An Analytic Investigation of the Bloch Nuclear Magnetic Resonance Flow Equations for the Analysis of General Fluid Flow

Abstract

Nuclear Magnetic Resonance (NMR) techniques now referred to as Magnetic Resonance Imaging (MRI) are used to study anatomy, physiology and pathology of human living tissues. In this study, the mathematical processes involved are examined. A second order time independent non-homogenous linear differential equation from the Bloch NMR equations is evolved. The parameters in the equations are equilibrium magnetization M_0, radio frequency rfB_1 (x,t) field, gyro-magnetic ratio of blood spin γ, velocity v as well as T_1 and T_2 relaxation times. A general method of solution of each equation under the influence of radio frequency magnetic field [rfB_1 (x,t)≠0] and in the absence of radio frequency magnetic field [rfB_1 (x,t) =0] is evolved. For the purpose of this study, the influence of the relaxation timeT_1 and T_2 are examined.