Scroll wave drift along steps, troughs and corners

TL;DR

This study experimentally and numerically investigates how scroll waves in excitable media drift along steps, troughs, and corners, revealing predictable behaviors influenced by geometry and vortex chirality, with implications for cardiac arrhythmias.

Contribution

It provides experimental validation of theoretical predictions on scroll wave drift along geometric features and explores complex interactions at corners and troughs.

Findings

Scroll waves are attracted to steps and drift along them with speeds proportional to the logarithm of height ratio.

Filaments in shallow regions terminate near step edges, while those in deep regions collide with step walls.

Numerical simulations replicate observed behaviors and reveal interactions like vortex encounters and symmetry breaking.

Abstract

Three-dimensional excitable systems can create nonlinear scroll waves that rotate around one-dimensional phase singularities. Recent theoretical work predicts that these filaments drift along step-like height variations. Here we test this prediction using experiments with thin layers of the Belousov-Zhabotinsky reaction. We observe that over short distances scroll waves are attracted towards the step and then rapidly commence a steady drift along the step line. The translating filaments always reside in the shallow subsystem and terminate on the step plateau near the edge. Accordingly filaments in the deep subsystem initially collide with and shorten at the step wall. The drift speeds obey the predicted proportional dependence on the logarithm of the height ratio and the direction depends on the vortex chirality. We also observe drift along the perimeter of rectangular plateaus and find that the filaments perform sharp turns at the corners. In addition, we investigate rectangular troughs for which vortices of equal chirality can drift in different directions. The latter two effects are reproduced in numerical simulations with the Barkley model. The simulations show that narrow troughs instigate scroll wave encounters that induce repulsive interaction and symmetry breaking. Similar phenomena could exist in the geometrical complicated ventricles of the human heart where reentrant vortex waves cause tachycardia and fibrillation.