Modeling electrode-based stimulation of muscle and nerve by ultrashort electric pulses

Numerical simulations of electrostimulation of frog gastrocnemius muscles have been carried out for pulse durations in the nanosecond regime. There are a number of potential advantages in using ultrashort pulses for electrical stimulation, and no previous electrostimulation work in the submicrosecond regime has been reported. A time-dependent, three-dimensional analysis model was developed and implemented for two cases: 1) direct stimulation via electrode contact and 2) indirect excitation through a saline-filled bath. The simulations yielded strength-duration (S-D) curves with pulse durations as short as 5 ns. Good agreement between the model predictions and experimental measurements was obtained. For example, with direct contact, a peak current of about 30 A was predicted for the shortest pulse; the measured value was 34 A. Calculations of the S-D curves for both direct and indirect stimulation yielded a good match with the available experimental data. A time constant of 160 μs was estimated; this value is indicative of a nerve-based response. The modeling also led to a demonstration of the nonthermal nature of electrostimulation with nanosecond pulses, even with an applied voltage of 5 kV. Finally, it was shown quantitatively that inhomogeneities in the nerve geometry and size can affect the S-D curve. For contact stimulation, the greatest potential for muscle twitching occurs at boundaries and within regions that have internal nonuniformity.