Simulation of Transmembrane Potential Propagation in Normal and Ischemic Tissue Using Aliev-Panfilov Model

Abstract

Mathematical modelling of heart's electrical activity is useful for understanding the details of heart's function, and developing methods for prediction, diagnosis and treatment of various heart diseases. In this work, we modelled the electrical activity of the heart in the three dimensional (3D) ventricular geometry based on transmembrane potential (TMP) distributions. The main intention in this study is to simulate TMP distributions using heart geometry obtained from Magnetic Resonance (MR) Images, and corresponding fiber structure obtained from Diffusion Weighted Images (DWI). Aliev-Panfilov model was used to describe electrical activity of the heart at tissue level, which focuses on the potential wavefront propagation. Using this model, it is also possible to include the anisotropy of the heart muscle in the calculations. Here, we first simulated 3 dimensional mapping of transmembrane distribution and propagation due to an ectopic stimulation on a normal ventricular geometry of the heart. Then, based on action potential morphology changes in a tissue with ischemia, we derived ischemic weight values and equation parameters for our model. By introducing ischemic regions on the ventricular geometry and applying ischemic weight values and parameters, we simulated TMP distribution and propagation in ventricular geometry with partial ischemia. Key words:Transmembrane potential propagation, Aliev-Panfilov model, normal and ischemic tissue, MRI, DWI. IntroductionCardiac arrhythmia refers to any abnormality or perturbation in the normal sequence of electrical impulses. Accordingly, cardiac arrhythmia is the main cause of morbidity and mortality in the developed world. Therefore, understanding mechanism of them is clinically important. Through investigating the underlying mechanism of the cardiac tissue, clinical methods has some disadvantages that make them insufficient for research purposes. These disadvantages are: 1) most of clinical method are invasive which has limited application in clinic 2) some lethal functional status of the heart such as ischemia, and myocardial infarction associated with ischemia, are difficult and sometimes impossible to investigate by clinical studies on patients. However, mathematical modelling with a simplified description of physical phenomena within mathematical description can be used as a good alternative for simulating, treatment, and prediction purposes. Cardiac mathematical models can be mainly divided to two categories; 1) cellular automata, that represents underlying structure by infinite, regular network or finite automaton working at each cell (node) of the network, 2) Reaction-diffusion methods, in which a system of non-linear partial differential equations are used to represent the excitation, distribution and propagation in an excitable media [1]. As in this study, we mainly focused on wave front properties rather than dynamics of ionic currents, therefore, we used reaction-diffusion models rather than the cellular models, which require small space and time int...