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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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Citations
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Playing at the Edge of Criticality: Expanded Whole-Brain Repertoire of Connectome-Harmonics
Atasoy, S., Deco, G., & Kringelbach, M. L. (2019) · Springer series on bio- and neurosystems · doi:10.1007/978-3-030-20965-0_2 · Cited by 17
An Electrophysiological Marker of Arousal Level in HumansPreprint
Lendner, J. D., Helfrich, R. F., Mander, B. A., Romundstad, L. G., Lin, J. J., Walker, M. P., Larsson, P. G., & Knight, R. T. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/625210 · Cited by 17
Wairagkar, M., Hayashi, Y., & Nasuto, S. J. (2019) · Frontiers in Systems Neuroscience · doi:10.3389/fnsys.2019.00066 · Cited by 16
Spatiotemporal Psychopathology – A novel approach to brain and symptoms
Northoff, G. (2022) · Nöro Psikiyatri Arşivi · doi:10.29399/npa.28146 · Cited by 19
Scale-Free Neural and Physiological Dynamics in Naturalistic Stimuli Processing
Lin, A., Maniscalco, B., & He, B. J. (2016) · eNeuro · doi:10.1523/eneuro.0191-16.2016 · Cited by 16
“Two well-studied forms of scale-free neural dynamics are the slow cortical potentials (SCPs; He et al., 2010) and amplitude fluctuations of brain oscillations (Linkenkaer-Hansen et al., 2001).”
BackgroundResultInfluentialEntanglement statistics in Markovian open quantum systems: A matter of mutation and selection
Carollo, F., & Pérez-Espigares, C. (2020) · Physical review. E · doi:10.1103/physreve.102.030104 · Cited by 14
“In this scenario, strong spatio-temporal correlations that are absent in equilibrium emerge [1–5] and stationary properties alone are not sufficient to understand the physics of the system, being required to study its trajectories and their statistical properties.”
BackgroundMüller, P. M., & Meisel, C. (2023) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1010919 · Cited by 16
Fractals and the Fock-Bargmann Representation of Coherent States
Vitiello, G. (2009) · Lecture notes in computer science · doi:10.1007/978-3-642-00834-4_3 · Cited by 16
“The power spectral densities in time and space of ECoGs from surface arrays conform to power-law distributions [16,17,18, 19 ,20].”
MethodHohlefeld, F. U., Ehlen, F., Krugel, L. K., Kühn, A. A., Curio, G., Klostermann, F., & Nikulin, V. V. (2013) · Neuroreport · doi:10.1097/wnr.0b013e328364c1a1 · Cited by 16
Rohlf, T. (2008) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/84/10004 · Cited by 16
A maximum likelihood based technique for validating detrended fluctuation analysis (ML-DFA)Preprint
Botcharova, M., Farmer, S. F., & Luc Berthouze, A. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1306.5075 · Cited by 16
“In Panel A, the minimum and maximum window sizes are set as suggested by [16].”
InfluentialFetterhoff, D., Kraft, R., Sandler, R., Opriș, I. C., Sexton, C. A., Marmarelis, V. Z., Hampson, R. E., & Deadwyler, S. A. (2015) · Frontiers in Systems Neuroscience · doi:10.3389/fnsys.2015.00130 · Cited by 15
“Scale-free dynamics are often associated with long-range temporal correlations (Linkenkaer-Hansen et al., 2001; Ciuciu et al., 2012) and quantified by the monofractal Hurst exponent.”
BackgroundMethodScale-specific dynamics of high-amplitude bursts in EEG capture behaviorally meaningful variability
Bansal, K., Garcia, J. O., Lauharatanahirun, N., Muldoon, S. F., Sajda, P., & Vettel, J. M. (2021) · NeuroImage · doi:10.1016/j.neuroimage.2021.118425 · Cited by 18
Caffeine induces age-dependent increases in brain complexity and criticality during sleep
Thölke, P., Arcand-Lavigne, M., Lajnef, T., Frenette, S., Carrier, J., & Jerbi, K. (2025) · Communications Biology · doi:10.1038/s42003-025-08090-z · Cited by 15
“Additionally, we also expanded on previous power spectral investigations of the effect of caffeine by disentangling periodic and aperiodic components in the EEG spectra.”
Lundqvist, M., Herman, P. A., Palva, J. M., Palva, S., Silverstein, D. N., & Lansner, A. (2013) · NeuroImage · doi:10.1016/j.neuroimage.2013.06.080 · Cited by 14
“Self-organized criticality has accordingly been proposed to underlie experimentally observed long-range temporal correlations of fast oscillations and to be crucial for the generation of ISFs (Linkenkaer-Hansen et al., 2001).”
BackgroundInfluentialSelf-citationUnifying and interpreting the spectral wavenumber content of EEGs, ECoGs, and ERPs
O’Connor, S. C., & Robinson, P. A. (2004) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2004.07.003 · Cited by 15
Communication activity in social networks: growth and correlations
Rybski, D., Buldyrev, S. V., Havlin, S., Liljeros, F., & Makse, H. A. (2011) · The European Physical Journal B · doi:10.1140/epjb/e2011-20172-4 · Cited by 15
The universal principles of self-organization and the unity of Nature and knowledge
Kurakin, A. V. (2007) · Cited by 14
Bumetanide As a Candidate Treatment for Behavioral Problems in Tuberous Sclerosis Complex
Vlaskamp, C., Poil, S., Jansen, F. E., Linkenkaer‐Hansen, K., Durston, S., Oranje, B., & Bruining, H. (2017) · Frontiers in Neurology · doi:10.3389/fneur.2017.00469 · Cited by 15
“(18)] to the amplitude envelop of band-pass filtered signal (FIR filter with a Blackman window, transition bandwidth 1 Hz) in the bands Alpha 8–13 and 6–13 Hz.”
BackgroundSelf-citationThe informational entropy endowed in cortical oscillations
Tozzi, A., Peters, J. F., & Çankaya, M. N. (2018) · Cognitive Neurodynamics · doi:10.1007/s11571-018-9491-3 · Cited by 15
On fractality of functional near-infrared spectroscopy signals: analysis and applications
Zhu, L., Haghani, S., & Najafizadeh, L. (2020) · Neurophotonics · doi:10.1117/1.nph.7.2.025001 · Cited by 16
Synaptic 1/f noise injection for overfitting suppression in hardware neural networks
Du, Y. J., Shao, W., Chai, Z., Zhao, H., Diao, Q., Gao, Y., Yuan, X., Wang, Q., Li, T., Zhang, W., et al. (2022) · Neuromorphic Computing and Engineering · doi:10.1088/2634-4386/ac6d05 · Cited by 15
“Similarly, it has been shown that both magnetoencephalography and electroencephalogram recordings of spontaneous neural activity in humans displayed 1/ f -like power spectra in the α , μ , and β frequency ranges [45].”
BackgroundJuárez-Martinez, E. L., van Andel, D. M., Sprengers, J. J., Avrămiea, A.-E., Oranje, B., Scheepers, F. E., Jansen, F. E., Mansvelder, H. D., Linkenkaer‐Hansen, K., & Bruining, H. (2022) · Frontiers in Neuroscience · doi:10.3389/fnins.2022.879451 · Cited by 15
Self-citationGonzalez, O. J. A., van Aerde, K. I., Mansvelder, H. D., van Pelt, J., & van Ooyen, A. (2014) · PLoS ONE · doi:10.1371/journal.pone.0100899 · Cited by 15
“amplitude alternating irregularly with episodes of low amplitude [3,26,27,28].”
BackgroundRobustness of functional networks at criticality against structural defects
Goodarzinick, A., Niry, M. D., Valizadeh, A., & Perc, M. (2018) · Physical review. E · doi:10.1103/physreve.98.022312 · Cited by 14
How Memory Conforms to Brain Development
Millán, A. P., Torres, J. J., & Marro, J. (2019) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2019.00022 · Cited by 14
“This in accordance with previous studies repeatedly reporting 1/f noise in brain activity under healthy conditions (Linkenkaer-Hansen et al., 2001; Voytek et al., 2015) and also in behavioral processes (Chialvo, 2010), which is related to the existence of temporal correlations within the data, and has been related to…”
BackgroundResultSELF-ORGANIZED CRITICALITY AND STOCHASTIC RESONANCE IN THE HUMAN BRAIN
Linkenkaer‐Hansen, K. (2002) · Aaltodoc (Aalto University) · Cited by 16
Self-citationKalamangalam, G. P., Long, S. S., & Chelaru, M. I. (2019) · Clinical Neurophysiology · doi:10.1016/j.clinph.2019.11.061 · Cited by 14
Scale-free dynamics of microstate sequence in negative schizophrenia and depressive disorder
Niu, Z., Jia, L., Liu, Y., Wang, Q., Li, Y., Yang, L., Xiaoli Li, A., & Wang, X. (2022) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2022.105287 · Cited by 14
Geertjens, L., van Voorst, T. W., Bouman, A., van Boven, M. A., Kleefstra, T., Verhage, M., Linkenkaer‐Hansen, K., Kasri, N. N., Cornelisse, L. N., & Bruining, H. (2022) · Genes · doi:10.3390/genes13020390 · Cited by 14
“We hav put forward that the concept of critical brain dynamics is a steppingstone to derive E/I ratios from neuronal oscillations measured with conventional EEG [57–60] (represented in Figure 4B) [58,61].”
MethodSelf-citation
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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