Reflections in excitable media linked to existence and stability of one-dimensional spiral waves

TL;DR

This paper investigates the existence and stability of one-dimensional spiral waves in excitable media, linking their properties to the likelihood of wave reflections that can cause cardiac arrhythmias, using numerical and analytical methods.

Contribution

It introduces a novel analysis of 1D spiral waves as time-periodic antisymmetric source defects and explores how system parameters influence reflection phenomena.

Findings

1D spiral waves are unstable periodic orbits linked to wave reflections.

Key parameters and physiological processes that promote or deter reflections are identified.

The study extends previous hypotheses about the instability and formation of 1D spirals.

Abstract

When propagated action potentials in cardiac tissue interact with local heterogeneities, reflected waves can sometimes be induced. These reflected waves have been associated with the onset of cardiac arrhythmias, and while their generation is not well understood, their existence is linked to that of one-dimensional (1D) spiral waves. Thus, understanding the existence and stability of 1D spirals plays a crucial role in determining the likelihood of the unwanted reflected pulses. Mathematically, we probe these issues by viewing the 1D spiral as a time-periodic antisymmetric source defect. Through a combination of direct numerical simulation and continuation methods, we investigate existence and stability of a 1D spiral wave in a qualitative ionic model to determine how the systems propensity for reflections are influenced by system parameters. Our results support and extend a previous hypothesis that the 1D spiral is an unstable periodic orbit that emerges through a global rearrangement of heteroclinic orbits and we identify key parameters and physiological processes that promote and deter reflection behavior.