Voxel Based Adaptive Meshless Method for Cardiac Electrophysiology Simulation

In this paper, an adaptive meshless method is described for solving the modified FitzHugh Nagumo equations on a set of nodes directly imported from the voxels of the medical images. The non-trivial task of constructing suitable meshes for complex geometries to solve the reaction-diffusion equations is circumvented by a meshfree implementation. The spatial derivatives arising in the reaction diffusion system are estimated using the Lagrangian form of scattered node radial basis function interpolant. Normal cardiac activation phenomena is fast, with a very steep upstroke and localised as compared to the size of the computational domain. To accurately capture this phenomena, a space adaptive method is presented where extra nodes are placed near the region of the activation front. The performance of the adaptive method is investigated first for synthetic geometry and then applied to a real-life geometry obtained from magnetic resonance imaging. Numerical results suggest that the presented method is capable of predicting realistic electrophysiology simulation effectively.