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

ABSTRACT

Numerous network and whole-brain modeling approaches use mean-field models, facilitating the study of dynamics due to their relative simplicity. They correspond to lumped descriptions of neuronal assemblies connected via synapses. Mean-field models do not usually consider the ionic composition of the extracellular space, which can change in physiological and pathological conditions, with strong effects on neuronal 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. Thus, the model provides a mean-field approximation, for locally homogeneous mesoscopic networks of biophysical neurons driven by an ion-exchange mechanism. The model can generate various physiological brain activities, including multi-stability during simulated healthy states, pathological spiking, 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 strongly synchronized neurons. The mean-field model exhibits emergent activity regimes qualitatively similar to those observed in weakly synchronized neuronal networks and experimentally observed in-vitro. This approach maintains a detailed biophysical level of description, such as the evolution of ionic concentrations while describing dynamics at the neural mass scale. Hence, these results may provide the missing link between high-level neural mass approaches, used in brain network modeling, and physiological parameters that drive the neuronal dynamics.