Large-excitability asymptotics for scroll waves in three-dimensional excitable media

Three-dimensional scroll waves are considered in a reaction-diffusion model of excitable media in the large excitability limit. Coordinates based on the scroll filament are defined and shown to provide a natural extension of the coordinates used for two-dimensional spiral waves. The leading-order free-boundary equations for interface motion in three dimensions are explicitly derived in these coordinates. Three specific examples are considered: straight twisted scroll waves, axisymmetric scroll waves, and helical scroll waves. The equations for the fields at leading and first order in the core region are given.