A generalized finite difference method for modeling cardiac electrical activation on arbitrary, irregular computational meshes

A generalized finite difference (GFD) method is presented that can be used to solve the bidomain equations modeling cardiac electrical activity. Classical finite difference methods have been applied by many researchers to the bidomain equations. However, these methods suffer from the limitation of requiring computational meshes that are structured and orthogonal. Finite element or finite volume methods enable the bidomain equations to be solved on unstructured meshes, although implementations of such methods do not always cater for meshes with varying element topology. The GFD method solves the bidomain equations on arbitrary and irregular computational meshes without any need to specify element basis functions. The method is useful as it can be easily applied to activation problems using existing meshes that have originally been created for use by finite element or finite difference methods. In addition, the GFD method employs an innovative approach to enforcing nodal and non-nodal boundary conditions. The GFD method performs effectively for a range of two and three-dimensional test problems and when computing bidomain electrical activation moving through a fully anisotropic three-dimensional model of canine ventricles.