A Study of Longitudinal and Transverse Relaxation Rates in Magnetic Resonance Imaging

Abstract

Two-second order non-homogenous linear differential equations from the Bloch Nuclear Magnetic Resonance (NMR) equations are evolved one as time-dependent and the other as time-independent. 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. However, for the purpose of this study, only T_1 and T_2 relaxation times are varied and analyzed for the measurement of the signals in relation to its effect on human anatomy.