Expansion of scroll wave filaments induced by chiral mismatch.

In three-dimensional excitable systems, scroll waves are rotating vortex states that consist of smoothly stacked spirals. This stacking occurs along one-dimensional phase singularities called filaments. If the system has a positive filament tension, these curves either straighten or collapse over time. The collapse can be prevented if the filament pins to a nonreactive object or a group of objects, but even in this case, the filament length does not typically grow. Using numerical simulations, we provide examples of filament growth induced by pinning, such as a scroll ring pinning to an inert trefoil knot, and explain the mechanism of this growth. Surprisingly, the corresponding filament loop thus not only persists in time but also steadily extends far from the pinning object.

Stabilization of collapsing scroll waves in systems with random heterogeneities.

In three-dimensional reaction-diffusion systems, excitation waves may form and rotate around a one-dimensional phase singularity called the filament. If the filament forms a closed curve, it will shrink over time and eventually collapse. However, filaments may pin to non-reactive objects present in the medium, reducing their rate of collapse or even allowing them to persist indefinitely. We use numerical simulations to study how different arrangements of non-reactive spheres affect the dynamics of circular filaments. As the filament contracts, it gets closer to and eventually touches and pins to objects in its path. This causes two possible behaviors. The filament can detach from the spheres in its path, slowing down the rate of contraction, or it can remain pinned to a collection of spheres. In general, more or larger spheres increase the chance that the filament remains pinned, but there are exceptions. It is possible for a small number of small spheres to support the filament and possible for the filament to pass through a large number of large spheres. Our work yields insights into the pinning of scroll waves in excitable tissue such as cardiac muscle, where scar tissue acts in a way similar to the non-reactive domains.