A neuronal population model based on cellular automata to simulate the electrical waves of the brain
Ali Khaleghi, Mohammad Reza Mohammadi, Kian Shahi, Ali Motie Nasrabadi
Abstract
Neural oscillations as synchronized activity of large numbers of neurons in the neural ensembles have always been a hot topic of research for experimental and theoretical studies because of their high importance in human behaviors and functions. Since there is not yet a comprehensive mathematical model for simulating brainwaves, we proposed a cellular automaton (CA) model of a neuronal population by considering the different states of an action potential at the cellular level and simple connectivity patterns . Some important characteristics of a neural network are included in the model, such as different states of activation of a neuron, and excitatory and inhibitory synapses. Our computational model can display different dynamics from fixed-point and limit-cycle to chaotic behaviors similar to different dynamics of a real neuronal population in the brain. Qualitative and quantitative comparisons of the real electroencephalogram data and the CA simulations in the linear and nonlinear domains demonstrated the efficiency of our CA network to simulate the electrical brain activity. Time series from the proposed model display a high-dimensional stochastic behavior that corresponds to the behavior of a healthy brain. Therefore, this model can be used to study biological neuronal populations and provide more insight into their different mechanisms.