Multimodal Transition and Excitability of a Neural Oscillator

Borkowski, L. S.

doi:10.12693/aphyspola.122.776

Cited by 2 publications

(10 citation statements)

References 28 publications

(43 reference statements)

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“…Using the FitzHugh Nagumo (FHN) model [33], they obtained a positive Lyapunov exponent which is consistent with experiments, where mutual desynchronization between similarly stimulated bers was observed. Their study is consistent with our analysis of the MMT within the HH [2527] and MorrisLecar [28] models. Since multimodal dynamics is common in electrically stimulated ANFs [3440], the current article may help to understand the response of ANFs to stimulation by a train of high-frequency current pulses.…”

Section: Introductionsupporting

confidence: 92%

“…It is clear from Fig. 2 and from earlier analysis [27,28] 2 , where the minimum of the excitation threshold occurs, is dominated by the 3:1 state and higher order states. Its mode-locking structure is essentially identical to that of monophasic monopolar stimulation shown in Fig.…”

Section: Methodsmentioning

confidence: 52%

“…Bistability at the threshold does not always imply the existence of MMT. As our recent study showed, neuron dynamics may be divided into four classes [28]. Only one of them displays MMT.…”

Section: Discussionmentioning

confidence: 97%

“…The MMT [25,26] and a dynamic instability [31,32] associated with it are key properties of many resonant neurons. MMT implies threshold bistability at nonresonant stimulation frequencies above the natural frequency of the neuron [28]. The converse is not always true.…”

Section: Discussionmentioning

confidence: 99%

“…Naturally, it should be kept in mind that a resonant neuron need not have the dynamics of the HH model [28] and the square root dependence of the ring rate on current amplitude is not always available. The optimal stimulation in clinical applications may include Gaussian noise superposed on the input signal [60].…”

Section: Discussionmentioning

confidence: 99%

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

Borkowski

2014

Acta Phys. Pol. A

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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 HodgkinHuxley 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 periodamplitude 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-rst pulses with an inter-phase gap approximately equal to 5 ms. The ring rate of the HodgkinHuxley 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 eect 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 eects at high stimulation frequency, such as multimodal transition, may provide an explanation for the therapeutic mechanism of deep brain stimulation.

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Section: Introductionsupporting

confidence: 92%

Section: Methodsmentioning

confidence: 52%

“…Bistability at the threshold does not always imply the existence of MMT. As our recent study showed, neuron dynamics may be divided into four classes [28]. Only one of them displays MMT.…”

Section: Discussionmentioning

confidence: 97%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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

Borkowski

2014

Acta Phys. Pol. A

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

Borkowski

2011

Preprint

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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.

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Multimodal Transition and Excitability of a Neural Oscillator

Cited by 2 publications

References 28 publications

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

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

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

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