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Broadband Criticality of Human Brain Network Synchronization

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  • Manfred G Kitzbichler
  • Marie L Smith
  • Søren R Christensen
  • Ed Bullmore

Abstract

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.Author Summary: Systems in a critical state are poised on the cusp of a transition between ordered and random behavior. At this point, they demonstrate complex patterning of fluctuations at all scales of space and time. Criticality is an attractive model for brain dynamics because it optimizes information transfer, storage capacity, and sensitivity to external stimuli in computational models. However, to date there has been little direct experimental evidence for critical dynamics of human brain networks. Here, we considered two measures of functional coupling or phase synchronization between components of a dynamic system: the phase lock interval or duration of synchronization between a specific pair of time series or processes in the system and the lability of global synchronization among all pairs of processes. We confirmed that both synchronization metrics demonstrated scale invariant behaviors in two computational models of critical dynamics as well as in human brain functional systems oscillating at low frequencies (

Suggested Citation

  • Manfred G Kitzbichler & Marie L Smith & Søren R Christensen & Ed Bullmore, 2009. "Broadband Criticality of Human Brain Network Synchronization," PLOS Computational Biology, Public Library of Science, vol. 5(3), pages 1-13, March.
    • Handle: RePEc:plo:pcbi00:1000314
    DOI: 10.1371/journal.pcbi.1000314
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    References listed on IDEAS

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    1. R. Chialvo, Dante, 2004. "Critical brain networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(4), pages 756-765.
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    8. Mikail Rubinov & Olaf Sporns & Jean-Philippe Thivierge & Michael Breakspear, 2011. "Neurobiologically Realistic Determinants of Self-Organized Criticality in Networks of Spiking Neurons," PLOS Computational Biology, Public Library of Science, vol. 7(6), pages 1-14, June.
    9. Christian Meisel & Alexander Storch & Susanne Hallmeyer-Elgner & Ed Bullmore & Thilo Gross, 2012. "Failure of Adaptive Self-Organized Criticality during Epileptic Seizure Attacks," PLOS Computational Biology, Public Library of Science, vol. 8(1), pages 1-8, January.
    10. Adrián Ponce-Alvarez & Gustavo Deco & Patric Hagmann & Gian Luca Romani & Dante Mantini & Maurizio Corbetta, 2015. "Resting-State Temporal Synchronization Networks Emerge from Connectivity Topology and Heterogeneity," PLOS Computational Biology, Public Library of Science, vol. 11(2), pages 1-23, February.
    11. Stoop, Ruedi & Kanders, Karlis & Lorimer, Tom & Held, Jenny & Albert, Carlo, 2016. "Big data naturally rescaled," Chaos, Solitons & Fractals, Elsevier, vol. 90(C), pages 81-90.
    12. Korosh Mahmoodi & Bruce J. West & Paolo Grigolini, 2018. "Self-Organized Temporal Criticality: Bottom-Up Resilience versus Top-Down Vulnerability," Complexity, Hindawi, vol. 2018, pages 1-10, March.
    13. David Samu & Anil K Seth & Thomas Nowotny, 2014. "Influence of Wiring Cost on the Large-Scale Architecture of Human Cortical Connectivity," PLOS Computational Biology, Public Library of Science, vol. 10(4), pages 1-24, April.
    14. Anna Barnes & Edward T Bullmore & John Suckling, 2009. "Endogenous Human Brain Dynamics Recover Slowly Following Cognitive Effort," PLOS ONE, Public Library of Science, vol. 4(8), pages 1-6, August.
    15. Todd Zorick & Mark A Mandelkern, 2013. "Multifractal Detrended Fluctuation Analysis of Human EEG: Preliminary Investigation and Comparison with the Wavelet Transform Modulus Maxima Technique," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-7, July.
    16. Baysal, Veli & Yılmaz, Ergin, 2021. "Chaotic Signal Induced Delay Decay in Hodgkin-Huxley Neuron," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    17. Rodrigo P. Rocha & Loren Koçillari & Samir Suweis & Michele Filippo De Grazia & Michel Thiebaut Schotten & Marco Zorzi & Maurizio Corbetta, 2022. "Recovery of neural dynamics criticality in personalized whole-brain models of stroke," Nature Communications, Nature, vol. 13(1), pages 1-18, December.
    18. Marcelo G Mattar & Michael W Cole & Sharon L Thompson-Schill & Danielle S Bassett, 2015. "A Functional Cartography of Cognitive Systems," PLOS Computational Biology, Public Library of Science, vol. 11(12), pages 1-26, December.
    19. Aguilar-Velázquez, D. & Guzmán-Vargas, L., 2017. "Synchronization and 1/f signals in interacting small-world networks," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 418-425.
    20. Allegrini, Paolo & Paradisi, Paolo & Menicucci, Danilo & Laurino, Marco & Bedini, Remo & Piarulli, Andrea & Gemignani, Angelo, 2013. "Sleep unconsciousness and breakdown of serial critical intermittency: New vistas on the global workspace," Chaos, Solitons & Fractals, Elsevier, vol. 55(C), pages 32-43.
    21. Fingelkurts, Andrew A. & Fingelkurts, Alexander A. & Neves, Carlos F.H., 2013. "Consciousness as a phenomenon in the operational architectonics of brain organization: Criticality and self-organization considerations," Chaos, Solitons & Fractals, Elsevier, vol. 55(C), pages 13-31.
    22. Martinez-Saito, Mario, 2022. "Discrete scaling and criticality in a chain of adaptive excitable integrators," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).

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