Inverse Problem of Electrocardiography: Estimating the Location of Cardiac Ischemia in a 3D Realistic Geometry

The inverse problem of electrocardiography (IPE) has been formulated in different ways in order to non invasively obtain valuable informations about the heart condition. Most of the formulations solve the IPE neglecting the dynamic behavior of the electrical wave propagation in the heart. In this work we take into account this dynamic behavior by constraining the cost function with the monodomain model. We use an iterative algorithm combined with a level set formulation and the use of a simple phenomenological model. This method has been previously presented to localize ischemic regions in a 2D cardiac tissue. In this work, we analyze the performance of this method in different 3D geometries. The inverse procedure exploits the spatiotemporal correlations contained in the observed data, which is formulated as a parametric adjust of a mathematical model that minimizes the misfit between the simulated and the observed data. Numerical results over 3D geometries show that the algorithm is capable of identifying the position and the size of the ischemic regions. For the experiments with a realistic anatomical geometry, we reconstruct the ischemic region with roughly a 47 % of false-positive rate and a 13 % false-negative rate under 10 % of input noise. The correlation coefficient between the reconstructed ischemic region and the ground truth exceeds the value of 0.70).