Brain activity modeling in general anesthesia: enhancing local mean-field models using a slow adaptive firing rate.

In this paper, an enhanced local mean-field model that is suitable for simulating the electroencephalogram (EEG) in different depths of anesthesia is presented. The main building elements of the model (e.g., excitatory and inhibitory populations) are taken from Steyn-Ross [M. L. Steyn-Ross, Phys. Rev. E 64, 011917 (2001), D. A. Steyn-Ross, Phys. Rev. E 64, 011918 (2001)] and Bojak and Liley [I. Bojak and D. T. Liley, Phys. Rev. E 71, 041902 (2005)] mean-field models and a new slow ionic mechanism is included in the main model. Generally, in mean-field models, some sigmoid-shape functions determine firing rates of neural populations according to their mean membrane potentials. In the enhanced model, the sigmoid function corresponding to excitatory population is redefined to be also a function of the slow ionic mechanism. This modification adapts the firing rate of neural populations to slow ionic activities of the brain. When an anesthetic drug is administered, the slow mechanism may induce neural cells to alternate between two levels of activity referred to as up and down states. Basically, the frequency of up-down switching is in the delta band (0-4 Hz) and this is the main reason behind high amplitude, low frequency fluctuations of EEG signals in anesthesia. Our analyses show that the enhanced model may have different working states driven by anesthetic drug concentration. The model is settled in the up state in the waking period, it may switch to up and down states in moderate anesthesia while in deep anesthesia it remains in the down state.