Sebastian Hirsch & Jürgen Braun 
Magnetic Resonance Elastography [PDF ebook] 
Physical Background And Medical Applications

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 (p SWE)
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

Ingolf Sack is professor for Experimental Radiology and Elastography at Charité – Universitätsmedizin Berlin, Germany. He received a Ph D in Chemistry at Freie Universität Berlin, Germany, for the development of methods in NMR spectroscopy. He worked at the Weizmann Institute in Rehovot, Israel, and at the Sunnybrook Hospital Toronto, Canada. Since 2003 he leads an interdisciplinary team of physicists, engineers, chemists and physicians which has pioneered pivotal developments in time-harmonic elastography of both MRI and ultrasound for many medical applications.

Sebastian Hirsch is a postdoctoral fellow in the Department of Radiology at the Charité – Universitätsmedizin Berlin, Germany. After studying physics at the University of Mainz, Germany, he joined Charité, where he works on pressure-sensitive MRE and the development of data acquisition strategies.
Jürgen Braun is an assistant professor at the Charité – Universitätsmedizin Berlin, Germany. He received his Ph D degree in physical chemistry from Albert-Ludwigs-University in Freiburg, Germany, for the elucidation of reaction kinetics with liquid and solid state NMR. He possesses long standing professional experience in elastography, medical engineering, and image processing.