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E-grāmata: Electro-magnetic Tissue Properties Mri

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(Kyung Hee Univ, Korea), (Philips Technologie Gmbh, Germany), (Yonsei Univ, Korea), (Cornell Univ, Usa)
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Electro-magnetic Tissue Properties MriPalielināt
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This is the first book that presents a comprehensive introduction to and overview of electro-magnetic tissue property imaging techniques using MRI, focusing on Magnetic Resonance Electrical Impedance Tomography (MREIT), Electrical Properties Tomography (EPT) and Quantitative Susceptibility Mapping (QSM). The contrast information from these novel imaging modalities is unique since there is currently no other method to reconstruct high-resolution images of the electro-magnetic tissue properties including electrical conductivity, permittivity, and magnetic susceptibility. These three imaging modalities are based on Maxwell's equations and MRI data acquisition techniques. They are expanding MRI's ability to provide new contrast information on tissue structures and functions.To facilitate further technical progress, the book provides in-depth descriptions of the most updated research outcomes, including underlying physics, mathematical theories and models, measurement techniques, computation issues, and other challenging problems.
Preface v
Foreword ix
1 Introduction
1(8)
1.1 Electro-magnetic Tissue Properties of Biological Tissues
2(2)
1.2 Three Electro-magnetic Tissue Property Imaging Modalities
4(1)
1.3 Mathematical Frameworks
5(2)
1.4 General Notations
7(2)
2 Electro-magnetism and MRI
9(68)
2.1 Basics of Electro-magnetism
10(21)
2.1.1 Maxwell's equations
10(1)
2.1.2 Electric field due to point charges in free space
11(5)
2.1.3 Molecular polarization
16(1)
2.1.4 Electrical bioimpedance for cylindrical subjects
17(1)
2.1.4.1 Conductivity and resistance at direct current
17(2)
2.1.4.2 Permittivity and capacitance
19(1)
2.1.4.3 Admittivity of a material including both mobile and immobile charges
20(1)
2.1.5 Boundary value problems in electrostatics
21(3)
2.1.6 Time-harmonic Maxwell's equations and eddy current model
24(4)
2.1.7 Magnetic field created by magnetic moment
28(3)
2.2 Magnetic Resonance Imaging
31(25)
2.2.1 MR signal and Larmor precession of spins ignoring relaxation effects
33(1)
2.2.1.1 Larmor precession of M in an external field B
33(3)
2.2.1.2 MR signal ignoring relaxation effects
36(1)
2.2.1.3 MR signal with gradient field
37(3)
2.2.1.4 One-dimensional imaging with frequency encoding
40(1)
2.2.1.5 Two-dimensional imaging with phase and frequency encoding
41(3)
2.2.2 On-resonance RF excitation to flip M toward the xy-plane
44(1)
2.2.2.1 Time-harmonic RF field B1
44(3)
2.2.2.2 Time-harmonic RF excitation and flip angle
47(4)
2.2.3 Signal detection and RF reciprocity principle
51(1)
2.2.3.1 RF reciprocity principle
52(3)
2.2.4 Relaxation effects
55(1)
2.3 Fourier Transform
56(3)
2.4 Image Processing
59(18)
2.4.1 Diffusion techniques for denoising: L1 vs. L2 minimization
60(3)
2.4.2 Segmentation
63(4)
2.4.3 Sparse sensing
67(4)
References
71(6)
3 Magnetic Resonance Electrical Impedance Tomography
77(114)
3.1 Overview and History of MREIT
78(5)
3.2 Overall Structure of MREIT
83(2)
3.3 Measurement of Internal Data Bz
85(7)
3.3.1 Noise analysis
88(3)
3.3.2 Pulse sequence
91(1)
3.4 Forward Model
92(10)
3.4.1 Boundary value problem in MREIT
93(5)
3.4.2 Computation of Bz
98(4)
3.5 Uniform Current Density Electrodes
102(7)
3.5.1 Mathematical model for uniform current electrode in half space
104(1)
3.5.2 Optimal geometry of non-uniform recessed electrodes
105(4)
3.6 Mathematical Model of MREIT for Stable Reconstruction
109(5)
3.6.1 Map from σ to Bz data
109(1)
3.6.2 Toward uniqueness of an MREIT problem
110(1)
3.6.2.1 Scaling uncertainty of σ
111(1)
3.6.2.2 Two linearly independent currents for uniqueness
112(2)
3.7 MREIT with Object Rotations
114(11)
3.7.1 Current density imaging
115(2)
3.7.1.1 Recovering a transversal current density J having Jz = 0 using Bz
117(2)
3.7.2 Early MREIT algorithms
119(1)
3.7.3 J-substitution algorithm
120(2)
3.7.3.1 J-substitution: Uniqueness
122(2)
3.7.3.2 J-substitution algorithm: Iterative scheme
124(1)
3.8 MREIT Without Subject Rotation
125(33)
3.8.1 Harmonic Bz algorithm
126(2)
3.8.1.1 Mathematical model and corresponding inverse problem
128(1)
3.8.1.2 Two-dimensional MREIT model
129(4)
3.8.1.3 Representation formula
133(4)
3.8.1.4 Local reconstruction using harmonic Bz algorithm
137(2)
3.8.1.5 Conductivity reconstructor using harmonic Bz algorithm
139(4)
3.8.1.6 Non-iterative harmonic Bz algorithm with transversally dominant current density
143(4)
3.8.1.7 A posteriori error estimate: two-dimensional MREIT model
147(5)
3.8.2 Variational Bz and gradient Bz decomposition algorithm
152(1)
3.8.2.1 Variational Bz algorithm
153(3)
3.8.2.2 Gradient Bz decomposition algorithm
156(2)
3.9 Anisotropic Conductivity Reconstruction Problem
158(5)
3.9.1 Definition of effective conductivity for a cubic sample
159(2)
3.9.2 Anisotropic conductivity reconstruction in MREIT
161(2)
3.10 Imaging Experiments
163(28)
3.10.1 Phantom experiment
163(1)
3.10.1.1 Non-biological phantom imaging
163(3)
3.10.1.2 Biological phantom imaging
166(1)
3.10.1.3 Contrast mechanism of apparent conductivity
167(3)
3.10.2 Animal experiment
170(1)
3.10.2.1 Postmortem animal imaging
170(3)
3.10.2.2 In vivo animal imaging
173(5)
3.10.3 In vivo human imaging
178(1)
3.10.4 Challenging problems and future directions
179(2)
Acknowledgments
181(1)
References
181(10)
4 MR-EPT
191(40)
4.1 Mathematical Model
193(15)
4.1.1 Central EPT equation
193(3)
4.1.2 Approximate EPT equation
196(5)
4.1.3 Boundary effects
201(3)
4.1.4 Anisotropy
204(2)
4.1.5 Local SAR
206(2)
4.2 Data Collection Method
208(4)
4.2.1 Amplitude
209(1)
4.2.2 Phase
209(3)
4.3 Image Reconstruction
212(2)
4.3.1 SNR and calculus operation kernel
212(1)
4.3.2 Main field strength and SNR
213(1)
4.4 Numerical Simulations
214(3)
4.4.1 Head model
214(3)
4.5 Experiments
217(5)
4.5.1 Phantom experiments
217(1)
4.5.2 Volunteer experiments
218(4)
4.6 Medical Applications
222(1)
4.7 Challenging Problems and Future Directions
223(8)
Acknowledgments
224(1)
References
225(6)
5 Quantitative Susceptibility Mapping
231(36)
5.1 Introduction
231(3)
5.2 Mathematical Model for Relating MRI Signal to Tissue Susceptibility
234(13)
5.2.1 The forward problem description
234(1)
5.2.1.1 Formulation of the forward problem from tissue magnetization to MRI measured field
234(3)
5.2.1.2 Inverse problem and mathematical analysis
237(3)
5.2.1.3 III-poised issue of the inverse problem from measured field to magnetization source
240(1)
5.2.2 Solutions to the inverse problem
241(1)
5.2.2.1 Morphology enabled dipole inversion (MEDI)
241(3)
5.2.2.2 Other forms of prior information for dipole inversion
244(1)
5.2.2.3 Condition the inverse problem well for precise solution --- Calculation of Susceptibility using Multiple Orientation Sampling (COSMOS)
245(2)
5.3 Data Acquisition Method
247(1)
5.4 Image Reconstruction Method
248(3)
5.4.1 The MEDI reconstruction algorithm
248(2)
5.4.2 Background field removal without affecting local fields
250(1)
5.5 Numerical Simulation
251(4)
5.6 Experimental Validation
255(11)
5.6.1 Validation of the reference standard COSMOS method
255(2)
5.6.2 Validation of the MEDI method
257(3)
5.6.3 Clinical applications
260(1)
5.6.3.1 Cerebral microhemorrhage
260(1)
5.6.3.2 Hemorrhage
261(1)
5.6.3.3 Deep brain stimulation
262(1)
5.6.3.4 Parkinson's disease
263(1)
5.6.3.5 Multiple sclerosis
264(2)
5.7 Challenging Problems and Future Directions
266(1)
Acknowledgments 267(1)
References 268(7)
Index 275
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