Washout filter aided mean field feedback desynchronization in an ensemble of globally coupled neural oscillators

Luo, Ming; Wu, Yongjun; Peng, Jianhua

doi:10.1007/s00422-009-0334-5

Cited by 45 publications

(29 citation statements)

References 43 publications

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“…In normal brain function, synchronization within and between neural populations is an important mechanism for neural signaling and information processing (Hauptmann et al 2005;Luo et al 2009). In recent years, synchronization has been extensively studied in different contexts by several researchers.…”

Section: Introductionmentioning

confidence: 99%

On the role of astrocytes in synchronization of two coupled neurons: a mathematical perspective

2011

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Based on recent findings, astrocytes, a subtype of glial cells, dynamically regulate the synaptic transmission of neuronal networks. In this research, a biologically inspired neuronal network model is constructed by connecting two Morris-Lecar neuron models. In this minimal network model, neuron-astrocyte interactions are considered in a functional-based procedure. Utilizing the developed model and according to the theoretical analysis carried out in the article, it is confirmed that, the astrocyte increases the threshold value of synchronization and provides appropriate feedback control in regulating the neural activities. Therefore, the healthy astrocyte has the potential to desynchronize the synchrony between two coupled neurons. Next, we investigate malfunction of the astrocyte in the regulatory feedback loop. Mathematically, we verify that pathologic astrocyte is no longer able to increase the synchronization threshold and therefore, it cannot compensate excessive increase in the excitation level. The main reason behind this is the fact that healthy astrocyte can optimally increase the input current of the individual neurons, while the so-called pathological astrocyte is unable to modify correctly the amount of this current. Consequently, disruptions of the signaling function of astrocyte initiate the hypersynchronous firing of neurons. In other words, reduction in neuron-astrocyte cross-talk will lead to synchronized firing of neurons. Therefore, our results propose that the astrocyte could have a key role in stabilizing neural activity.

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Section: Introductionmentioning

confidence: 99%

On the role of astrocytes in synchronization of two coupled neurons: a mathematical perspective

2011

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“…Other studies rely on phase models. The mean-field feedback is applied using a particular resonant filter (Tukhlina et al, 2007; Luo et al, 2009) or a purely proportional feedback (without derivative terms) is analyzed with a finite-dimensional model, using an approach based on Lyapunov functions (Franci et al, 2011, 2012). The model of Rubin and Terman is exploited in Leondopulos (2007), Liu et al (2011).…”

Section: Introductionmentioning

confidence: 99%

Closing the loop of deep brain stimulation

Carron

Chaillet

Filipchuk

et al. 2013

Front. Syst. Neurosci.

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High-frequency deep brain stimulation is used to treat a wide range of brain disorders, like Parkinson's disease. The stimulated networks usually share common electrophysiological signatures, including hyperactivity and/or dysrhythmia. From a clinical perspective, HFS is expected to alleviate clinical signs without generating adverse effects. Here, we consider whether the classical open-loop HFS fulfills these criteria and outline current experimental or theoretical research on the different types of closed-loop DBS that could provide better clinical outcomes. In the first part of the review, the two routes followed by HFS-evoked axonal spikes are explored. In one direction, orthodromic spikes functionally de-afferent the stimulated nucleus from its downstream target networks. In the opposite direction, antidromic spikes prevent this nucleus from being influenced by its afferent networks. As a result, the pathological synchronized activity no longer propagates from the cortical networks to the stimulated nucleus. The overall result can be described as a reversible functional de-afferentation of the stimulated nucleus from its upstream and downstream nuclei. In the second part of the review, the latest advances in closed-loop DBS are considered. Some of the proposed approaches are based on mathematical models, which emphasize different aspects of the parkinsonian basal ganglia: excessive synchronization, abnormal firing-rate rhythms, and a deficient thalamo-cortical relay. The stimulation strategies are classified depending on the control-theory techniques on which they are based: adaptive and on-demand stimulation schemes, delayed and multi-site approaches, stimulations based on proportional and/or derivative control actions, optimal control strategies. Some of these strategies have been validated experimentally, but there is still a large reservoir of theoretical work that may point to ways of improving practical treatment.

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“…Other models and feedback schemes similar to (3)-(4) have been considered in the literature for the study of desynchronization via mean-field feedback [22][23][24]35,[41][42][43][44][48][49][50], achieving encouraging results that support this control strategy. Apart from computational studies [22][23][24], several analytical results have been derived.…”

Section: Comparison With Existing Approachesmentioning

confidence: 77%

“…Motivated by the same medical problem, different works have appeared about the physics of a population of interconnected oscillators under the effect of a mean-field feedback [22,23,35,[42][43][44]49,50], mostly relying on numerical analysis. On the one hand, these studies have shown that mean-field feedback DBS is a promising strategy for desynchronizing pathological neuronal populations.…”

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confidence: 99%

Desynchronization and inhibition of Kuramoto oscillators by scalar mean-field feedback

Franci

Chaillet

Panteley

et al. 2012

Math. Control Signals Syst.

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International audienceMotivated by neuroscience applications, and in particular by the deep brain stimulation treatment for Parkinson's disease, we have recently derived a simplified model of an interconnected neuronal population under the effect of its mean-field proportional feedback. In this paper, we rely on that model to propose conditions under which proportional mean-field feedback achieves either oscillation inhibition or desynchronization. More precisely, we show that for small natural frequencies, this scalar control signal induces an inhibition of the collective oscillation. For the closed-loop system, this situation corresponds to a fixed point which is shown to be almost globally asymptotically stable in the fictitious case of zero natural frequencies and all-to-all coupling and feedback. In the case of an odd number of oscillators, this property is shown to be robust to small natural frequencies and heterogencities in both the coupling and feedback topology. On the contrary, for large natural frequencies, we show that scalar proportional mean-field feedback is able to induce desynchronization. After having recalled a formal definition for desynchronization, we show how it can be induced in a network of originally synchronized oscillators

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Washout filter aided mean field feedback desynchronization in an ensemble of globally coupled neural oscillators

Cited by 45 publications

References 43 publications

On the role of astrocytes in synchronization of two coupled neurons: a mathematical perspective

On the role of astrocytes in synchronization of two coupled neurons: a mathematical perspective

Closing the loop of deep brain stimulation

Desynchronization and inhibition of Kuramoto oscillators by scalar mean-field feedback

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