Fundamentals of In Vivo Magnetic Resonance
Spin Physics, Relaxation Theory, and Contrast Mechanisms
1. Edition March 2024
288 Pages, Softcover
Wiley & Sons Ltd
Fundamentals of In Vivo Magnetic Resonance
Authoritative reference explaining why and how the most important, radiation-free technique for elucidating tissue properties in the body works
In Vivo Magnetic Resonance helps readers develop an understanding of the fundamental physical processes that take place inside the body that can be probed by magnetic resonance imaging (MRI) and magnetic resonance spectroscopy (MRS), uniquely bridging the gap between the physics of magnetic resonance (MR) image formation and the in vivo processes that influence the detected signals, thereby equipping the reader with the mathematical tools essential to study the spin interactions leading to various contrast mechanisms.
With a focus on clinical relevance, this book equips readers with practical knowledge that can be directly applied in medical settings, enabling informed decision-making and advancements in the field of medical imaging. The material arises from the lecture notes for a Stanford University Department of Radiology course taught for over 15 years.
Aided by clever illustrations, the book takes a step-by-step approach to explain complex concepts in a comprehensible manner. Readers can test their understanding by working on approximately 60 sample problems.
Written by two highly qualified authors with significant experience in the field, In Vivo Magnetic Resonance includes information on:
* The fundamental imaging equations of MRI
* Quantum elements of magnetic resonance, including linear vector spaces, Dirac notation, Hilbert Space, Liouville Space, and associated mathematical concepts
* Nuclear spins, covering external and internal interactions, chemical shifts, dipolar coupling, J-coupling, the spin density operator, and the product operator formalism
* In vivo MR spectroscopy methods
* MR relaxation theory and the underlying sources of image contrast accessible via modern clinical MR imaging techniques
With comprehensive yet accessible coverage of the subject and a wealth of learning resources included throughout, In Vivo Magnetic Resonance is an ideal text for graduate students in the fields of physics, biophysics, biomedical physics, and materials science, along with lecturers seeking classroom aids.
1.1. A Brief History of MR
1.2. NMR vs MRI
1.3. The Roadmap
1.4. Historical Notes
Chapter 2. Classical Description of MR
2.1. Nuclear Magnetism
2.2. Net Magnetization and the Bloch Equations
2.3. Rf Excitation and Reception
2.4. Spatial Localization
2.5. The MRI Signal Equation
2.6. Exercises
2.7. Historical Notes
Chapter 3. Quantum Description of MR
3.1. Introduction
3.1.1. Why QM for magnetic resonance?
3.1.2. Historical developments
3.1.3. Wavefunctions
3.2. Mathematics of QM
3.2.1. Linear vector spaces
3.2.2. Dirac notation and Hilbert Space
3.2.3. Liouville Space
3.3. The Six Postulates of QM
3.4. MR in Hilbert Space
3.4.1. Review of spin operators
3.4.2. Single spin in a magnetic field: longitudinal and transverse magnetization
3.4.3. Ensemble of spins in a magnetic field
3.5. MR in Liouville Space
3.5.1. Statistical mixture of quantum states
3.5.2. The density operator
3.5.3. The Spin-lattice Disconnect
3.5.4. Hilbert space vs Liouville space
3.5.5. Observations about the spin density operator
3.5.6. Solving the Liouville-von Neuman equation
3.6. Exercises
3.7. Historical Notes
Chapter 4. Nuclear Spins
4.1. Review of the Spin Density Operator and the Hamiltonian
4.2. External Interactions
4.3. Internal Interactions
4.3.1. Chemical shift
4.3.2. Dipolar coupling
4.3.3. J-coupling
4.4. Summary of the Nuclear Spin Hamiltonian
4.5. Exercises
4.6. Historical Notes
Chapter 5. Product Operator Formulism
5.1. The Density Operator, Populations, and Coherences
5.1.1. Spin systems and associated density operators
5.1.2. Density matrix calculations
5.2. POF for Single-Spin Coherence Space
5.3. POF for Two-Spin Coherence Space
5.4. Branch Diagrams
5.5. Multiple Quantum Coherences and 2D NMR
5.6. Polarization Transfer
5.7. Spectral Editing
5.7.1. J-difference editing
5.7.2. Multiple quantum filtering
5.8. Exercises
5.9. Historical Notes
Chapter 6. In vivo MRS
6.1. 1H MRS
6.1.1. Acquisition methods
6.1.2. Detectable metabolites and applications
6.2. 31P-MRS
6.3. 13C-MRS
6.3.1. Acquisition methods
6.3.2. 13C infusion studies
6.3.3. Hyperpolarized 13C
6.4. Deuterium Metabolic Imaging
6.5. 23Na-MRI
6.6. Exercises
Chapter 7. Relaxation Fundamentals
7.1. Basic Principles
7.1.1. Molecular motion
7.1.2. Stochastic processes
7.1.3. A simple model of relaxation
7.2. Dipolar Coupling
7.2.1. The Solomon equations
7.2.2. Calculating transition rates
7.2.3. Nuclear Overhauser Effect
7.3. Chemical Exchange
7.3.1. Introduction
7.3.2. Effects on longitudinal magnetization
7.3.3. Effects on transverse magnetization
7.3.4. Examples
7.4. In vivo Water
7.4.1. Hydration layers
7.4.2. Tissue relaxation times
7.4.3. Magic angle effects
7.4.4. Magnetization Transfer Contrast (MTC)
7.4.5. Chemical Exchange Saturation Transfer (CEST)
7.5. Exercises
7.6. Historical Notes
Chapter 8. Redfield Theory of Relaxation
8.1. Perturbation theory and the Interaction Frame of Reference
8.2. Calculating Relaxation Times
8.3. Relaxation mechanisms
8.3.1. Dipolar coupling revisited
8.3.2. Scalar relaxation of the 1st kind and 2nd kind
8.3.3. Chemical Shift Anisotropy (CSA)
8.4. Relaxation in the Rotating Frame
8.4.1. Physics of T1r
8.4.2. The spin-lock experiment
8.4.3. Applications
8.5. Illustrative Examples
8.5.1. Hyperpolarized 13C-urea
8.5.2. Hyperpolarized 13C-Pyr
8.6. Exercises
8.7. Historical Notes
Chapter 9. MRI Contrast Agents
9.1. Paramagnetic Relaxation Enhancement
9.1.1. Solomon-Bloembergen-Morgan theory
9.1.2. Gd3+-based T1 contrast agents
9.2. T2 and T2* Contrast Agents
9.2.1. T2, diffusion, and outer-sphere relaxation
9.2.2. SPIOs and USPIOs
9.3. PARACEST Contrast Agents
9.4. Contrast Agents in the Clinic
9.4.1. Gd-based agents
9.4.2. Iron-based agents
9.5. Exercises
Chapter 10. In vivo Examples
10.1. Relaxation properties of brain
10.1.1. Morphological imaging
10.1.2. Perfusion imaging
10.1.3. Diffusion-Weighted Imaging (DWI)
10.1.4. Imaging myelin
10.1.5. Susceptibility-Weighted Imaging (SWI)
10.2. Relaxation properties of blood
10.2.1. Hemoglobin and red blood cells
10.2.2. MRI blood oximetry
10.2.3. functional Magnetic Resonance Imaging (fMRI)
10.2.4. MRI of hemorrhage
10.3. Relaxation properties of cartilage
10.3.1. T2 mapping
10.3.2. DWI
10.3.3. T1r mapping and dispersion
10.3.4. gagCEST
10.3.5. dGEMRIC
10.3.6. Ultrashort TE (UTE) imaging
10.3.7. Sodium MRI
10.3.8. Summary
10.4. Synopsis
10.5. Exercises
Exercise Solutions
References
Index
Keshav Datta, PhD, is Vice President, Research & Development, at VIDA Diagnostics Inc., Coralville, IA, USA, a precision lung health company, accelerating therapies to patients through AI-powered lung intelligence. He is also a Consulting Research Scientist at Stanford University, Stanford, CA, USA.
