Mathematical approach to unpinning of spiral waves anchored to an obstacle with high-frequency pacing

Spiral waves are observed in wide variety of reaction-diffusion systems. Those observed in cardiac tissues are important since they are related to serious disease that threatens human lives, such as atrial or ventricular fibrillation. We consider the unpinning of spiral waves anchored to a circular obstacle on excitable media using high-frequency pacing. Here, we consider two types of the obstacle; i.e., that without any diffusive interaction with the environment, and that with diffusive interaction. We found that the threshold frequency for success in unpinning is lower for the obstacle with diffusive interaction than for the one without it. We discuss the threshold frequency based on the angular velocity of a chemical wave anchoring the obstacle.