Mathematical Concept of the Bloch FlowEquations for General Magnetic Resonance Imaging: A Review
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Date
2011-03-18
Journal Title
Journal ISSN
Volume Title
Publisher
Wiley Online Library
Abstract
The recent analytical solutions to the Bloch NMR equations for a general RF
excitation have opened many possibilities for further investigations to NMR theory and
experiments even at the molecular level. Fortunately, many of the most important but hidden
applications of blood flow and general physiological fluid flow parameters can be
revealed without too much difficulty if appropriate mathematical techniques are used to
explore the new NMR equations derived from the Bloch equations. Generally, we should be
very much concerned with analytical results that the Bloch NMR flow equations can provide
for different physical, biomedical, geophysical, medical, and environmental situations especially
at the molecular level for the purpose of interdisciplinary approach to solve difficult
problems. It can be motivating, exciting, and rewarding if attention are focused on the possible
application of these analytical techniques and methods suitable for describing each of
the various normal and pathological biological conditions. Most solutions presented in this
study are described both in isotropic and anisotropic geometries with minimum mathematical
assumptions. We discussed a general expression for the diffusion coefficients in the
common geometries. These analytical results can prove to be very invaluable in the analysis
of restricted flows. It is so much special because it could tell us when restricted flows occur
and also reveal the causes of such restriction. Such knowledge can help in finding the
causes of many diseases (whose causes are yet unknown) and suggest the best treatment
Description
Staff Publication
Keywords
Bloch NMR flow equations;, diffusion coefficient;, NMR diffusion equation;, magnetic resonance imaging (MRI)