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 neuron subject to periodic train of biphasic rectangular current pulses. One of the simpler ways to understand the behavior of 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 cathodicrst pulses with an inter-phase gap approximately equal to 5 ms. The ring rate of the Hodgkin Huxley 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 ring state coexist and transition to ring is a discontinuous one. We found a multimodal transition in the regime of irregular ring 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 e ect 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 e ects at high stimulation frequency, such as multimodal transition, may provide an explanation for the therapeutic mechanism of deep brain stimulation.