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Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations
Open accessAbstract
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.
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“The power spectra of neural signals typically follow a power-law form (), indicating temporal correlations that persist across multiple timescales (He et al. 2010; Miller et al. 2009; Linkenkaer-Hansen et al. 2001; Touboul and Destexhe 2010).”
From The myth of the Bayesian brain (2025) · cites this paper as Linkenkaer-Hansen et al. 2001
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“The main steps from the broadband signal to the quantification of LRTC using DFA have been explained in detail previously (Hardstone et al., 2012; Linkenkaer-Hansen et al., 2001).”
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“LRTC is traditionally estimated on an amplitude envelope of narrowband EEG oscillations, which requires long EEG segments (Linkenkaer-Hansen et al., 2001).”
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BackgroundIntellectually able adults with autism spectrum disorder show typical resting-state EEG activity
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Self-citationCross-Species Investigation on Resting State Electroencephalogram
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Scaling behaviour in music and cortical dynamics interplay to mediate music listening pleasure
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Self-organized criticality as a framework for consciousness: A review study
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“(2001), who focused on the temporal fluctuations employing a method called detrended fluctuation analysis and reported scale-free temporal statistics in EEG data (Linkenkaer-Hansen et al., 2001).”
MethodSpike-phase coupling patterns reveal laminar identity in primate cortex
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“Nonetheless, the multitaper applied in rsEEG deals with the unadjusted full spectra of AM power (Supplementary Figure 15, left column), whereas the Detrended Fluctuation analysis (DFA; Linkenkaer-Hansen et al., 2001) and FOOOF algorithm can handle the aperiodic component (Donoghue et al.”
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“This signature has been observed in amplitude fluctuations of 10- and 20-Hz oscillation ( Linkenkaer-Hansen et al. 2001 ), as well as in ‘‘durations’’ of synchronized activity (Gong et al. 2003).”
Herzog, N., Steinfath, T. P., & Tarrasch, R. (2021) · Frontiers in Neuroscience · doi:10.3389/fnins.2021.632922 · Cited by 26
“Neural Correlates of Sustained Attention Long-range temporal correlations (LRTC) are an indicator for temporal autocorrelations in the amplitude fluctuations of ongoing neuronal oscillations and were suggested to indicate when neuronal systems operate at a near-critical point (Linkenkaer-Hansen et al., 2001; Nikulin a…”
BackgroundIntrinsic dynamics and topography of sensory input systems
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Phase synchronization and measure of criticality in a network of neural mass models
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“Quick reorganization of neural networks during processing demands would be possible by the critical state dynamics of spontaneous oscillations (Linkenkaer-Hansen et al. 2001), thus scaling phenomena would be an essential characteristic of complex, adaptive, healthy systems.”
BackgroundLong-Range Temporal Correlations in Resting EEG
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EEG, Temporal Correlations, and Avalanches
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“, narrow band filtering (or not) and squaring of the signal, versus using wavelet methods to isolate the amplitude envelope of the signal (without squaring) (Linkenkaer-Hansen et al., 2001; Parish et al., 2004).”
MethodModulation of critical brain dynamics using closed-loop neurofeedback stimulation
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“To assess the statistical significance of the DFA exponents without making assumptions about the theoretical distribution of data, the exponents were computed for phase-shuffled data (Linkenkaer-Hansen, et al. 2001,Prichard and Theiler.”
Self-citationNegative mood and mind wandering increase long-range temporal correlations in attention fluctuations
Irrmischer, M., van der Wal, C. N., Mansvelder, H., & Linkenkaer-Hansen, K. (2018) · PLoS ONE · doi:10.1371/journal.pone.0196907 · Cited by 27
Self-citationModel selection for identifying power-law scaling
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Thoughts about thinking: cognition according to the second law of thermodynamics
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“TCs have been shown to characterize information processing, and their maximization is a hallmark for criticality (29, 45, 46).”
Dissipative neurodynamics in perception forms cortical patterns that are stabilized by vortices
Freeman, W., & Vitiello, G. (2009) · Journal of Physics Conference Series · doi:10.1088/1742-6596/174/1/012011 · Cited by 25
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“…processes are difficult to generalize to other repeated measures of human activity that exhibit 1/f noise, such as speech acoustics (Kello et al., 2008) and affect ratings (Delignières et al., 2004), and repeated measures of human neural activity as well (Linkenkaer-Hansen et al., 2001).”
BackgroundBuilding a minimum frustration framework for brain functions over long time scales
Tozzi, A., Flå, T., & Peters, J. F. (2016) · Journal of Neuroscience Research · doi:10.1002/jnr.23748 · Cited by 24
Relationships between short and fast brain timescales
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Dynamics of high frequency brain activity
Moffett, S. X., O’Malley, S. M., Man, S., Hong, D., & Martin, J. V. (2017) · Scientific Reports · doi:10.1038/s41598-017-15966-6 · Cited by 25
Lombardi, F., Shriki, O., Herrmann, H. J., & de Arcangelis, L. (2021) · Neurocomputing · doi:10.1016/j.neucom.2020.05.126 · Cited by 29
Mariani, B., Nicoletti, G., Bisio, M., Maschietto, M., Oboe, R., Leparulo, A., Suweis, S. S., & Vassanelli, S. (2021) · Frontiers in Systems Neuroscience · doi:10.3389/fnsys.2021.709677 · Cited by 24
Intentional systems: Review of neurodynamics, modeling, and robotics implementation
Kozma, R. (2007) · Physics of Life Reviews · doi:10.1016/j.plrev.2007.10.002 · Cited by 26
“The importance of long-distance correlations has been emphasized by numerous brain theorists [72–79].”
BackgroundSmith, R. J., Sugijoto, A., Rismanchi, N., Hussain, S. A., Shrey, D. W., & Lopour, B. A. (2017) · Brain Topography · doi:10.1007/s10548-017-0588-5 · Cited by 25
“a scaling constant termed the Hurst parameter (Linkenkaer-Hansen et al. 2001).”
Shalev, N., Bauer, A. R., & Nobre, A. C. (2019) · Current Opinion in Psychology · doi:10.1016/j.copsyc.2019.06.003 · Cited by 23
“2 Hz is supported by modelling data [61], local field-potential recordings in monkeys [62], and human electrophysiology [63].”
MethodDynamic Functional Connectivity as a complex random walk: Definitions and the dFCwalk toolbox
Arbabyazd, L., Lombardo, D., Blin, O. J., Didic, M., Battaglia, D. A., & Jirsa, V. (2020) · MethodsX · doi:10.1016/j.mex.2020.101168 · Cited by 25
“…(strictly speaking, DFA is undefined in this case) In Battaglia et al. [5] we have found that resting state dFC streams are generally persistent (“pink noise” like, long-term correlations) for window sizes W > ~ 20 s, in line with frequent reports of persistence in neural activity [24 , 33] .”
Mapping and modeling age-related changes in intrinsic neural timescales
Wu, K., & Gollo, L. L. (2025) · Communications Biology · doi:10.1038/s42003-025-07517-x · Cited by 26
“By combining empirical results and neuron network modeling, this study puts forward the idea that altered network properties due to aging increase the distance to criticality, explaining the reduced intrinsic timescales observed with advanced aging.”
Dynamics of spontaneous alpha activity correlate with language ability in young children
Kwok, E. Y. L., Cardy, J. O., Allman, B. L., Allen, P., & Herrmann, B. (2018) · Behavioural Brain Research · doi:10.1016/j.bbr.2018.10.024 · Cited by 26
An EEG-Based Neuromarketing Approach for Analyzing the Preference of an Electric Car
Raiesdana, S., & Mousakhani, M. (2022) · Computational Intelligence and Neuroscience · doi:10.1155/2022/9002101 · Cited by 24
“Results of this work verified that transition from resting state to emotion-based or attention-based mental activity, and then the emergence of decision-making/ preference cognition is accompanied by the presence of stochastic effects and high-dimensional character of the dynamics [35].”
BackgroundSpontaneous Spiking Is Governed by Broadband Fluctuations
Davis, Z. W., Muller, L., & Reynolds, J. H. (2022) · Journal of Neuroscience · doi:10.1523/jneurosci.1899-21.2022 · Cited by 26
Does throbbing pain have a brain signature?
Mo, J., Maizels, M., Ding, M., & Ahn, A. H. (2013) · Pain · doi:10.1016/j.pain.2013.02.013 · Cited by 24
“In turn, slow modulations of EEG activity in the alpha band are thought to be of great relevance to brain function because these large-scale, brain-wide network oscillations appear to be the basis for communication between distant but functionally related regions of the brain [28–30,37].”
BackgroundEftaxias, K., Kapiris, P., Balasis, G., Peratzakis, A., Karamanos, K., Kopanas, J., Antonopoulos, G., & Nomicos, K. (2006) · Natural hazards and earth system sciences · doi:10.5194/nhess-6-205-2006 · Cited by 24
“Note that a self-organized 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 (Linkenkaer-Hansen et al., 2001).”
BackgroundTaylor, T. J., Hartley, C., Šimon, P., Kiss, I. Z., & Luc Berthouze, A. (2013) · The Journal of Mathematical Neuroscience · doi:10.1186/2190-8567-3-5 · Cited by 24
“Are there other markers of criticality that may be more amenable to characterisation and that should be considered instead of, or in addition to, the statistics of event sizes? The need for such markers in neuroscience has been recognised (see [29] for example) and a number of studies have investigated long-range temp…”
BackgroundOptimally fuzzy temporal memoryPreprint
Shankar, K. H., & Howard, M. W. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1211.5189 · Cited by 24
“Such long range correlations can be found in statistics of natural images [2–4], speech and music [5], brain activity [6], economics [7] and even in human cognition [8–10].”
BackgroundHohlefeld, F. U., Ehlen, F., Tiedt, H. O., Krugel, L. K., Horn, A., Kühn, A. A., Curio, G., Klostermann, F., & Nikulin, V. V. (2015) · Neuroscience · doi:10.1016/j.neuroscience.2015.04.013 · Cited by 23
“…et al., 2001; Kello et al., 2010), which indicates the interdependence of remote parts in the signal, across tens and hundreds of seconds, as frequently shown in cortical EEG (e.g., Linkenkaer-Hansen et al., 2001, 2007; Nikulin and Brismar, 2004; Palva et al., 2013; Hohlefeld et al., 2013b).”
InfluentialNolte, G., Aburidi, M., & Engel, A. K. (2019) · Scientific Reports · doi:10.1038/s41598-019-42732-7 · Cited by 23
Relationship between regional white matter hyperintensities and alpha oscillations in older adults
Kumral, D., Čėsnaitė, E., Beyer, F., Hofmann, S., Hensch, T., Sander, C., Hegerl, U., Haufe, S., Villringer, A., Witte, A. V., et al. (2021) · Neurobiology of Aging · doi:10.1016/j.neurobiolaging.2021.10.006 · Cited by 23
Detrended Fluctuation Analysis of the Human EEG during Listening to Emotional Music
Gao, T., Wu, D., Huang, Y.-L., & Yao, D. (2007) · Cited by 23
Botcharova, M., Luc Berthouze, A., Brookes, M. J., Barnes, G. R., & Farmer, S. F. (2015) · Frontiers in Physiology · doi:10.3389/fphys.2015.00183 · Cited by 22
“A similar approach has been used inmany recent studies, e.g., (Linkenkaer-Hansen et al., 2001).”
MethodSelf-organization and Emergence of Dynamical Structures in Neuromorphic Atomic Switch Networks
Stieg, A. Z., Avizienis, A. V., Sillin, H. O., Aguilera, R., Shieh, H.-H., Martin‐Olmos, C., Sandouk, E. J., Aono, M., & Gimzewski, J. K. (2013) · Springer eBooks · doi:10.1007/978-3-319-02630-5_10 · Cited by 23
Heterogeneity of synaptic input connectivity regulates spike-based neuronal avalanches
Wu, S., Zhang, Y., Cui, Y., Li, H., Wang, J., Guo, L., Xia, Y., Yao, D., Xu, P., & Guo, D. (2018) · Neural Networks · doi:10.1016/j.neunet.2018.10.017 · Cited by 24
“Furthermore, previous studies have also shown the whole-brain activity dynamics measured with noninvasive techniques, such as electroencephalography (EEG) and functional magnetic resonance imaging (fMRI), can also be well described by power-law statistics [13, 14].”
Kim, J. W., Shin, H.-B., & Robinson, P. (2009) · Clinical Neurophysiology · doi:10.1016/j.clinph.2009.04.018 · Cited by 21
Evaluating and Comparing Measures of Aperiodic Neural ActivityPreprint
Donoghue, T., Hammonds, R., Lybrand, E., Waschke, L., Gao, R., & Voytek, B. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.09.15.613114 · Cited by 23
“Notably, dfa in particular is often applied to analyze the properties of the amplitude envelope of narrowband filtered time series (Hardstone et al., 2012; Linkenkaer-Hansen et al., 2001).”
BackgroundA measure centrality index for systematic empirical comparison of consciousness theories
Chis-Ciure, R., Melloni, L., & Northoff, G. (2024) · Neuroscience & Biobehavioral Reviews · doi:10.1016/j.neubiorev.2024.105670 · Cited by 22
Altered Brain Criticality in Schizophrenia: New Insights From Magnetoencephalography
Alamian, G., Lajnef, T., Pascarella, A., Lina, J., Knight, L., Walters, J., Singh, K. D., & Jerbi, K. (2022) · Frontiers in Neural Circuits · doi:10.3389/fncir.2022.630621 · Cited by 36
Zhu, J.-Q., Sundh, J., Spicer, J., Chater, N., & Sanborn, A. N. (2023) · Psychological Review · doi:10.1037/rev0000427 · Cited by 31
Yang, B., Zhang, H., Jiang, T., & Yu, S. P. (2023) · iScience · doi:10.1016/j.isci.2023.107963 · Cited by 23
Fractals as macroscopic manifestation of squeezed coherent states and brain dynamics
Vitiello, G. (2012) · Journal of Physics Conference Series · doi:10.1088/1742-6596/380/1/012021 · Cited by 22
Scale-free dynamics and critical phenomena in cortical activity
Boonstra, T. W., He, B. J., & Daffertshofer, A. (2013) · Frontiers in Physiology · doi:10.3389/fphys.2013.00079 · Cited by 22
“Moreover, fluctuations in electrophysiological and neuroimaging signals reveal prevalent scale-free dynamics (Linkenkaer-Hansen et al., 2001; He, 2011).”
BackgroundFedele, T., Blagovechtchenski, E., Nazarova, M. A., İşcan, Z., Moiseeva, V., & Nikulin, V. V. (2016) · Neuroscience · doi:10.1016/j.neuroscience.2016.06.015 · Cited by 23
“…shown that LRTC are present in the amplitude dynamics of many neuronal oscillations including theta, alpha and beta frequency bands and may extend for tens of seconds (Linkenkaer-Hansen et al., 2001, 2004, 2007; Nikulin and Brismar, 2005; Montez et al., 2009; Palva et al., 2013; Smit et al., 2013).”
Klaus, A., & Plenz, D. (2016) · PLoS Biology · doi:10.1371/journal.pbio.1002582 · Cited by 18
Scale-Free Amplitude Modulation of Neuronal Oscillations Tracks Comprehension of Accelerated Speech
Borges, A. F. T., Giraud, A., Mansvelder, H. D., & Linkenkaer‐Hansen, K. (2017) · Journal of Neuroscience · doi:10.1523/jneurosci.1515-17.2017 · Cited by 25
“Scale-free dynamics are a hallmark of resting-state neuronal activity, when synchronous cell assemblies form in a largely selforganized manner (Pritchard, 1992; Linkenkaer-Hansen et al., 2001; Freeman et al., 2003; Van de Ville et al., 2010; Poil et al., 2012).”
BackgroundMethodSelf-citationBongers, A., Flynn, A. B., & Northoff, G. (2019) · Neuroscience Research · doi:10.1016/j.neures.2019.10.011 · Cited by 22
“Therefore, relying on the method established by Wen and Liu (2016), one can separate fractal and oscillatory components in order to apply analysis (calculation of PLE or DFA) specifically to the fractal component.”
Method
Metadata
- Authors
- Linkenkaer-Hansen, K., Nikouline, V. V., Palva, J. M., & Ilmoniemi, R. J.
- Affiliations
- Helsinki University Hospital (FI)
- University of Helsinki (FI)
- Venue
- The Journal of Neuroscience
- Publisher
- Society for Neuroscience
- Published
- 2001-02-15
- Volume
- 21
- Issue
- 4
- Pages
- 1370-1377
- ISSN
- 0270-6474 (ISSN-L)
- 1529-2401
- PMC
- PMC6762238
- OpenAlex
- W2139852582
- Cited by
- 1,149
- References
- 50
- Citations by year
- 2026: 63 · 2025: 70 · 2024: 63 · 2023: 53 · 2022: 76 · 2021: 60 · 2020: 63 · 2019: 57 · 2018: 65 · 2017: 66 · 2016: 62 · 2015: 43 · 2014: 53 · 2013: 48 · 2012: 45
- FWCI
- 6.12
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Journal of Neuroscience (publishedVersion, cc-by-nc-sa)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- Funders
- Helsingin ja Uudenmaan Sairaanhoitopiiri
- Academy of Finland
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
- Keywords
- long-range temporal correlations, power-law scaling, neural oscillations, spontaneous neuronal activity, self-organized criticality, neural network reorganization, scaling exponents
- MeSH terms
- Adult, Biological Clocks, Brain, Computer Simulation, Electroencephalography, Female, Humans, Male, Models, Neurological, Nerve Net, Occipital Lobe, Parietal Lobe, Signal Processing, Computer-Assisted, Stochastic Processes, Time Factors, Visual Perception, Magnetoencephalography, Fractals
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