing
3.8 Summary of factors affecting image quality
3.9 Human visual psychophysics + image perception
3.10 Problems
4. Reconstruction of Objects from Projections
4.1 Formation of projections
4.2 Reconstruction from projections
4.3 Central Slice Theorem
4.4 Conventional tomography
4.5 Back projection
4.6 Filtered back projection: the Radon Transform; band limited objects; discrete filters; physical interpretation, summary
4.7 Limitations in reconstruction from projections: incomplete data, statistical limitations and propagation of noise, effects of finite number of projections, artifacts
4.8 Radial projections and reconstructions
4.9 Algebraic and model based reconstructions
4.10 Problems
5. X-Radiographic Imaging; Image Formation
5.1 Overview of X-ray imaging: radiography, fluoroscopy, CT, digital radiography
5.2 Production and characteristics of X-rays
5.3 X-radiographic imaging: physical properties relevant for imaging
5.4 X-ray interactions with tissues: classical scattering, photoelectric effect, Compton effect
5.5 Origins of contrast in X-ray imaging; relation to tissue composition
5.6 Effects of scatter; spectral effects
5.7 X-ray contrast materials
5.8 Image formation in radiography: transfer functions for projection imaging, magnification, effect of focal spot, motion blurring
5.9 Image recording: PSF of films and screens; detector quantum efficiency and noise in X-ray images; model of array of photon counters, derivation of characteristic curve and effects; propagation of signal and noise in and image quality in digital radiography
5.10 Problems
6. Nuclear Imaging: Image Formation
6.1 Overview of nuclear medicine: radioactivity, radioisotopes, radiopharmaceuticals, detectors
6.2 Image formation in projection imaging; effects of collimators, countrate
6.3 Design of cameras
6.4 Image formation in SPECT and PET; effects of attenuation, scatter
6.5 Reconstruction theory
6.6 Sensitivity and resolution considerations in nuclear imaging
6.7 Problems
7. Nuclear Magnetic Resonance Imaging: Image Formation
7.1 Overview
7.2 Equilibrium and dynamics of spin systems
7.3 Image formation
7.4 Effects of relaxation
7.5 Classes of pulse sequences
7.6 Signal and noise ratio in MR imaging
7.7 Problems
8. Nuclear Magnetic Resonance Imaging: Design of Systems
8.1 The Bo magnet
8.2 Bo shims
8.3 Gradient coils
8.4 The radiofrequency coil
8.5 The NMR receiver and signal processing
8.6 Problems
9. Nuclear Magnetic Resonance Imaging: Physical Properties Relevant for Imaging [1] Relaxation
9.1 Classical description of relaxation in solutions
9.2 Relaxation by dipole-dipole interactions
9.3 Relaxation mechanisms in biological tissues
9.4 Anderson-Weiss theory
9.5 MRI contrast agents: paramagnetic relaxation effects, susceptibility effects
9.6 Chemical shift and J-coupling effects
9.7 Problems
9.8 Appendix: Simple quantum theory of spin 1/2 nuclei
9.8.1 States of a system of spins
9.8.2 Transitions between states
9.8.3 Quantum form of the Bloch equations
9.8.4 Quantum description of a spin echo
9.8.5 Quantum description of relaxation
10. Nuclear Magnetic Resonance Imaging: Physical Properties Relevant for Imaging [2] Motion and Flow
10.1 Effects of gradients, phase dispersion, q space
10.2 Effects of incoherent motion; diffusion, IVIM, turbulent flow
10.3 Spin tagging and tissue deformation
10.4 Time of flight effects, ASL, perfusion
10.5 Phase contrast effects
10.6 Problems
11. Ultrasound Imaging: Image Formation
11.1 Introduction
11.2 Overview of ultrasonic imaging
11.3 Physics of sound waves and vibrations
11.4 Image formation with ultrasound: transducers as sound radiators; sound fields from transducers; equivalent circuits of transducers; the impulse responses of a transducer
11.5 Sound propagation in uniform layers of tissue: homogeneous wave equation, reflection, refraction, behavior of pulses at smooth interfaces
11.6 Design of ultrasonic pulse echo imaging systems; limits on resolution
11.7 Image artifacts
11.8 Problems
12. Ultrasound Imaging: Physical Properties Relevant for Imaging
12.1 Characteristic Impedance, sound velocity, elastic properties of tissues
12.2 Inhomogeneous wave equation
12.3 Scattering of sound pulses: continuum description of backscattering; scattering from discrete scatterers, approaches to tissue characterization
12.4 Absorption: factors affecting absorption; wave equation with absorption
12.5 Non-linear waves; cavitation
12.6 Doppler effect: scattering from blood, signal processing and physics of flow measurements
12.7 Problems
14. Physiological Function from Imaging
14.1 Compartmental modeling and simple tracer kinetics
14.2 Measurement of blood flow and organ function using imaging:
14.2.1 Assessment of brain function
14.2.2 Assessment of cardiac function
14.3 Problem
Detalles del producto
Detalles del producto
- Edición: 1
- Última edición
- Publicado: 24 de septiembre de 2026
- Idioma: Inglés
Sobre los autores
Sobre los autores
AA
Adam W. Anderson
Adam W. Anderson, Ph.D. is Professor of Biomedical Engineering and Radiology and Radiological Sciences at Vanderbilt University and a member of the Vanderbilt University Institute of Imaging Science. Dr. Anderson received his doctorate in Physics from Yale University in 1990 and has been engaged on research in MRI for the past 30 years. He is a Fellow of the American Institute of Medical and Biological Engineering and the International Society of Magnetic Resonance in Medicine. His current research focuses on improving methods of diffusion and high field MRI for characterizing brain structure and function.
Afiliaciones y experiencia
Professor of Biomedical Engineering and Radiology and Radiological Sciences, Vanderbilt University, USACC
Charles F. Caskey
Charles Caskey, Ph.D. is an Associate Professor of Radiology and Radiological Sciences and Biomedical Engineering at Vanderbilt University and director of the Laboratory of Acoustic Therapy and Imaging in the Vanderbilt University Institute of Imaging Science. Dr. Caskey received his doctoral degree for studies of the bioeffects of ultrasound during microbubble-enhanced drug delivery at the University of California at Davis. He has made many contributions to the fields of contrast-enhanced ultrasound, MR-guided focused ultrasound, and ultrasound neuromodulation. His current research focuses on developing new uses for ultrasound applications, such as neuromodulation, drug delivery, and functional imaging.
Afiliaciones y experiencia
Associate Professor of Radiology and Radiological Sciences and Biomedical Engineering, Vanderbilt University, USAJG
John C. Gore
John C. Gore, Ph.D., holds the Hertha Ramsey Cress Chair in Medicine and is a University Professor of Radiology and Radiological Sciences, Biomedical Engineering, Physics and Astronomy, and Molecular Physiology and Biophysics at Vanderbilt University, where he also directs the Vanderbilt University Institute of Imaging Science. Dr. Gore obtained his B.Sc. in Physics from the University of Manchester in 1972, a Ph.D. in Physics from the University of London in 1976, and a BA degree in Law from Ealing College, London in 1982. He is a member of the National Academy of Engineering and an elected Fellow of the American Association for the Advancement of Science, the American Institute of Medical and Biological Engineering, the International Society for Magnetic Resonance in Medicine (ISMRM), the American Physical Society, the National Academy of Inventors, the International Academy of Medical and Biological Engineering, and the Institute of Physics (UK). He is also a Distinguished Investigator of the Academy of Radiology Research and Overseas Fellow of the Royal Society of Medicine (UK). He is editor-in-chief of the journal Magnetic Resonance Imaging. and an Honorary Professor at Zhejiang University in China. His research is focused on the development and applications of biomedical imaging techniques, especially magnetic resonance imaging.
Afiliaciones y experiencia
University Professor of Radiology and Radiological Sciences, Biomedical Engineering, Physics and Astronomy, and Molecular Physiology and Biophysics, Vanderbilt University, USATP
Todd E. Peterson
Todd Peterson, Ph.D., is Associate Professor of Radiology & Radiological Sciences at Vanderbilt University and Director of Nuclear Imaging and Radiochemistry in the Institute of Imaging Science, Vanderbilt University Medical Center. After completing his graduate training in experimental nuclear physics at Indiana University, he conducted his postdoctoral research in the University of Arizona's Center for Gamma-Ray Imaging. A primary research focus throughout his career has been the application of semiconductor detectors to high-resolution SPECT. His research also has spanned a wide range of applications of PET, SPECT, and CT imaging in both preclinical and clinical research. He is a Fellow of both the American Institute for Medical and Biological Engineering and the Society of Nuclear Medicine and Molecular Imaging.
Afiliaciones y experiencia
Associate Professor of Radiology & Radiological Sciences, Vanderbilt University, USA