Modeling neuronal avalanches and long-range temporal correlations at the emergence of collective oscillations: continuously varying exponents mimic M/EEG results

We revisit the CROS (CRitical OScillations) model which was recently proposed as an attempt to reproduce both scale-invariant neuronal avalanches and long-range temporal correlations. With excitatory and inhibitory stochastic neurons locally connected in a two-dimensional disordered network, the model exhibits a transition where alpha-band oscillations emerge. Precisely at the transition, the fluctuations of the network activity have nontrivial detrended fluctuation analysis (DFA) exponents, and avalanches (defined as supra-threshold activity) have power law distributions of size and duration. We show that, differently from previous results, the exponents governing the distributions of avalanche size and duration are not necessarily those of the mean-field directed percolation universality class (3/2 and 2, respectively). Instead, in a narrow region of parameter space, avalanche exponents obtained via a maximum-likelihood estimator vary continuously and follow a linear relation, in good agreement with results obtained from M/EEG data. In that region, moreover, the values of avalanche and DFA exponents display a spread with positive correlations, reproducing human MEG results. Author summary Since the first experimental observation of scale-invariant neuronal avalanches, the idea that the brain could be operating near a phase transition has received much attention. But if the brain is critical, what is the phase transition? Experimentally, the sizes and durations of local field potential (LFP) avalanches were power-law distributed with exponents 3/2 and 2. Theoretically, these are the exponents of a critical branching process, a coincidence which has inspired many models with a common feature: a phase transition from a silent (absorbing) to an active phase. These models, however, struggle with another experimental result: brain activity can also exhibit long-range temporal correlations (LRTCs, another fingerprint of a critical system). An attempt to model both phenomena was put forward via the CROS (CRitical OScillations) model, in which neuronal avalanches and LRTCs were observed at a transition where alpha-band oscillations emerge. We show that the avalanche exponents of the CROS model do not necessarily agree with those of a critical branching process, but can vary near the transition region, just like the exponents governing LRTCs. Moreover, the spread of exponents observed in the model is in good agreement with experimental results from human MEG data.