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

摘要

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 regularizationapproach to the inverse problem of electrocardiography. To differentiatebetween the need for nonlinear treatment and the need forregularization, two simple models were chosen. In the first model, theinverse problem was highly ill-conditioned (matrix conditionno.>lOE6). The epicardial potentials (17 points) are to be restoredfrom the surface potentials (17 points). The cardiac source wasrepresented by a concentric cap of distribution of dipoles-near theepicardium-in a homogenous volume conductor. Several values for thesource angle were taken for both linear calculations and training theANN. For this model, regularization was needed even without geometricuncertainties. In the second model, the inverse problem was relativelywell-conditioned (matrix condition no.<20), where the cardiac sourcewas represented by six current dipoles in a homogenous spherical volumeconductor of radius R=1. Body surface potentials were calculated at 41measuring points on the body sphere. The potentials calculated from the64 possible combinations of dipoles status were used to get the transfermatrix