Estimation of Synaptic Conductance in the Spiking Regime for the McKean Neuron Model

In this work, we aim at giving a first proof of concept to address the estimation of synaptic conductances when a neuron is spiking, a complex inverse non-linear problem which is an open challenge in neuroscience. Our approach is based on a simplified model of neuronal activity, namely a piecewise linear version of the FitzHugh-Nagumo model. This simplified model allows a precise knowledge of the non-linear f-I curve by using standard techniques of non-smooth dynamical systems. In the regular firing regime of the neuron model, we obtain an approximation of the period which, in addition, improves previous approximations given in the literature up-to-date. By knowing both this expression of the period and the current applied to the neuron, and then solving an inverse problem with a unique solution, we are able to estimate the steady synaptic conductance of the cell’s oscillatory activity. Moreover, the method gives also good estimations when the synaptic conductance varies slowly in time.