Self-organized criticality and structural dynamics in evolving neuronal networks: A modified sandpile model

Abstract

We investigate a modified sandpile model on a directed network with evolving weighted links as a model for the dynamics and structural evolution of the brain. The main goal is to derive the distribution of neuronal avalanches as well as the distribution of connection weights between voxels. In this non-Abelian sandpile model, the node dynamics represent the evolution of voltages across different voxels and follow the Bak-Tang-Wiesenfeld (BTW) threshold spiking rules. The directed link weights, representing connections among the voxels, evolve according to Hebb’s rule and spike-timing-dependent plasticity (STDP). Additionally, mechanisms for pruning and adding new connections are introduced to the model. Our simulations reveal that the size distribution of spike avalanches follows a power-law distribution with a mean-field exponent of $3/2$. Moreover, the steady-state link weight distribution also exhibits power-law scaling with an exponent of 1. We discuss the parallels between these findings and the distributions of neuronal avalanches and connectivity observed in some results from the Human Connectome Project, emphasizing the significance of structural changes in the brain’s critical dynamics.