Action potential dynamics on heterogenous neural networks: from kinetic to macroscopic equations

TL;DR

This paper develops a kinetic and macroscopic model for action potential dynamics in heterogeneous neural networks, incorporating neuron connection variability and brain structure, and analyzes how heterogeneity affects potential propagation and synchronization.

Contribution

It introduces a coupled kinetic-macroscopic framework that accounts for heterogeneity in neural connections and brain topology, advancing understanding of neural dynamics.

Findings

Heterogeneity influences membrane potential propagation.

Synchronization depends on network topology.

Equilibria are characterized in both kinetic and macroscopic models.

Abstract

In the context of multi-agent systems of binary interacting particles, a kinetic model for action potential dynamics on a neural network is proposed, accounting for heterogeneity in the neuron-to-neuron connections, as well as in the brain structure. Two levels of description are coupled: in a single area, pairwise neuron interactions for the exchange of membrane potential are statistically described; among different areas, a graph description of the brain network topology is included. Equilibria of the kinetic and macroscopic settings are determined and numerical simulations of the system dynamics are performed with the aim of studying the influence of the network heterogeneities on the membrane potential propagation and synchronization.