  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.
