Modeling the Electrical Function of the Human Heart

This thesis deals with finding answers to the question, whether it is possible and feasible to model cardiac electrical activity employing exclusively isotropic conductivities, although the heart is known to own pronounced anisotropic properties. For this purpose the effects of two numerical methods – the boundary element method (BEM) and the finite element method (FEM) – were investigated on both the forward problem and the inverse problem of electrocardiography. In the next step potential implications and consequences with respect to the body surface potentials were figured out when isotropic electrical conductivities were applied. By realistically modeling of the human cardiac fibrous structure a ventricular model was generated, which represented one compartment – apart from lungs, blood mass, and the torso surface – of a volume conductor model. Employing this model four different heart rhythms were simulated applying a cellular automaton, and the epi-, endocardial and myocardial electrical influences on the body surface potentials for each rhythm were computed. Further the influence of cardiac isotropic or anisotropic conductivities on the accuracy of determining cardiac activation times was studied by solving the inverse problem. It could be shown, that approximating electrical cardiac activity by isotropic conductivities yielded for a satisfactory accuracy depending on the intended application. This was also emphasized by the high mean correlation coefficient of more than 92 % between the body surface potentials and the epiand endocardial ventricular anisotropic electrical activity for the four different rhythms during the depolarization sequence. Additionally it could be figured out, that inverse algorithms, which had a low sensitivity with respect to potential amplitudes but which owned a high sensitivity regarding potential patterns, also delivered results with satisfactory accuracy when isotropic electrical conductivities were applied.