Eikonal-based initiation of fibrillatory activity in thin-walled cardiac propagation models

Reentrant arrhythmias can be simulated in electrophysiological models of electrical impulse propagation governed by a reaction-diffusion system. To facilitate the initiation of a large number of independent episodes of simulated arrhythmias with controllable level of complexity, a new approach is proposed for thin-walled geometries in which depolarization wave dynamics is essentially two-dimensional. Points representing phase singularities are first randomly distributed over the epicardial surface and are assigned a topological charge (direction of rotation). A qualitatively-correct phase map is then reconstructed on the whole surface by interpolation. The eikonal-diffusion equation is used to iteratively regularize the phase map based on a priori information on wavefront propagation. An initial condition for the reaction-diffusion model is created from the resulting phase map with multiple functional/anatomical reentries. Results in an atrial model demonstrate the ability to generate statistical realizations of the same dynamics and to vary the level of complexity measured by the number of phase singularities. A library of 100 simulations with an average number of phase singularities ranging from 1 to 10 is created. An extension to volumetric patient-specific atrial models including fiber orientation and a fast conducting system is presented to illustrate possible applications.