A Meshfree Method for Solving Cardiac Electrical Propagation

We present a novel numerical scheme to accurately and efficiently simulate the spatiotemporal electrical propagation for three dimensional heart model. A meshfree particle representation of myocardial volume is first developed, upon which the electrical propagation can be obtained using the element-free Galerkin (EFG) method for the FitzHugh-Nagumo model. This method is based on a sufficient amount of sampling nodes of the three-dimensional myocardial volume, but without the needs to construct the often expensive and complicated mesh structure between these nodes. Compared to the traditional finite element method, this new approach provides a more efficient numerical method to model the effects of the myocardial geometrical complexity and material inhomogeneity/anisotropicness. Experiments on synthetic and real heart geometries with uniform and nonuniform diffuse materials are presented. Related implementation issues are also discussed