A mathematical analysis of Stenosis Geometry, NMR magnetizations and signals based on the Bloch NMR flow equations, Bessel and Boubaker polynomial expansions

Abstract

Magnetic resonance imaging (MRI) has great potential in modern medical imaging, as it is noninvasive and provides comprehensive information about stenostic and nonstenostic plaque and myocardial viability. The aim of this paper is to model the variation of NMR magnetization and signals over a stenosis under cylindrical geometry, based on the Bloch NMR flow equations. A cylindrical coordinate is constructed such that its maximum radius indicates a totally blocked blood vessel. A differential equation in terms of NMR transverse magnetization was solved for blood molecules which tunnel through the plaque and could be located at the centre of the plaque or any other point within the plaque. Such analysis can be very useful for assessing the relative importance of several flow parameters such as pressure loss due to friction and due to dynamic losses. Analytical expressions are proposed as guides to future investigations. Furthermore, new parameters were derived, which may allow one to accurately define the fluid resistance to shear or flow and to measure the adhesive/cohesive or frictional fluid property. These new parameters are directly or inversely dependent on the length or diameter of the stenosis and the dynamic viscosity of blood flow