Predicting filament drift in twisted anisotropy

Excitable media with twisted anisotropy have recently been attracting significant interest because of their applicability to wave propagation in heart tissue. Here we consider the dynamics of an intramural scroll wave whose filament lies initially within an arbitrary layer of mutually parallel cardiac fibers, and drifts parallel to itself from layer to layer. Earlier simulations have demonstrated that such a filament stabilizes in a layer whose fiber direction is the same as its own. In the present paper we analytically derive the trajectory of the filament, and obtain good agreement with earlier numerical data. For sufficiently sparse scrolls, our analysis predicts an equilibrium alignment perpendicular rather than parallel to the fibers.