Wave-train induced unpinning of weakly anchored vortices in excitable media

A free vortex in excitable media can be displaced and removed by a wave-train. However, simple physical arguments suggest that vortices anchored to large inexcitable obstacles cannot be removed similarly. We show that unpinning of vortices attached to obstacles smaller than the core radius of the free vortex is possible through pacing. The wave-train frequency necessary for unpinning increases with the obstacle size and we present a geometric explanation of this dependence. Our model-independent results suggest that decreasing excitability of the medium can facilitate pacing-induced removal of vortices in cardiac tissue.

💡 Research Summary

The paper investigates how rotating vortices (spiral waves) in excitable media can be detached (“unpinned”) from inexcitable obstacles by an externally applied wave‑train, a process that is well‑known for free vortices but thought to be impossible for vortices anchored to large obstacles. Using generic two‑dimensional reaction‑diffusion models (FitzHugh‑Nagumo, Barkley, etc.), the authors systematically vary the obstacle radius (R) and the free‑vortex core radius (r_c), treating the ratio (R/r_c) as the key geometric parameter. Numerical simulations reveal that when the obstacle is smaller than the vortex core ((R<r_c)), a periodic wave‑train of appropriate frequency can gradually shift the vortex core away from the obstacle. Each incoming wavefront collides with the obstacle boundary at an angle (\theta); this collision produces a small displacement of the core, and repeated collisions produce a step‑wise drift that eventually frees the vortex.

A central quantitative finding is that the minimal pacing frequency (f_{\text{min}}) required for unpinning grows roughly linearly with obstacle size. By measuring the wave propagation speed (c) and the spacing between successive wavefronts (\lambda=c/f), the authors derive a geometric relation:

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