Volume conductor model of transcutaneous electrical stimulation with kilohertz signals

Incorporating high-frequency components in transcutaneous electrical stimulation (TES) waveforms may make it possible to stimulate deeper nerve fibers since the impedance of tissue declines with increasing frequency. However, the mechanisms of high-frequency TES remain largely unexplored. We investigated the properties of TES with frequencies beyond those typically used in neural stimulation.

We implemented a multilayer volume conductor model including dispersion and capacitive effects, coupled to a cable model of a nerve fiber. We simulated voltage- and current-controlled transcutaneous stimulation, and quantified the effects of frequency on the distribution of potentials and fiber excitation. We also quantified the effects of a novel transdermal amplitude modulated signal (TAMS) consisting of a non-zero offset sinusoidal carrier modulated by a square-pulse train.

The model revealed that high-frequency signals generated larger potentials at depth than did low frequencies, but this did not translate into lower stimulation thresholds. Both TAMS and conventional rectangular pulses activated more superficial fibers in addition to the deeper, target fibers, and at no frequency did we observe an inversion of the strength-distance relationship. Current regulated stimulation was more strongly influenced by fiber depth, whereas voltage regulated stimulation was more strongly influenced by skin thickness. Finally, our model reproduced the threshold-frequency relationship of experimentally measured motor thresholds.

The model may be used for prediction of motor thresholds in TES, and contributes to the understanding of high-frequency TES.