Analysis of electrostimulation and electroporation by high repetition rate bursts of nanosecond stimuli

Exposures to short-duration, strong electric field pulses have been utilized for stimulation, ablation, and the delivery of molecules into cells. Ultrashort, nanosecond duration pulses have shown unique benefits, but they require higher field strengths. One way to overcome this requirement is to use trains of nanosecond pulses with high repetition rates, up to the MHz range. Here we present a theoretical model to describe the effects of pulse trains on the plasma membrane and intracellular membranes modeled as resistively charged capacitors. We derive the induced membrane potential and the stimulation threshold as functions of pulse number, pulse duration, and repetition rate. This derivation provides a straightforward method to calculate the membrane charging time constant from experimental data. The derived excitation threshold agrees with nerve stimulation experiments, indicating that nanosecond pulses are not more effective than longer pulses in charging nerve fibers. The derived excitation threshold does not, however, correctly predict the nanosecond stimulation of cardiomyocytes. We show that a better agreement is possible if multiple charging time constants are considered. Finally, we expand the model to intracellular membranes and show that pulse trains do not lead to charge buildup, but can create significant oscillations of the intracellular membrane potential.