Akademik Veri Yönetim Sistemi
7th International Conference on Mathematics “An Istanbul Meeting for World Mathematicians”, İstanbul, Türkiye, 11 - 13 Temmuz 2023, ss.135-143
Here we study the application of our recently invented statistical model of a small neural population (Borisenok, 2022) to control and suppress epileptiform behavior. The model describes the neural population as a set of three coupled ordinary differential equations describing the rates of the low-synchronized, highly-synchronized, and hyper-synchronized neurons. The corresponding control stimuli modeling electrical stimulating pulses or, alternatively, optogenetic stimulation, are added to the RHS of our master equations to perform the feedback algorithm for stabilization or tracking the hyper-synchronized epileptiform phase in the population. The control goal corresponds to the full suppression of such a phase. The control algorithm works in completely autonomic mode and does not demand any external observer. The practical realization of our proposed approach opens a gate for a new type of microscopic device: being implanted into the brain they are capable to make efficient control over potential seizures even without active monitoring from outside.
Keywords: Small neuron populations, neural excitations, master equation, hypersynchronization, epileptiform dynamics, feedback control.