Drift of scroll waves in thin layers caused by thickness features: asymptotic theory and numerical simulations

TL;DR

This paper develops an asymptotic theory and numerical simulations to analyze how sharp variations in layer thickness influence the drift of scroll waves in thin excitable media, extending understanding beyond filament tension effects.

Contribution

It introduces a novel two-step asymptotic approach to quantify the impact of layer thickness features on scroll wave dynamics, distinct from previous curvature-based models.

Findings

Asymptotic predictions match numerical simulations.

Scroll wave drift is significantly affected by sharp thickness variations.

The theory applies to various geometrical features like steps, ridges, and disks.

Abstract

A scroll wave in a very thin layer of excitable medium is similar to a spiral wave, but its behaviour is affected by the layer geometry. We identify the effect of sharp variations of the layer thickness, which is separate from filament tension and curvature-induced drifts described earlier. We outline a two-step asymptotic theory describing this effect, including asymptotics in the layer thickness and calculation of the drift of so perturbed spiral waves using response functions. As specific examples, we consider drift of scrolls along thickness steps, ridges, ditches, and disk-shaped thickness variations. Asymptotic predictions agree with numerical simulations.