Optimizing Inverse Electrocardiographic Problem: Hybrid and High-Order Finite Element Method

One type of inverse problems in electrocardiography (ECG) is to non-invasively reconstruct epicardial electric potentials from body-surface measurements. We study how to design the finite element discretization of such problem, so as to optimize the conditioning and stability of the resulting numerical system. The inverse ECG problem is ill-posed, requiring different discretization strategies from its corresponding forward problem (see Fig.1 ). We developed two new techniques: 1) a unified finite element framework that accepts tetrahedral, hexahedral and prismatic elements, and 2) a high-order finite element method with a flexible hierarchical structure. We plan to integrate these techniques into the ECG toolkit within SCIRun. The toolkit will facilitate realistic simulation of clinical applications such as ischemia and arrhythmia.