Effect of Relaxation Time from Improved Bloch NMR Fluid Flow Equation on Area under NMR Spectrum of Blood Spinning Protons using Fourier Transform Method

This study aims to develop a new NMR spectrum governing equation. It also investigates theoretically the effect of transverse relaxation times of arterial, venous, and capillary blood samples on the area under the spectrum of blood proton spins. Laplace transform method was used to build the NMR signal equation, which is the solution of the improved Bloch NMR time-dependent fluid flow equation. Furthermore, Fourier transform signal processing technique was used to convert the NMR signal to the NMR spectrum. MATLAB and Origin Pro software tools were utilized as primary tools for d*ata generation and simulation purposes. The results for arterial, venous, and capillary blood samples illustrated that the area under the spectrum (As) varied as a function of changes in the transverse relaxation time, T2. Firstly, for arterial blood, when T2 = 228 ms, 245 ms, 262 ms, and 279 ms, the computed values of As = 0.02155 Aradm-1s-1, 0.02150 Aradm-1s-1, 0.02141 Aradm-1s-1, and 0.02097 Aradm-1s-1, respectively. Additionally, for venous blood, when T2 = 158 ms, 173 ms, 188 ms, and 203 ms, the computed values of As = 0.02416 Aradm-1s-1, 0.02334 Aradm-1s-1, 0.02270 Aradm-1s-1, and 0.02259 Aradm-1s-1 respectively. In conclusion, for capillary blood, when T2 = 10 ms, 73 ms, 136 ms, and 199 ms, the computed values of As = 0.00127 Aradm-1s-1, 0.01365 Aradm-1s-1, 0.02697 Aradm-1s-1, and 0.02530 Aradm-1s-1 respectively. These results mean that as blood circulates through the human blood vessels, the number of spinning protons changes due to varying transverse relaxation times of arterial, venous, and capillary blood. The results of the simulation may be used by spectroscopists to verify experimental results in order to determine the number of nuclei, resonant frequency, and chemical shift of nuclei in a sample