Boundary-layer analysis of waves propagating in an excitable medium: Medium conditions for wave-front-obstacle separation

In an excitable medium, wave breaks are essential for spiral wave formation. Although wave breaks can result from collisions between a wave and an obstacle, it is only when the resultant wave fragments separate from the obstacle (wave-front-obstacle separation) that a spiral wave will begin to develop. We explored collisions between a piecewise linear obstacle and an incident wave front while varying the excitability of the media and the angle between the linear obstacle segments. Wave-front-obstacle separation was observed to occur within the small boundary layer of the order of the wave-front thickness. Conditions for wave-front-obstacle separation were determined by the relationship between reaction-diffusion flows within this boundary-layer region. We developed a theoretical characterization of the boundary-layer region that permits estimation of the critical values of medium parameters and obstacle geometry that define the transition from wave-front-obstacle attachment to wave-front-obstacle separation. Theoretical predictions revealed good agreement with results of the numerical simulations.