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

This research work investigated the effect of the transverse relaxation times of arterial, venous, and capillary blood samples on the area under the NMR spectrum of signal generated from blood proton spins. The study was carried out theoretically by simulating and generating data from the newly developed governing equation for the NMR spectrum, which was derived using Fourier transform signal processing technique. The results for arterial blood samples showed that when the transverse relaxation time of arterial blood sample is 228 <i>ms</i>, 245 <i>ms,</i> 262 <i>ms</i>, and 279 <i>ms</i>, respectively, the computed values of area under the spectrum were 0.02155 <i>Aradm</i>^<em>-1</em><i>s</i>^<em>-1</em>, 0.02150<i> Aradm</i>^<em>-1</em><i>s</i>^<em>-1</em>, 0.02141<i> Aradm</i>^<em>-1</em><i>s</i>^<em>-1</em>, and 0.02097<i> Aradm</i>^<em>-1</em><i>s</i>^<em>-1</em> respectively. Additionally, the results for the venous blood samples showed that when the transverse relaxation time of venous blood sample is 158 <i>ms</i>, 173 <i>ms</i>, 188 <i>ms</i>, and 203 <i>ms</i>, the computed values of the area under the spectrum were 0.02416<i> Aradm</i>^<em>-1</em><i>s</i>^<em>-1</em>, 0.02334<i> Aradm</i>^<em>-1</em><i>s</i>^<em>-1</em>, 0.02270<i> Aradm</i>^<em>-1</em><i>s</i>^<em>-1</em>, and 0.02259<i> Aradm</i>^<em>-1</em><i>s</i>^<em>-1</em>, respectively. To conclude, the results for capillary blood showed that when the transverse relaxation time of capillary blood is 10 <i>ms</i>, 73 <i>ms</i>, 136 <i>ms</i>, and 199 <i>ms</i>, respectively, the computed values of area under the spectrum were 0.00127<i>Aradm</i>^<em>-1</em><i>s</i>^<em>-1</em>, 0.01365<i>Aradm</i>^<em>-1</em><i>s</i>^<em>-1</em>, 0.02697<i>Aradm</i>^<em>-1</em><i>s</i>^<em>-1</em>, and 0.02530<i> Aradm</i>^<em>-1</em><i>s</i>^<em>-1</em>, respectively. These results mean that for varied transverse relaxation times of arterial, venous, and capillary blood samples, the number of blood protons varies over time as blood circulates through the human vessels.