Detection of Phase Singularities in Triangular Meshes

Abstract

Phase singularities have become a key marker in animal and computer models of atrial and ventricular fibrillation. However, existing algorithms for the automatic detection of phase singularities are limited to regular, quadratic mesh grids. We present an algorithm to automatically and exactly detect phase singularities in triangular meshes. For each node an oriented path inscribing the node with one unit of spatial discretization is identified. At each time step the phase information is calculated for all nodes. The so-called topological charge is also computed for each node. A non-zero (+/- 2pi) charge is obtained for all nodes with a path enclosing a phase singularity. Thus all charged nodes belonging to the same phase singularity have to be clustered. With the use of the developed algorithm, phase singularities can be detected in triangular meshes with an accuracy of below 0.2 mm - independent of the type of membrane kinetics used. With the possibility to detect phase singularities automatically and exactly, important quantitative data on cardiac fibrillation can be gained.