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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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InfluentialEditorial: On the relation of dynamics and structure in brain networks
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On the Autocorrelation Function of 1/f Noises
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MethodSpectral decay vs. correlation dimension of EEG
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BackgroundSelf-citationCriticality in Cortex: Neuronal Avalanches and Coherence Potentials
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“The Detrended Fluctuation Analysis (DFA) was developed for studying the power-law long-range correlation present in different non-stationary time series [8] where its features were discovered in neural brain oscillations [9,10].”
BackgroundComplex Dynamics of Propagating Waves in a Two-Dimensional Neural Field
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“0 indicates the presence of scale-free temporal correlations (autocorrelations) (Linkenkaer-Hansen et al., 2001; Chen et al., 2002; Gao et al., 2006).”
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Self-citationPerformance of dry electrode with bristle in recording EEG rhythms across brain state changes
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MethodIt's about Space, It's about Time, Neuroeconomics and the Brain Sublime
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Robust Statistical Detection of Power-Law Cross-Correlation
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“It has been shown that neuronal activity in the human brain relates to critical dynamics, with persistent power-law correlations extending over multiple time scales 27,28 .”
Attenuation of temporal correlations of neuronal oscillations in patients with mild spastic diplegia
Gao, F., Wu, X., Feng, Y., & Jia, H. (2017) · Scientific Reports · doi:10.1038/s41598-017-14879-8 · Cited by 10
The self in art therapy – Brain-based assessment of the drawing process
Lin, Y. S., Hartwich, P., Wolff, A., Golesorkhi, M., & Northoff, G. (2020) · Medical Hypotheses · doi:10.1016/j.mehy.2020.109596 · Cited by 11
Self-regulated critical brain dynamics originate from high frequency-band activity in the MEG
Dürschmid, S., Reichert, C., Walter, N., Hinrichs, H., Heinze, H., Ohl, F. W., Tononi, G., & Deliano, M. (2020) · PLoS ONE · doi:10.1371/journal.pone.0233589 · Cited by 10
Cruz, G., Grent-‘t-Jong, T., Krishnadas, R., Palva, J. M., Palva, S., & Uhlhaas, P. J. (2021) · NeuroImage Clinical · doi:10.1016/j.nicl.2021.102722 · Cited by 11
Self-citationStead, M., Worrell, G. A., & Litt, B. (2005) · Complexity · doi:10.1002/cplx.20088 · Cited by 11
“Recently, DFA has been used to demonstrate the presence of LRTC with power-law scaling in human EEG recorded from the scalp [13, 14].”
BackgroundMethodFractal Analysis of EEG Upon Auditory Stimulation During Waking and Hypnosis in Healthy Volunteers
Lee, J., & Koo, B. (2012) · International Journal of Clinical and Experimental Hypnosis · doi:10.1080/00207144.2012.675294 · Cited by 12
“Lee, Kim, Kim, Park, & Kim, 2002 ; Linkenkaer-Hansen, Nikouline, Palva, & Ilmoniemi, 2001 ; Linkenkaer-Hansen, Nikulin, Palva, Kaila, & Ilmoniemi, 2004 ; Nikulin & Brismar, 2004 , 2005).”
Battaglia, D. A., Boudou, T., Hansen, E. C. A., Lombardo, D., Chettouf, S., Daffertshofer, A., McIntosh, A. R., Zimmermann, J., Ritter, P., & Jirsa, V. (2017) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/107243 · Cited by 15
On the agreement between small-world-like OFC model and real earthquakesPreprint
Ferreira, D. S. R., Papa, A. R. R., & Menezesd, R. (2016) · Cited by 11
Defining and measuring proximity to criticality based on univariate time series
Sooter, J. S., Fontenele, A. J., Barreiro, A. K., Ly, C., Hengen, K. B., & Shew, W. L. (2026) · Proceedings of the National Academy of Sciences · doi:10.1101/2025.08.03.668332 · Cited by 15
Preconfigured architecture of the developing mouse brain
Chini, M., Hnida, M., Kostka, J. K., Chen, Y., & Hanganu‐Opatz, I. L. (2024) · Cell Reports · doi:10.1016/j.celrep.2024.114267 · Cited by 11
“…(SUA) firing rates 15–17 ; spike transmission probability 10,17 ; pairwise correlations among spike trains 18 ; and power of the local field potential (LFP), 19,20 electroencephalogram (EEG), 21–23 magnetoencephalogram (MEG), 22–24 and blood-oxygen-level-dependent (BOLD) 25 signals.”
Harnessing Long-Range Temporal Correlations for Advanced Epilepsy Classification
Grubov, V., Kuc, A. K., Kurkin, S., Andrikov, D. A., Павлович, У. Н., Maksimenko, V., Karpov, O. E., & Hramov, A. E. (2025) · PRX Life · doi:10.1103/prxlife.3.013005 · Cited by 10
Janjarasjitt, S., & Loparo, K. A. (2013) · Journal of the Korean Physical Society · doi:10.3938/jkps.63.1659 · Cited by 10
Nonlinear analysis of electroencephalogram signals while listening to the holy Quran
Vaghefi, M., Nasrabadi, A. M., Golpayegani, S. M. R. H., Mohammadi, M. R., & Gharibzadeh, S. (2019) · Journal of Medical Signals & Sensors · doi:10.4103/jmss.jmss_37_18 · Cited by 10
“Self‐similarity parameter or scaling exponent may be considered as an indicator of neural fluctuation dynamics, whose mean amplitude is strongly dependent on fluctuation activities.[49] Exponent scaling value was >0 and if α = 0.”
BackgroundInfrared Radiation of Graphene Electrothermal Film Triggered Alpha and Theta Brainwaves
Lu, Y., Yang, R., Dai, Y., Yuan, D., Yu, X., Liu, C., Feng, L., Shen, R., Wang, C., Dai, S., et al. (2022) · Small Science · doi:10.1002/smsc.202200064 · Cited by 11
“Electroencephalogram (EEG) is a record of the oscillations of the brain electric potential[36], including detailed signals that provide information about underlying neural activities in the human brain.[37] Considering the convenience,”
BackgroundKat, R., Linkenkaer‐Hansen, K., Koopmans, M. A., Houtman, S. J., Bruining, H., & Kas, M. J. (2024) · Cerebral Cortex · doi:10.1093/cercor/bhae201 · Cited by 10
Self-citationChiarucci, R., Madeo, D., Loffredo, M. I., Castellani, E., Santarcangelo, E. L., & Mocenni, C. (2014) · Scientific Reports · doi:10.1038/srep05610 · Cited by 10
Measuring brain temperature without a thermometer
Papo, D. (2014) · Frontiers in Physiology · doi:10.3389/fphys.2014.00124 · Cited by 10
“The relaxation time is considerably slower than exponential (Linkenkaer-Hansen et al., 2001; Buiatti et al., 2007; Ciuciu et al., 2012; Zilber et al., 2012).”
BackgroundAguilera, M., Barandiaran, X. E., Bedía, M. G., & Arbeloa, F. J. S. (2015) · PLoS ONE · doi:10.1371/journal.pone.0117465 · Cited by 10
“Long-range correlations in the form of 1/f patterns have been extensively found in EEG/MEGmeasurements of brain activity in alpha, mu, and beta oscillations [13].”
BackgroundLin, D. C., Sharif, A. H., & Kwan, H. C. (2006) · Biological Cybernetics · doi:10.1007/s00422-006-0094-4 · Cited by 10
“…except some deviation in the large increment of S6 (crosses) address these two prominent features of the brain dynamics, rather than the scaling of EEG in the α frequency band (Freeman 2004; Hwa and Ferree 2002; Stam and de Bruin, 2004; Linkenkaer-Hansen et al. 2001; Bhattacharya et al. 2000).”
BackgroundMethodResultInfluentialDehghani, N., Bédard, C., Cash, S. S., Halgren, E., & Alain Destexhe, A. (2010) · Journal of Computational Neuroscience · doi:10.1007/s10827-010-0252-5 · Cited by 10
“First, in contrast to prior studies (such as Novikov et al. 1997; Linkenkaer-Hansen et al. 2001), we calculated the frequency scaling of all the sensors and did not confine our analysis to a specific region.”
MethodResultIntra, F. S., Avrămiea, A.-E., Irrmischer, M., Poil, S., Mansvelder, H. D., & Linkenkaer‐Hansen, K. (2018) · Frontiers in Human Neuroscience · doi:10.3389/fnhum.2018.00159 · Cited by 11
“The main steps from the broadband signal to the quantification of LRTC using DFA have been explained in detail previously (Linkenkaer-Hansen et al., 2001; Hardstone et al., 2012).”
MethodSelf-citationLessons From Astronomy and Biology for the Mind—Copernican Revolution in Neuroscience
Northoff, G. (2019) · Frontiers in Human Neuroscience · doi:10.3389/fnhum.2019.00319 · Cited by 11
EEG Correlates of Learning From Speech Presented in Environmental Noise
Eqlimi, E., Bockstael, A., Coensel, B. D., Schönwiesner, M., Talsma, D., & Botteldooren, D. B. (2020) · Frontiers in Psychology · doi:10.3389/fpsyg.2020.01850 · Cited by 10
“Long-range temporal correlations (LRTC) are the most common measures with which to quantify how slowly the autocorrelations of the signal decay in power-law function (Linkenkaer-Hansen et al., 2001; Nikulin and Brismar, 2005; Palva et al., 2013).”
BackgroundSelf-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. (2019) · Springer eBooks · doi:10.1007/978-3-319-76375-0_14 · Cited by 10
Spivey, M. J. (2020) · The MIT Press eBooks · doi:10.7551/mitpress/12818.001.0001 · Cited by 37
Long-term correlations in the surface behavior of dolphins
Ferrer‐i‐Cancho, R., & Lusseau, D. (2006) · Europhysics Letters (EPL) · doi:10.1209/epl/i2005-10596-9 · Cited by 10
Dopaminergic modulation of the spectral characteristics in the rat brain oscillatory activity
Valencia, M., López‐Azcárate, J., Nicolás, M. J., Alegre, M., & Artieda, J. (2012) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2011.12.019 · Cited by 10
Trajectory of frequency stability in typical development
Frohlich, J., Andrei Irimia, A., & Jeste, S. (2014) · Brain Imaging and Behavior · doi:10.1007/s11682-014-9339-3 · Cited by 10
“1997), and amplitude fluctuations (Linkenkaer-Hansen et al. 2001) as well as power spectral density (Pritchard 1992) in Table 1 Interpretations of frequency metastability”
Estimation of eigenvalues, eigenvectors and scores in FDA models with dependent errors
Beran, J., & Liu, H. (2016) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2016.02.002 · Cited by 10
An EEG nicotinic acetylcholine index to assess the efficacy of pro-cognitive compounds
Simpraga, S., Mansvelder, H. D., Groeneveld, G. J., Prins, S., Hart, E. P., Poil, S., & Linkenkaer‐Hansen, K. (2018) · Clinical Neurophysiology · doi:10.1016/j.clinph.2018.08.014 · Cited by 9
Self-citationTemporal structure of brain oscillations predicts learned nocebo responses to pain
Thomaidou, M. A., Blythe, J. S., Houtman, S. J., Veldhuijzen, D. S., van Laarhoven, A. I. M., & Evers, A. W. M. (2021) · Scientific Reports · doi:10.1038/s41598-021-89368-0 · Cited by 10
Attending to the Stream of Consciousness – A Methodological Challenge
Cosmelli, D. J. (2008) · Springer eBooks · doi:10.1007/978-3-540-70573-4_5 · Cited by 10
Rapid self-organized criticality: Fractal evolution in extreme environments
Halley, J. D., Warden, A. C., Sadedin, S., & Li, W. (2004) · Physical Review E · doi:10.1103/physreve.70.036118 · Cited by 10
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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