Finite element investigation of the effect of conductivity changes in ischemic heart tissue on electrocardiography

Electrocardiography (ECG) is a common diagnostic tool based on reading potentials on the human torso and make deductions about heart health. Many quasistatic numerical studies exist in the literature that tackles forward and the inverse problem of ECG. While the abnormal transmembrane potential of the ischemic tissue is taken into account in these studies, the decreased conductivity due to this pathology has been largely ignored. In the first part of this study, we have investigated numerically the effect of ischemic conductivities on the torso potentials, and the effect of these torso potentials on the solution of the inverse problem. To achieve this objective, a finite element code has been written to solve the bidomain problem on realistic two-dimensional torso geometries, and a related optimization code is written that uses the finite element code. Our results show that the ischemic conductivity has a noticeable effect on the torso potentials but makes a small difference when locating the ischemic region in the inverse problem. In the second part of this thesis work, a novel iterative scheme for the solution of the inverse problem has been developed. The method is based on the parameterization of the location of the ischemic regions, where the parameters are determined using sensitivity analysis and finite element optimization. It has been observed that the method succesfully locates the ischemic region.