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

Abstract

ABSTRACTNumerous 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.Significance StatementIn this study, we applied mathematical formalism to estimate the mean-field behaviors of a large neuronal ensemble taking into account the ion-exchange between the intracellular and extracellular space. The model demonstrates different brain activities including resting state, spiking behavior, and seizure, as a function of the extracellular ion concentration. The relevant parameter regime for different brain activities is extracted mainly in terms of ion concentration and heterogeneity of individual neurons in the network. This neural mass model enables studying the influence of changes in extracellular ionic conditions on whole brain dynamics in health and disease. The effect of external stimulus current and conductance-based coupling of neural masses are also analyzed.