Steady-State Analysis for Oxygen Diffusion in Infarcted Myocardial Tissue

Myocardial infarction (MI), commonly known as a heart attack, can cause restriction in blood supply and oxygen shortage. The current stem cell therapy aims to rebuild lost myocardial tissue including its vasculature after MI. However, it should be determined how many vessels myocardial fibers need and how these vessels should be distributed to deliver enough oxygen to maintain their normal function. Mathematical modeling is a good approach to systematically determine the number and distributions of vessels that are needed. In this study, we employ Boundary Element Method combined with Fast Multipole Algorithm to predict the level of hypoxia after MI. Morphology of cardiac tissue based on available morphometric images is used for simulation. Steady state solutions for oxygen level distribution in both normal and infarcted heart are achieved. The numerical studies show that the developed FMBEM can effectively handle the diffusion process in the real world.