R. M. Arthur, "Spherical-Harmonic Approximation to the Forward-Problem of Electrocariology," J. of Electrocardiology, vol. 32, pp. 22-33, 1999.

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 (RE) of 0.036. REs 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.

Key words: Cardiac sources, forward problem, spherical harmonics, torso model