Alternating Direction Implicit Method for the Electro-Cardiology Models

Abstract

Electrophysiology is an area of science that led to innovative experimentations between clinicians and scientists. Studying and understanding cardiac dynamics plays a key role in designing therapies, preoperative planning, and studying arrhythmias, fibrillations and other cardiac anomalies. Exploring the heart dynamics in three dimensions in vivo is difficult, and hence an alternative is needed. Mathematical modelling offers a valuable, yet computationally expensive tool for such exploration. The mathematical models of the electrical activity of the heart consist of a system of nonlinear partial differential equations coupled with a system of stiff ordinary differential equations. Numerical simulation of this coupled system requires accurate space and time discretization. In this work, an Alternating Direction Implicit Method (ADI) is presented as a new numerical scheme for solving the electrical model of the heart. Two-dimensional numerical results are presented illustrating the advantages and robustness of this proposed method. Comparison with the Crank-Nicolson Adams Bashforth (CNAB) method is demonstrated and the advantages of ADI are explained in terms of run time and memory consumption.