Cardiac Electrophysiology Meshfree Modeling Through the Mixed Collocation Method

We present the meshfree mixed collocation method (MCM) for cardiac electrophysiology simulation. Capitalizing on the meshfree property of MCM, we introduce an immersed grid approach for automated generation of meshfree node grids from medical image data. This approach allows us to avoid the time-consuming mesh generation and processing that mesh-based methods like the finite element method (FEM) require. We employ the MCM to solve the cardiac monodomain model considering electrical propagation in 2D tissue sheets, 3D tissue slabs, and a realistic biventricular anatomy. We demonstrate that the solutions obtained by the MCM are in good agreement with the FEM, particularly when immersed grid is used. These findings confirm the suitability of the MCM for cardiac electrophysiology simulation and make the MCM a promising alternative to the FEM for cardiac electrical investigations.