Surface integration and least-squares procedures for the inverse recovery of cardiac multipole components

A simulation study was performed to evaluate different recovery procedures for computing the multipole components of the cardiac electrical activity. A series of dipolar potential distributions was first generated on a realistic numerical model of the human torso. Then, different procedures based on surface integration (SI) and least-squares (LS) minimization were used to compute the multipole components. The parameters of a single moving dipole (SMD) computed from the estimated multipoles were compared with those of the original dipole source. For a finite and homogeneous simulation as well as recovery medium, the results showed that SI employing the potentials over all 1216 surface elements of the torso model was not affected by the various numerical approximations used to perform the integration (e.g., rms error for the SMD position, p = 0.7 mm). By integrating the potentials with truncated capping surfaces at the neck and the waist, the recovery errors increased (p = 2.1 mm). Sampling the potentials at 63 sites, followed by interpolation over the rest of the torso surface, severely affected the SI results for the SMD (p = 6.4 mm), as compared with LS minimization using also 63 values (p = 0.9 mm). With lungs and intraventricular blood masses in the simulation medium but a finite and homogeneous recovery medium, SI was less effective (p = 10.8 mm) than LS (p = 8.6 mm). Adequate compensation for the effects of lungs was obtained by including regions of lower electrical conductivity in the recovery medium for LS, and by a correction matrix for SI. In general, LS gave better results than SI, but with a higher initial computation time.