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

Abstract

Electric stimulation of various parts of the nervous system is a widely used therapeutic method and a principle of operation of prosthetic devices. Its usefulness has been proven in areas such as treatment of neurological disorders and cochlear prostheses. However the dynamic mechanisms underlying these applications are not well understood. In order to shed some light on this problem we study the response of the Hodgkin-Huxley (HH) neuron subject to periodic train of biphasic rectangular current pulses. One of the simpler ways to understand the behavior of a such a nonlinear system is the analysis of the global bifurcation diagram in the period-amplitude plane.For short pulses the topology of this diagram is approximately invariant with respect to the pulse polarity and shape details. The lowest excitation threshold for charge-balanced input was obtained for cathodic-first pulses with an inter-phase gap (IPG) approximately equal 5ms. The firing rate of the HH neuron stimulated at the frequency of its natural resonance is a square root function of the pulse amplitude. At nonresonant frequencies the quiescent state and the firing state coexist and transition to firing is a discontinuous one. We found a multimodal transition (MMT) in the regime of irregular firing between the 2:1 and 3:1 locked-in states. This transition separates the regime of odd-only multiples of the stimulus period from the regime where modes of both parities participate in the response. A strong antiresonant effect was found between the states 3:1 and 4:1, where the modes (2 + 3n) : 1, where n = 0, 1, 2, . . ., were entirely absent. The antiresonant effects at high stimulation frequency, such as MMT, may provide an explanation for the therapeutic mechanism of deep brain stimulation.