Alternans and Spiral Breakup in an Excitable Reaction-Diffusion System: A Simulation Study

Abstract

The determination of the mechanisms of spiral breakup in excitable media is still an open problem for researchers. In the context of cardiac electrophysiological activities, spiral breakup exhibits complex spatiotemporal pattern known as ventricular fibrillation. The latter is the major cause of sudden cardiac deaths all over the world. In this paper, we numerically study the instability of periodic planar traveling wave solution in two dimensions. The emergence of stable spiral pattern is observed in the considered model. This pattern occurs when the heart is malfunctioning (i.e., ventricular tachycardia). We show that the spiral wave breakup is a consequence of the transverse instability of the planar traveling wave solutions. The alternans, that is, the oscillation of pulse widths, is observed in our simulation results. Moreover, we calculate the widths of spiral pulses numerically and observe that the stable spiral pattern bifurcates to an oscillatory wave pattern in a one-parameter family of solutions. The spiral breakup occurs far below the bifurcation when the maximum and the minimum excited states become more distinct, and hence the alternans becomes more pronounced.

Spiral waves: linear and nonlinear theory

“…More dramatic instabilities cause spiral breakup, where the compression and expansion of the waves emitted by the spiral wave grow in time and space, leading to filamentation and complex dynamics; see for instance [59] for experiments and [2,6,7,39] for analysis. The compression and expansion can be modulated in the lateral direction of wave trains, leading to different fragmentation phenomenologies; see [32,55]. Spatiotemporal growth of perturbations has been described in terms of properties of dispersion relations at wave trains [74] and the resulting subcritical instabilities are often very sensitive to noise and domain size.…”

A Two-Stage Model Identification Method for Simulation of Electrical Wave Propagation in Heart Tissue

“…Several simplified models of cardiac cells were developed in the literature, including Fenton-Karma model [4], Minimal model [5], and FitzHugh-Nagumo (FHN) model [6]. FHN is one of the best-known simplified models, which is popularly used and modified in many studies to better describe the electrical properties of heart tissue [7,8]. The well-know Aliev-Panfilov [9] model is modified from the FHN model to restore the refractoriness and the restitution curve of cardiac tissue.…”