Automated derivation of mean field models from spiking neural networks for the simulation of brain dynamics

Abstract

A mean field model (MFM) is a mesoscopic description of neuronal population dynamics that can reduce the complexity of neural microcircuits into equations preserving key functional properties. The generation of a MFM is a complex mathematical process that starts with the incorporation of single neuron input/output relationships and local connectivity. Once neuron electroresponsiveness and synaptic properties are defined, in principle, the process can be automatized. Here we develop a tool for automatic MFM derivation from biophysically grounded spiking networks (Auto-MFM) by performing micro-to-mesoscale parameter remapping, estimating input/output relationships specific for different neuronal populations (i.e., transfer functions), and optimizing transfer function parameters. Auto-MFM was tested using a spiking cerebellar circuit as a generative model. The cerebellar MFM derived with Auto-MFM accurately reproduced cerebellar population dynamics of the corresponding spiking network, matching mean and time-varying firing rates across a wide range of stimulation patterns. Auto-MFM allowed us to model and explore physiological and pathological circuit variants; indeed, it was used to map ataxia-related structural connectivity alterations of the cerebellar network, in which Purkinje cells with simplified dendritic structure altered the cerebellar connectivity. Furthermore, Auto-MFM was used to create a library of cerebellar MFMs by sweeping the level of the excitatory conductance at mossy fiber - granule cell synapse, which is altered in several neuropathologies. Auto-MFM is thus proving a flexible and powerful tool to generate region-specific MFMs of healthy and pathological brain networks to be embedded in brain digital models.