Unstable Spiral Waves and Local Euclidean Symmetry in a Model of Cardiac Tissue

TL;DR

This study analyzes unstable spiral waves in a cardiac tissue model, examining their properties, stability, and drift, and how boundary effects and discretization influence their dynamics, shedding light on spiral chaos mechanisms.

Contribution

It introduces methods to compute unstable spiral waves in arbitrary domains and explores how boundary and discretization effects impact their behavior and stability.

Findings

Unstable spiral waves can be computed numerically on various domain shapes.

Boundary effects influence spiral wave stability and drift.

Finite size and discretization break local Euclidean symmetry, affecting spiral dynamics.

Abstract

This paper investigates the properties of unstable single-spiral wave solutions arising in the Karma model of two-dimensional cardiac tissue. In particular, we discuss how such solutions can be computed numerically on domains of arbitrary shape and study how their stability, rotational frequency, and spatial drift depend on the size of the domain as well as the position of the spiral core with respect to the boundaries. We also discuss how the breaking of local Euclidean symmetry due to finite size effects as well as the spatial discretization of the model is reflected in the structure and dynamics of spiral waves. This analysis allows identification of a self-sustaining process responsible for maintaining the state of spiral chaos featuring multiple interacting spirals.