Dynamics of a coupled epileptic network with time delay

Yulin Guan; Xue Zhang; Yulin Guan; Xue Zhang

doi:10.3934/mmc.2022003

Mathematical Modelling and Control

2022, Volume 2, Issue 1: 13-23. doi: 10.3934/mmc.2022003

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Research article

Dynamics of a coupled epileptic network with time delay

Yulin Guan ,
Xue Zhang ^,

College of Science, Northeastern University, Shenyang, 110000, China

Received: 14 December 2021 Revised: 23 February 2022 Accepted: 02 March 2022 Published: 08 March 2022

Epilepsy is considered as a brain network disease. Epileptic computational models are developed to simulate the electrophysiological process of seizure. Some studies have shown that the epileptic network based on those models can be used to predict the surgical outcome of patients with drug-resistant epilepsy. Most studies focused on the causal relationship between electrophysiological signals of different brain regions and its impact on seizure onset, and there is no knowledge about how time delay of electrophysiological signal transmitted between those regions related to seizure onset. In this study, we proposed an epileptic model with time delay between network nodes, and analyzed whether the time delay between nodes of epileptic network can cause seizure like event. Our results showed that the time delay between nodes may drive the network from normal state to seizure-like event through Hopf bifurcation. The time delay between nodes of epileptic computational network alone may induce seizure-like event. Our analysis suggested that the time delay of electrophysiological signals transmitted between different regions may be an important factor for seizure happening, which provide a deeper understanding of the epilepsy, and a potential new path for epilepsy treatment.
- epilepsy,
- stability,
- seizure-like event,
- Hopf bifurcation,
- time delay
Citation: Yulin Guan, Xue Zhang. Dynamics of a coupled epileptic network with time delay[J]. Mathematical Modelling and Control, 2022, 2(1): 13-23. doi: 10.3934/mmc.2022003

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Abstract

Epilepsy is considered as a brain network disease. Epileptic computational models are developed to simulate the electrophysiological process of seizure. Some studies have shown that the epileptic network based on those models can be used to predict the surgical outcome of patients with drug-resistant epilepsy. Most studies focused on the causal relationship between electrophysiological signals of different brain regions and its impact on seizure onset, and there is no knowledge about how time delay of electrophysiological signal transmitted between those regions related to seizure onset. In this study, we proposed an epileptic model with time delay between network nodes, and analyzed whether the time delay between nodes of epileptic network can cause seizure like event. Our results showed that the time delay between nodes may drive the network from normal state to seizure-like event through Hopf bifurcation. The time delay between nodes of epileptic computational network alone may induce seizure-like event. Our analysis suggested that the time delay of electrophysiological signals transmitted between different regions may be an important factor for seizure happening, which provide a deeper understanding of the epilepsy, and a potential new path for epilepsy treatment.

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