The inverse problem of phase singularity distribution: An eikonal approach

The aim of this paper is to develop a tool to construct initial conditions for a cardiac propagation model, in which phase singularities are positioned at predefined locations. Our approach relies on the eikonal-diffusion equation (extended to handle reentrant activations) to generate phase maps describing reentries around phase singularities. Through a mapping between phase and cell state, these phase maps are used to create initial conditions from which evolution is simulated in the monodomain framework. This method was applied to initiate functional reentries in an atrial model. Reentrant circuits were placed at 24 different anatomical locations. Phase singularities tracked during the simulations meandered in the vicinity of the desired locations specified in the eikonal problem. The results suggest that this tool could help in the creation of a library of different forms of simulated arrhythmias.