The Appearance Order of Varying Intervals Introduces Extra Modulation Effects on Neuronal Firing Through Non-linear Dynamics of Sodium Channels During High-Frequency Stimulations

Electrical pulse stimulation in the brain has shown success in treating several brain disorders with constant pulse frequency or constant inter-pulse interval (IPI). Varying IPI may offer a variety of novel stimulation paradigms and may extend the clinical applications. However, a lack of understanding of neuronal responses to varying IPI limits its informed applications. In this study, to investigate the effects of varying IPI, we performed both rat experiments and computational modeling by applying high-frequency stimulation (HFS) to efferent axon fibers of hippocampal pyramidal cells. Antidromically evoked population spikes (PSs) were used to evaluate the neuronal responses to pulse stimulations with different IPI patterns including constant IPI, gradually varying IPI, and randomly varying IPI. All the varying IPI sequences were uniformly distributed in the same interval range of 10 to 5 ms (i.e., 100 to 200 Hz). The experimental results showed that the mean correlation coefficient of PS amplitudes to the lengths of preceding IPI during HFS with random IPI (0.72 ± 0.04, n = 7 rats) was significantly smaller than the corresponding correlation coefficient during HFS with gradual IPI (0.92 ± 0.03, n = 7 rats, P < 0.001, t-test). The PS amplitudes induced by the random IPI covered a wider range, over twice as much as that induced by the gradual IPI, indicating additional effects induced by merely changing the appearance order of IPI. The computational modeling reproduced these experimental results and provided insights into these modulatory effects through the mechanism of non-linear dynamics of sodium channels and potassium accumulation in the narrow peri-axonal space. The simulation results showed that the HFS-induced increase of extracellular potassium ([K(+)](o)) elevated the membrane potential of axons, delayed the recovery course of sodium channels that were repeatedly activated and inactivated during HFS, and resulted in intermittent neuronal firing. Because of non-linear membrane dynamics, random IPI recruited more neurons to fire together following specific sub-sequences of pulses than gradual IPI, thereby widening the range of PS amplitudes. In conclusion, the study demonstrated novel HFS effects of neuronal modulation induced by merely changing the appearance order of the same group of IPI of pulses, which may inform the development of new stimulation patterns to meet different demands for treating various brain diseases.