Theoretical Implementation of Stochastic Epileptic Oscillator Using a Tripartite Synaptic Neuronal Network Model

Epilepsy is a neurological disorder, always coming with abnormal brain seizures activity of complex randomness and unpredictability, which have brought obstacles for the improvement of epileptic treatment. However, the mechanism of the epileptic randomness has not been unfolded. Inspired by the recent experimental finding that astrocyte G protein coupled receptor involves in the stochastic epileptic seizures, we proposed a cortical tripartite synaptic network of neurons and astrocytes with the G protein noise, which is capable to explain the stochastic process of epileptic seizures in the involvement of the G protein noise, a Gaussian distributed noise which explains the heterogeneity of the G protein types and the nonuniform environmental effect. Based on this model, we have discussed the dynamical stochastic induction process of the epileptic seizures statistically by performing totally 60 simulation trials. Our simulation results showed that the increase of the noise intensity could induce the epileptic seizures state coexisting with the increase of frequency and in vitro epileptic depolarization blocks. Meanwhile, there has been a bistable state of the noise intensity for the neurons switching among the regular sparse spiking and the epileptic seizure state. This random presence of epileptic seizure state would be absent when the noise intensity continues to increase, then the neurons start to stay in epileptic seizures steadily, but with an increase of the epileptic depolarization block duration. The simulation results also shed light on the fact that the calcium signals in astrocytes have played significant roles in the pattern formation of both the random and steady epileptic seizure state. Our results on the stochastic process of the epileptic seizures could provide potential theory for improvement for the epileptic prediction and treatment.