Fundamentals of In Vivo Magnetic Resonance

Daniel M. Spielman, PhD, is Professor of Radiology at Stanford University, Stanford, CA, USA. He is a fellow of both the American Institute for Medical & Biological Engineering (AIMBE) and International Society of Magnetic Resonance in Medicine (ISMRM), and has received multiple teaching awards including the ISMRM Outstanding Teacher Award (2005) and Stanford Department of Radiology Research Faculty of the Year (2022). 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.

Chapter 1. Introduction

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