TABLE 3.

Results of studies on criticality in sleep.

References	Population	Cerebral activity measure	Criticality measure	Main findings
Freeman et al., 2006	1 epileptic human with intracranial electrodes on the right inferior temporal gyrus	iEEG	Neuronal avalanche	• Slow-wave sleep is accompanied by a loss of scale-free activity, thus deviating from criticality. • Increased synaptic input in the awake state seems to shift neocortex away from criticality Diminished input in slow wave sleep allows return toward criticality, but with some added risk of instability and seizures.
Ribeiro et al., 2010	14 rats with electrodes in V1, S1 and hippocampus	MEA/LFP	Neuronal avalanche	• SWS is associated with a deviation from a power-law distribution.
Dehghani et al., 2012	2 cats with electrodes in M1; 3 monkeys with electrodes in M1 and PMd; 2 humans with pharmaco-resistent epilepsy with electrodes in middle temporal gyrus	LFP	Neuronal avalanche	• There is an absence of power-law scaling of neuronal avalanches in all examined recordings, including SWS and REM sleep.
Allegrini et al., 2013	29 whole-night human recordings	hdEEG	Neuronal avalanche	• In NREM sleep, criticality breaks down and is restored during REM sleep.
Meisel et al., 2013	8 healthy adults during 40h of sustained wakefulness followed by sleep	EEG	Neuronal avalanche	• Sleep restriction creates a progressive distance from criticality toward states characterized by an imbalance toward excitation (supercritical). • Sleep shows to be restoring the critical state by recovering power-law characteristics.
Paradisi et al., 2013	29 whole-night recordings	EEG	DFA	• SWS is accompanied by a deviation of criticality using DFA.
Priesemann et al., 2013	5 adults with refractory partial epilepsy presurgical evaluation	LFP	Neuronal avalanche	• Neuronal avalanches differ depending on the vigilance states: SWS shows large avalanches, wakefulness shows intermediate avalanches, and REM sleep shows small avalanches. • Authors suggest that SWS is closest to the critical state.
Tagliazucchi et al., 2013	51 non-sleep deprived subjects	EEG/fMRI	Hurst exponent	• N2 and N3 show a decreased temporal complexity in specific brain regions using BOLD spontaneous fluctuations display.
Allegrini et al., 2015	29 whole-night human recordings	hdEEG	DFA	• While neuronal avalanches seem to be qualitatively unchanged in N2 and N3, a deviation from criticality is found using DFA. • The authors suggest that a new kind of self-organized criticality emerges in sleep, characterized by the absence of thermodynamical feedback of the order on the control parameter, making way for a more auto-organized system.
Meisel et al., 2017b	23 rats	LFP	ACF	• The long timescales found in wake and REM sleep are abolished during NREM sleep, which may explain the lack of responsiveness and loss of consciousness in this state.
Bocaccio et al., 2019	58 non-sleep deprived subjects	EEG/fMRI	Neuronal avalanche	• There is a significant effect of sleep stage on the scaling parameters of the cluster size power-law distributions. Post hoc statistical tests show that differences are maximal between wakefulness and N2 sleep.
Wang et al., 2019	20 rats: 10 controls and 10 with lesions of the parafacial zone (PZ)	PSG	DFA	• Bursts in θ and δ rhythms exhibit a complex temporal organization, with long-range power-law correlations and a robust duality of power law and exponential-like duration distributions, typical features of systems self-organizing at criticality.
Lombardi et al., 2020	10 rats	EEG	DFA	• The presence of transient bursts in θ and δ cortical rhythms is found during the sleep-wake cycle. These bursts exhibit a complex temporal organization typical of non-equilibrium systems self-organizing at criticality. • An anti-correlation between θ and δ bursts is found throughout the sleep-wake cycle, a further sign of critical behavior.

ACF, autocorrelation function; DFA, detrended fluctuation analysis; EEG, electroencephalography; fMRI, functional magnetic resonance imaging; hdEEG, high-density electroencephalography; iEEG, intracranial electroencephalography; LFP, local field potential; MEA, multielectrode arrays; M1, primary motor area; OSA, obstructive sleep apnea; PMd, dorsal premotor cortex; S1: primary somatosensory cortex; V1, primary visual area.