A hybrid model for large neural network description

TL;DR

This paper introduces a hybrid modeling approach combining discrete and continuous models to efficiently describe neural population dynamics, validated on cerebellar microcircuits, capturing complex behaviors with reduced computational cost.

Contribution

The paper presents a novel hybrid model integrating conductance-based ODEs and PDEs for neural populations, enabling efficient large-scale neural simulations.

Findings

Successfully reconstructed cerebellar granular layer activity

Captured microcircuit synchronization and traveling waves

Achieved significant computational cost reduction

Abstract

The aim of the present paper is to efficiently describe the membrane potential dynamics of neural populations formed by species having a high density difference in specific brain areas. We propose a hybrid model whose main ingredients are a conductance-based model (ODE system) and its continuous counterpart (PDE system) obtained through a limit process in which the number of neurons confined in a bounded region of the brain is sent to infinity. Specifically, in the discrete model each cell of the low-density populations is individually described by a set of time-dependent variables, whereas in the continuum model the high-density populations are described as a whole by a small set of continuous variables depending on space and time. Communications among populations, which translate into interactions among the discrete and the continuous models, are the essence of the hybrid model we present here. Such an approach has been validated reconstructing the ensemble activity of the granular layer network of the Cerebellum, leading to a computational cost reduction. The hybrid model reproduced interesting dynamics such as local microcircuit synchronization, travelling waves, center-surround and time-windowing.