An inverse procedure is proposed and tested which aims at recovering the a priori unknown functional and structural information from global signals of living brains activity. To this end we consider a Leaky-Integrate and Fire (LIF) model with short term plasticity neurons, coupled via a directed network. Neurons are assigned a specific current value, which is heterogenous across the sample, and sets the firing regime in which the neuron is operating in. The aim of the method is to recover the distribution of incoming network degrees, as well as the distribution of the assigned currents, from global field measurements. The proposed approach to the inverse problem implements the reductionist Heterogenous Mean-Field approximation. This amounts in turn to organizing the neurons in different classes, depending on their associated degree and current. When tested again synthetic data, the method returns accurate estimates of the sought distributions, while managing to reproduce and interpolate almost exactly the time series of the supplied global field. Finally, we also applied the proposed technique to longitudinal wide-field fluorescence microscopy data of cortical functionality in groups of awake Thy1-GCaMP6f mice. Mice are induced a photothrombotic stroke in the primary motor cortex and their recovery monitored in time. An all-to-all LIF model which accommodates for currents heterogeneity allows to adequately explain the recorded patterns of activation. Altered distributions in neuron excitability are in particular detected, compatible with the phenomenon of hyperexcitability in the penumbra region after stroke.
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