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E-raamat: Magnetic Resonance Elastography - Physical Background and Medical Applications: Physical Background and Medical Applications [Wiley Online]

Jurgen Braun, Ingolf Sack, Sebastian Hirsch

Formaat: 456 pages
Ilmumisaeg: 11-Jan-2017
Kirjastus: Blackwell Verlag GmbH
ISBN-10: 3527696016
ISBN-13: 9783527696017

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Wiley Online
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Formaat: 456 pages
Ilmumisaeg: 11-Jan-2017
Kirjastus: Blackwell Verlag GmbH
ISBN-10: 3527696016
ISBN-13: 9783527696017

Teised raamatud teemal:

Rohkem infot Wiley Online kohta

Raamatu kodulehekülg: https://onlinelibrary.wiley.com/doi/book/10.1002/9783527696017

Magnetic resonance elastography (MRE) is a medical imaging technique that combines magnetic resonance imaging (MRI) with mechanical vibrations to generate maps of viscoelastic properties of biological tissue. It serves as a non-invasive tool to detect and quantify mechanical changes in tissue structure, which can be symptoms or causes of various diseases. Clinical and research applications of MRE include staging of liver fibrosis, assessment of tumor stiffness and investigation of neurodegenerative diseases.
The first part of this book is dedicated to the physical and technological principles underlying MRE, with an introduction to MRI physics, viscoelasticity theory and classical waves, as well as vibration generation, image acquisition and viscoelastic parameter reconstruction.
The second part of the book focuses on clinical applications of MRE to various organs. Each section starts with a discussion of the specific properties of the organ, followed by an extensive overview of clinical and preclinical studies that have been performed, tabulating reference values from published literature. The book is completed by a chapter discussing technical aspects of elastography methods based on ultrasound.

About the Authors

xiii

Foreword

Preface

xvii

Acknowledgments

xix

Notation

xxi

List of Symbols

xxiii

Introduction

(6)

Part I Magnetic Resonance Imaging

(54)

1 Nuclear Magnetic Resonance

(14)

1.1 Protons in a Magnetic Field

(1)

1.2 Precession of Magnetization

(3)

1.2.1 Quadrature Detection

(2)

1.3 Relaxation

(1)

1.4 Bloch Equations

(1)

1.5 Echoes

(2)

1.5.1 Spin Echoes

(2)

1.5.2 Gradient Echoes

(1)

1.6 Magnetic Resonance Imaging

(6)

1.6.1 Spatial Encoding

(1)

1.6.1.1 Slice Selection

(1)

1.6.1.2 Phase Encoding

(1)

1.6.1.3 Frequency Encoding

(3)

2 Imaging Concepts

(18)

2.1 k-Space

(3)

2.2 k-Space Sampling Strategies

(7)

2.2.1 Segmented Image Acquisition

(1)

2.2.1.1 Fast Low-Angle Shot (FLASH)

(1)

2.2.1.2 Balanced Steady-State Free Precession (bSSFP)

(2)

2.2.2 Echo-Planar Imaging (EPI)

(2)

2.2.3 Non-Cartesian Imaging

(1)

2.3 Fast Imaging

(8)

2.3.1 Fast Imaging Strategies

(1)

2.3.2 Partial Fourier Imaging

(1)

2.3.3 Parallel Imaging

(1)

2.3.3.1 GRAPPA

(1)

2.3.4 Impact of Fast Imaging on SNR and Scan Time

(4)

3 Motion Encoding and MRE Sequences

(20)

3.1 Motion Encoding

(14)

3.1.1 Gradient Moment Nulling

(2)

3.1.2 Encoding of Time-Harmonic Motion

(4)

3.1.3 Fractional Encoding

(1)

3.2 Intra-Voxel Phase Dispersion

3.3 Diffusion-Weighted MRE

(1)

3.4 MRE Sequences

(8)

3.4.1 FLASH-MRE

(2)

3.4.2 bSSFP-MRE

(2)

3.4.3 EPI-MRE

(4)

Part II Elasticity

(84)

4 Viscoelastic Theory

(68)

4.1 Strain

(4)

4.2 Stress

(1)

4.3 Invariants

(1)

4.4 Hooke's Law

(1)

4.5 Strain-Energy Function

(1)

4.6 Symmetries

(4)

4.7 Engineering Constants

(5)

4.7.1 Young's Modulus and Poisson's Ratio

(1)

4.7.2 Shear Modulus and Lame's First Parameter

(1)

4.7.3 Compressibility and Bulk Modulus

(2)

4.7.4 Compliance and Elasticity Tensor for a Transversely Isotropic Material

(1)

4.8 Viscoelastic Models

(12)

4.8.1 Elastic Model: Spring

(1)

4.8.2 Viscous Model: Dashpot

(1)

4.8.3 Combinations of Elastic and Viscous Elements

(6)

4.8.4 Overview of Viscoelastic Models

(3)

4.9 Dynamic Deformation

(12)

4.9.1 Balance of Momentum

(4)

4.9.2 Mechanical Waves

(2)

4.9.2.1 Complex Moduli and Wave Speed

(1)

4.9.3 Navier--Stokes Equation

(1)

4.9.4 Compression Modulus and Oscillating Volumetric Strain

100

(1)

4.9.5 Elastodynamic Green's Function

101

(2)

4.9.6 Boundary Conditions

103

(1)

4.10 Waves in Anisotropic Media

104

(6)

4.10.1 The Christoffel Equation

105

(1)

4.10.2 Waves in a Transversely Isotropic Medium

106

(4)

4.11 Energy Density and Flux

110

(4)

4.11.1 Geometric Attenuation

113

(1)

4.12 Shear Wave Scattering from Interfaces and Inclusions

114

(17)

4.12.1 Plane Interfaces

115

(3)

4.12.2 Spatial and Temporal Interfaces

118

(3)

4.12.3 Wave Diffusion

121

(4)

4.12.3.1 Green's Function of Waves and Diffusion Phenomena

125

(1)

4.12.3.2 Amplitudes and Intensities of Diffusive Waves

126

(5)

5 Poroelasticity

131

(14)

5.1 Navier's Equation for Biphasic Media

133

(9)

5.1.1 Pressure Waves in Poroelastic Media

136

(4)

5.1.2 Shear Waves in Poroelastic Media

140

(2)

5.2 Poroelastic Signal Equation

142

(3)

Part III Technical Aspects and Data Processing

145

(98)

6 MRE Hardware

147

(14)

6.1 MRI Systems

147

(6)

6.2 Actuators

153

(8)

6.2.1 Technical Requirements

153

(1)

6.2.2 Practicality

153

6.2.3 Types of Mechanical Transducers

154

(7)

7 MRE Protocols

161

(4)

8 Numerical Methods and Postprocessing

165

(26)

8.1 Noise and Denoising in MRE

165

(11)

8.1.1 Denoising: An Overview

165

(2)

8.1.2 Least Squares and Polynomial Fitting

167

(1)

8.1.3 Frequency Domain (k-Space) Filtering

168

(1)

8.1.3.1 Averaging

168

(2)

8.1.3.2 LTI Filters in the Fourier Domain

170

(2)

8.1.3.3 Band-Pass Filtering

172

(1)

8.1.4 Wavelets and Multi-Resolution Analysis (MRA)

172

(2)

8.1.5 FFT versus MRA in vivo

174

(1)

8.1.6 Sparser Approximations and Performance Times

175

(1)

8.2 Directional Filters

176

(3)

8.3 Numerical Derivatives

179

(8)

8.3.1 Matrix Representation of Derivative Operators

182

(1)

8.3.2 Anderssen Gradients

183

(3)

8.3.3 Frequency Response of Derivative Operators

186

(1)

8.4 Finite Differences

187

(4)

9 Phase Unwrapping

191

(8)

9.1 Flynn's Minimum Discontinuity Algorithm

193

(2)

9.2 Gradient Unwrapping

195

(1)

9.3 Laplacian Unwrapping

196

(3)

10 Viscoelastic Parameter Reconstruction Methods

199

(30)

10.1 Discretization and Noise

201

(3)

10.2 Phase Gradient

204

(1)

10.3 Algebraic Helmholtz Inversion

205

(3)

10.3.1 Multiparameter Inversion

207

(1)

10.3.2 Helmholtz Decomposition

207

(1)

10.4 Local Frequency Estimation

208

(2)

10.5 Multifrequency Inversion

210

(4)

10.5.1 Reconstruction of φ

211

(2)

10.5.2 Reconstruction of |G*|

213

(1)

10.6 k-MDEV

214

(3)

10.7 Finite Element Method

217

(7)

10.7.1 Weak Formulation of the One-Dimensional Wave Equation

218

(1)

10.7.2 Discretization of the Problem Domain

219

(1)

10.7.3 Basis Function in the Discretized Domain

220

(1)

10.7.4 FE Formulation of the Wave Equation

221

(3)

10.8 Direct Inversion for a Transverse Isotropic Medium

224

(1)

10.9 Waveguide Elastography

225

(4)

11 Multicomponent Acquisition

229

(4)

12 Ultrasound Elastography

233

(10)

12.1 Strain Imaging (SI)

235

(1)

12.2 Strain Rate Imaging (SRI)

235

(1)

12.3 Acoustic Radiation Force Impulse (ARFI) Imaging

235

(2)

12.4 Vibro-Acoustography (VA)

237

(1)

12.5 Vibration-Amplitude Sonoelastography (VA Sono)

237

(1)

12.6 Cardiac Time-Harmonic Elastography (Cardiac THE)

237

(1)

12.7 Vibration Phase Gradient (PG) Sonoelastography

238

(1)

12.8 Time-Harmonic Elastography (1D/2D THE)

238

(1)

12.9 Crawling Waves (CW) Sonoelastography

238

(1)

12.10 Electromechanical Wave Imaging (EWI)

239

(1)

12.11 Pulse Wave Imaging (PWI)

239

(1)

12.12 Transient Elastography (TE)

240

(1)

12.13 Point Shear Wave Elastography (pSWE)

240

(1)

12.14 Shear Wave Elasticity Imaging (SWEI)

240

(1)

12.15 Comb-Push Ultrasound Shear Elastography (CUSE)

241

(1)

12.16 Supersonic Shear Imaging (SSI)

241

(1)

12.17 Spatially Modulated Ultrasound Radiation Force (SMURF)

241

(1)

12.18 Shear Wave Dispersion Ultrasound Vibrometry (SDUV)

241

(1)

12.19 Harmonic Motion Imaging (HMI)

242

(1)

Part IV Clinical Applications

243

(108)

13 MRE of the Heart

245

(18)

13.1 Normal Heart Physiology

245

(5)

13.1.1 Cardiac Fiber Anatomy

247

(2)

13.1.2 Wall Shear Modulus versus Cavity Pressure

249

(1)

13.2 Clinical Motivation for Cardiac MRE

250

(2)

13.2.1 Systolic Dysfunction versus Diastolic Dysfunction

250

(2)

13.3 Cardiac Elastography

252

(11)

13.3.1 Ex vivo SWI

253

(1)

13.3.2 In vivo SDUV

253

(1)

13.3.3 In vivo Cardiac MRE in Pigs

254

(2)

13.3.4 In vivo Cardiac MRE in Humans

256

(1)

13.3.4.1 Steady-State MRE (WAV-MRE)

256

(3)

13.3.4.2 Wave Inversion Cardiac MRE

259

(1)

13.3.5 MRE of the Aorta

260

(3)

14 MRE of the Brain

263

(20)

14.1 General Aspects of Brain MRE

264

(1)

14.1.1 Objectives

264

(1)

14.1.2 Determinants of Brain Stiffness

264

(1)

14.1.3 Challenges for Cerebral MRE

264

(1)

14.2 Technical Aspects of Brain MRE

265

(12)

14.2.1 Clinical Setup for Cerebral MRE

265

(1)

14.2.2 Choice of Vibration Frequency

266

(3)

14.2.3 Driver-Free Cerebral MRE

269

(1)

14.2.4 MRE in the Mouse Brain

270

(7)

14.3 Findings

277

(6)

14.3.1 Brain Stiffness Changes with Age

272

(1)

14.3.2 Male Brains Are Softer than Female Brains

273

(1)

14.3.3 Regional Variation in Brain Stiffness

274

(1)

14.3.4 Anisotropic Properties of Brain Tissue

274

(2)

14.3.5 The in vivo Brain Is Compressible

276

(1)

14.3.6 Preliminary Findings of MRE with Functional Activation

277

(1)

14.3.7 Demyelination and Inflammation Reduce Brain Stiffness

277

(2)

14.3.8 Neurodegeneration Reduces Brain Stiffness

279

(1)

14.3.9 The Number of Neurons Correlates with Brain Stiffness

280

(1)

14.3.10 Preliminary Conclusions on MRE of the Brain

280

(3)

15 MRE of Abdomen, Pelvis, and Intervertebral Disc

283

(42)

15.1 Liver

283

(28)

15.1.1 Epidemiology of Chronic Liver Diseases

286

(1)

15.1.2 Liver Fibrosis

287

(2)

15.1.2.1 Pathogenesis of Liver Fibrosis

289

(2)

15.1.2.2 Staging of Liver Fibrosis

291

15.1.2.3 Noninvasive Screening Methods for Liver Fibrosis

292

(1)

15.1.2.4 Reversibility of Liver Fibrosis

293

(1)

15.1.2.5 Biophysical Signs of Liver Fibrosis

293

(1)

15.1.3 MRE of the Liver

294

(1)

15.1.3.1 MRE in Animal Models of Hepatic Fibrosis and Liver Tissue Samples

294

(1)

15.1.3.2 Early Clinical Studies and Further Developments

295

(8)

15.1.3.3 MRE of Nonalcoholic Fatty Liver Disease

303

(1)

15.1.3.4 Comparison with other Noninvasive Imaging and Serum Biomarkers

304

(3)

15.1.3.5 MRE of the Liver for Assessing Portal Hypertension

307

(2)

15.1.3.6 MRE in Liver Grafts

309

(1)

15.1.3.7 Confounders

310

(1)

15.2 Spleen

311

(3)

15.2.1 MRE of the Spleen

311

(3)

15.3 Pancreas

314

(1)

15.3.1 MRE of the Pancreas

315

(1)

15.4 Kidneys

315

(3)

15.4.1 MRE of the Kidneys

316

(2)

15.5 Uterus

318

(1)

15.5.1 MRE of the Uterus

318

(1)

15.6 Prostate

319

(2)

15.6.1 MRE of the Prostate

320

(1)

15.7 Intervertebral Disc

321

(4)

15.7.1 MRE of the Intervertebral Disc

322

(3)

16 MRE of Skeletal Muscle

325

(8)

16.1 In vivo MRE of Healthy Muscles

326

(4)

16.2 MRE in Muscle Diseases

330

(3)

17 Elastography of Tumors

333

(18)

17.1 Micromechanical Properties of Tumors

333

(3)

17.2 Ultrasound Elastography of Tumors

336

(3)

17.2.1 Ultrasound Elastography in Breast Tumors

337

(1)

17.2.2 Ultrasound Elastography in Prostate Cancer

338

(1)

17.3 MRE of Tumors

339

(12)

17.3.1 MRE of Tumors in the Mouse

340

(2)

17.3.2 MRE in Liver Tumors

342

(2)

17.3.3 MRE of Prostate Cancer

344

(1)

17.3.3.1 Ex Vivo Studies

344

(1)

17.3.3.2 In Vivo Studies

345

(1)

17.3.4 MRE of Breast Tumors

345

(1)

17.3.4.1 In Vivo MRE of Breast Tumors

346

(1)

17.3.5 MRE of Intracranial Tumors

347

(4)

Part V Outlook

351

(4)

Dimensionality

351

(1)

Sparsity

352

(1)

Heterogeneity

353

(1)

Reproducibility

353

(2)

A Simulating the Bloch Equations

355

(2)

B Proof that Eq. (3.8) Is Sinusoidal

357

(2)

C Proof for Eq. (4.1)

359

(2)

D Wave Intensity Distributions

361

(6)

D.1 Calculation of Intensity Probabilities

361

(1)

D.2 Point Source in 3D

362

(1)

D.3 Classical Diffusion

363

(2)

D.4 Damped Plane Wave

365

(2)

References

367

(50)

Index

417

Ingolf Sack is professor for Experimental Radiology and Elastography at Charité - Universitätsmedizin Berlin, Germany. He received a PhD 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 PhD 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.

Püsilink: https://www.kriso.ee/db/9783527696017_pe.html

E-raamat: Magnetic Resonance Elastography - Physical Background and Medical Applications: Physical Background and Medical Applications [Wiley Online]

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