Theoretical foundations of studying criticality in the brain

Complex systems, when poised near a critical point of a phase transition between order and disorder, exhibit a dynamics comprising a scale-free mixture of order and disorder which is universal, i.e. system-independent (1-5). It allows systems at criticality to adapt swiftly to environmental changes (i.e., high susceptibility) as well as to flexibly process and store information. These unique properties prompted the conjecture that the brain might operate at criticality (1), a view supported by the recent description of neuronal avalanches in cortex in vitro (6-8), in anesthetized rats (9) and awake primates (10), and in neuronal models (11-16). Despite the attractiveness of this idea, its validity is hampered by the fact that its theoretical underpinning relies solely on the replication of sizes and durations of avalanches, which reflect only a portion of the rich dynamics found at criticality. Here we show experimentally five fundamental properties of avalanches consistent with critic …

The critical brain hypothesis receives increasing support from recent experimental results. It postulates that the brain is at a critical point between an ordered and a chaotic regime, sometimes referred to as the "edge of chaos." Another central observation of neuroscience is the principle of excitation-inhibition balance: Certain brain networks exhibit a remarkably constant ratio between excitation and inhibition. When this balance is perturbed, the network shifts away from the critical point, as may for example happen during epileptic seizures. However, it is as of yet unclear what mechanisms balance the neural dynamics towards this excitation-inhibition ratio that ensures critical brain dynamics. Here we introduce a simple yet biologically plausible toy model of a self-organized critical neural network with a self-organizing excitation to inhibition ratio. The model only requires a neuron to have local information of its own recent activity and changes connections between neurons a …

Much evidence seems to suggest the cortex operates near a critical point, yet a single set of exponents defining its universality class has not been found. In fact, when critical exponents are estimated from data, they widely differ across species, individuals of the same species, and even over time, or depending on stimulus. Interestingly, these exponents still approximately hold to a dynamical scaling relation. Here we show that the theory of quasicriticality, an organizing principle for brain dynamics, can account for this paradoxical situation. As external stimuli drive the cortex, quasicriticality predicts a departure from criticality along a Widom line with exponents that decrease in absolute value, while still holding approximately to a dynamical scaling relation. We use simulations and experimental data to confirm these predictions and describe new ones that could be tested soon.

The observation of apparent power laws in neuronal systems has led to the suggestion that the brain is at, or close to, a critical state and may be a self-organised critical system. Within the framework of self-organised criticality a separation of timescales is thought to be crucial for the observation of power-law dynamics and computational models are often constructed with this property. However, this is not necessarily a characteristic of physiological neural networks-external input does not only occur when the network is at rest/a steady state. In this paper we study a simple neuronal network model driven by a continuous external input (i.e. the model does not have an explicit separation of timescales from seeding the system only when in the quiescent state) and analytically tuned to operate in the region of a critical state (it reaches the critical regime exactly in the absence of input-the case studied in the companion paper to this article). The system displays avalanche dynami …

Such avalanches have been claimed to be generically scale-invariant – i.e. power-law distributed – with many exciting implications in Neuroscience. Recently, a self-organized model has been proposed by Levina, Herrmann and Geisel to justify such an empirical finding. Given that (i) neural dynamics is dissipative and (ii) there is a loading mechanism “charging” progressively the background synaptic strength, this model/dynamics is very similar in spirit to forest-fire and earthquake models, archetypical examples of non-conserving self-organization, which have been recently shown to lack true criticality. Here we show that cortical neural networks obeying (i) and (ii) are not generically critical; unless parameters are fine tuned, their dynamics is either sub- or super-critical, even if the pseudo-critical region is relatively broad.