Inverse Recovery of Two Moving Dipoles from Simulated Surface Potential Distributions on a Realistic Human Torso Model

We tested a procedure to recover two moving dipole (TMD) parameters from bidipolar potential distributions generated over the surface of a numerical human torso model, using 120 surface sampling points. The surface distributions were computed for either a finite homogeneous torso (T1), a finite torso with lungs (T2), or a finite torso with lungs and blood masses (T3). Inverse calculations were carried out to initially recover the multipole series components (15, 24, or 35 terms) using either a finite homogeneous torso (I1) or a finite torso with lungs (I2), and a least-squares difference procedure. Next, the TMD parameters were obtained by fitting these multipole series components (15 or 24 terms) to the multipole series components estimated from the Brody shift equations, using the Levenberg-Marquardt iterative algorithm and a series of initial estimates for the TMD solution. A simulation run involved 253 different input dipole-pair combinations and 20 initial estimates. The correct TMD solution almost always coincided with that yielding the minimum residue, which was also the solution obtained by the largest fraction of initial estimates. The lowest rms position error of 2.7 mm was obtained with a T1-I1 torso combination, and with 35 recovered multipole series components and 24 Brody shift equations. Larger errors were obtained using a lower number of recovered multipole series components and Brody shift equations, or pairs of parallel or antiparallel dipoles, or dipoles of unequal amplitude.