Finite element refinements for inverse electrocardiography: Hybrid shaped elements and high-order element truncation

We study how finite element method (FEM) can be selected to optimize numerical discretization of the inverse electrocardiographic (ECG) problem. Due to its ill-posedness, the inverse ECG problem poses different discretization requirements from its forward problem counterpart. Conventional refinements effective for the forward problem may become ineffective when applied to the inverse problem. We propose two refining methods specifically tackling the ill-posedness of the inverse problem. One is hybrid-shaped elements involving quadrilateral/triangular elements in 2D and prismatic/tetrahedral elements in 3D. Another method uses high-order FEM, extracts from the resulting system the linear component and solves the linear part only. Simulations on realistic human torso models demonstrate that both methods improve both the discrete problem's conditioning and the inverse solution, indicating our strategies might provide guidelines for mesh generation in practical biomedical simulations.