The dynamics of three-dimensional scroll waves in excitable media

Abstract

We investigate the motion of the central filament of a scroll wave in excitable medium. We assume that two-dimensional spiral solutions are known and use these solutions to produce slowly varying scroll waves in three-dimensional space. Using standard ideas from perturbation theory (multiscale techniques) we find equations governing the motion of the central filament of the scroll and the twist of the scroll wave. These equations are specialized to the case of a circular filament with uniformly distributed twist, to determine the collapse or expansion and vertical drift of the spiral filament and to a helical filament with drift. The predictions of these equations are in good qualitative agreement with the numerical experiments.