The ANN as a technique to solve the inverse problem of electrocardiography: the effect of the training margin on the errors caused by geometric uncertainties in an eccentric homogenous spherical model

Artificial neural networks (ANN) were previously proposed by the author as a technique for solving the inverse problem of electrocardiography. The aim of the paper is to find the training limits of the input data for this problem and the related probability of output errors. Using a model of a homogeneous spherical body, the cardiac source was represented by six current dipoles located on the surface of an eccentric heart sphere. Body surface potentials were calculated at 26 measuring points for (19×64) cases representing the all possible combinations of dipole status (64) in the following (19) cases; the basic case, 8 cases of uncertainty in heart radius r_o, 8 cases of angular uncertainty in θ, and 2 cases in φ of the spherical coordinates. The data base for 64×19 cases was used to test the response of the ANN for each group of training. The statistical output error E was calculated in each case (E=Nf×100/64×6, where Nf is the number of false outputs). The obtained results showed that the ANN accepted the training data within a limited margin, beyond which the data would appear to be contradictory