Contribution of dielectric dispersions to voltage waveforms arising from electrical stimulation

This study presents an analysis of the effect of incorporating a subset of the complete set of dielectric dispersions in electric field models of implanted electrical stimulation. An analytic volume conductor model was used to determine the voltage waveform at a distance of 5mm from a point current stimulus for 17 different biological tissues. The RMS error of the voltage waveform resulting from the incorporation of a subset of all poles with respect to the voltage waveform resulting from the incorporation of the complete set of dispersive poles was calculated. The stimulus amplitude necessary to elicit action potential propagation in a myelinated mammalian nerve fibre in each of the dispersive models was also determined using a multi-compartment cable axon model. It was found that, for all tissues, removal of dispersions with pole frequencies greater than 1 MHz had a negligible effect on the threshold stimulation amplitude, suggesting that they may be neglected when constructing volume conductor models of electrical stimulation. However, removal of low-frequency dispersions below 1 MHz resulted in greater reductions in the threshold stimulus amplitudes necessary for activation of axons, with errors of up to 86% observed.