The Laplacian inverse problem of electrocardiography: an eccentric spheres study

The eccentric spheres model of the heart-torso system is used to study the inverse problem of electrocardiography using measurements of the Laplacian of the body surface potential distribution. Electrical activity is simulated on the six main regions of the inner surface by considering a limited number of current dipoles placed within the inner sphere. The resulting outer surface potential and Laplacian distributions are then calculated in a forward sense. Varying amounts of random noise are added to these distributions before a zero-order Tikhonov regularization scheme is used to recover the inner surface potential distribution. Comparing the calculated and original inner surface distributions indicates that measurements of the outer surface Laplacian can more accurately reconstruct epicardial potentials than measurements of the outer surface potentials. These distributions are more accurate in that the extrema are placed very close to their original positions and are of nearly the same magnitude. Also, multiple extrema and high potential gradients are recovered.