Modeling and simulation of a network of neurons regarding Glucose Transporter Deficiency induced epileptic seizures

Ariel Leslie; Jianzhong Su; Ariel Leslie; Jianzhong Su

doi:10.3934/era.2022092

Electronic Research Archive

2022, Volume 30, Issue 5: 1813-1835. doi: 10.3934/era.2022092

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Modeling and simulation of a network of neurons regarding Glucose Transporter Deficiency induced epileptic seizures

Ariel Leslie ,
Jianzhong Su ^,

Department of Mathematics, University of Texas at Arlington, 411 S. Nedderman Dr, Arlington, TX 76019, USA

Received: 06 October 2021 Revised: 29 December 2021 Accepted: 06 January 2022 Published: 30 March 2022

Epilepsy is a complex phenomena of a system of highly intensive and synchronized neurons simultaneously firing which can be traced to spatial and temporal patterns. Seizures are a well known physical feature for all types of epileptic disorders. The rhythms, patterns, and oscillatory dynamics explain the mechanistic nature of neurons especially in absence seizures. Previous models such as Wilson-Cowan (1973), introduced brain models showing the dynamics of a network of neurons consisting of excitatory and inhibitory neurons. Taylor et al. (2014) then adapted the Wilson-Cowan model to epileptic seizures using a thalamo-cortical based theory. Fan et al. (2018) projects that thalamic reticulus nuclei control spike wave discharges specifically in absence seizures. We identify brain activity patterns specific to Glucose (G1D) Transport Deficiency Epilepsy in a network model based on electroencephalogram device (EEG) data. Additionally, we study the EEG patterns to identify the plausible mechanism that causes G1D epileptic behavior. Our coupled thalamo-cortical model goes beyond a connection in a logical unidirectional pattern shown by Fan or in a bidirectional small world pattern. Our model is a network based on paired correlation of EEG signals more analogous to realistic seizure activity. Using our model, we are able to study stability analysis for equilibrium and periodic behavior. We also identify parameter values which cause synchronized activity or more stable activity. Lastly, we identify a synchronization index and sensitivity analysis regarding parameters that directly affect Spike Wave Discharges and other spiking behavior. We will show how our 32-unit data-driven network model reflects G1D seizure dynamics and discuss the limitations of the model.
- epilepsy,
- excitatory,
- neurons,
- functional connectives,
- mathematical modeling
Citation: Ariel Leslie, Jianzhong Su. Modeling and simulation of a network of neurons regarding Glucose Transporter Deficiency induced epileptic seizures[J]. Electronic Research Archive, 2022, 30(5): 1813-1835. doi: 10.3934/era.2022092

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Abstract

Epilepsy is a complex phenomena of a system of highly intensive and synchronized neurons simultaneously firing which can be traced to spatial and temporal patterns. Seizures are a well known physical feature for all types of epileptic disorders. The rhythms, patterns, and oscillatory dynamics explain the mechanistic nature of neurons especially in absence seizures. Previous models such as Wilson-Cowan (1973), introduced brain models showing the dynamics of a network of neurons consisting of excitatory and inhibitory neurons. Taylor et al. (2014) then adapted the Wilson-Cowan model to epileptic seizures using a thalamo-cortical based theory. Fan et al. (2018) projects that thalamic reticulus nuclei control spike wave discharges specifically in absence seizures. We identify brain activity patterns specific to Glucose (G1D) Transport Deficiency Epilepsy in a network model based on electroencephalogram device (EEG) data. Additionally, we study the EEG patterns to identify the plausible mechanism that causes G1D epileptic behavior. Our coupled thalamo-cortical model goes beyond a connection in a logical unidirectional pattern shown by Fan or in a bidirectional small world pattern. Our model is a network based on paired correlation of EEG signals more analogous to realistic seizure activity. Using our model, we are able to study stability analysis for equilibrium and periodic behavior. We also identify parameter values which cause synchronized activity or more stable activity. Lastly, we identify a synchronization index and sensitivity analysis regarding parameters that directly affect Spike Wave Discharges and other spiking behavior. We will show how our 32-unit data-driven network model reflects G1D seizure dynamics and discuss the limitations of the model.

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