Mathematics, Game Theory and Algebra Compedium, Volume 3

Abstract

During the past decade, major breakthroughs in magnetic resonance imaging (MRI) quality were made by means of great improvement in scanner hardware and pulse sequences. Some advanced MRI techniques have truly revolutionized the detection of disease states and MRI can now-within a few minutes-acquire important quantitative information non-invasively from an individual in any plane or volume at comparatively high resolution. However, the very basic physics of this promising technological breakthrough is not well understood. Parameters that are measured from time to time in advanced MRI seem to be logically and functionally related but the theoretical facility to optimally explore them is still missing. In a single experimental investigation, for example, few of huge amount of information available are effectively used. 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.