Research of Dynamic Modes in the Mathematical Model of Elementary Thalamocortical Cell

Kolosov, Anton; Nuidel, I. V.; Yakhno, V. G.

doi:10.18500/0869-6632-2016-24-5-72-83

Cited by 5 publications

(7 citation statements)

References 3 publications

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“…Однако механизмы перехода между нормальным и патологическим состояниями в таких больших моделях изучить очень проблематично из-за большой размерности и большого числа параметров. В пределе некоторые результаты могут быть получены, если перейти к рассмотрению мозга как сплошной среды, как это сделано в [11], но такое моделирование не всегда согласуется с современными представлениями о наличии большого числа дальних связей между нейронами коры и таламуса, хотя может быть полезно для некоторых типов активности, например, при изучении распространяющейся депрессии [12].…”

Section: Introductionunclassified

The Modeling of Spike-Wave Discharges in Brain with Small Oscillatory Neural Networks

Kapustnikov¹,

Sysoeva²,

Sysoev³

2020

Math.Biol.Bioinf.

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A pathology of coupling architecture in the thalamo-cortical system is considered the main cause of absence epilepsy, the eletroencephalographic primary manifestation of which are spike-wave discharges. The immediate cause of the discharges may be in increase of intracortical connectivity or external stimulation of cortex or thalamus. At the same time, the mechanisms of discharge termination are still not clear; so from the point of view of the dynamical system theory, the spike-wave discharge can be considered as a long transient process. In this paper, we propose a simple mathematical model of network with 14 identical Fitzhugh–Nagumo neurons, which is organized in accordance with modern ideas about thalamo-cortical brain network. In this model, long transients in response to short-term pulse driving from a separate neuron, representing the nervus trigeminus, are shown to be possible. Bifurcation analysis reveals such transients to develop in the system approximately the bifurcation of the cycle birth from the condensation of phase trajectories. The model may be useful for detailed studies of the thalamo-cortical system. It also can be used to investigate effects of electrical brain stimulation and pharmacological interventions, and to test the methods for evaluating connectivity in brain.

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Section: Introductionunclassified

The Modeling of Spike-Wave Discharges in Brain with Small Oscillatory Neural Networks

Kapustnikov¹,

Sysoeva²,

Sysoev³

2020

Math.Biol.Bioinf.

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“…Figures 3 and 4 demonstrate three states of the system: before an exposure to external signal, during exposure to a high-frequency external signal, and after the exposure. All these states are characterized by the natural frequency of the thalamocortical system, which depends on the mean amplitude of the external signal [7]. "High frequency exposure" means that the frequency of the external signal is substantially higher than the natural frequency of the thalamocortical unit cell.…”

Section: Resultsmentioning

confidence: 99%

“…The present study addressed the focused model of the thalamocortical function without considering structures of the internal modules, i.e., the specific thalamic nucleus; the inhibitory reticular nonspecific thalamic nucleus, or the cortex areas associated with the thalamic nuclei [7].…”

Section: Methodsmentioning

confidence: 99%

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Using a Phenomenological Mathematical Model to Reproduce the Interaction of Endogenous and Exogenous Oscillations under Neurocontrol

Nuidel¹,

Kolosov²,

Demareva³

et al. 2019

Sovrem Tehnol Med

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The aim of the study was to evaluate the possibility of using a phenomenological mathematical model of the thalamocortical unit cell to describe the frequency-time responses of the real thalamocortical system (namely, various alpha rhythm modulations) and reproduce the signal dynamics in the process of neurobiocontrol. Materials and Methods. The experimental part of this study (the resonant neurobiocontrol with double feedback based on the BioFeedBack2 software-hardware complex) was carried out according to the hybrid protocol: background-before/after: 2-minute record of the baseline vertex EEG (the active electrode-Cz grounding and the reference electrodes held on the earlobes); frequency scan during 210 s: exposure to pulsed infrared radiation with an increasing rate of from 8 to 14 Hz (frequency step-0.1 Hz, time step-3 s) and a music-like sound signal, the tone and volume of which determined by the peak amplitude in the spectrum of the current EEG in the range of 8-14 Hz. The characteristic feedback time is 10 ms, the frequency accuracy is 0.2-0.4 Hz. Periodic noise pulses, presented with a frequency related to the baseline heart rate, have been added to the sound signal. For the calculations, a previously developed phenomenological model of the thalamocortical unit cell was used. The model incorporates interacting modules simulating the major neuronal modules of the brain, i.e., the thalamus, the cortex and the thalamic reticular nuclei. Results and Discussion. Using the proposed phenomenological mathematical model of the thalamocortical unit cell, we obtained frequency-time responses of the model signal, which reproduces the frequency pattern of the real EEG signal. The model simulates the situation when the baseline alpha rhythm changes in response to an external factor with the known thalamocortical parameters. In the future, this information will improve the current feedback procedures of biocontrol aimed at enhancing the cognitive power of the brain. Appropriate training will allow controlling the alpha rhythm frequency (neurobiolcontrol) in such a way that, by the objective psychophysical criteria, the subjects will have their cognitive activity enhanced, and, by the subjective assessment, their well-being will improve. Conclusion. In this study, a neuro-informational approach to personalized brain rhythm management is demonstrated. It is now possible to reproduce individual features of a complex information processing system using the proposed phenomenological model of the thalamocortical unit cell.

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“…Computational models on SWD generation made a great contribution to our understanding of the pathophysiology of absence epilepsy [5][6][7]. Currently there are a number of models that are quite distinct from each other including phenomenological [8] and biophysical models [9][10][11]; thalamic [12], cortical [13,14] and thalamo-cortical [15], micro- [12,16], meso- [17][18][19][20][21] and macroscale [7,16,[22][23][24][25][26][27][28] models were described. Most models aim to reproduce the characteristics of SWDs, but some of them focus on effect of abnormal activity in thalamo-cortical networks, most often the thalamus was considered as the initiation site for SWDs [29][30].…”

Section: Introductionmentioning

confidence: 99%

Dynamical mesoscale model of absence seizures in genetic models

et al. 2020

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A mesoscale network model is proposed for the development of spike and wave discharges (SWDs) in the cortico-thalamo-cortical (C-T-C) circuit. It is based on experimental findings in two genetic models of childhood absence epilepsy-rats of WAG/Rij and GAERS strains. The model is organized hierarchically into two levels (brain structures and individual neurons) and composed of compartments for representation of somatosensory cortex, reticular and ventroposteriomedial thalamic nuclei. The cortex and the two thalamic compartments contain excitatory and inhibitory connections between four populations of neurons. Two connected subnetworks both including relevant parts of a C-T-C network responsible for SWD generation are modelled: a smaller subnetwork for the focal area in which the SWD generation can take place, and a larger subnetwork for surrounding areas which can be only passively involved into SWDs, but which is mostly responsible for normal brain activity. This assumption allows modeling of both normal and SWD activity as a dynamical system (no noise is necessary), providing reproducibility of results and allowing future analysis by means of theory of dynamical system theories. The model is able to reproduce most timefrequency changes in EEG activity accompanying the transition from normal to epileptiform activity and back. Three different mechanisms of SWD initiation reported previously in experimental studies were successfully reproduced in the model. The model incorporates also a separate mechanism for the maintenance of SWDs based on coupling analysis from experimental data. Finally, the model reproduces the possibility to stop ongoing SWDs with high frequency electrical stimulation, as described in the literature.

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Research of Dynamic Modes in the Mathematical Model of Elementary Thalamocortical Cell

Cited by 5 publications

References 3 publications

The Modeling of Spike-Wave Discharges in Brain with Small Oscillatory Neural Networks

The Modeling of Spike-Wave Discharges in Brain with Small Oscillatory Neural Networks

Using a Phenomenological Mathematical Model to Reproduce the Interaction of Endogenous and Exogenous Oscillations under Neurocontrol

Dynamical mesoscale model of absence seizures in genetic models

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