Criticality in RSNs

On the multiple aspects of criticality

Ton, Robert; Deco, Gustavo; Daffertshofer, Andreas


Brain activity at rest displays well-structured spatio-temporal patterns. These patterns have been shown to have clinical and functional relevance[1] and are believed to provide insight into the general architecture of the human brain.

Several studies using M/EEG suggest that the brain operates at a critical state. Hallmarks of critical systems are scale-free (spectral) distribution functions that typically obey power laws [2] and may stem from multi-scale entropies [3]. In simulations studies, criticality is also an important notion. There that notion refers to a critical value of the control parameter leading to isolated bifurcations in model behavior. A very consistent finding is that correlations between model and data are maximal at the cusp of such bifurcations [4,5]. In fact, that led to the idea that the brain operates close to critical states. Network dynamics close to such a parameter regime do show critical dynamics [6] and attractor multi-stability [7] – but is criticality therefore mandatory for the brain to function optimally? Being so close to the critical parameter might come with high risk for catastrophic events. Does this put this ‘optimality’ at stake?.

Using a phase reduction approach to a network of oscillating neural masses we observed a (time-delayed) balance between attracting and repulsive force. We argue that this balance causes network behavior to be insensitive to coupling strength and only moderately (and continuously) dependent on delay. The network dynamics suggests that our model is in a permanently critical state, as evidenced by a broad – or even flat – potential of the drift coefficient in the corresponding Fokker-Planck equation describing the evolution of the probability density of the degree of synchrony across the network.

We conclude that critical behavior of brain activity does not necessarily imply that the brain operates at the cusp of isolated bifurcations. Our model suggests that the experimentally observed criticality is the result of a self-organization rendering parameter specifics less crucial for the brain’s macroscopic behavior.


References
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