Direct inference of the spectra of pericardial potentials using the boundary-element method

New methods, based on Tikhonov regularization, were developed to infer the magnitude and phase of pericardial potentials directly. These methods were tested in an adult-male torso model using measured human epicardial potentials. With 1% noise added to body-surface potentials, regularization with an optimal parameter at each frequency from 1 to 100 Hz gave an average relative error (RE) in inferred spectral magnitudes of 0.44. Regularization with the composite-residual-smoothing-operator (CRESO) parameter increased the RE slightly to 0.47. With 10% additive noise, 10 mm overestimation of heart radius, and a 10 mm error in heart position, the average CRESO parameter from 1 to 100 Hz gave an average RE of 0.71. Performance was frequency dependent. The smallest REs occurred at low frequencies. With 1% noise, optimal regularization gave average REs of 0.20, 0.40, and 0.53 in the 1-15, 15-46, and 46-100 Hz bands, respectively. Direct inference of spectral magnitudes was more accurate than Fourier transformation of inferred time-domain waveforms. Results suggest that when heart size and location are not known, minimum REs in spectral estimates are found using an overestimated heart size and a regularization parameter which is the average value over the frequency band of interest.