Understanding the relation between the structure of brain networks and their functions is a fundamental open question. Simple models of neural activity have proven to be effective in describing features of whole-brain spontaneous activity when tuned at their critical point. Here, we show how the interplay between criticality and structural networks is crucial in driving collective behaviors such as global oscillations [1].

We study analytically a stochastic Greenberg-Hastings cellular automaton widely used to describe brain dynamics [2]. For the first time, we solve its mean-field continuous-time version, showing the presence of a bistable region between a high-activity and a low-activity phase, as well as the lack of no collective oscillations.

We then study numerically the model on an empirical connectome between mesoscopic brain regions [3]. We find that the underlying network structure changes drastically the phenomenology of the model, smoothing the bistability into a continuous transition. Crucially, we find that the system now displays a large peak in the power-spectrum, signaling the emergence of collective oscillations in the system. The peak of the power-spectrum is maximal where both the variance of the average activity and the autocorrelation time peak, suggesting that a critical-like transition might be present. By comparing our results with ad-hoc null models of the connectome, we find that both sparsity and heterogeneous weights are fundamental ingredients in promoting the emergence of this continuous transition. Yet, higher-order structures are likely needed to fully explain the emerging dynamics appearing in the connectome – shedding light on the role of the underlying network structure in the emergence of collective patterns in the brain.

[1] G. Barzon, G. Nicoletti, B. Mariani, M. Formentin, and S. Suweis, “Criticality and network structure drive emergent oscillations in a stochastic whole-brain model”, J. Phys. Complex. 3 025010 (2022)
[2] A. Haimovici, E. Tagliazucchi, P. Balenzuela, and D. R. Chialvo, “Brain organization into resting state networks emerges at criticality on a model of the human connectome”, Phys Rev Lett 110 178101 (2013)
[3] P. Hagmann, L. Cammoun, X. Gigandet, R. Meuli, C. J. Honey, V. J. Wedeen, and O. Sporns, “Mapping the structural core of human cerebral cortex,” PLoS Biol 6(7) (2008)

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