A mathematical model of the Bloch NMR equations for quantitative analysis of blood flow in blood vessels with changing cross-section—I

Recently, magnetic resonance imaging has moved away from merely depicting the morphology of objects or disease states and is now concerned with creating spatially localized representations of dynamics and function. Dynamical measurements of blood flow, is one example of this trend. Improving these techniques requires an understanding of the basic physics that govern imaging technology and the functions of biological systems. This presentation is focused on mathematical modeling of the Bloch NMR flow equations into Bessel functions of the first and the second kind. The model is tailored towards understanding the basic physics of extracting the relevant flow parameters by which velocity quantification can be made in blood vessels with changing cross-section to solve real problems in medicine and biology.