Finite Element Discretization Strategies for the Inverse Electrocardiographic (ECG) Problem

Successful employment of numerical techniques for the forward and inverse electrocardiographic (ECG) problems requires the ability to both quantify and minimize approximation errors introduced as part of the discretization process. Conventional finite element discretization and refinement strategies effective for the forward problem may become inappropriate for the inverse problem because of its ill-posed nature. This conjecture leads us to develop discretization strategies specifically for the inverse ECG problem. By quantitatively analyzing the connection between the ill-posedness of the continuum inverse problem and the illconditioning of its discretized version, we propose strategies involving hybrid-shaped finite elements to discretize the inverse ECG problem effectively and efficiently. We also propose the criteria for evaluating the quality of the resultant discrete system. The efficacy of the strategies are demonstrated on a realistic torso model in both two and three dimensions.