Reaction-diffusion waves in the vicinity of obstacles: The eikonal approach

The behaviour of excitable reaction-diffusion waves in the presence of non-excitable obstacles and boundaries is a complex phenomenon and portends pathological consequences in physiological systems such as cardiac tissue. The objective is to investigate, with the aid of the eikonal equation, the behaviour of three-dimensional waves in the proximity of spherical obstacles, and the extent to which this behaviour can be inferred by a study of the surface waves. The main conclusion is that an expanding spherical wave located symmetrically between identical spherical obstacles, is not stabilized as a stationary sphere by the Neumann conditions.