Modeling and simulation of cardiac electric activity in a human cardiac tissue with multiple ischemic zones

In this work, a human ventricular model (ten Tusscher and Panfilov model) coupled with the tissue level monodomain model is used to analyze the influence of multiple myocardial ischemia on the human cardiac tissue. The existence and uniqueness of the ischemic model comprising the monodomain model with a discontinuous ionic model for the human cardiac tissue is discussed. The coupled system of partial differential equation and ordinary differential equations are solved numerically using [Formula: see text] finite elements in space and Backward Euler finite difference scheme in time. The apriori finite element error estimate for the numerical scheme has been shown to be of [Formula: see text]. Essentially, we evaluate the impact of the increasing size of the ischemic region and the presence of the multiple ischemic regions having equal or different intensities on the neighboring healthy part of the cardiac tissue. We examine both the individual and the combined influence of two types of ischemia, Hyperkalemia (with the variation of the extracellular potassium ion concentration, [Formula: see text]) and Hypoxia (with the variation of intracellular Adenosine triphosphate (ATP) concentration via parameter [Formula: see text]) on the cardiac electrical activity of cardiac tissue. We observe that with the increase in the ischemic region size by a factor five times, there is an additional almost 10% drop in the action potential duration (APD) in the neighboring healthy regions. The combined effect of Hyperkalemia and Hypoxia brings an additional 12% drop in APD in the ischemic subregions and an additional 5% drop in APD in the neighboring healthy part of the cardic tissue in comparison to the only Hyperkalemic ischemia. When the Hyperkalemic and/or Hypoxic degeneracy of a ischemic zone is non-uniform then innercore degeneracy has greater influence on resting potential and APD of outercore of variable intensity ischemic zone than the other way. Also, increasing the number of ischemic subregions from 2 to 4 leads to a 4% drop in APD.