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.