Theory, Dynamics and Applications of Magnetic Resonance Imaging-I

Abhishek Gupta, Timothy Stait-Gardner, Bahman Ghadirian, William S. Price, Michael Oluwaseun Dada, Omotayo Bamidele Awojoyogbe  © by the authors

ISBN: 978-1-940366-10-4
Published Date: October, 2014
Pages: 143
Paperback: $89
Publisher: Science Publishing Group
To purchase hard copies of this book, please email: book@sciencepublishinggroup.com
Book Description

There can be few better examples of the complex and unanticipated interactions of basic research and technological innovation than the development of magnetic resonance imaging (NMR/MRI) techniques for multidisciplinary research. The method has the rather unusual and attractive features that it is totally non-destructive and non-invasive and for these reasons it has interesting applications in almost all fields of research.

An ideal approach to exhaust the complex and unanticipated interactions of basic research and technological innovation offered by magnetic resonance techniques would be to find generalized ( time dependent and time independent) analytical solutions and models to the Bloch NMR equations. The advantages of such solutions are related to the fact that the magnetizations and signals obtainable from them may constitute an array of parameters that are uniquely informative for functional and dynamical studies of living and nonliving matters.

Unfortunately, the basic physics of extracting the relevant information from the solution of Bloch NMR equations to accurately understand the theory, dynamics and applications of magnetic resonance imaging (MRI) is still not yet fully available. Additionally, it may be noteworthy to mention that, analytical solutions to the Bloch NMR flow equations have deliberately, perhaps unintentionally been omitted in the literature. Presently, there are no simple closed solutions known to the Bloch NMR flow equations for a general radiofrequency (rF) excitation. Therefore the Mathematical formulations and models based on the Bloch NMR flow equations presented in this book can be taken as definitions of new functions to be studied in detail.

Volume I of this book is intended to present basic theory of MRI and develop several fundamental equations which can be invaluable for quantitative and qualitative analysis of NMR magnetizations and signals. Fortunately, analytical solutions to these equations are available in standard Mathematics, Physics, Chemistry and Engineering textbooks. These solutions can then be used to reveal without too much difficulty many of the most important but hidden applications of magnetic resonance imaging.

Volume I is intentionally divided into only two chapters to focus the minds of our readers on the array of MRI innovations expected in Volume II.

Author Introduction

Omotayo Bamidele Awojoyogbe, Department of Physics, Federal University of Technology, Minna, Niger State, Nigeria.
Abhishek Gupta, Nanoscale Organisation and Dynamics Group, School of Science and Health, University of Western Sydney, Australia.
Timothy Stait-Gardner, Nanoscale Organisation and Dynamics Group, School of Science and Health, University of Western Sydney, Australia.
Bahman Ghadirian, Nanoscale Organisation and Dynamics Group, School of Science and Health, University of Western Sydney, Australia.
William S. Price, Nanoscale Organisation and Dynamics Group, School of Science and Health, University of Western Sydney, Australia.
Michael Oluwaseun Dada, Department of Physics, Federal University of Technology, Minna, Niger State, Nigeria.

Table of Contents
  • The Whole Book

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  • Front Matter

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  • Chapter 1 Fundamental Concept for the Theory, Dynamics and Applications of MRI

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    1. 1.1 Introduction
    2. 1.2 Preliminary Concepts
    3. 1.2.1 Nuclear Spin and Magnetic Moment
    4. 1.2.2 Radiofrequency Pulse and Signal Detection
    5. 1.2.3 Relaxation
    6. 1.3 MRI Theory
    7. 1.3.1 Gradients - One Dimensional Imaging
    8. 1.3.2 Three Dimensional Imaging - Spatial Encoding
    9. 1.3.3 Slice Selection
    10. 1.3.4 Phase Encoding
    11. 1.3.5 Frequency Encoding
    12. 1.3.6 Raw Data Matrix, K - Space and Q - Space
    13. 1.3.7 Image Reconstruction
    14. 1.4 MRI Contrast
    15. 1.4.1 Endogenous Sources
    16. 1.4.2 Exogenous Sources - Contrast Agents
    17. 1.5 Applications
    18. References
  • Chapter 2 Fundamental Mathematical Formulation for the Theory, Dynamics and Applications of Magnetic Resonance Imaging

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    1. 2.1 Introduction
    2. 2.2 The Bloch NMR Equations
    3. 2.3 The General Bloch NMR Flow Equation
    4. 2.4 The Time - Independent Bloch NMR Flow Equation
    5. 2.5 The Time - Dependent Bloch NMR Flow Equation
    6. 2.6 Diffusion MRI Equation
    7. 2.7 Wave MRI Equation
    8. 2.8 The Bessel Equation
    9. 2.9 The NMR Schrodinger Wave Equation
    10. 2.10 Time - Dependent NMR Schrodinger Equaion
    11. 2.11 NMR Legendre Equation and Boubaker Polynomial
    12. 2.12 Sturm - Liouville Problem
    13. 2.13 The Diffusion - Advection Equation
    14. 2.14 The Euler NMR Equation
    15. 2.15 Analytical Solutions to the Generalized Bloch NMR Flow Equation
    16. 2.16 Solutions to the NMR Travellling Wave Equation
    17. 2.17 MRI Bessel Equation
    18. 2.18 Equation of Motion for Pulsed NMR
    19. 2.19 Application to Molecular Imaging
    20. 2.20 The Hermite Polynomials
    21. 2.21 Application to Multiple Sclerosis
    22. 2.22 Bloch - Torrey Equation for NMR Studies of Molecular Diffusion
    23. 2.23 Adiabatic Model of Bloch NMR Flow Equation
    24. 2.24 Application of Time Dependent Bloch NMR Equation and Pennes Bioheat Equation to Theranostics
    25. 2.25 Summary
    26. 2.26 Conclusion
    27. References
  • Back Matter

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