Response of the Hodgkin-Huxley neuron to a periodic sequence of biphasic pulses

TL;DR

This study analyzes how Hodgkin-Huxley neurons respond to periodic biphasic pulses, revealing optimal stimulation parameters, bifurcation behaviors, and resonance effects that influence neuronal firing patterns and thresholds.

Contribution

It provides new insights into the response dynamics of Hodgkin-Huxley neurons to biphasic pulses, including bifurcation structures and resonance phenomena, under various stimulus conditions.

Findings

Optimal charge-balanced stimulation with cathodic-first pulses and 5 ms IPG.

Resonant frequencies produce continuous firing rate changes with amplitude.

Nonresonant frequencies show coexistence of quiescent and firing states, with discontinuous transitions.

Abstract

We study the response of the Hodgkin-Huxley neuron stimulated periodically by biphasic rectangular current pulses. The optimal response for charge-balanced input is obtained for cathodic-first pulses with an inter-phase gap (IPG) approximately equal 5 ms. For short pulses the topology of the global bifurcation diagram in the period-amplitude plane is approximately invariant with respect to the pulse polarity and shape details. If stimuli are delivered at neuron's resonant frequencies the firing rate is a continuous function of pulse amplitude. At nonresonant frequencies the quiescent state and the firing state coexist over a range of amplitude values and the transition to excitability is a discontinuous one. There is a multimodal odd-all transition between the 2:1 and 3:1 locked-in states. A strong antiresonant effect is found between the states 3:1 and 4:1, where the modes (2+3n):1, $n=0,1,2,...$, are entirely absent. At high frequencies the excitation threshold is a nonmonotonic function of the stimulus and the perithreshold region is bistable, with the quiescent state coexisting with either a regular or chaotic firing.