BPES-related mathematical development for the phase shift due to RF magnetic field in heart inferior coronary artery NMR imaging

Abstract

It is known that most cardiovascular emergencies are caused by coronary artery disease. Nevertheless, in the last decade’s related literature, data about mathematical models of heart and heart vessels along with NMR/MRI features is not accordingly abundant. In fact there are inherent difficulties in developing this type of mathematical models to completely describe the real or ideal geometries of heart arterial system. In this study, a mathematical formulation for the NMR diffusion partial differential equation derived from the Bloch NMR flow equations to describe in detail the activities in lower heart coronary artery is presented. Based on the Bloch NMR flow equations, we deduce analytical expressions to describe in detail the NMR transverse magnetizations and signals as a function of some NMR flow and geometrical parameters which are invaluable for the analysis of blood flow in heart vessels. The boundary conditions are inherently introduced based on the properties of the Boubaker polynomials expansion scheme BPES.