Computational Molecular Magnetic Resonance Imaging for Neuro-oncology

Cover
Mini Title
Computational MolecularMagnetic Resonance Imagingfor Neuro-oncology
Copyright
Preface
Acknowledgments
Contents
List of Figures
List of Tables
Book Review
Chapter 1: General Introduction
1.1 Molecular or Cellular Processes Associated with Disease Conditions
1.2 Molecular Imaging
1.3 Importance of Molecular Imaging in Human Medicine
1.4 Molecular Imaging Techniques
1.5 Significance of MRI Techniques
Chapter 2: Fundamental Physics of Nuclear Magnetic Resonance
2.1 Overview of Magnetic Resonance Imaging
2.1.1 Principles of Magnetic Resonance Imaging
2.1.2 Physics of Magnetic Resonance Imaging
2.1.3 Magnetic Resonance Imaging Equipment
2.1.3.1 The Magnet
2.1.3.2 Gradients
2.1.3.3 RF System
2.1.4 Image Acquisition and Computation
2.1.5 Image Contrast
2.1.6 Applications of MR Imaging
2.1.6.1 Physiological MR Imaging
2.1.6.2 Magnetic Resonance Angiography (MRA)
2.1.6.3 Functional Imaging
2.1.6.4 Spectroscopic Imaging
2.1.6.5 Diffusion Imaging
2.2 MR Contrast Agents and Their Physicochemical Basis
2.2.1 Methods of Generating Contrast in MR Agents
2.2.2 Atomic Basis of Magnetic Resonance
2.2.3 Relaxivity and T1, T2, T2* Contrast Agents
2.2.4 Chemistry of T1 Agents
2.2.5 T2 Agents
2.2.6 Functionalization of MR Contrast Agents
2.3 Principles of Optics in Magnetic Resonance
2.3.1 Bloch Equations in Optics
2.4 Computational Science
2.4.1 Computational Science and Problem Solving
2.4.2 Advantages of Computational Model
2.5 Compressed Sensing MRI and Computational Science
2.6 MRI in Molecular Imaging
2.7 Theoretical Treatment of Magnetic Resonance
2.7.1 Theoretical Background of Magnetic Resonance
2.7.1.1 Paramagnetism and Curie´s Law
2.7.1.2 Magnetic Susceptibility
2.7.1.3 Larmor Precession
Spin Equation of Motion
Spin Precession
2.7.1.4 NMR Relaxation
Equilibrium States
The Relaxation Process
2.7.1.5 Spin Interactions
2.7.1.6 Spin-Lattice and Spin-Spin Relaxation
2.7.2 The Bloch Equations
2.7.2.1 The Rotating Frame of Reference
2.7.2.2 The Equivalence Principle
2.7.2.3 Transformation to the Rotating Frame
2.7.2.4 Equation of Motion in the Fictitious Field
2.7.2.5 Rotating Field and Oscillating Field
Rotating and Counter-Rotating Components
The Effective Magnetic Field
Resonant Transverse Field
2.7.2.6 Excitation Pulses
2.7.2.7 Harmonic Oscillator Model of NMR and Dynamic Magnetic Susceptibility
Time Response of Damped Oscillator
Frequency Response of Damped Oscillator
Linearity and Superposition
Fourier Duality
Complex Susceptibility
Dynamic Magnetic Susceptibility
2.7.2.8 The Transverse Relaxation Function
Response to Linearly Polarized Magnetic Field
2.7.2.9 Linearity and Saturation
Conditions for Linearity
Saturation
Non-Adiabatic Condition
Adiabatic Condition
2.7.3 Quantum and Classical Descriptions of Spin Motion
2.7.3.1 Quantum and Classical Treatment
2.7.3.2 The Heisenberg Equation
2.7.3.3 Equation of Motion for Magnetic Moment Operator
2.7.3.4 Evaluation of Commutators
2.7.3.5 Computation of Expectation Values
2.7.4 Quantum Treatment of NMR Relaxation
2.7.4.1 Relaxation, Resonance and Equilibrium State
2.7.4.2 Expectation Values of Quantum Operators
2.7.4.3 Systems in Equilibrium
2.7.4.4 Curie´s Law for Systems with Interactions
2.7.4.5 Behaviour of Magnetization in Pulsed NMR
The Hamiltonian and Approximations
Quantum Responses Due to 90 and 180 Pulses
Relaxation of Longitudinal and Transverse Magnetization
2.7.4.6 Quantum Mechanical Description of Spin in a Static Field Bo
Equation of Motion for the System
2.7.4.7 Quantum Mechanical Description of Spin in a Rotating Magnetic Field
2.7.4.8 Quantum Mechanical Pictures for Description of Physical Systems
The Heisenberg Picture
The Schrödinger Picture
The Interaction (Dirac) Picture
2.7.5 Modelling and Differential Equations in Computational MRI
2.7.6 Formulation of the Bloch Equations for Treatment of Fluids in Motion
2.7.6.1 Kinematic of Fluids in Motion
2.7.6.2 The Bloch NMR Flow Equations
2.7.6.3 NMR Flow at Constant Fluid Velocity
The General Bloch NMR Flow Equation for Constant Fluid Velocity
Time-Independent Bloch NMR Flow Equation for Constant Fluid Velocity
Time-Dependent Bloch NMR Flow Equation for Constant Fluid Velocity
2.7.7 Diffusion Process in Magnetic Resonance
2.7.7.1 Multidimensional Diffusion with Constant Diffusion Coefficient
2.7.7.2 Multidimensional Diffusion with Variable Diffusion Coefficient
2.7.8 Advection-Diffusion in Nuclear Magnetic Resonance
2.7.8.1 One-Dimensional Diffusion-Advection with Constant Diffusion Coefficient
2.7.8.2 Multidimensional Diffusion-Advection with Constant Diffusion Coefficient
2.7.8.3 Multidimensional Diffusion-Advection with Variable Diffusion Coefficient
2.7.9 Justification for Assumption of the Nature of Transverse Magnetization
2.7.10 Variable Fluid Flow Corrections to the Bloch NMR Flow Equation
2.7.10.1 NMR Flow with Variable Fluid Velocity
The General Bloch NMR Flow Equation for Variable Fluid Velocity
The Time-Independent Bloch NMR Flow Equation for Variable Fluid Velocity
2.7.10.2 Derivation of Diffusion Equation with Variable Diffusion Coefficient
2.7.10.3 One-Dimensional Diffusion-Advection with Variable Diffusion Coefficient
2.7.10.4 Multidimensional Diffusion and Diffusion-Advection with Variable Diffusion Coefficient
Chapter 3: Radiofrequency Identification System for Computational Diffusion Magnetic Resonance Imaging Based on Bloch´s NMR Fl...
3.1 Introduction
3.2 Mathematical Analysis
3.3 Development of Non-gradient MRI
3.4 A New Method for Diffusion MRI
3.5 Computational Analysis
3.6 Discussion
3.7 Conclusion
Chapter 4: Radio-Frequency Identification System for Computational Magnetic Resonance Imaging of Blood Flow at Suction Points
4.1 Introduction to Blood Flow and MRI
4.2 Analytical Method
4.3 Analysis of Blood Flow at Suction Points
4.4 Computational Analysis of Blood Flow at Suction Points
4.5 RF ID and Velocity Data Generation for Different Tissues
4.6 Conclusion
Chapter 5: A Computational MRI Based on Bloch´s NMR Flow Equation, MRI Fingerprinting and Python Deep Learning for Classifying...
5.1 Introduction
5.2 Computational Modelling of the Bloch NMR Flow Equation
5.3 Relaxometry Data
5.4 Computation of Magnetic Resonance Signal Dataset
5.5 Data Visualization
5.6 Linear Regression
5.7 Machine Learning
5.7.1 Logistic Regression
5.7.2 Support Vector Machine
5.7.3 Naive Bayes
5.7.4 Decision Tree
5.7.5 Random Forest
5.7.6 Extra Trees
5.7.7 K Nearest Neighbors
5.7.8 XGBoost
5.8 Shallow Deep Learning
5.9 Deep Neural Network
5.10 Discussions
5.11 Conclusion
Chapter 6: Analysis of the Hydrogen-Like Atom for Neuro-Oncology Based on Bloch´s NMR Flow Equation
6.1 Background to Quantum Mechanical Treatment of Bloch Flow Equation
6.2 Quantum Mechanical Understanding of Classical NMR/MRI
6.3 Mathematical Representation of NMR/MRI in Quantum Mechanical Domain
6.4 Formulation of the Yukawa Potential for NMR Wave Equation
6.5 Formulation of the Coulomb Potential for NMR Wave Equation
6.6 Quantum Neuro-Oncology
6.7 Analysis of Radiofrequency Pulse as a Function of Radial Distance of the Atoms
6.8 Discussion
6.9 Conclusion
Chapter 7: Quantum Mechanical Model of the Bloch NMR Flow Equations for Transport Analysis of Quantum-Drugs in Microscopic Blo...
7.1 Introduction
7.2 Quantum Mechanical Model of Bloch NMR Flow Equations
7.3 Application to Nanotechnology
7.4 Quantum Drugs Model
7.5 Application of the WKB Approximation
7.6 The Tunnelling Effect of Quantum Drugs
7.7 Description of QM-Designed Drugs in Protein-Structured Nanomachines
7.8 Conclusion
Chapter 8: Application of ``R´´ Machine Learning for Magnetic Resonance Relaxometry Data Representation and Classification of ...
8.1 Introduction
8.2 Dataset of NMR Relaxometry for Three Classes of Brain Tumor
8.3 Statistical Summary of the MRI Relaxometry Dataset
8.4 Visualization of the MRI Relaxometry Dataset
8.5 Model Construction
8.6 Model Prediction
8.7 Discussion of Results
8.8 Conclusion
Chapter 9: Advanced Magnetic Resonance Image Processing and Quantitative Analysis in Avizo for Demonstrating Radiomic Contrast...
9.1 Potential Application of Radiomics
9.2 Factors Affecting Radiomic Feature Quantification
9.3 Machine Learning in Radiomics
9.4 Semi-Supervised Learning
9.5 Deep Learning
9.6 Research Opportunities and Challenges
9.7 Procedures in Advanced Image Processing and Quantitative Analysis
9.7.1 Processing Grayscale Images in Avizo
9.7.2 Interpretation as 2D Image or 3D Stack
9.7.3 Binarization of Grayscale Images
9.7.4 Image Separation
9.7.5 Image Analysis
9.7.6 Extracted Numerical Data
9.7.7 Visualizations of Extracted Data
9.7.8 Interactive Selection of the Data
9.8 Image-Based Filtering
9.9 Discussion
9.10 Conclusion
Chapter 10: Computational Analysis of Magnetic Resonance Imaging Contrast Agents and Their Physico-Chemical Variables
10.1 Analytical Method for Monitoring the Dynamics of Responsive Contrast Agents
10.2 Bloch NMR Flow Model for Contrast Agents Moving in 1 D Tissue Spaces
10.3 Application of Model to Cardiovascular Disease
10.4 Computational Monitoring the Dynamics of Contrast Agents
10.5 Computational Model for Comparative Analysis of MRI Contrast Agents
10.6 Development of Machine Learning Classification Algorithm for Screening MRI Contrast Agents
10.6.1 Data Preparation
10.6.2 Data Visualization
10.6.3 XGBoost Model for Classification
10.7 Bridging the Gap Between Computational Models and Experimental Imaging
10.8 Discussion
10.9 Conclusion
Chapter 11: General Conclusion
Bibliography
Index