 
Summary: J. OF ELECTROCARDIOLOGY, 32:2233, 1999 1
SphericalHarmonic Approximation to
the Forward Problem of Electrocardiology
R. Martin Arthur, PhD
Abstract Forwardproblem solutions were approximated us
ing sphericalharmonic series on an adultmale torso model
with heart and lungs. These approximations were found using
only a knowledge of torsomodel 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 fifthdegree
series for eight distributed doublelayer sources had an average
relative error (RE) of 0.036. REs were similar with and without
torso inhomogeneities. The fifthdegree series solution (36 terms)
was found four times faster than the conventional method and
provided a data reduction factor of about 20 in the 715node
torso model studied. Sphericalharmonic series transform surface
potentials into an orthogonal basis set whose spatialfrequency
