Spiral-generation mechanism in the two-dimensional FitzHugh-Nagumo system

Abstract

Spiral waves are a mathematical concept that organizes spatio-temporal dynamics in dissipative, spatially extended biological, physical and chemical systems. They support a variety of important phenomena, such as re-entrant cardiac arrhythmias and spatial patterns in chemical reactions. In this paper we consider a two-dimensional (2D) disturbance wave that can make the pulse wave travel around the disturbance and generate a self-sustaining spiral wave. The use of a region temporarily refractory as a disturbance in formatwave is a novelmechanism for generating activity in spiral shape. In addition, it is robust for a wide variety of refractory areas and geometry shapes. This situationmodels the appearance of abnormal electrical activity in the heart, where the disturbance is a cardiac tissue in damage. We present a Finite Element Method (FEM) scheme for the two-dimensional FitzHugh-Nagumo (FHN) system to simulate the spiral-generation mechanism in cardiac tissue. This scheme is based on the semiimplicit Eyres algorithm and we present some numerical results to demonstrate the effectiveness and usefulness of the present technique.