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Response of the Hodgkin-Huxley Neuron to a Periodic Sequence of Biphasic Pulses

100%

Borkowski L.

vol. 125

issue 1

145-154

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 cathodic-first pulses with an inter-phase gap approximately equal to 5 ms. The firing 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 firing state coexist and transition to firing is a discontinuous one. We found a multimodal transition 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 multimodal transition, may provide an explanation for the therapeutic mechanism of deep brain stimulation.

Multimodal Transition and Excitability of a Neural Oscillator

80%

Borkowski L.

Acta Physica Polonica A

2012

vol. 122

issue 4

776-780

We analyze the response of the Morris-Lecar model to a periodic train of short current pulses in the period-amplitude plane. For a wide parameter range encompassing both class 2 and class 3 behavior in the Hodgkin classification there is a multimodal transition between the set of odd modes and the set of all modes. It is located between the 2:1 and 3:1 locked-in regions. It is the same dynamic instability as the one discovered earlier in the Hodgkin-Huxley model and observed experimentally in squid giant axons. It appears simultaneously with the bistability of the states 2:1 and 3:1 in the perithreshold regime. These results imply that the multimodal transition may be a universal property of resonant neurons.

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2 Acta Physica Polonica A

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Response of the Hodgkin-Huxley Neuron to a Periodic Sequence of Biphasic Pulses

Multimodal Transition and Excitability of a Neural Oscillator