Effect of Transverse Relaxation Rate on Time-Dependent Magnetic Resonance Imaging

Abstract

Magnetic Resonance Imaging (MRI), developed from nuclear magnetic resonance involves a non-invasive medical approach towards studying the anatomy, physiology and pathology of human tissues. In this study, attempt is made at expressing mathematically the processes involved in MRI for diagnosis and possible treatment of diseases within the human body. A time-dependent second -order non-homogeneous linear differential equation from the Bloch (NMR) equation is evolved. The parameters in the equations are M_0, radio frequency rfB_1 f(x,t) field, gyromagnetic ratio of blood spin γ as well as T_1 and T_2 relaxation times. the solution obtained will be examined when the system is under an influence of a driving force, F_0 cos wt and γB_1 (t)=cos⁡wt is the radio frequency field. However, for the purpose of this study, only relaxation times are varied and analyzed for measurement of the signals in relation to its effect on human anatomy.