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

A scroll wave in a very thin layer of excitable medium is similar to a spiral wave, but its behavior 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.