Modeling propagation velocity of activity fronts in two-dimensional neuronal networks

Abstract

This study investigates the propagation of neuronal activity fronts inspired by experiments in one- and two-dimensional neuronal cultures, and by using theoretical and numerical approaches. We derive analytical expressions for the propagation velocity for random geometric networks and exponentially distributed connectivity networks, focusing on the inter-neuronal dynamics and simplifying the intra-neuronal processes. Theoretical results are validated against numerical simulations of such networks using the Izhikevich model of spiking neurons, highlighting the impact of network structure on pulse dynamics. The measured velocities in both 1D and 2D models are constant across space, which is consistent with experimental findings. However, there is a velocityconnectivity dependency that is expected. Additionally, network noise and neuron variability also play a crucial role in initiating or shaping front velocity. Our models and simulations provide insights into how network structure influences the key macroscopic observable that is activity propagation.