Spherical-harmonic approximation to the forward problem of electrocardiology

Abstract

Forward-problem solutions were approximated using spherical-harmonic series on an adult male torso model with heart and lungs. These approximations were found using only a knowledge of torso-model geometry and were not based on a prior solution for surface potentials. Because these series depend only on polar and azimuthal angles, they allow continuous estimation of the forward-problem solution over the torso without further knowledge of the torso geometry. Compared to the conventional method, potentials estimated from fifth-degree series for eight distributed double-layer sources had an average relative error of 0.036. Relative errors were similar with and without torso inhomogeneities. The fifth-degree series solution (36 terms) was found four times faster than the conventional method and provided a data reduction factor of about 20 in the 715-node torso model studied. Spherical-harmonic series transform surface potentials into an orthogonal basis set whose spatial-frequency content increases with increasing degree. Consequently, these series may provide a structure for the systematic study of the effect on forward-problem solutions of both changes in torso shape and inclusion of inhomogeneities.