The ANN as a nonlinear regularization technique to solve the inverse problem of electrocardiography

The inverse problem of electrocardiography is ill-conditioned, which amplifies the errors generated by the geometric uncertainties. Linear regularization treatment is not enough for this problem. Therefore, the authors introduced the ANN as a nonlinear regularization approach to the inverse problem of electrocardiography. To differentiate between the need for nonlinear treatment and the need for regularization, two simple models were chosen. In the first model, the inverse problem was highly ill-conditioned (matrix condition no.>lOE6). The epicardial potentials (17 points) are to be restored from the surface potentials (17 points). The cardiac source was represented by a concentric cap of distribution of dipoles-near the epicardium-in a homogenous volume conductor. Several values for the source angle were taken for both linear calculations and training the ANN. For this model, regularization was needed even without geometric uncertainties. In the second model, the inverse problem was relatively well-conditioned (matrix condition no.<20), where the cardiac source was represented by six current dipoles in a homogenous spherical volume conductor of radius R=1. Body surface potentials were calculated at 41 measuring points on the body sphere. The potentials calculated from the 64 possible combinations of dipoles status were used to get the transfer matrix.