Tracking of Arbitrary Regimes for Spiking and Bursting in the Hodgkin-Huxley Neuron

Borisenok, Sergey; Ünal, Zeynep

doi:10.20319/mijst.2017.32.560576

Cited by 2 publications

(3 citation statements)

References 32 publications

(37 reference statements)

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“…The dynamical set ( 6)-( 7) can be equipped with the control inputs mimicking the external perturbations of the neural clusters with the electrical (Rattay, 1999) or optogenetic (Joshi et al, 2020) signals. In this case, the set of control algorithms can be applied to detect (Borisenok and Ünal, 2017;Borisenok, 2021) and suppress (Borisenok et al, 2018;Borisenok, 2022) the epileptiform dynamics.…”

Section: Discussionmentioning

confidence: 99%

Statistical Model for Excitation and Hypersynchronization in the Small Neural Populations

Borisenok

2022

EJOSAT

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The mathematical modeling of epileptic seizures appearing in small neural populations can follow a few alternative ways: modeling of individual cells and their interaction vs. modeling groups and clusters on neurons. The purpose of this work is invention of a novel continuous (population-based) model for the appearance of the hyper-synchronized firing cells of the epileptiform type. In the same time, we use here the master equations based on the transition probabilities among different states of the cell excitation and hyper-synchronization. We developed an ODE model combining the dynamical equations for different sub-populations (unexcited, excited, and, as our novelty, hypersynchronized). Our model may serve as a simple but powerful tool to analyze the appearance and development of epileptiform dynamics in artificial neural networks. It can cover different cases of microepilepsy, and also may open the gate for studying drug-resistant epilepsy regime. Our dynamical set can be extended with the control inputs mimicking the external perturbations of the neural clusters with the electrical or optogenetic signals. In this case, the set of control algorithms can be applied to detect and suppress the epileptiform dynamics. Thus, the dynamic processes of epilepsy in small neural populations do not demand necessary the development of detailed models for individual neurons. Even the ‘averaged’ dynamical set for the unexcited, excited and hypersynchronized sub-populations can serve as an efficient tool for investigation and numerical simulations of microscopic seizures.

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Section: Discussionmentioning

confidence: 99%

Statistical Model for Excitation and Hypersynchronization in the Small Neural Populations

Borisenok

2022

EJOSAT

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“…The achievability of the stabilization/tracking goal in the HH dynamical system for the speed gradient algorithm has been proved numerically in (Borisenok & Ünal, 2017). Now the differential equation for the action potential v looks like this: .…”

Section: Speed Gradient Feedbackmentioning

confidence: 98%

“…The achievability of the goal for arbitrary stabilization/tracking via target attractor feedback has been discussed in (Borisenok & Ünal, 2017).…”

Section: 'Quantum States' Of Hh Neuronmentioning

confidence: 99%

Quantum Algorithms With Controlled Hodgkin-Huxley Neurons

Borisenok

2021

mijst

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Tracking of Arbitrary Regimes for Spiking and Bursting in the Hodgkin-Huxley Neuron

Abstract: Abstract

Cited by 2 publications

References 32 publications

Statistical Model for Excitation and Hypersynchronization in the Small Neural Populations

Statistical Model for Excitation and Hypersynchronization in the Small Neural Populations

Quantum Algorithms With Controlled Hodgkin-Huxley Neurons

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