A Mathematical Model of 99mTc-ECD Diffusion in Brain for Epileptic Patients

Abstract

This research develops diffusion equation to describe behavior of the $^{99\mathrm{m}}\text{Tc-ECD}$ diffusion in epileptic patient's brain SPECT image over time. The equation was approximated the numerical solution at steady state by central difference approximation. Then they were compared with the real data around interested point that may be epileptogenic by relative error. In the result, the rate constant of $^{99\mathrm{m}}\text{Tc-ECD}$ diffusion in brain area $D_{1}= 1. 10657$ unit²/min and the rate constant of $^{99\mathrm{m}}\text{Tc-ECD}$ diffusion in ventricle area $D_{2}=1$ unit²/min that has relative error around 26.81%. The numerical solution show the $^{99\mathrm{m}}\text{Tc-ECD}$ diffusion in brain SPECT image is homogeneous diffusion.