Criticality and network structure drive emergent oscillations in a stochastic whole-brain model

Abstract

Understanding the relation between the structure of brain networks and its functions is a fundamental open question. Simple models of neural activity based on real anatomical networks have proven effective in describing features of whole-brain spontaneous activity when tuned at their critical point. In this work, we show that indeed structural networks are a crucial ingredient in the emergence of synchronized oscillations in a whole-brain stochastic model at criticality. We study such model in the mean-field limit, providing an analytical understanding of the associated first-order phase transition, arising from the presence of a bistable region in the parameters space. Then, we derive the power spectrum in the linear noise approximation and we show that, in the mean-field limit, no global oscillations emerge. Finally, by adding back an underlying brain network structure with homeostatic normalization, we numerically show how the bi-stability region is disrupted and concomitantly a synchronized phase with maximal dynamic range is observed. Hence, both the structure of brain networks and criticality are fundamental in driving the collective coordinated responses and maximal sensitivity of whole-brain stochastic models.