The human brain spontaneously generates neural oscillations with a large variability in frequency, amplitude, duration, and recurrence. Little, however, is known about the long-term spatiotemporal structure of the complex patterns of ongoing activity. A central unresolved issue is whether fluctuations in oscillatory activity reflect a memory of the dynamics of the system for more than a few seconds.We investigated the temporal correlations of network oscillations in the normal human brain at time scales ranging from a few seconds to several minutes. Ongoing activity during eyes-open and eyes-closed conditions was recorded with simultaneous magnetoencephalography and electroencephalography. Here we show that amplitude fluctuations of 10 and 20 Hz oscillations are correlated over thousands of oscillation cycles. Our analyses also indicated that these amplitude fluctuations obey power-law scaling behavior. The scaling exponents were highly invariant across subjects. We propose that the large variability, the long-range correlations, and the power-law scaling behavior of spontaneous oscillations find a unifying explanation within the theory of self-organized criticality, which offers a general mechanism for the emergence of correlations and complex dynamics in stochastic multiunit systems. The demonstrated scaling laws pose novel quantitative constraints on computational models of network oscillations. We argue that critical-state dynamics of spontaneous oscillations may lend neural networks capable of quick reorganization during processing demands. Key words: spontaneous oscillations; large-scale dynamics; temporal properties; correlations; scaling behavior; selforganized criticality; complexityOscillations at various frequencies are a prominent feature of the spontaneous electroencephalogram (EEG) (Berger, 1929;Connors and Amitai, 1997) and are believed to reflect functional states of the brain (Llinás, 1988;Steriade et al., 1993;Arieli et al., 1996;Herculano-Houzel et al., 1999;Tsodyks et al., 1999). These oscillations arise from correlated activity of a large number of neurons whose interactions are generally nonlinear (Steriade et al., 1990(Steriade et al., , 1993Lopez da Silva, 1991). The intrinsic neural properties and intricate patterns of connectivity add further complexity to the behavior of neural systems (Llinás, 1988;Connors and Amitai, 1997;Destexhe et al., 1998). The mechanisms and dynamics of network oscillations have been widely studied with electrophysiological recordings (Destexhe et al., 1998(Destexhe et al., , 1999, as well as with computational models (Destexhe et al., 1998;Stam et al., 1999). Neural oscillations in vivo exhibit large variability in both amplitude and frequency. The dynamic nature of these fluctuations, however, has remained unclear. Particularly for the human electroencephalogram, 8 -13 Hz oscillations have attracted widespread interest in this context. However, the complexity of the EEG has rendered it impossible to reliably distinguish the waxing and waning of oscillations o...

Scale-free fluctuations are ubiquitous in behavioral performance and neuronal activity. In time scales from seconds to hundreds of seconds, psychophysical dynamics and the amplitude fluctuations of neuronal oscillations are governed by power-law-form longrange temporal correlations (LRTCs). In millisecond time scales, neuronal activity comprises cascade-like neuronal avalanches that exhibit power-law size and lifetime distributions. However, it remains unknown whether these neuronal scaling laws are correlated with those characterizing behavioral performance or whether neuronal LRTCs and avalanches are related. Here, we show that the neuronal scaling laws are strongly correlated both with each other and with behavioral scaling laws. We used source reconstructed magneto-and electroencephalographic recordings to characterize the dynamics of ongoing cortical activity. We found robust power-law scaling in neuronal LRTCs and avalanches in resting-state data and during the performance of audiovisual threshold stimulus detection tasks. The LRTC scaling exponents of the behavioral performance fluctuations were correlated with those of concurrent neuronal avalanches and LRTCs in anatomically identified brain systems. The behavioral exponents also were correlated with neuronal scaling laws derived from a resting-state condition and with a similar anatomical topography. Finally, despite the difference in time scales, the scaling exponents of neuronal LRTCs and avalanches were strongly correlated during both rest and task performance. Thus, long and short time-scale neuronal dynamics are related and functionally significant at the behavioral level. These data suggest that the temporal structures of human cognitive fluctuations and behavioral variability stem from the scaling laws of individual and intrinsic brain dynamics.spontaneous activity | threshold detection | criticality H uman cognitive and behavioral performance is highly variable and exhibits slow fluctuations that are salient in continuous performance tasks (CPTs) (1). Psychophysical time series have been known since the early 1950s to be nonrandomly clustered (2), and later studies have shown that hit-rate and/or reaction-time fluctuations in CPT data are fractal and power-law autocorrelated across hundreds of seconds (3-9). The biological origins and relevance of these dynamic, however, remain unclear (10, 11).Similar to those in behavioral performance, the fluctuations of collective neuronal activity at many levels of the nervous system are scale-free and governed by power-law scaling laws. On short time scales (10 −3 −10 −1 s), negative deflections in local field potentials form spatiotemporal cascades of activity, "neuronal avalanches" (32-34), the size and lifetime distributions of which are power laws akin to those of a critical branching process (33). Neuronal avalanches characterize spontaneous neuronal network activity in organotypic cultures (32), brain slices in vitro (35), and monkey (34) and human cortex (36) in vivo. In monkey cortex, the avalanche...

Recent years of research have shown that the complex temporal structure of ongoing oscillations is scale-free and characterized by long-range temporal correlations. Detrended fluctuation analysis (DFA) has proven particularly useful, revealing that genetic variation, normal development, or disease can lead to differences in the scale-free amplitude modulation of oscillations. Furthermore, amplitude dynamics is remarkably independent of the time-averaged oscillation power, indicating that the DFA provides unique insights into the functional organization of neuronal systems. To facilitate understanding and encourage wider use of scaling analysis of neuronal oscillations, we provide a pedagogical explanation of the DFA algorithm and its underlying theory. Practical advice on applying DFA to oscillations is supported by MATLAB scripts from the Neurophysiological Biomarker Toolbox (NBT) and links to the NBT tutorial website . Finally, we provide a brief overview of insights derived from the application of DFA to ongoing oscillations in health and disease, and discuss the putative relevance of criticality for understanding the mechanism underlying scale-free modulation of oscillations.

Criticality has gained widespread interest in neuroscience as an attractive framework for understanding the character and functional implications of variability in brain activity. The metastability of critical systems maximizes their dynamic range, storage capacity, and computational power. Power-law scaling-a hallmark of criticality-has been observed on different levels, e.g., in the distribution of neuronal avalanches in vitro and in vivo, but also in the decay of temporal correlations in behavioral performance and ongoing oscillations in humans. An unresolved issue is whether power-law scaling on different organizational levels in the brain-and possibly in other hierarchically organized systems-can be related. Here, we show that critical-state dynamics of avalanches and oscillations jointly emerge in a neuronal network model when excitation and inhibition is balanced. The oscillatory activity of the model was qualitatively similar to what is typically observed in recordings of human resting-state MEG. We propose that homeostatic plasticity mechanisms tune this balance in healthy brain networks, and that it is essential for critical behavior on multiple levels of neuronal organization with ensuing functional benefits. Based on our network model, we introduce a concept of multi-level criticality in which power-law scaling can emerge on multiple time scales in oscillating networks. IntroductionSynchronous brain activity is thought to be crucial for neural integration, cognition, and behavior (Fries, 2005;Buzsáki, 2006). The multi-scale properties of synchronous cell assemblies, however, remain poorly understood. While probing activity at different scales, several investigators have begun to consider self-organized criticality (SOC) as an overriding neuronal organizing principle (Linkenkaer-Hansen et al., 2001;Beggs and Plenz, 2003;Haldeman and Beggs, 2005;Kinouchi and Copelli, 2006;Levina et al., 2007;Plenz and Thiagarajan, 2007;Gireesh and Plenz, 2008;Poil et al., 2008;Petermann et al., 2009;Chialvo, 2010;He et al., 2010;Millman et al., 2010;Rubinov et al., 2011). The SOC theory holds that slowly driven, interaction-dominated threshold systems will be attracted to a critical point, with the system balanced between order and disorder (Bak et al., 1987;Bak, 1996;Jensen, 1998).This critical state is characterized by scale-free probability distributions. In cortical slices, neuronal avalanches of local field potential activity are governed by a power-law (i.e., scale-free) distribution of event sizes with an exponent of Ϫ1.5, as expected for a critical branching process (Beggs and Plenz, 2003). Similar results have also been found in vivo ). This finding inspired the development of computational models that were capable of producing power-law-distributed neuronal avalanches through a process of self-organization, thereby providing theoretical support for SOC in neuronal systems (Levina et al., 2007;Millman et al., 2010;Rubinov et al., 2011). Models have shown that networks in a critical state display differing resp...

The presence of various ongoing oscillations in the brain is correlated with behavioral states such as restful wakefulness or drowsiness. However, even when subjects aim to maintain a high level of vigilance, ongoing oscillations exhibit large amplitude variability on time scales of hundreds of milliseconds to seconds, suggesting that the functional state of local cortical networks is continuously changing. How this volatility of ongoing oscillations influences the perception of sensory stimuli has remained essentially unknown.We investigated the relationship between prestimulus neuronal oscillations and the subjects' ability to consciously perceive and react to somatosensory stimuli near the threshold of detection. We show that, for prestimulus oscillations at ϳ10, 20, and 40 Hz detected over the sensorimotor cortex, intermediate amplitudes were associated with the highest probability of conscious detection and the shortest reaction times. In contrast, for 10 and 20 Hz prestimulus oscillations detected over the parietal region, the largest amplitudes were associated with the best performance.Our data indicate that the prestimulus oscillatory activity detected over sensorimotor and parietal cortices has a profound effect on the processing of weak stimuli. Furthermore, the results suggest that ongoing oscillations in sensory cortices may optimize the processing of sensory stimuli with the same mechanism as noise sources in intrinsic stochastic resonance.

Encoding and retention of information in memory are associated with a sustained increase in the amplitude of neuronal oscillations for up to several seconds. We reasoned that coordination of oscillatory activity over time might be important for memory and, therefore, that the amplitude modulation of oscillations may be abnormal in Alzheimer disease (AD). To test this hypothesis, we measured magnetoencephalography (MEG) during eyes-closed rest in 19 patients diagnosed with early-stage AD and 16 agematched control subjects and characterized the autocorrelation structure of ongoing oscillations using detrended fluctuation analysis and an analysis of the life-and waiting-time statistics of oscillation bursts. We found that Alzheimer's patients had a strongly reduced incidence of alpha-band oscillation bursts with long life-or waiting-times (< 1 s) over temporo-parietal regions and markedly weaker autocorrelations on long time scales (1-25 seconds). Interestingly, the life-and waiting-times of theta oscillations over medial prefrontal regions were greatly increased. Whereas both temporo-parietal alpha and medial prefrontal theta oscillations are associated with retrieval and retention of information, metabolic and structural deficits in early-stage AD are observed primarily in temporo-parietal areas, suggesting that the enhanced oscillations in medial prefrontal cortex reflect a compensatory mechanism. Together, our results suggest that amplitude modulation of neuronal oscillations is important for cognition and that indices of amplitude dynamics of oscillations may prove useful as neuroimaging biomarkers of early-stage AD.Alzheimer's disease ͉ magnetoencephalography ͉ neuronal oscillations ͉ resting-state brain activity ͉ temporal correlations P sychological and neuroimaging data suggest that the brain performs many important functions during rest, such as retrieval and manipulation of information in short-term memory, and problem-solving and planning (1, 2). These resting-state functions may represent an essential aspect of human selfawareness and are susceptible to impairment in brain-related disorders including depression, schizophrenia, and dementia (3).Neuroimaging has identified anatomical patterns of activity that are remarkably consistent across resting-state experiments, most notably in the precuneus, lateral parietal and medial prefrontal cortices (4, 5). The existence of such a ''resting-state network'' has been suggested to reflect a ''default mode'' of brain operation in the absence of goal-directed behavior (6). Coordination of anatomically distributed activity during rest has been studied extensively by computing correlations between neuronal signals from different brain areas (Fig. 1). This approach has revealed aberrant resting-state networks in Alzheimer disease (AD) (7-9) and other disorders (4, 10, 11).For cognitive processing, coordination of local brain activity over time may be just as important as the coordination of simultaneous activity in anatomically distinct brain regions and may be refl...

The cortical processing of consciously perceived and unperceived somatosensory stimuli is thought to be identical during the first 100 -120 ms after stimulus onset. Thereafter, the electrophysiological correlates of conscious perception have been shown to be reflected in the N1 component of the evoked response as well as in later (Ͼ200 ms) nonstimulus-locked ␥-band (28 -50 Hz) oscillatory activity. To evaluate more specifically the time course and correlation of neuronal oscillations with conscious perception, we recorded neuromagnetic responses to threshold-intensity somatosensory stimuli. We show here that cortical broadband activities phase locked to the subsequently perceived stimuli in somatosensory, frontal, and parietal regions as early as 30 -70 ms from stimulus onset, whereas the phase locking to the unperceived stimuli was weak and primarily restricted to somatosensory regions. Such stimulus locking also preceded the perceived stimuli, indicating that the phase of ongoing cortical activities biases subsequent perception. Furthermore, the data show that the stimulus locking was present in the -(4 -8 Hz), ␣-(8 -14 Hz), ␤-(14 -28 Hz), and ␥-(28 -40 Hz) frequency bands, of which the widespread ␣-band component was dominant for the consciously perceived stimuli but virtually unobservable for the unperceived stimuli. Our results show that the neural correlates of conscious perception are already found during the earliest stages of cortical processing from 30 to 150 ms after stimulus onset and suggest that ␣-frequency-band oscillations have a role in the neural mechanisms of sensory awareness.

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