An Introduction to MRI for Medical Physicists and Engineers

An Introduction to MRI for Medical Physicists and Engineers  Price Reduced!

Author:  Anthony Wolbarst and Nathan Yanasak
ISBN:  9781930524583
Published:  June 2019 | 318 pp | eBook

Price:   $ 95.95      List Price 120.00


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Table of Contents

Preface

1. Introduction to MRI

1.1 A Stratospheric, Warp-Speed Sketch of NMR and MRI
 
The nuclear magnetic moment is proportional to the nuclear spin
 
Some Notes on Vectors
 
First picture of NMR: quasi-quantum mechanical (spin-up/spin-down along Bz and the z-axis)
 
MRI of a 1D patient
 
Second picture of NMR: classical (magnetization precessing in x-y plane)
 
Proton spin relaxation
 
Longitudinal proton spin relaxation time, T1
 
Transverse proton spin relaxation time, T2
 
T1-weighted and T2-w clinical images
1.2 Uniqueness of MRI
1.3 A Real MRI Case Study
 
Computed tomography (CT)
 
MRI: T1-w, T2-w, and FLAIR imaging
 
Magnetic resonance spectroscopy (MRS)
 
Functional MRI (f MRI)
 
Diffusion tensor MR imaging (DTI)
 
MRI-guided fine-needle biopsy
 
Positron emission tomography?
 
Treatment guidance and follow-up
1.4 A Brief History of MRI: Bloch, Purcell, Damadian, Lauterbur, et. al.
1.5 A Clinical Caveat

2. Quasi-Quantum, Two-State Picture of Proton NMR in a Single Voxel

2.1 A Brief Review of Electromagnetism
 
Fields, Maxwell’s equations, and the wave equation
 
Photons
2.2 Magnetic Fields within Matter: Magnetic Susceptibility
 
Applied main, gradient, and RF fields at a voxel
 
Spontaneous magnetic fields that affect T1 and T2
 
Magnetic susceptibility: diamagnetism, paramagnetism, and ferromagnetism induced by B0
2.3 Nuclear Magnetic Dipole Moment
 
Proton-proton dipole interaction
2.4 Proton Spin-Up and Spin-Down States
2.5 NMR at the Larmor Resonance Frequency
2.6 Preliminary Demonstration of the NMR Phenomenon in Water

3. Proton Density MR Study of a 1D Multi-Voxel Patient and the Quality of the Image

3.1 The Three Distinct Applied Magnetic Fields in 1D MRI
3.2 Encoding of x-Position with an x-Gradient, and the Local NMR Resonance Frequency
3.3 Proton Density (PD) MRI of a Multi-Voxel, One-Dimensional Patient
3.4 Measures of Image Quality: Contrast, Resolution, and the MTF
 
Contrast (C)
 
Resolution (R)
 
Glimpse of the modulation transfer function (MTF)
3.5 Stochastic Noise, Signal-to-Noise Ratio, Contrast-Detail Curves, and the DQE
 
Stochastic noise
 
Signal-to-noise ratio (SNR)
 
Contrast-detail curves
 
Detective quantum efficiency (DQE)
3.6 Judging Performance with ROC Curves
 
True positives (TP), false negatives (FN), etc.
 
Sensitivity, selectivity, and accuracy
 
Receiver operating characteristic (ROC) curves
 
Bayes’ theorem
3.7 Some MR Artifacts
 
Nonlinear gradient-field artifact
 
Chemical shift artifact
 
Susceptibility artifact

4. Magnetization of a Voxel

4.1 The Magnetization, m(x,t), of the Voxel at Location x
4.2 Thermal Equilibrium: The Battle between Energy and Entropy
4.3 The Magnitude of m(t) at Thermal Equilibrium, m0 ≡ m(∞), and Its Impact on Image Quality
4.4 Effect of Field Strength, |B0|, on Image Quality
4.5 Spin Population Dynamics
4.6 Stimulated Radiative Transitions and Spin System Saturation
4.7 Stimulated Non-Radiative Spin Transitions and T1 Relaxation

5. Mathematical Machinations

5.1 Two Simple but Essential Functions
 
Exponential decay and growth
 
Sinusoidal oscillation
5.2 Scalar (Dot) Product of Vectors and Functions
 
Spectral analysis of real vectors
 
Into the complex plane
 
Orthonormal sinusoidal basis vectors
5.3 Fourier Series Expansion of a Function Periodic in Time or Space
 
Basis vectors, and the Dirac delta function
 
Series truncation
5.4 Fourier Integrals and Transforms
 
FT [LSF(x)] = MTF(v)
 
Patient motion artifacts and the Fourier Shift Theorem
5.5 Vectors in a 1D k-Space
5.6 Digital Representations of Symbols and Images
 
Pixel size and grayscale
 
Data compression
5.7 Noise, Statistics, and Probability Distribution Functions
 
Elementary statistical notions
 
Notes on the Poisson distribution
 
NEX×SNR
 
Rician Distribution
5.8 Sampling an Analog Signal
 
Shannon-Nyquist sampling theorem
 
Aliasing artifact
5.9 Resolution vs. Detectability
 
Resolution
 
Detectability requires enough size, sufficiently high contrast, and low noise

6. Classical Approach to Proton MRI in a Voxel

6.1 Normal Modes of Oscillation
6.2 Resonance at the Normal Mode Frequency
 
Precession and nutation of a gyroscope
6.3 In a Voxel, Classical Precession of m(t) about B0 at vLarmor; The Bloch Equations
6.4 Classical View of NMR
6.5 Grand Entrance of the 90° Pulse
6.6 Laboratory Frame of Reference vs. One Rotating at vLarmor

7. Free Induction Decay Imaging of a 1D Patient (without the Decay)

7.1 Saturation-Recovery in a Single Voxel, Assuming Unrealistically Slow Spin Relaxation
7.2 Improving the SNR with Quadrature Detection
7.3 Net Nuclear Magnetization from All the Voxels in the 1D Phantom Together
7.4 Selecting the z-Slice (or in 1D, the Row of Voxels) for Imaging
7.5 Signal from the 1D Phantom
7.6 FID Imaging of the 1D Phantom: Encoding Voxel x-Position Again with an x-Gradient
7.7 1D Image Reconstruction by Way of Frequency-Space
7.8 1D Image Reconstruction by Way of k-Space
7.9 Connections between Image Space and k-Space
 
Resolution in real space is inversely proportional to the width of the FOVk in k-space
7.10 Phase Waves

8. MRI Instrumentation

8.1 Main Magnet
 
MRI superconducting magnets
 
Fringe fields
 
Permanent magnets and electromagnets
8.2 Gradient Coils
8.3 The MRI RF System Is Like an AM Radio Transmitter/Receiver Pair
 
Super-heterodyne AM radio
 
New MRI machines employ direct detection, not an IF stage
 
Signal Bandwidth
8.4 Antennae/RF Coils
 
Signal-to-noise ratio, again
8.5 Phased Array of Receiver Coils

9. T1 (Longitudinal, Spin-Lattice) Relaxation

9.1 The Longitudinal Proton Spin-Relaxation Time, T1, in a Single Voxel
9.2 Exponential Regrowth of mz(t) toward m0 at the Rate 1/T1: m(t) = m0 (1 – e(–t/T1))
9.3 The Bloch Equations, Including T1 Relaxation
9.4 Biophysical Mechanism of Proton T1 Relaxation: Spontaneous, Random, vLarmor Fluctuations
 
in the Local Bz(t), Created by the Tissues Themselves, Can Induce Spin-State Transitions
9.5 Tumbling Frequencies of Water Molecules in Three Aqueous Environments
9.6 T1 Increases with the Strength of the Main Field, B0
9.7 Determining T1 in a Voxel
9.8 T1 MRI in a 1D Patient
9.9 Speeding Things Up: Short TRs and Small Flip Angles

10. T2 (Transverse, Spin-Spin) Relaxation

10.1 Transverse (Spin-Spin) Proton Relaxation: Spin De-Phasing in the x-y Plane with Characteristic Time T2
10.2 Biophysics of Proton T2 Relaxation
10.3 Static Field de-Phasing, at the Rate 1/TSFd-P , and the Spin-Echo Sequence that Removes It
10.4 1/T2* is 1/T2 Speeded Up by 1/TSFd-P
10.5 Shape of an NM Resonance Line
10.6 Magnetization Transfer (MT) Imaging
10.7 Contrast Agents such as Gadolinium Chelates

11. The Spin-Echo Pulse Sequence

11.1 Spin-Echo (SE) RF Pulse Sequence in a Single Voxel: 90°–180°– read
11.2 Put Another Way…
11.3 And More Realistically…
11.4 The Spin-Echo RF Pulse Sequence Eliminates the TSFd-P Effect
11.5 Selecting TE and TR for T1-Weighted SE
11.6 Optimizing the T1 Contrast for a Pair of Nearby Voxels
11.7 T2-weighted and PD-w for SE
11.8 SE Reconstruction of the Image of a 1D Patient from a Single Line in k-Space
11.9 Dealing with Unwanted Phase Changes in the Echo Signal Caused by Gradients
11.10 Following a Simple Trajectory through 1D k-Space
11.11 Inversion Recovery (IR) in a Voxel: 180°–90°–180°– read

12. Image Reconstruction in Two Dimensions

12.1 Selection of a Two-Dimensional Slice
12.2 Waves in 2D Real Space and Vectors in 2D k-space
12.3 Phase Encoding of Voxel y-Position
12.4 A 2D, 4-Voxel Spin-Echo/Spin-Warp Example
 
Preliminary study: Gy = Gx = 0
 
First S-E repetition: Gy = 0 throughout, but Gx on during readout
 
Second S-E repetition: Gy is on for the time tphase before readout
 
Solving the four equations for the four unknowns, mi
12.5 The General Spin-Echo, Spin-Warp Echo Data Acquisition Process

13. Fast Imaging

13.1 Time to Acquire a Slice-Image
13.2 Multiple Slice Imaging
 
On Calculating the Numbers of Batches and of Slices per Batch
13.3 Stack of 2D Slices vs. 3D Block of Tissue
13.4 Fast Spin Echo vs. Conventional Spin Echo—More Readouts per Excitation
13.5 Gradient Echo (GE) / Gradient Recall Echo (GRE)—Reducing the Repetition Time (TR)
13.6 Echo Planar Imaging (EPI)—Many More Readouts per Excitation
13.7 k-Space Has (Approximate) Conjugate Symmetry, and its Data are Redundant
13.8 Under-sampling of k-space in Combination with Phased Array Coils
13.9 Frequency- and Phase-Encoding Similarities
13.10 Cartesian vs. Non-Cartesian Readout

14. Fluid Motion in One Dimension

14.1 Water and Blood Flow
14.2 Magnetic Resonance Angiography (MRA)
14.3 Perfusion Imaging
14.4 Diffusion Tensor Imaging (DTI)
14.5 Functional MRI (fMRI) with the Blood Oxygenation Level Dependent (BOLD) Effect

15. MRI Device Quality Assurance and Safety

15.1 Daily/Weekly/Monthly Quality Assurance Checks by Technologists, and the Semi-Annual QA by a Medical Physicist
15.2 Accreditation by the American College of Radiology Every Three Years
15.3 MR Safety Requires Eternal Vigilance (Regulations, Restricted Access, Records…)
15.4 Danger from the Main Magnet and Its Fringe Fields: Beware of Aneurysm Clips and Pacemakers,
 
and of Flying Screwdrivers, Wheelchairs, and Oxygen Bottles
15.5 Biological Hazards from Switching Gradients and RF Fields, etc.
15.6 Contrast Agents and Injectors
15.7 On Siting, Installing, and Accepting an MRI Device

16. On the Horizon: Imaging with a Crystal Ball

16.1 Evolution: Ongoing Changes
 
Quantitative imaging, including MR fingerprinting
 
Compressed sensing
 
Inexpensive low-field MRI
 
High-field imaging
 
MRI on elements other than hydrogen; nuclear hyperpolarization
 
Helium-free MRI
 
Quiet imaging
 
Combining MRI with PET, NIR, US, etc.
 
Zero-quantum imaging
 
Radiation therapy treatment planning and follow-up
16.2 Revolution: Quantum Computers and Artificial Intelligence Quantum Artificial intelligence (AI)
16.3 Conclusion

Symbols and Abbreviations

Fundamental Equations

References and Sources

Index