Mean-field approximation of network of biophysical neurons driven by conductance-based ion exchange

ABSTRACT

Numerous network and whole brain modeling approaches make use of mean-field models. Their relative simplicity allows studying network dynamics at a large scale. They correspond to lumped descriptions of neuronal assemblies connected via synapses. mean-field models do not consider the ionic composition of the extracellular space, which can change in physiological and pathological conditions, with strong effects on neuron activity. Here we derive a mean-field model of a population of Hodgkin–Huxley type neurons, which links the neuronal intra- and extra-cellular ion concentrations to the mean membrane potential and the mean synaptic input in terms of the synaptic conductance. The model can generate various physiological brain activities including multi-stability at resting states, as well as pathological spiking and bursting behaviors, and depolarization block. The results from the analytical solution of the mean-field model agree with the mean behavior of numerical simulations of large-scale networks of neurons. The mean-field model is analytically exact for non-autonomous ion concentration variables and provides a mean-field approximation in the thermodynamic limit, for locally homogeneous mesoscopic networks of biophysical neurons driven by an ion-exchange mechanism. These results may provide the missing link between high-level neural mass approaches which are used in the brain network modeling and physiological parameters that drive the neuronal dynamics.