Simulation of cardiac perfusion by contrast in the myocardium using a formulation of flow in porous media

This paper presents a computational model that characterizes the spatio-temporal dynamics of blood perfusion in cardiac myocardium. Specifically, we are interested in reproducing qualitative images obtained by contrast-enhanced exams, which are widely used in clinical medicine to evaluate the blood perfusion in the heart. The application of contrast allows the detection of injuries, ischemic regions, fibrosis or tumors. Here we focus on the pathological case associated to subendocardial infarct. In our modeling, we will consider the tissue of cardiac myocardium as a porous media, i.e. a solid region with empty spaces. To this end, the modeling was based on differential equations and Darcy’s Law, which correlates tissue permeability, pressure difference and the blood flow in the cardiac tissue.