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 format wave is a novel mechanism for generating activity in spiral shape. In addition, it is robust for a wide variety of refractory areas and geometry shapes. This situation models 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 semi implicit Eyres algorithm and we present some numerical results to demonstrate the effectiveness and usefulness of the present technique.