Topological charge-density method of identifying phase singularities in cardiac fibrillation

Spiral waves represent the key motifs of typical self-sustained dynamical patterns in excitable systems such as cardiac tissue. The motion of phase singularities (PSs) that lies at the center of spiral waves captures many qualitative and, in some cases, quantitative features of their complex dynamics. Recent clinical studies suggested that ablating the tissue at PS locations may cure atrial fibrillation. Here, we propose a different method to determine the location of PSs. Starting from the definition of the topological charge of spiral waves, we obtain the expression of the topological charge density in a discrete case. With this expression, we can calculate the topological charge at each grid in the space directly, so as to accurately identify the position of PSs.

Automated summary

Spiral waves in excitable systems are key motifs of self-sustained dynamical patterns, with phase singularities capturing the complexity of their dynamics. Clinical studies have shown that ablating tissue at phase singularity locations may cure atrial fibrillation. The authors propose a method to determine phase singularity locations by calculating the topological charge at each grid point in space.