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 .
We study analytically a stochastic Greenberg-Hastings cellular automaton widely used to describe brain dynamics . 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 . 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.
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