Initiation of two-armed spiral waves pinned to obstacles in simulated excitable media

Propagating excitations in forms of spiral waves occur in various excitable media governed by reaction-diffusion mechanisms. They have an important impact on human health since they correspond to cardiac arrhythmia and potentially cause life-threatening fibrillation. The spiral waves and the corresponding pathological conditions stay longer when the spiral waves are pinned to unexcitable obstacles, e.g., blood vessels or scars in the heart. We present a method to initiate two-armed spiral waves pinned to a circular obstacle. The initiation is successful when the obstacle diameter is larger than a critical value that increases with the system excitability. This due to the fact the areas close to the partitions sufficiently recover for the next excitation. For obstacles smaller than the critical diameter, the spiral waves fail to be pinned and subsequently two separate free spiral waves occupy the system. While the free spiral waves depend solely on the excitability, the two-armed pinned spiral waves are influenced by both the obstacle size and the excitability.