Predicting the duration of chaotic transients in excitable media

Abstract

The spatiotemporal dynamics of excitable media may exhibit chaotic transients. We investigate this transient chaos in the 2D Fenton–Karma model describing the propagation of electrical excitation waves in cardiac tissue and compute the average duration of chaotic transients in dependence on model parameter values. Furthermore, other characteristics like the dominant frequency, the size of the excitable gap, pseudo ECGs, the number of phase singularities and parameters characterizing the action potential duration restitution curve are determined and it is shown that these quantities can be used to predict the average transient time using polynomial regression.

Focusing on transient chaos

“…In this section, we provide an overview of contributions to the focus issue, which describe the emergence of transient chaos in various applications, including self-organization of active particles [8], dynamics of power grids [9], applications in medicine [10] and magnetohydrodynamics [11], as well as in machine learning [12].…”

“…Transient complex spatiotemporal dynamics can also be found in cardiac tissue, where it is associated with cardiac arrhythmias such as ventricular fibrillation. This dysfunction of the heart muscle is studied by Aron et al [10] using the 2D Fenton-Karma model, which is a minimal model for the electrophysiology of ventricular myocytes. The paper presents numerical evidence that the average length of the exponentially distributed chaotic transients in the Fenton-Karma model is functionally linked to the features commonly used to characterize excitable media (e.g., the dominant frequency, the size of the excitable gap, or the shape of the action-potential duration restitution curve).…”