Mathematics, Game Theory and Algebra Compedium, Volume 3

Abstract

Magnetic resonance sequences have been developed to label the position of a spin, albeit indirectly, through the Larmore frequency. This provides the basis for measuring diffusion. However, the interpretation of the data is complicated by the effects of restricted geometries and the mathematical modeling required to account for this becomes nontrivial especially in cylindrical and spherical geometries. Generally one have to resort to numerical methods and/or approximations to model diffusion within restricted geometries depending on the experimental conditions. Based on the new NMR diffusion equation, parts I and II of this study intend to provide a very straightforward theoretical background for measuring diffusion of water protons and specific chemicals encountered in most common advanced MRI methods including diffusion MRI, perfusion MRI, functional MRI.