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.

In this paper we study a harmonic function method for dipolar source reconstruction, and implemented the numerical simulations. We propose a new error estimate and provide a rigorous proof of the estimate. Then, we validate our method in computer-simulated data and study its numerical stability in different noise levels. It is shown that the harmonic function method can be used to quickly and accurately locate the active regions in EEG source reconstruction.