Two Theorems Concerning the Quadrupole Applicable to Electrocardiography

The first part of the paper discusses various representations for the electric scalar potential, and develops a procedure for determining the magnitude of the quadrupole term of the multipole expansion from a knowledge of its five components. The terms in the multipole expansion for an equivalent cardiac generator depend on the location in the heart region chosen as the origin. In the second part of the paper, an optimum dipole location is defined as the point where the dipole term alone gives the best fit to the potential on a least squares basis. If the heart is well represented by a dipole plus quadrupole, with the z-axis chosen to coincide with the dipole moment p, the optimum dipole location is given by