INVESTIGATION OF ALGORITHMS FOR SOLVING THE ELECTRO-CARDIAC ACTIVITY

Abstract

Mathematical models are used to simulate the behavior of the electrical activity of a single cell or multiple cells of the heart. Single cell models contain a system of ODEs (ordinary differential equations) while multi-cell models consist of a coupled system of ODEs and PDEs (partial differential equations). We present different algorithms to explore the efficiency of different solvers for simulating cardiac models. We use operator splitting methods to split the coupled system of equations into the ODE and PDE parts. Then, we examine different solvers for simulating each part separately. Experiments shows that solving the ODE part contributes significantly to the total work required for the simulation of the multi-cell models. Therefore, utilizing efficient solution methods for this part of the problem is a requirement. The goal of this research is investigating efficient algorithms for solving these mathematical models.