Abstract
The human brain spontaneously generates neural oscillations with a large variability in frequency, amplitude, duration, and recurrence. Little, however, is known about the longterm 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 eyesopen and eyesclosed 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 powerlaw scaling behavior. The scaling exponents were highly invariant across subjects. We propose that the large variability, the longrange correlations, and the powerlaw scaling behavior of spontaneous oscillations find a unifying explanation within the theory of selforganized 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 criticalstate dynamics of spontaneous oscillations may lend neural networks capable of quick reorganization during processing demands.
 spontaneous oscillations
 largescale dynamics
 temporal properties
 correlations
 scaling behavior
 selforganized criticality
 complexity
Oscillations 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; HerculanoHouzel 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, 1993; Lopez 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, 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 over epochs longer than 2–15 sec from that of filtered white noise (Paluš, 1996; Cerf et al., 1997; Stam et al., 1999). This suggests that the underlying neural populations are unlikely to obey entirely lowdimensional dynamics.
Recent studies have demonstrated that a large variety of complex processes, including forest fires (Malamud et al., 1998), earthquakes (Bak, 1997), financial markets (Mantegna and Stanley, 1995; Lux and Marchesi, 1999), heartbeats (Peng et al., 1995), and human coordination (Gilden et al., 1995; Chen et al., 1997), exhibit unexpected statistical similarities, most commonly powerlaw scaling behavior of a particular observable. Scaling behavior (or scalefree behavior) means that no characteristic scales dominate the dynamics of the underlying process. Scalefree behavior can be revealed with scaling analysis, which quantifies the fluctuations of a parameter as a function of the scale at which the parameter is evaluated. Scalefree behavior reflects a tendency of complex systems to develop correlations that decay more slowly and extend over larger distances in time and space than the mechanisms of the underlying process would suggest (Bassingthwaighte et al., 1994; Barabási and Stanley, 1995; Bak, 1997). The longrange correlations build up through local interactions until they extend throughout the entire system. After this stage, the dynamics of the system exhibit powerlaw scaling behavior, and the underlying process operates in a critical state, a phenomenon often termed selforganized criticality (SOC) (Bak et al., 1987, 1988). Unlike deterministic approaches aimed at finding lowdimensional chaos, the SOC framework allows for a highdimensional character of the dynamics and for the presence of stochastic effects.
We have investigated whether noninvasively recorded spontaneous oscillations in the human brain show scaling behavior. Here we demonstrate the presence of longrange temporal correlations and powerlaw scaling behavior of oscillations at ∼10 and 20 Hz.
Parts of this work have been published previously in abstract form (LinkenkaerHansen et al., 2000).
MATERIALS AND METHODS
Recordings and experimental conditions. Spontaneous brain activity from 10 normal subjects (aged 20–30 years, one female) was recorded simultaneously with magnetoencephalography (MEG) and EEG using a wholescalp magnetometer array containing 122 planar gradiometers (Knuutila et al., 1993) and a 64channel EEG cap (Virtanen et al., 1996). The study was approved by the Ethics Committee of the Department of Radiology of the Helsinki University Central Hospital. The subjects were seated in a magnetically shielded room and instructed to relax with eyes open or closed in two 20 min recording sessions. The MEG and EEG data were sampled at 300 Hz and the pass band of 0.3–90 Hz.
Data analysis. The amplitude of neural oscillations was estimated with wavelet filtering and subsequently evaluated for the presence of temporal correlations using the autocorrelation function (ACF) and detrended fluctuation analysis (DFA). As control for the neural origin of temporal correlations, we used an MEG reference recording and surrogate data.
Wavelet filtering. The signals were filtered with a Morlet wavelet; the modulus of the complexvalued outcome, W(t,f) , represents the amplitude of the signal at a time range centered at t and in a frequency band centered at f (Torrence and Compo, 1998). For each frequency band, we centered the wavelet at the peak frequency determined individually with amplitude spectra. The widths of the wavelet in the time and frequency domains are expressed as the attenuation by a factor of e
^{2}and denoted t_{e}
andf_{e}
, respectively:
Temporal correlations. Temporal correlations of oscillations were quantified with the ACF and the DFA applied to the modulus of the wavelet filtered signals, i.e., to the amplitude envelope of the oscillations at a given frequency.
The autocorrelation function gives a measure of how a signal is correlated with itself at different time delays. When normalized, the autocorrelation attains its maximum value of one at zero time lag, decays toward zero with increasing time lag for (finite) correlated signals, and fluctuates around and close to zero at time lags free of correlations.
The detrended fluctuation analysis has been developed for quantifying correlation properties in nonstationary signals, e.g., in physiological time series, because longrange correlations—revealed by an ACF analysis—can arise also as an artifact of the “patchiness” of nonstationary data (Peng et al., 1994, 1995). In DFA, the modulus of the wavelettransformed signal at center frequency f is first integrated to produce a vector y of the cumulative sum of the signal amplitude around its average value:
Reference data. Broadband environmental noise is often temporally correlated. To verify that intrinsic sensor noise or environmental disturbances did not cause any of the effects reported here, a 20 min MEG recording without a subject in the instrument was performed and subjected to identical analyses as the real data.
Surrogate data. For the EEG data, we used socalled surrogate data as control, which are commonly used as a control when probing a signal for a nonrandom temporal structure (Ivanov et al., 1996). Surrogate signals have identical power spectra with the original signals but do not have temporal correlations; they were generated by first computing the Fourier transforms of the original signals, randomizing the Fourier phases while preserving the moduli, and then performing inverse Fourier transforms.
RESULTS
Oscillatory activity in occipital and rolandic regions
Amplitude spectra were computed for the 122 MEG and the 64 EEG channels. For all 10 subjects and both conditions, we detected prominent peaks in the alpha frequency band (8–13 Hz) in MEG and EEG channels over the occipital and parietal regions (Fig.2 A,B). For both MEG and EEG data, we selected the four channels with the largest alpha rhythm amplitude for further analysis for each subject and condition (the same channels were used for the “eyesopen” and the “eyesclosed” conditions). The peak alpha frequency was 10.4 ± 0.6 Hz (mean ± SD).
Mu rhythm (8–13 Hz) was detected in MEG channels over the right somatosensory cortex in nine subjects (Fig. 2 C). Additionally, in these subjects, one (∼21 Hz in six subjects) or two (∼16 and ∼21 Hz in three subjects) peaks in the beta frequency band (15–25 Hz) were observed over the somatosensory region (Fig.2 C). The four channels with the largest amplitude of mu rhythm were selected for further analysis for each subject; for the three subjects having two peaks in the beta range, we analyzed the component having the higher frequency. The peak frequencies were 10.7 ± 0.5 Hz (mu rhythm) and 21.3 ± 1.2 Hz (beta rhythm).
In terms of scaling analysis, the pronounced peaks in the amplitude spectra at 10 Hz show that the dynamics of broadband spontaneous activity is not scalefree; rather, it is dominated by a characteristic time scale of ∼100 msec. In the following sections, we address whether also the amplitude fluctuations of spontaneous oscillations have characteristic scales, which would imply a typical duration of oscillatory bursts.
Fractal appearance of spontaneous alpha oscillations
Wavelet analysis was used to estimate the amplitude of the signals in narrow frequency bands (Fig. 3) (see Materials and Methods). The wavelet was centered at the peak frequency of a given frequency band determined from the amplitude spectra of individual subjects. Highly irregular amplitude fluctuations were observed in both conditions for the occipital MEG alpha rhythm (Fig.3 A,B). To visualize the trend of the amplitude fluctuations at different scales of temporal resolution, the waveletfiltered original and surrogate signals were first downsampled from 300 to 15 Hz. Both the original and the surrogate signals were highly irregular at time scales <12 sec (Fig.3 C, top). Downsampling the signals to 1.5 Hz and enlarging the displayed interval to 120 sec reveals larger variability in the alpha activity than for the surrogate data (Fig. 3 C,middle). Finally, the display of the entire 1200 sec at a resolution of ∼10 sec still shows large amplitude changes for the alpha but only minor ripples for the surrogate data (Fig.3 C, bottom).
The appearance of large variability at many scales (as in Fig.3 C) is epitomical of fractal objects and is increasingly being acknowledged to hint about the presence of spatial and temporal correlations at many scales (Bassingthwaighte et al., 1994;Barabási and Stanley, 1995; Bak, 1997). This is in contrast to the variability of signals from uncorrelated or strongly noisedominated processes that appear even when measured at coarse scales.
Temporal correlations of spontaneous alpha oscillations
To quantify the temporal structure of the alpha rhythm amplitude fluctuations, we used power spectrum and autocorrelation analyses. Power spectrum analysis measures the contribution of different frequencies to the total power of a signal. In the amplitude envelope of alpha oscillations, the presence of preferred modulation frequencies of oscillations would thus produce peaks in the power spectrumP(f). We, however, observed a linear decay of power with increasing frequency in doublelogarithmic coordinates in the range of 0.005–0.5 Hz; i.e., a 1/f ^{β} type of a power spectrum: P(f) ≈f ^{−β} (Fig.4). For the MEG data, powerlaw exponents were β _{closed} = 0.44 ± 0.09 (mean ± SD; r ^{2} = 0.94) and β _{open} = 0.52 ± 0.12 (r ^{2} = 0.89). The reference recording gave rise to a whitenoise spectrum withβ _{ref} = 0.03 (r ^{2} = 0.02), thus ruling out 1/f ^{β} type of modulation of background 10 Hz noise. The EEG data yielded exponentsβ _{closed} = 0.36 ± 0.17 andβ _{open} = 0.51 ± 0.12. The differences in exponents between the two conditions (eyesclosed vs eyesopen) or between recording modalities were not significant (twotailed ttests; all nonsignificant differences in this paper have a p > 0.1). As a further control, we used surrogate data (see Materials and Methods); this also resulted in a whitenoise spectrum: β _{sur} = 0.05 (r ^{2} = 0.05). The 1/f ^{β} power spectra indicate a lack of a characteristic time scale for the duration and recurrence of oscillations and are characteristic for fractal signals.
We then computed autocorrelation functions for the waveletfiltered MEG and EEG data. The autocorrelation analysis indicated the presence of statistically significant correlations up to time lags of >100 sec (Fig. 5). The decay of the autocorrelation function was slow over two decades and well fitted by a power law: ACF(t) ≈t ^{−γ} (Fig. 5). The MEG data yielded γ_{closed} = 0.58 ± 0.23 (r ^{2} = 0.99) and γ_{open} = 0.73 ± 0.31 (r ^{2} = 0.97), whereas the EEG data yielded exponents γ_{closed} = 0.52 ± 0.35 (r ^{2} = 0.97) and γ_{open} = 0.81 ± 0.32 (r ^{2} = 0.98). The behavior of the autocorrelation functions is in congruence with 1/f ^{β} type of power spectra. The differences between the two conditions and between the exponents derived from MEG versus EEG data were not significant.
These results indicate that the irregular patterns of amplitude fluctuations of alpha oscillations evident from Figure 3 are embedded with correlations at many time scales. The decrease in correlation with temporal distance appears to be governed by a powerlaw.
Spontaneous alpha oscillations exhibit robust powerlaw scaling behavior
The power spectrum analysis and autocorrelation analyses used in the previous section are not optimal for the quantification of correlations in potentially nonstationary data, because longrange correlations (revealed by an autocorrelation analysis) can arise also as an artifact of the “patchiness” of nonstationary data. Thus, to further consolidate the presence of longrange correlations, we implemented the detrended fluctuation analysis (see Materials and Methods).
DFA was applied to the same amplitude time series of alpha oscillations as analyzed in the previous section. The selfsimilarity parameter α of the DFA is the powerlaw exponent characterizing the temporal correlations; uncorrelated signals yield a selfsimilarity parameter α = 0.5. This was confirmed using identically waveletfiltered reference recordings and surrogate data, which yielded α _{ref} = 0.508 and α _{sur} = 0.496, respectively (Fig. 6 A,B). For the α oscillations, on the other hand, we discovered robust powerlaw scaling behavior across conditions and recording modalities in 10 of 10 subjects (Fig.6 A,B). The onset of the loglog linear increase of the DFAfluctuation parameter, F, was at a window size of ∼5 sec (this is the lower limit in the DFA method because of the integration by the wavelet in the time domain), and the powerlaw scaling persisted until at least 300 sec. To obtain reliable scaling statistics for time scales larger than ∼300 sec, longer data series would be needed because of the generally large variability of the rootmeansquare fluctuation from one window to the other. The MEG data yieldedα _{closed} = 0.71 ± 0.06 andα _{open} = 0.71 ± 0.05 for conditions eyesclosed and eyesopen, respectively (Fig.6 A). The EEG data yieldedα _{closed} = 0.68 ± 0.07 andα _{open} = 0.70 ± 0.04 (Fig.6 B). The difference in selfsimilarity parameters between the two conditions was not statistically significant, and very similar selfsimilarity parameters were obtained also for the two recording modalities, despite the different sensitivity of MEG and EEG to the underlying currents (Hari and Ilmoniemi, 1986).
The selfsimilarity parameter α may be viewed as an index of the dynamics of the neural oscillations, whereas the mean amplitude relates to the strength of oscillatory activity. That these two measures convey complementary information about neural activity was indicated by the analysis of their correlation (Fig. 6 C). The mean amplitude and α _{open} were not correlated in either MEG or EEG data, whereasα _{close} was weakly, albeit significantly, negatively correlated with the mean amplitude for both MEG and EEG (p < 0.04;r ^{2} < 0.51; Spearman correlation). These correlations are surprising because a decrease in signaltonoise ratio biases the estimated selfsimilarity parameter toward that of the reference recording (α _{ref} ≅ 0.5). This thus indicates that noise (either environmental or from the sensors) has negligible contribution to the selfsimilarity parameters estimated for alpha oscillations.
To quantify the apparent stability of the selfsimilarity parameters across subjects, conditions, and recording techniques relative to the variability of the mean amplitudes, we compared for each subject the ratioα _{closed}/α _{open}with the corresponding ratio of the mean oscillation amplitude. This normalization eliminates amplitude effects caused by intersubject variability in head size, position in the instrument, etc. The amplitude ratio varied considerably across subjects but was always larger than unity (MEG, 1.98 ± 0.87; EEG, 1.81 ± 0.98) (Fig. 6 D), reflecting the well known high level of alpha rhythm activity when eyes are closed (Fig. 2 A). The ratios of scaling exponents, on the other hand, were near unity (MEG, 1.04 ± 0.12; EEG, 1.00 ± 0.13) (Fig.6 D). Linear correlations between amplitude and scaling exponent ratios were nonsignificant in both MEG and EEG data, and the SD of the amplitude ratios was significantly larger than for the exponent ratios (p < 0.0001; Fisher's test).
The DFA results indicate that, for the 10 Hz oscillations from the occipital region, spontaneous activity is robustly characterized by longrange temporal correlations that decay as powerlaw functions and with remarkably invariant scaling exponents. It has been pointed out recently that the scaling parameters of genuine longrange correlated processes obey the following relation: α = (2 −γ)/2 = (1 + β)/2 (Rangarajan and Ding 2000). Using γ and β from the previous section, good agreement is found for the predicted and the measuredα. Thus, together, DFA, autocorrelation, and power spectrum analyses provide robust evidence in support for powerlaw scaling behavior, as well as for the lack of characteristic time scales for the modulation of the alpha rhythm amplitude.
Generality of longrange temporal correlations and powerlaw scaling behavior of spontaneous oscillations
To test whether scaling behavior was unique to alpha rhythmicity or a more general property of largescale network oscillations, we applied the DFA and autocorrelation analyses to oscillations detected with MEG at the mu and beta frequency bands over the right somatosensory region in the eyesclosed condition (Fig.2 C).
Robust powerlaw scaling was indeed evident for both mu and beta oscillations over a range of approximately two decades. The selfsimilarity parameters obtained for mu and beta oscillations were significantly different: α _{mu} = 0.73 ± 0.09 and α _{beta} = 0.68 ± 0.07 (p < 0.005) (Fig.7 A); however, comparingα _{mu} withα _{closed} (the occipital alpha) indicated that 10 Hz oscillations from the rolandic and occipital regions had similar scaling properties (significance level of the difference, p > 0.3). The powerlaw decays of the autocorrelation functions were characterized by exponents γ_{mu} = 0.46 ± 0.35 and γ_{beta} = 0.70 ± 0.36 (Fig. 7 B); the difference in these exponents, as well as the differences in mean amplitudes of the mu and beta oscillations, were significant (p < 0.04). Nevertheless, correlations were not found between the magnitude of the selfsimilarity parameters and of the mean amplitudes for either the mu or beta rhythms, nor did the ratios of the exponents and of the amplitudes correlate linearly (Fig.7 C). The lack of correlation between the selfsimilarity parameters and amplitudes makes it unlikely that the difference in scaling exponents results from the lower signaltonoise ratio of beta oscillations. Differential scaling parameters of mu and beta oscillations suggest that the neural mechanisms and/or networks underlying these two rhythms are distinct. This interpretation is in agreement with reports on differential reactivity and anatomical origin of somatosensory mu and beta oscillations (Hari and Salmelin, 1997). In line with the results on alpha oscillations, we also found for the somatosensory oscillations that the ratios of mu and beta rhythm scaling exponents were more stable than the corresponding mean amplitude measures (exponent ratio, 1.09 ± 0.08; amplitude ratio, 1.41 ± 0.18; the difference in SD of the ratios,p < 0.002; Fisher's test).
The presence of powerlaw scaling behavior in amplitude fluctuations of mu and beta frequency bands in the somatosensory region indicates that these statistical characteristics are not unique to the occipitoparietal alpha rhythm.
DISCUSSION
We have investigated the largescale dynamics of network oscillations in the normal human brain. To the best of our knowledge, this is the first characterization of the temporal correlations in spontaneous oscillations at time scales ranging from a few seconds to several minutes. Our results indicate that spontaneous alpha, mu, and beta oscillations have significant temporal correlations for at least a couple of hundred seconds during resting conditions (eyesopen and eyesclosed). The decay of correlation was characterized by powerlaw scaling. The selfsimilarity parameters obtained with the detrended fluctuation analysis were highly invariant across subjects. The simultaneously recorded MEG and EEG agreed quantitatively in their estimates of the scaling exponents characterizing the occipital alpha rhythm dynamics. Oscillations at 8–13 and 15–25 Hz had different scaling properties, which suggests that distinct neural networks and/or mechanisms underlie these oscillations.
The correlated nature of spontaneous oscillations
It has often been noted that spontaneously occurring synchrony in cell populations appears in an irregular manner both temporally and spatiotemporally (Traub et al., 1989; Destexhe et al., 1999; Tsodyks et al., 1999). Previous studies have reported that 10 Hz oscillations are generated with great variability every 5–20 sec and last for ∼0.5–10 sec (Lopez da Silva, 1991; Destexhe et al., 1998). It has remained unknown, however, to what extent oscillatory activity beyond these time scales is statistically dependent. The present scaling analyses indicate that successive oscillations indeed are correlated, even over thousands of oscillation cycles (Figs. 47).
Scaling analysis is used increasingly in many fields of science to characterize complex phenomena. It can be used to test a model for its ability to generate scalefree behavior (Ivanov et al., 1998). Alternatively, transitions in scaling behavior from one parameter range to another can reveal scales at which different mechanisms influence the system dynamics (Barabási and Stanley, 1995; Peng et al., 1995; Ivanov et al., 1996). The stability of scaling exponents obtained here (Figs. 6 C,D, 7 C) suggests that scaling exponents may indeed be useful quantitative hallmarks of also the dynamic processes underlying spontaneous brain oscillations. The good quantitative agreement of the scaling exponents derived from MEG and EEG data reflects that scaling exponents are quantitative indices of relative fluctuations and do not depend on the unit of choice or the method used to measure the underlying dynamic process.
Moreover, the results of the power spectrum analysis indicated that bursts of oscillations are not modulated at any characteristic or dominant time scale (Fig. 4). The correlated nature of these oscillations suggests that “a burst” is only a part of a series of connected events and that the fractal structure of the signal reflects a hierarchy of bursts within bursts rather than a succession of individual or independent bursts. This we shall address further in the next section.
Local interactions as a mechanism underlying longrange temporal correlations and scaling behavior
One of the defining aspects of population oscillations is the ability of neural networks to establish spatiotemporal correlations with millisecond range precision and over large distances mainly through local synaptic connections (Traub et al., 1989). Here we describe a general framework of how local interactions create largescale dynamics, which could account for the longrange temporal correlations and the powerlaw scaling behavior observed for spontaneous oscillations.
Since the first reports on selforganized criticality (Bak et al., 1987, 1988), ample evidence has indicated that several complex systems selforganize through local interactions to a critical state with longrange spatiotemporal correlations (Bak et al., 1989; Mantegna and Stanley, 1995; Boettcher and Paczuski, 1996; Paczuski et al., 1996;Bak, 1997; Malamud et al., 1998; Lux and Marchesi, 1999). This state is termed “critical” because similar scaling behavior can be observed in equilibrium systems when finetuning a parameter to the point at which the system undergoes a phase transition. In nonequilibrium systems, however, this complex state can be “selforganized” and emerge purely under the dynamics of the system. In this case, the local rules of interaction sculpt the dynamics across many scales, and no characteristic scale can be identified.
Neural networks host the common features of SOC systems, such as a large number of units (neurons), local and nonlinear interactions between neurons, externally imposed perturbations, a certain amount of stochastic variation of internal parameters, and ability to store information in spatial patterns. In analogy with the scalefree behavior of SOC systems, we propose that the powerlaw form of the amplitude dynamics of spontaneous oscillations may not be highly dependent on the specific mechanisms underlying the generation of the population oscillations. A fundamental prerequisite for the emergence of a critical state, however, is that the network oscillations are associated with synaptic plasticity. Structural memory affecting the recruitment of neurons into future population oscillations is critical to ensure a degree of correlation. The exact values of the powerlaw exponents, on the other hand, may be related to both the biophysical mechanisms and the neural architecture underlying the oscillations. In line with this, our results showed that mu and alpha oscillations scaled similarly, but beta oscillations had a significantly smaller scaling exponent than mu and alpha.
A selforganized critical process, as the source of the temporal power laws, would further suggest that similar power laws exist also for parameters in the spatial domain. Based on the analogy with other SOC systems, one prediction is powerlaw statistics for the probability that a number of neurons, n, is recruited into an oscillatory event. Quantification of spatial correlations may, however, require invasive studies with greater spatial resolution than the present MEG and EEG measurements.
Possible functional significance of selforganized scalefree dynamics
The functional significance of the scalefree behavior of oscillations may be diverse. Temporal correlations of spontaneous network oscillations, as we have described here, may be the physiological correlate of behavioral results such as the 1/f ^{β} noise in the human judgement of temporal intervals (Gilden et al., 1995) and the longrange correlations observed for synchronization errors in human coordination (Chen et al., 1997). Thus, in terms of mechanisms, it may be the dynamic structural memory of the neural networks (see previous section) that constrain perception and behavior to powerlaw statistical patterns, even in situations in which humans attempt to avoid such correlations.
From a theoretical point of view and based on simulations, it has been argued that a state of criticality would be optimal for a network to swiftly adapt to new situations (Alstrøm and Stassinopoulos 1995;Stassinopoulos and Bak, 1995; Bonabeau, 1997; Chialvo and Bak, 1999). In the critical state, the spatiotemporal correlations are highly susceptible to perturbations; the dynamics may be viewed as balancing between a predictable stable pattern of activity and uncorrelated random behavior. Thus, if the “fractal” structure of neural oscillations indeed arises from selforganized neural network dynamics poised at criticality, one would expect the ongoing activity to be effectively disrupted by externally imposed perturbations. This, in fact, has been observed. During eventrelated desynchronization (ERD), spontaneous 8–13 Hz oscillations are suppressed rapidly (approximately within one cycle) by sensory stimulation (Hari and Salmelin, 1997;Nikouline et al., 2000), memory search (Kaufman et al., 1991), or motor activity (Pfurtscheller, 1989; Crone et al., 1998). Furthermore, the mapping of ERD on the cortical surface has revealed transitions from spatially diffuse to focused and somatotopically specific patterns of alpha suppression (Crone et al., 1998), consistent with the picture of spontaneous cortical states being driven into stimulus specific configurations of correlated neural activity (Tsodyks et al., 1999). We suggest that the widespread and rapid onset of ERD reflects longrange spatial correlations in the neural networks. Because all oscillations studied here showed surprisingly robust scaling behavior, we tentatively propose that, under normal physiological conditions, neural networks in general may operate in a critical state, thereby lending them capable of quick reorganization during processing demands.
Further studies are needed to determine how the powerlaw scaling exponents are affected by various experimental, pharmacological, or pathological conditions and whether current computational models of spontaneous network oscillations agree qualitatively and quantitatively with the present findings.
Footnotes

This work was supported by the Danish Natural Science Research Council, The Danish Research Agency, Center for International Mobility (Helsinki), and Helsinki University Central Hospital Research funds. J.M.P. was supported by the Academy of Finland and by the Juselius Foundation. We thank T. L. van Zuijen, J. Sinkkonen, and M. Kesäniemi for discussions. Wavelet software provided by C. Torrence and G. Compo (http://paos.colorado.edu/research/wavelets) was modified for this study.
Correspondence should be addressed to Klaus LinkenkaerHansen, BioMag Laboratory, P.O. Box 442, FIN00029 HUS, Finland. Email:klaus{at}oliivi.huch.fi.