Magnetic Resonance Elastography

Foreword
Preface

Introduction

PART I. Magnetic Resonance Imaging

NUCLEAR MAGNETIC RESONANCE
Protons in a Magnetic Field
Precession of Magnetization
Relaxation
Bloch Equations
Echoes
Magnetic Resonance Imaging

IMAGING CONCEPTS
k-Space
k-Space Sampling Strategies

MOTION ENCODING AND MRE SEQUENCES
Motion Encoding
Intra-Voxel Phase Dispersion
Diffusion-Weighted MRE
MRE Sequences

PART II. Elasticity

VISCOELASTIC THEORY
Strain
Stress
Invariants
Hooke's Law
Strain-Energy Function
Symmetries
Engineering Constants
Viscoelastic Models
Dynamic Deformation
Waves in Anisotropic Media
Energy Density and Flux
Shear Wave Scattering from Interfaces and Inclusions

POROELASTICITY
Navier Equations for Biphasic Media
Poroelastic Signal Equation

PART III. Technical Aspects and Data Processing

MRE HARDWARE
MRI Systems
Actuators

MRE PROTOCOLS

NUMERICAL METHODS AND POST-PROCESSING
Noise and Denoising in MRE
Directional Filters
Numerical Filters
Finite Differences

PHASE UNWRAPPING
Flynn's Minimum Discontinuity Algorithm
Gradient Unwrapping
Laplacian Unwrapping

VISCOELASTIC PARAMETER RECONSTRUCTION METHODS
Discretization and Noise
Phase Gradient
Algebraic Helmholtz Inversion
Local Frequency Estimation
Multifrequency Inversion
k-MDEV
Finite Element Method
Direct Inversion for a Transverse Isotropic Medium
Waveguide Elastography

MULTI-COMPONENT ACQUISITION

ULTRASOUND ELASTOGRAPHY
Strain Imaging (SI)
Strain-Rate Imaging (SRI)
Acoustic Radiation Force Impulse (ARFI) Imaging
Vibro-Acoustography (VA)
Vibration-Amplitude Sonoelastography (VA Sono)
Cardiac Time-Harmonic Elastography (cardiac THE)
Vibration Phase Gradient (PG) Sonoelastography
Time-Harmonic Elastography (1D/2D THE)
Crawling Waves (CW) Sonoelastography
Electromechanical Wave Imaging (EWI)
Pulse Wave Imaging (PWI)
Transient Elastography (TE)
Point Shear Wave Elastography (pSWE)
Shear Wave Elasticity Imaging (SWEI)
Comb-Push Ultrasound Shear Elastography (CUSE)
Supersonic Shear Imaging (SSI)
Spatially Modulated Ultrasound Radiation Force (SMURF)
Shear Wave Dispersion Ultrasound Vibrometry (SDUV)
Harmonic Motion Imaging (HMI)

PART IV. Clinical Applications

MRE OF THE HEART
Normal Heart Physiology
Clinical Motivation for Cardiac MRE
Cardiac Elastography

MRE OF THE BRAIN
General Aspects of Brain MRE
Technical Aspects of Brain MRE
Findings

MRE OF ABDOMEN, PELVIS AND INTERVERTEBRAL DISC
Liver
Spleen
Pancreas
Kidneys
Uterus
Prostate
Intervertebral Disc

MRE OF SKELETAL MUSCLE
In Vivo MRE of Healthy Muscles
MRE in Muscle Diseases

ELASTOGRAPHY OF TUMORS
Micromechanical Properties of Tumors
Ultrasound Elastography of Tumors
MRE of Tumors

PART V. Outlook

APPENDICES
Simulating the Bloch Equations
Proof that eq. (3.8) is Sinusoidal
Proof for eq. (4.1)
Wave Intensity Distributions