This book covers the latest developments in tissue electrical conductivity and current density imaging, increasingly popular as well as challenging applications of MRI. These applications are enabled by the acquisition of high-quality MR phase images. This book provides a practical description of the MRI physics needed to understand and acquire phase images in MRI and the key details required to reconstruct them into conductivity, current density or electric field distributions. Comprehensive details are provided about the electrical properties of biological tissues, computational modeling considerations, experimental methods, construction of non-biological and biological phantoms and MRI pulse sequences. An inclusive review of image reconstruction algorithms, and their potential applications is provided for applications directed at determining current density or electric fields, such as in transcranial DC or AC stimulation techniques; as well as electrical conductivity reconstructions that may be of use in quantitative MRI applications used to detect cancer or other pathologies. This is an excellent book for undergraduate and graduate students beginning to explore phase, current density, and conductivity imaging in MRI, and will also be of great use to researchers interested in the area of MR-based electrical property imaging.
Author(s): Rosalind Sadleir, Atul Singh Minhas
Series: Advances in Experimental Medicine and Biology, 1380
Publisher: Springer
Year: 2022
Language: English
Pages: 210
City: Cham
Preface
Contents
1 Electromagnetic Properties and the Basis for CDI, MREIT, and EPT
1.1 Electrical Properties of Tissue
1.1.1 What Underlies Tissue Electromagnetic Properties
1.1.1.1 Ionic Conductivities
1.1.1.2 Membranes and Solid Tissues
1.1.1.3 Relaxation Models of Tissue Properties
1.1.1.4 Relationship Between Diffusion and Conductivity
1.1.2 Anisotropic Tissue Properties
1.1.3 Active Membrane Properties
1.1.4 Tissue Properties
1.1.5 Measurement of Impedance Properties
1.1.5.1 Electrode Properties
1.1.5.2 Conductivity Cell and Dependence on Geometry
1.1.5.3 High-Frequency (>50 MHz) Properties
1.1.6 Methods for Reconstructing Electrical Property Images Using MR-Based Methods
1.1.6.1 History
1.1.6.2 CDI and MREIT
1.1.6.3 MREPT
1.1.7 Other Electromagnetic Properties Measureable Using MRI
References
2 Modeling for Electromagnetic Characterization, Prediction, and Reconstruction
2.1 Introduction
2.2 Overview of the Finite Element Approach
2.3 Partial Differential Equations
2.4 The Finite Element Method
2.5 The Shape Function
2.6 Formulating the Global Solution Matrix
2.7 Shape Functions for Linear Elements
2.7.1 Rectangular Linear Elements
2.7.2 Hexahedral Elements
2.7.3 Triangular Elements
2.7.4 Tetrahedral Elements
2.8 An Example Problem
2.9 Assembly of the Overall Matrix Equation
2.10 Solution of the System of Equations
2.11 Sampling Solutions
2.12 Accounting for Anisotropy
2.13 Grading
2.14 Higher-Order Elements
2.15 Segmentation of Image Data into Realistic Geometry Models
2.15.1 Segmentation Procedures
2.15.2 Exporting Segmentation Information to a Finite Element Solver
2.15.3 Adding Anisotropy to Models
2.16 COMSOL Modeling
2.16.1 Electric Current Modeling
2.16.2 Magnetic and Electric Fields Modeling Combined
2.16.3 Modeling of High-Frequency Electromagnetic Properties
Appendix 1: Formulation of the Functional for Laplace or Poisson Equations
Formulation of the Functional for a Finite Element Mesh
Minimizing the Functional
Appendix 2: Extraction of Data from Finite Element Models
Partial Volume
Finite Element Sampling
Example Code Using COMSOL
References
3 Magnetic Resonance Imaging Basics
3.1 Introduction
3.2 MRI Hardware
3.2.1 Magnet
3.2.2 Gradient and Shim Coils
3.2.3 Radiofrequency Coils
3.2.4 Spectrometer
3.2.5 Power Amplifiers
3.2.6 Preamplifier
3.3 Nuclear Magnetic Resonance
3.3.1 Spin System of Hydrogen Nucleus
3.3.2 Magnetic Moment and Magnetization
3.3.3 Interaction of Magnetic Moments with External Magnetic Field
3.3.4 Susceptibility and Magnetic Materials
3.3.5 Radiofrequency Excitation
3.3.6 Relaxation
3.3.7 Bloch Equations in General Form with T1 and T2
3.3.8 Signal Generation in NMR
3.4 Magnetic Resonance Imaging
3.4.1 Initial Condition Inside an MRI Scanner
3.4.2 Application of Magnetic Field Gradients
3.4.3 K-Space in MRI
3.4.4 Mathematical Expression of MRI K-Space Signal
3.4.5 Discrete K-Space
3.4.6 Pulse Sequences in MRI
3.5 Image Reconstruction in MRI
3.5.1 Fourier Reconstruction of MRI Data
3.5.2 Parallel Imaging
3.6 Magnitude and Phase Images in MRI
3.7 MRI Applications Exploiting Imaging Artifacts
3.8 Signal and Noise in MRI
3.8.1 SNR Calculation Methods
3.8.2 SNR Formulation in MRI
3.9 Common MR Image Formats
3.9.1 DICOM
3.9.2 NIfTI
References
4 Phantom Construction and Equipment Configurations for Characterizing Electrical Properties Using MRI
4.1 Introduction
4.2 Electrical Property Phantoms
4.2.1 Phantom Types
4.2.2 T1, Conductivity, and Permittivity Modifiers
4.2.3 Properties of Different Gelling Agents
4.2.4 Phantom Body
4.3 Measuring Electrical Parameters
4.3.1 Two-Probe Method
4.3.2 Four-Probe Method
4.3.3 Temperature Dependence
4.4 MREIT Electrodes
4.4.1 Copper Electrodes
4.4.2 Carbon-Hydrogel Electrodes
4.4.3 Carbon Rubber Electrodes
4.4.4 Internal Electrodes
4.4.5 Electrode Preparation and Placement
4.5 MREIT Constant Current Sources
4.5.1 Constant Current Source (CCS-KHU)
4.5.2 Control Program
4.5.3 PC Interface
4.5.4 Constant Current Source
4.5.5 Voltmeter
4.5.6 Discharge Circuit
4.5.7 Switch Module
4.5.8 Trigger Pulse Interface
4.5.9 Commercial Current Sources for MREIT
4.6 Steps in a Typical MREIT or MREPT Study
4.7 Previous MREIT Studies
4.7.1 MREIT
4.7.2 Non-biological Phantoms
4.7.3 Biological Phantoms
4.7.4 In Vivo Studies
4.8 MREPT
4.9 Summary
References
5 MR Current Density and MREIT Data Acquisition
5.1 Introduction
5.2 Experiment Setup
5.2.1 System Configurations/Magnetic Resonance Imaging Scanner
5.2.2 TTL Triggers
5.3 Data Acquisition
5.4 Measurement of Bz
5.4.1 Noise in MREIT
5.4.2 MRI Pulse Sequences for MREIT
5.4.3 MREIT Data Preprocessing
5.4.3.1 MR Phase Corrections
5.4.3.2 Current Density and Conductivity Image Reconstruction
5.4.4 Clinical Applications of MREIT
5.4.4.1 MREIT During tES Therapy
5.4.4.2 3D Head Model Generation
5.4.4.3 MREIT During Electroporation
5.4.5 Summary
References
6 Magnetic Resonance Current Density Imaging (MR-CDI)
6.1 Introduction
6.2 Preliminaries
6.3 Current Density Imaging via Ampere's Law
6.4 Current Density Reconstruction Algorithms from one Component of Magnetic Flux Density data
6.4.1 Current Density Reconstruction Using the Discretized Bio-Savart Law
6.4.2 Seo's Method
6.4.3 Projected Current Density Algorithm
6.4.4 Model-Based Algorithm
6.5 Correction of Stray Magnetic Field
6.5.1 BL-Field Correction
6.5.2 BE-Field Correction
6.6 Conclusion
Appendix 1
Directional Derivative Operator
Directional Derivative for Noisy Data
Numerical Implementation of the Directional Derivative
Appendix 2
References
7 Magnetic Resonance Electrical Impedance Tomography
7.1 Introduction
7.2 Preliminaries
7.2.1 Fundamental Equations for MREIT
7.2.2 Characteristics of Bz Distributions
7.3 Approaches to the MREIT Inverse Problem
7.4 Isotropic Image Reconstruction Algorithms in MREIT
7.4.1 Sensitivity-Based Algorithm
7.4.2 J-Substitution Algorithm
7.4.3 Harmonic Bz Algorithm
7.4.4 Transversal J-Substitution Algorithm
7.4.5 Non-iterative Harmonic Bz Algorithm
7.4.6 Dual-Loop Algorithm
7.5 Anisotropic Image Reconstruction Algorithms in MREIT
7.5.1 Seo's Algorithm
7.5.2 Axial Anisotropic Conductivity Reconstruction Algorithm
7.5.3 Other Anisotropic Image Reconstruction Algorithms
7.6 Diffusion Tensor Magnetic Resonance Electrical Impedance Tomography: DT-MREIT
7.6.1 Non-iterative DT-MREIT Algorithm
7.6.2 Diffusion-Weighted J-Substitution Algorithm
7.7 Image Reconstruction Toolbox
7.8 Conclusion
Appendix 1
Appendix 2
References
8 Magnetic Resonance Electrical Properties Tomography (MREPT)
8.1 Introduction
8.2 MREPT Data Acquisition
8.3 Pulse Sequences and Data Processing for B1 Magnitude Measurement
8.3.1 Examples of B1 Magnitude Measurements
8.3.2 Pulse Sequences and Data Processing for B1 Phase Measurement
8.3.3 Examples of B1 Phase Measurement
8.4 MREPT Image Reconstruction
8.4.1 Physical Background
8.4.2 Numerics
8.4.3 Advanced EPT Reconstruction Techniques
8.4.4 Permittivity Reconstruction
8.5 MREPT Experiments
8.5.1 Phantom Experiment
8.5.2 In Vivo Human Experiment
8.5.3 Examples of Phantom/In Vivo Reconstructions
8.5.4 Preclinical Experiments
Appendix
References
Index
