A deformable finite element derived finite difference method for cardiac activation problems

We present a finite element (FE) derived finite difference (FD) technique for solving cardiac activation problems over deforming geometries using a bidomain framework. The geometry of the solution domain is defined by a FE mesh and over these FEs a high resolution FD mesh is generated. The difference points are located at regular intervals in the normalized material space within each of the FEs. The bidomain equations are then transformed to the embedded FD mesh which provides a solution space that is both regular and orthogonal. The solution points move in physical space with any deformation of the solution domain, but the equations are set up in such a way that the solution is invariant as it is constructed in material space. The derivation of this new solution technique is presented along with a series of examples that demonstrate the accuracy of this bidomain framework.