The DOI matches its Crossref record; 53 of the 53 references it cites were found in a registry or an index.
Broadband Criticality of Human Brain Network Synchronization
Open accessAbstract
Self-organized criticality is an attractive model for human brain dynamics, but there has been little direct evidence for its existence in large-scale systems measured by neuroimaging. In general, critical systems are associated with fractal or power law scaling, long-range correlations in space and time, and rapid reconfiguration in response to external inputs. Here, we consider two measures of phase synchronization: the phase-lock interval, or duration of coupling between a pair of (neurophysiological) processes, and the lability of global synchronization of a (brain functional) network. Using computational simulations of two mechanistically distinct systems displaying complex dynamics, the Ising model and the Kuramoto model, we show that both synchronization metrics have power law probability distributions specifically when these systems are in a critical state. We then demonstrate power law scaling of both pairwise and global synchronization metrics in functional MRI and magnetoencephalographic data recorded from normal volunteers under resting conditions. These results strongly suggest that human brain functional systems exist in an endogenous state of dynamical criticality, characterized by a greater than random probability of both prolonged periods of phase-locking and occurrence of large rapid changes in the state of global synchronization, analogous to the neuronal "avalanches" previously described in cellular systems. Moreover, evidence for critical dynamics was identified consistently in neurophysiological systems operating at frequency intervals ranging from 0.05-0.11 to 62.5-125 Hz, confirming that criticality is a property of human brain functional network organization at all frequency intervals in the brain's physiological bandwidth.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Several lines of evidence point to fractal-like (1/f) self-similarity over different spatio-temporal scales in brain dynamics and structure [76,77].”
From Consciousness in the universe (2014) · cites this paper as [77]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“there does appear to be evidence for some kind of scale-invariance in neurophysiological processes (Section 3.2 [76,77]).”
From Consciousness in the universe (2014) · cites this paper as [77]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Collective dynamics of ‘small-world’ networks
Watts, D. J., & Strogatz, S. H. (1998) · Nature · doi:10.1038/30918 · Cited by 43,060
Tzourio-Mazoyer, N., Landeau, B., Papathanassiou, D., Crivello, F., Etard, O., Delcroix, N., Mazoyer, B., & Joliot, M. (2002) · NeuroImage · doi:10.1006/nimg.2001.0978 · Cited by 16,319
Multimodel Inference: Understanding AIC and BIC in Model Selection
Burnham, K. P., & Anderson, D. R. (2004) · Sociological Methods & Research · doi:10.1177/0049124104268644 · Cited by 11,648
PIKOVSKY, A. S., Rosenblum, M., & Kurths, J. (2001) · Cambridge University Press eBooks · doi:10.1017/cbo9780511755743 · Cited by 8,250
Chemical Oscillations, Waves, and Turbulence
Kuramoto, Y. (1984) · Springer series in synergetics · doi:10.1007/978-3-642-69689-3 · Cited by 7,242
Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
Onsager, L. (1944) · Physical Review · doi:10.1103/physrev.65.117 · Cited by 6,634
Synchronization a universal concept in nonlinear sciences
PIKOVSKY, A. S., Rosenblum, M. G., & Kurths, J. (2001) · Cited by 5,640
A mechanism for cognitive dynamics: neuronal communication through neuronal coherence.
Fries, P. (2005) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2005.08.011 · Cited by 4,284
Gray, C. M., König, P., Engel, A. K., & Singer, W. (1989) · Nature · doi:10.1038/338334a0 · Cited by 4,183
Beitrag zur Theorie des Ferromagnetismus
Ising, E. (1925) · Zeitschrift für Physik · doi:10.1007/bf02980577 · Cited by 3,871
The Kuramoto model: A simple paradigm for synchronization phenomena
Acebrón, J. A., Bonilla, L. L., Vicente, C. J. P., Ritort, F., & Spigler, R. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.77.137 · Cited by 3,579
Neuronal Synchrony: A Versatile Code for the Definition of Relations?
Singer, W. (1999) · Neuron · doi:10.1016/s0896-6273(00)80821-1 · Cited by 2,581
Efficiency and Cost of Economical Brain Functional Networks
Achard, S., & Bullmore, E. (2007) · PLoS Computational Biology · doi:10.1371/journal.pcbi.0030017 · Cited by 2,553
Self-citationAchard, S., Salvador, R., Whitcher, B., Suckling, J., & Bullmore, E. (2006) · The Journal of Neuroscience · doi:10.1523/jneurosci.3874-05.2006 · Cited by 2,393
Self-citationNeuronal Avalanches in Neocortical Circuits
Beggs, J. M., & Plenz, D. (2003) · The Journal of Neuroscience · doi:10.1523/jneurosci.23-35-11167.2003 · Cited by 2,325
Spatiotemporal signal space separation method for rejecting nearby interference in MEG measurements
Taulu, S., & Simola, J. (2006) · Physics in Medicine and Biology · doi:10.1088/0031-9155/51/7/008 · Cited by 1,526
Modulation of Neuronal Interactions Through Neuronal Synchronization
Womelsdorf, T., Schoffelen, J.-M., Oostenveld, R., Singer, W., Desimone, R., Engel, A. K., & Fries, P. (2007) · Science · doi:10.1126/science.1139597 · Cited by 1,367
Neurophysiological Architecture of Functional Magnetic Resonance Images of Human Brain
Salvador, R. M., John Suckling, A., Coleman, M. R., Pickard, J. D., Menon, D. K., & Bullmore, E. T. (2005) · Cerebral Cortex · doi:10.1093/cercor/bhi016 · Cited by 1,334
Self-citationLong-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations
Linkenkaer-Hansen, K., Nikouline, V. V., Palva, J. M., & Ilmoniemi, R. J. (2001) · The Journal of Neuroscience · doi:10.1523/jneurosci.21-04-01370.2001 · Cited by 1,149 · cited 1×
“Power law scaling of human neurophysiological processes has been previously described in both functional MRI and MEG or electrophysiological datasets [ 14 ,15,43].”
MethodNonlinear multivariate analysis of neurophysiological signals
Pereda, E., Quiroga, R. Q., & Bhattacharya, J. (2005) · Progress in Neurobiology · doi:10.1016/j.pneurobio.2005.10.003 · Cited by 1,066
Petzold, L. R. (1983) · SIAM Journal on Scientific and Statistical Computing · doi:10.1137/0904010 · Cited by 1,063
Adaptive reconfiguration of fractal small-world human brain functional networks
Bassett, D. S., Meyer-Lindenberg, A., Achard, S., Duke, T., & Bullmore, E. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0606005103 · Cited by 814
Self-citationHistory of the Lenz-Ising Model
Brush, S. G. (1967) · Reviews of Modern Physics · doi:10.1103/revmodphys.39.883 · Cited by 739
Beggs, J. M., & Plenz, D. (2004) · Journal of Neuroscience · doi:10.1523/jneurosci.0540-04.2004 · Cited by 583
Suppression of Interference and Artifacts by the Signal Space Separation Method
Taulu, S., Kajola, M., & Simola, J. (2004) · Brain Topography · doi:10.1023/b:brat.0000032864.93890.f9 · Cited by 541
The Temporal Correlation Hypothesis of Visual Feature Integration
Gray, C. M. (1999) · Neuron · doi:10.1016/s0896-6273(00)80820-x · Cited by 541
The criticality hypothesis: how local cortical networks might optimize information processing
Beggs, J. M. (2008) · Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rsta.2007.2092 · Cited by 533
Hierarchical Organization Unveiled by Functional Connectivity in Complex Brain Networks
Zhou, C., Zemanová, L., Zamora‐López, G., Hilgetag, C. C., & Kurths, J. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.238103 · Cited by 504
Haldeman, C. L., & Beggs, J. M. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.058101 · Cited by 464
Lachaux, J.-P., Antoine Lutz, A., Rudrauf, D., Cosmelli, D. J., Quyen, M. L. V., Martinerie, J. M., & Varela, F. J. (2002) · Neurophysiologie Clinique · doi:10.1016/s0987-7053(02)00301-5 · Cited by 370
Complexity, contingency, and criticality.
Bak, P., & Paczuski, M. (1995) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.92.15.6689 · Cited by 337
Fractional Gaussian noise, functional MRI and Alzheimer's disease
Maxim, V., Sendur, L., Fadili, J. M., John Suckling, A., Gould, R. L., Howard, R. J., & Bullmore, E. T. (2005) · NeuroImage · doi:10.1016/j.neuroimage.2004.10.044 · Cited by 270
Self-citationChialvo, D. R. (2004) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2004.05.064 · Cited by 266
Clustered Organization of Cortical Connectivity
Hilgetag, C. C., & Kaiser, M. (2004) · Neuroinformatics · doi:10.1385/ni:2:3:353 · Cited by 251
A model for neuronal oscillations in the visual cortex
Schuster, H. G., & Wagner, P. D. (1990) · Biological Cybernetics · doi:10.1007/bf00203633 · Cited by 213
Gene expression dynamics in the macrophage exhibit criticality
Nykter, M., Price, N. D., Aldana, M., Ramsey, S. A., Kauffman, S. A., Hood, L., Yli-Harja, O. P., & Shmulevich, I. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0711525105 · Cited by 203
Fractal connectivity of long-memory networks
Achard, S., Bassett, D. S., Meyer‐Lindenberg, A., & Bullmore, E. T. (2008) · Physical Review E · doi:10.1103/physreve.77.036104 · Cited by 133
Self-citationSelf-organized critical neural networks
Bornholdt, S., & Röhl, T. (2003) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.67.066118 · Cited by 130
Wink, A. M., Bullmore, E. T., Barnes, A., Bernard, F., & John Suckling, A. (2008) · Human Brain Mapping · doi:10.1002/hbm.20593 · Cited by 128
Self-citationCritical Scale Invariance in a Healthy Human Heart Rate
Kiyono, K., Struzik, Z. R., Aoyagi, N., Sakata, S., Hayano, J., & Yamamoto, Y. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.178103 · Cited by 115
Neural Networks Debunk Phrenology
Knight, R. T. (2007) · Science · doi:10.1126/science.1144677 · Cited by 104
Self-organized criticality and scale-free properties in emergent functional neural networks
Shin, C.-W., & Kim, S. (2006) · Physical Review E · doi:10.1103/physreve.74.045101 · Cited by 102
John Suckling, A., Wink, A. M., Bernard, F., Barnes, A., & Bullmore, E. T. (2008) · Journal of Neuroscience Methods · doi:10.1016/j.jneumeth.2008.06.037 · Cited by 98
Self-citationMode-Locking and the Transition to Chaos in Dissipative Systems
Bak, P., Bohr, T., & Jensen, M. H. (1985) · Physica Scripta · doi:10.1088/0031-8949/1985/t9/007 · Cited by 85
Adaptive learning by extremal dynamics and negative feedback
Bak, P., & Chialvo, D. R. (2001) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.63.031912 · Cited by 78
Self‐organized criticality and the development of EEG phase reset
Thatcher, R. W., North, D. M., & Biver, C. J. (2008) · Human Brain Mapping · doi:10.1002/hbm.20524 · Cited by 74
Bullmore, E. T., Brammer, M. J., Bourlon, P., Alarcón, G., Polkey, C. E., Elwes, R. D. C., & Binnie, C. D. (1994) · Electroencephalography and Clinical Neurophysiology · doi:10.1016/0013-4694(94)00181-2 · Cited by 67
Self-citationGong, P., Nikolaev, A. R., & van Leeuwen, C. (2007) · Physical Review E · doi:10.1103/physreve.76.011904 · Cited by 65
The Brain: What is Critical About It?
Chialvo, D. R., Balenzuela, P., Fraiman, D., Ricciardi, L. M., Buonocore, A., & Pirozzi, E. (2008) · AIP conference proceedings · doi:10.1063/1.2965095 · Cited by 41
Time-varying spectral analysis in neurophysiological time series using Hilbert wavelet pairs
Whitcher, B. J., Craigmile, P. F., & Brown, P. (2005) · Signal Processing · doi:10.1016/j.sigpro.2005.07.002 · Cited by 32
Functional modulation of power-law distribution in visual perception
Shimono, M., Owaki, T., Amano, K., Kitajo, K., & Takeda, T. (2007) · Physical Review E · doi:10.1103/physreve.75.051902 · Cited by 12
High-resolution intersubject averaging and a coordinate system for the cortical surface
Fischl, B., Sereno, M. I., Tootell, R. B. H., & Dale, A. M. (1999) · Human Brain Mapping · doi:10.1002/(sici)1097-0193(1999)8:4
- Self-citation
Flagged first, then by citations
Cited by
Sorted by citations
Complex brain networks: graph theoretical analysis of structural and functional systems
Bullmore, E., & Sporns, O. (2009) · Nature Reviews Neuroscience · doi:10.1038/nrn2575 · Cited by 11,820
Self-citationThe free-energy principle: a unified brain theory?
Friston, K. (2010) · Nature Reviews Neuroscience · doi:10.1038/nrn2787 · Cited by 8,120
Functional and Effective Connectivity: A Review
Friston, K. J. (2011) · Brain Connectivity · doi:10.1089/brain.2011.0008 · Cited by 3,415
The economy of brain network organization
Bullmore, E., & Sporns, O. (2012) · Nature Reviews Neuroscience · doi:10.1038/nrn3214 · Cited by 3,284
Self-citationThe role of the posterior cingulate cortex in cognition and disease
Leech, R., & Sharp, D. J. (2014) · Brain · doi:10.1093/brain/awt162 · Cited by 2,247
Metadata
- Authors
- Kitzbichler, M. G., Smith, M. L., Christensen, S. R., & Bullmore, E.
- Affiliations
- University of Cambridge (GB)
- MRC Cognition and Brain Sciences Unit (GB)
- GlaxoSmithKline (United Kingdom) (GB)
- Venue
- PLoS Computational Biology
- Publisher
- Public Library of Science (PLoS)
- Published
- 2009-03-20
- Volume
- 5
- Issue
- 3
- Pages
- e1000314
- ISSN
- 1553-734X (ISSN-L)
- 1553-7358
- PMC
- PMC2647739
- OpenAlex
- W2115990221
- Cited by
- 527
- References
- 52
- Citations by year
- 2026: 10 · 2025: 16 · 2024: 14 · 2023: 28 · 2022: 28 · 2021: 31 · 2020: 25 · 2019: 38 · 2018: 37 · 2017: 37 · 2016: 24 · 2015: 24 · 2014: 39 · 2013: 44 · 2012: 54
- FWCI
- 21.21
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- PLoS Computational Biology (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- BIROn (Birkbeck, University of London) (acceptedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Apollo (University of Cambridge) (submittedVersion, cc-by)
- Apollo (cc-by)
- Funders
- GlaxoSmithKline
- Wellcome Trust
- Medical Research Council
- National Institute of Mental Health
- 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
- self-organized criticality, functional brain networks, phase synchronization, power-law scaling, neuronal avalanches, Ising model, Kuramoto model, resting-state brain dynamics, functional MRI, magnetoencephalography
- MeSH terms
- Action Potentials, Animals, Biological Clocks, Brain, Computer Simulation, Cortical Synchronization, Humans, Models, Neurological, Nerve Net, Synaptic Transmission, Neurons
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
