  An inverse procedure is developed and tested to recover functional and
structural information from global signals of brains activity. The method
assumes a leaky-integrate and fire model with excitatory and inhibitory
neurons, coupled via a directed network. Neurons are endowed with a
heterogenous current value, which sets their associated dynamical regime. By
making use of a heterogenous mean-field approximation, the method seeks to
reconstructing from global activity patterns the distribution of in-coming
degrees, for both excitatory and inhibitory neurons, as well as the
distribution of the assigned currents. The proposed inverse scheme is first
validated against synthetic data. Then, time-lapse acquisitions of a zebrafish
larva recorded with a two-photon light sheet microscope are used as an input to
the reconstruction algorithm. A power law distribution of the in-coming
connectivity of the excitatory neurons is found. Local degree distributions are
also computed by segmenting the whole brain in sub-regions traced from
annotated atlas.
