Impact of Relaxation Time from Improved Bloch NMR Fluid Flow Equation on NMR Signal of Blood Proton Spins using Laplace Transform Method

Nuclear Magnetic Resonance (NMR) is a non-destructive spectroscopic technique in which the magnetization of a sample, such as human blood, changes by the application of both an external and radio frequency (RF) field to the sample. NMR is a non-invasive tool used in medicine and surgery for getting valuable information on blood flowing along the human blood vessels. In the existing work done on NMR signal, which is the transient state solution of the Bloch NMR fluid flow equation, it is noted that some NMR blood flow parameters, such as static magnetic field and Larmor precessional frequency of blood-spinning protons, are missing in the existing NMR signal equation. In order to solve this problem to generate accurate NMR signal results. This study developed a new NMR signal equation that contains the missing NMR parameter. Furthermore, the signal equation was used to investigate the effect of transverse relaxation times of arterial, venous, and capillary blood, respectively, on the NMR signal of blood proton spins. Laplace transform method was utilized to obtain the NMR signal, which is the closed-form solution of the improved Bloch NMR fluid flow time-dependent equation. MATLAB and Origin Pro software tools were utilized for the generation and simulation of data. Results of the simulation and analysis showed that for varied relaxation times of arterial, venous, and capillary blood, the NMR signal generated from the blood proton spins decreased with increasing time. This means that the blood proton spins gradually lose their alignment of magnetic moments, which is due to the interactions between neighboring blood proton spins. The results obtained from the simulations may be used as a means of validating the experimental results obtained from an NMR/Magnetic resonance imaging machine by providing a theoretical basis for comparison with the experimental data.