Annihilation dynamics during spiral defect chaos revealed by particle models

Pair-annihilation events are ubiquitous in a variety of spatially extended systems and are often studied using computationally expensive simulations. Here we develop an approach in which we simulate the pair-annihilation of spiral wave tips in cardiac models using a computationally efficient particle model. Spiral wave tips are represented as particles with dynamics governed by diffusive behavior and short-ranged attraction. The parameters for diffusion and attraction are obtained by comparing particle motion to the trajectories of spiral wave tips in cardiac models during spiral defect chaos. The particle model reproduces the annihilation rates of the cardiac models and can determine the statistics of spiral wave dynamics, including its mean termination time. We show that increasing the attraction coefficient sharply decreases the mean termination time, making it a possible target for pharmaceutical intervention. Many physical systems exhibit annihilation events during which pairs of objects collide and are removed from the system. These events occur in a number of soft-matter and active-matter systems that exhibit spatiotemporal patterning. For example, topological defects in nematic liquid crystals can develop motile topological defects that annihilate when they meet 1,2. Pair-wise annihilation of defects or singularities also plays a role in a number of biological systems. In bacterial biofilms, for instance, imperfect cell alignment results in point-like defects that carry half-integer topological charge and can annihilate in pairs. These topological defects explain the formation of layers and have been proposed as a model for the buckling of biofilms in colonies of nematically ordered cells3,4.