Cited by 45Neural dynamics and brain functionFunctional Brain Connectivity StudiesPhilosophy and Theoretical Science

Criticality as a determinant of integrated information Φ in human brain networks

Open access
Kim, Hyoungkyu, Lee, UnCheol·2019·Entropy

Published version of a preprint

Abstract

Integrated information theory (IIT) describes consciousness as information integrated across highly differentiated but irreducible constituent parts in a system. However, in a complex dynamic system such as the brain, the optimal conditions for large integrated information systems have not been elucidated. In this study, we hypothesized that network criticality, a balanced state between a large variation in functional network configuration and a large constraint on structural network configuration, may be the basis of the emergence of a large Φ, a surrogate of integrated information. We also hypothesized that as consciousness diminishes, the brain loses network criticality and Φ decreases. We tested these hypotheses with a large-scale brain network model and high-density electroencephalography (EEG) acquired during various levels of human consciousness under general anesthesia. In the modeling study, maximal criticality coincided with maximal Φ. The EEG study demonstrated an explicit relationship between Φ, criticality, and level of consciousness. The conscious resting state showed the largest Φ and criticality, whereas the balance between variation and constraint in the brain network broke down as the response rate dwindled. The results suggest network criticality as a necessary condition of a large Φ in the human brain.

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.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.3390/e21100981

Cites

6 of 6 references verified0 citation errors · 0 not checkable

Statistics

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.

A few free checks a day · papers already verified open instantly · results are public

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?

  • Some surrogate measures of Φ have been successfully applied to altered levels of consciousness in humans and relate to network factors such as topological modularity or critical dynamics.

    “Furthermore, some surrogate measures of Φ have been successfully applied to altered levels of consciousness in humans (Kim et al., 2018) and also shown to relate to network factors such as topological modularity (Kim et al., 2018) or critical dynamics (Kim and Lee, 2019).”

    From Conscious Processing and the Global Neuronal Workspace Hypothesis (2020) · cites this paper as Kim and Lee, 2019

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Research works printed but not linked: 68

  1. [1]Oizumi M. Albantakis L. Tononi G. From the phenomenology to the mechanisms of consciousness: Integrated Information Theory 3.0 PLoS Comput Biol. 2014 10 e1003588 10.1371/journal.pcbi.1003588 24811198 PMC4014402 · DOI · Paper page
  2. [3]Tononi G. Boly M. Massimini M. Koch C. Integrated information theory: From consciousness to its physical substrate Nat. Rev. Neurosci. 2016 17 450 461 10.1038/nrn.2016.44 27225071 · DOI · Paper page
  3. [5]Tononi G. Integrated information theory of consciousness: An updated account Arch. Ital. Biol. 2012 150 56 90 10.4449/aib.v149i5.1388 23165867 · DOI
  4. [6]Tononi G. Information integration: Its relevance to brain function and consciousness Arch. Ital. Biol. 2010 148 299 322 10.4449/AIB.V148I3.1224 21175016 · DOI
  5. [7]Bak P. Tang C. Wiesenfeld K. Self-organized criticality Phys. Rev. A 1988 38 364 374 10.1103/PhysRevA.38.364 9900174 · DOI
  6. [8]Bak P. Paczuski M. Complexity, contingency, and criticality Proc. Natl. Acad. Sci. USA 1995 92 6689 6696 10.1073/pnas.92.15.6689 11607561 PMC41396 · DOI
  7. [10]Werner G. Metastability, criticality and phase transitions in brain and its models Biosystems 2007 90 496 508 10.1016/j.biosystems.2006.12.001 17316974 · DOI
  8. [11]Hesse J. Gross T. Self-organized criticality as a fundamental property of neural systems Front. Syst. Neurosci. 2014 8 166 10.3389/fnsys.2014.00166 25294989 PMC4171833 · DOI · Paper page
  9. [12]Tagliazucchi E. Balenzuela P. Fraiman D. Chialvo D.R. Criticality in large-scale brain FMRI dynamics unveiled by a novel point process analysis Front. Physiol. 2012 3 15 10.3389/fphys.2012.00015 22347863 PMC3274757 · DOI
  10. [13]Hidalgo J. Grilli J. Suweis S. Muñoz M.A. Banavar J.R. Maritan A. Information-based fitness and the emergence of criticality in living systems Proc. Natl. Acad. Sci. USA 2014 111 10095 10100 10.1073/pnas.1319166111 24982145 PMC4104871 · DOI
  11. [14]Haimovici A. Tagliazucchi E. Balenzuela P. Chialvo D.R. Brain organization into resting state networks emerges at criticality on a model of the human connectome Phys. Rev. Lett. 2013 110 178101 10.1103/PhysRevLett.110.178101 23679783 · DOI · Paper page
  12. [15]Marinazzo D. Pellicoro M. Wu G. Angelini L. Cortés J.M. Stramaglia S. Information transfer and criticality in the Ising model on the human connectome PLoS ONE 2014 9 e93616 10.1371/journal.pone.0093616 24705627 PMC3976308 · DOI
  13. [16]Moon J.-Y. Lee U. Blain-Moraes S. Mashour G.A. General relationship of global topology, local dynamics, and directionality in large-scale brain networks PLoS Comput. Biol. 2015 11 e1004225 10.1371/journal.pcbi.1004225 25874700 PMC4397097 · DOI · Paper page
  14. [17]Cocchi L. Gollo L.L. Zalesky A. Breakspear M. Criticality in the brain: A synthesis of neurobiology, models and cognition Prog. Neurobiol. 2017 158 132 152 10.1016/j.pneurobio.2017.07.002 28734836 · DOI
  15. [18]Beggs J.M. The criticality hypothesis: How local cortical networks might optimize information processing Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 2008 366 329 343 10.1098/rsta.2007.2092 17673410 · DOI · Paper page
  16. [19]Khajehabdollahi S. Abeyasinghe P.M. Owen A.M. Soddu A. The emergence of integrated information, complexity, and consciousness at criticality bioRxiv 2019 10.1101/521567 PMC7516800 33286113 · DOI
  17. [20]Kim M. Mashour G.A. Moraes S.-B. Vanini G. Tarnal V. Janke E. Hudetz A.G. Lee U. Functional and Topological Conditions for Explosive Synchronization Develop in Human Brain Networks with the Onset of Anesthetic-Induced Unconsciousness Front. Comput. Neurosci. 2016 10 10.3389/fncom.2016.00001 PMC4720783 26834616 · DOI
  18. [21]Kim M. Kim S. Mashour G.A. Lee U. Relationship of topology, multiscale phase synchronization, and state transitions in human brain networks Front. Comput. Neurosci. 2017 11 55 10.3389/fncom.2017.00055 28713258 PMC5492767 · DOI
  19. [22]Beggs J.M. Timme N. Being critical of criticality in the brain Front. Physiol. 2012 3 163 10.3389/fphys.2012.00163 22701101 PMC3369250 · DOI
  20. [23]Lee H. Golkowski D. Jordan D. Berger S. Ilg R. Lee J. Mashour G.A. Lee U. Avidan M.S. Blain-Moraes S. Relationship of critical dynamics, functional connectivity, and states of consciousness in large-scale human brain networks Neuroimage 2019 188 228 238 10.1016/j.neuroimage.2018.12.011 30529630 · DOI
  21. [24]Yoon S. Sorbaro Sindaci M. Goltsev A.V. Mendes J.F.F. Critical behavior of the relaxation rate, the susceptibility, and a pair correlation function in the Kuramoto model on scale-free networks Phys. Rev. E 2015 91 32814 10.1103/PhysRevE.91.032814 25871164 · DOI
  22. [25]Moretti P. Muñoz M.A. Griffiths phases and the stretching of criticality in brain networks Nat. Commun. 2013 4 2521 10.1038/ncomms3521 24088740 · DOI
  23. [26]Moon J.-Y. Kim J. Ko T.-W. Kim M. Iturria-Medina Y. Choi J.-H. Lee J. Mashour G.A. Lee U. Structure shapes dynamics and directionality in diverse brain networks: Mathematical principles and empirical confirmation in three species Sci. Rep. 2017 7 46606 10.1038/srep46606 28425500 PMC5397857 · DOI
  24. [27]Breakspear M. Dynamic models of large-scale brain activity Nat. Neurosci. 2017 20 340 352 10.1038/nn.4497 28230845 · DOI · Paper page
  25. [28]Gong G. He Y. Concha L. Lebel C. Gross D.W. Evans A.C. Beaulieu C. Mapping anatomical connectivity patterns of human cerebral cortex using in vivo diffusion tensor imaging tractography Cereb. Cortex 2008 19 524 536 10.1093/cercor/bhn102 18567609 PMC2722790 · DOI · Paper page
  26. [29]Hoppensteadt F.C. Izhikevich E.M. Weakly Connected Neural Networks 1st ed. Springer-Verlag New York, NY, USA 1997
  27. [30]Breakspear M. Heitmann S. Daffertshofer A. Generative models of cortical oscillations: Neurobiological implications of the kuramoto model Front. Hum. Neurosci. 2010 4 190 10.3389/fnhum.2010.00190 21151358 PMC2995481 · DOI
  28. [31]Nakagawa T.T. Woolrich M. Luckhoo H. Joensson M. Mohseni H. Kringelbach M.L. Jirsa V. Deco G. How delays matter in an oscillatory whole-brain spiking-neuron network model for MEG alpha-rhythms at rest Neuroimage 2014 87 383 394 10.1016/j.neuroimage.2013.11.009 24246492 · DOI
  29. [32]Flores F.J. Hartnack K.E. Fath A.B. Kim S.-E. Wilson M.A. Brown E.N. Purdon P.L. Thalamocortical synchronization during induction and emergence from propofol-induced unconsciousness Proc. Natl. Acad. Sci. USA 2017 114 E6660 E6668 10.1073/pnas.1700148114 28743752 PMC5558998 · DOI
  30. [33]Deco G. Cabral J. Saenger V.M. Boly M. Tagliazucchi E. Laufs H. Van Someren E. Jobst B. Stevner A. Kringelbach M.L. Perturbation of whole-brain dynamics in silico reveals mechanistic differences between brain states Neuroimage 2018 169 46 56 10.1016/j.neuroimage.2017.12.009 29225066 · DOI
  31. [34]Deco G. Cabral J. Woolrich M.W. Stevner A.B.A. van Hartevelt T.J. Kringelbach M.L. Single or multiple frequency generators in on-going brain activity: A mechanistic whole-brain model of empirical MEG data Neuroimage 2017 152 538 550 10.1016/j.neuroimage.2017.03.023 28315461 PMC5440176 · DOI
  32. [35]Jobst B.M. Hindriks R. Laufs H. Tagliazucchi E. Hahn G. Ponce-Alvarez A. Stevner A.B.A. Kringelbach M.L. Deco G. Increased stability and breakdown of brain effective connectivity during slow-wave sleep: Mechanistic insights from whole-brain computational modelling Sci. Rep. 2017 7 4634 10.1038/s41598-017-04522-x 28680119 PMC5498661 · DOI
  33. [36]Zhang H. Watrous A.J. Patel A. Jacobs J. Theta and alpha oscillations are traveling waves in the human neocortex Neuron 2018 98 1269 1281.e4 10.1016/j.neuron.2018.05.019 29887341 PMC6534129 · DOI
  34. [37]Naruse Y. Matani A. Miyawaki Y. Okada M. Influence of coherence between multiple cortical columns on alpha rhythm: A computational modeling study Hum. Brain Mapp. 2009 31 703 715 10.1002/hbm.20899 PMC6870997 19890847 · DOI
  35. [38]Caminiti R. Ghaziri H. Galuske R. Hof P.R. Innocenti G.M. Evolution amplified processing with temporally dispersed slow neuronal connectivity in primates Proc. Natl. Acad. Sci. USA 2009 106 19551 19556 10.1073/pnas.0907655106 19875694 PMC2770441 · DOI · Paper page
  36. [39]Blain-Moraes S. Tarnal V. Vanini G. Alexander A. Rosen D. Shortal B. Janke E. Mashour G.A. Neurophysiological correlates of sevoflurane-induced unconsciousness Anesthesiol. J. Am. Soc. Anesthesiol. 2015 122 307 316 10.1097/ALN.0000000000000482 PMC4301983 25296108 · DOI
  37. [40]Beggs J.M. Plenz D. Neuronal avalanches in neocortical circuits J. Neurosci. 2003 23 11167 11177 10.1523/JNEUROSCI.23-35-11167.2003 14657176 PMC6741045 · DOI · Paper page
  38. [41]Brochini L. de Andrade Costa A. Abadi M. Roque A.C. Stolfi J. Kinouchi O. Phase transitions and self-organized criticality in networks of stochastic spiking neurons Sci. Rep. 2016 6 35831 10.1038/srep35831 27819336 PMC5098137 · DOI
  39. [42]Kim H. Moon J.-Y. Mashour G.A. Lee U. Mechanisms of hysteresis in human brain networks during transitions of consciousness and unconsciousness: Theoretical principles and empirical evidence PLoS Comput. Biol. 2018 14 e1006424 10.1371/journal.pcbi.1006424 30161118 PMC6135517 · DOI
  40. [43]Lv P. Guo L. Hu X. Li X. Jin C. Han J. Li L. Liu T. Modeling dynamic functional information flows on large-scale brain networks Proceedings of Medical Image Computing and Computer-Assisted Intervention (MICCAI 2013) Springer Berlin/Heidelberg, Germany 2013 698 705 24579202
  41. [44]Schmidt R. LaFleur K.J.R. de Reus M.A. van den Berg L.H. van den Heuvel M.P. Kuramoto model simulation of neural hubs and dynamic synchrony in the human cerebral connectome BMC Neurosci. 2015 16 54 10.1186/s12868-015-0193-z 26329640 PMC4556019 · DOI
  42. [45]Deco G. Kringelbach M.L. Jirsa V.K. Ritter P. The dynamics of resting fluctuations in the brain: Metastability and its dynamical cortical core Sci. Rep. 2017 7 3095 10.1038/s41598-017-03073-5 28596608 PMC5465179 · DOI
  43. [46]Stanley H.E. Wong V.K. Introduction to phase transitions and critical phenomena Am. J. Phys. 1972 40 927 928 10.1119/1.1986710 · DOI
  44. [47]Oizumi M. Tsuchiya N. Amari S. Unified framework for information integration based on information geometry Proc. Natl. Acad. Sci. USA 2016 113 14817 14822 10.1073/pnas.1603583113 27930289 PMC5187746 · DOI
  45. [49]Kitazono J. Kanai R. Oizumi M. Efficient algorithms for searching the minimum information partition in Integrated Information Theory Entropy 2018 20 173 10.3390/e20030173 PMC7512690 33265264 · DOI
  46. [51]Stam C.J. Nolte G. Daffertshofer A. Phase lag index: Assessment of functional connectivity from multi channel EEG and MEG with diminished bias from common sources Hum. Brain Mapp. 2007 28 1178 1193 10.1002/hbm.20346 17266107 PMC6871367 · DOI
  47. [52]Lee U. Lee H. Müller M. Noh G.-J. Mashour G.A. Genuine and spurious phase synchronization strengths during consciousness and general anesthesia PLoS ONE 2012 7 e46313 10.1371/journal.pone.0046313 23056281 PMC3462801 · DOI
  48. [53]Wen P. Li Y. EEG human head modelling based on heterogeneous tissue conductivity Australas. Phys. Eng. Sci. Med. 2006 29 235 240 10.1007/BF03178571 17058584 · DOI
  49. [54]Oostenveld R. Fries P. Maris E. Schoffelen J.-M. FieldTrip: Open source software for advanced analysis of MEG, EEG, and invasive electrophysiological data Comput. Intell. Neurosci. 2011 2011 156869 10.1155/2011/156869 21253357 PMC3021840 · DOI · Paper page
  50. [55]Deco G. Jirsa V.K. Ongoing cortical activity at rest: Criticality, multistability, and ghost attractors J. Neurosci. 2012 32 3366 3375 10.1523/JNEUROSCI.2523-11.2012 22399758 PMC6621046 · DOI
  51. [56]Tagliazucchi E. Chialvo D.R. Siniatchkin M. Amico E. Brichant J.-F. Bonhomme V. Noirhomme Q. Laufs H. Laureys S. Large-scale signatures of unconsciousness are consistent with a departure from critical dynamics J. R. Soc. Interface 2016 13 20151027 10.1098/rsif.2015.1027 26819336 PMC4759808 · DOI
  52. [57]Hudetz A.G. Humphries C.J. Binder J.R. Spin-glass model predicts metastable brain states that diminish in anesthesia Front. Syst. Neurosci. 2014 8 234 10.3389/fnsys.2014.00234 25565989 PMC4263076 · DOI
  53. [58]Lee U. Mashour G.A. Kim S. Noh G.-J. Choi B.-M. Propofol induction reduces the capacity for neural information integration: Implications for the mechanism of consciousness and general anesthesia Conscious. Cogn. 2009 18 56 64 10.1016/j.concog.2008.10.005 19054696 · DOI
  54. [59]Tagliazucchi E. The signatures of conscious access and its phenomenology are consistent with large-scale brain communication at criticality Conscious. Cogn. 2017 55 136 147 10.1016/j.concog.2017.08.008 28846872 · DOI
  55. [60]Arsiwalla X.D. Verschure P.F.M.J. The global dynamical complexity of the human brain network Appl. Netw. Sci. 2016 1 16 10.1007/s41109-016-0018-8 30533508 PMC6245215 · DOI
  56. [61]Mediano P.A.M. Farah J.C. Shanahan M. Integrated Information and Metastability in Systems of Coupled Oscillators Arxiv Prepr. 2016 1606.08313
  57. [62]Hu X. Boccaletti S. Huang W. Zhang X. Liu Z. Guan S. Lai C.-H. Exact solution for first-order synchronization transition in a generalized Kuramoto model Sci. Rep. 2014 4 7262 10.1038/srep07262 25434404 PMC4248286 · DOI
  58. [63]Ko T.-W. Ermentrout G.B. Partially locked states in coupled oscillators due to inhomogeneous coupling Phys. Rev. E Stat. Nonlin Soft Matter Phys. 2008 78 16203 10.1103/PhysRevE.78.016203 18764031 · DOI
  59. [64]Bédard C. Destexhe A. Macroscopic models of local field potentials and the apparent 1/f noise in brain activity Biophys. J. 2009 96 2589 2603 10.1016/j.bpj.2008.12.3951 19348744 PMC2711281 · DOI
  60. [65]Liang Z. King J. Zhang N. Intrinsic organization of the anesthetized brain J. Neurosci. 2012 32 10183 10191 10.1523/JNEUROSCI.1020-12.2012 22836253 PMC3422560 · DOI · Paper page
  61. [66]Liu X. Ward B.D. Binder J.R. Li S.-J. Hudetz A.G. Scale-free functional connectivity of the brain is maintained in anesthetized healthy participants but not in patients with unresponsive wakefulness syndrome PLoS ONE 2014 9 e92182 10.1371/journal.pone.0092182 24647227 PMC3960221 · DOI
  62. [67]Lee U. Mashour G.A. Role of network science in the study of anesthetic state transitions Anesthesiology 2018 129 1029 1044 10.1097/ALN.0000000000002228 29683806 PMC6191341 · DOI
  63. [68]Priesemann V. Valderrama M. Wibral M. Le Van Quyen M. Neuronal avalanches differ from wakefulness to deep sleep—evidence from intracranial depth recordings in humans PLoS Comput. Biol. 2013 9 e1002985 10.1371/journal.pcbi.1002985 23555220 PMC3605058 · DOI
  64. [69]Lee U. Oh G. Kim S. Noh G. Choi B. Mashour G.A. Brain networks maintain a scale-free organization across consciousness, anesthesia, and recovery: Evidence for adaptive reconfiguration Anesthesiology 2010 113 1081 1091 10.1097/ALN.0b013e3181f229b5 20881595 PMC2962769 · DOI
  65. [70]Krzemiński D. Kamiński M. Marchewka A. Bola M. Breakdown of long-range temporal correlations in brain oscillations during general anesthesia Neuroimage 2017 159 146 158 10.1016/j.neuroimage.2017.07.047 28750775 · DOI
  66. [71]Meisel C. Storch A. Hallmeyer-Elgner S. Bullmore E. Gross T. Failure of adaptive self-organized criticality during epileptic seizure attacks PLoS Comput. Biol. 2012 8 e1002312 10.1371/journal.pcbi.1002312 22241971 PMC3252275 · DOI
  67. [72]Bonachela J.A. de Franciscis S. Torres J.J. Muñoz M.A. Self-organization without conservation: Are neuronal avalanches generically critical? J. Stat. Mech. Theory Exp. 2010 2010 P02015 10.1088/1742-5468/2010/02/P02015 · DOI
  68. [74]Huang Z. Vlisides P.E. Tarnal V.C. Janke E.L. Keefe K.M. Collins M.M. McKinney A.M. Picton P. Harris R.E. Mashour G.A. Brain imaging reveals covert consciousness during behavioral unresponsiveness induced by propofol Sci. Rep. 2018 8 13195 10.1038/s41598-018-31436-z 30181567 PMC6123455 · DOI

Cited by

Sorted by citations

Authors
Kim, H., & Lee, U.
Affiliations
University of Michigan (US)
Corresponding author
Lee, UnCheol
Venue
Entropy
Publisher
MDPI AG
Published
2019-10-08
Volume
21
Issue
10
Pages
981
ISSN
1099-4300 (ISSN-L)
OpenAlex
W2980277777
Cited by
45
References
6
Citations by year
2026: 4 · 2025: 4 · 2024: 9 · 2023: 9 · 2022: 10 · 2021: 7 · 2020: 2
FWCI
2.76
Type
journal article
Language
en
Open access
Locations
  • Entropy (publishedVersion, cc-by)
  • bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by-nc-nd)
  • PubMed Central (publishedVersion, cc-by)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
Funders
National Institutes of Health (R01 GM098578)
Topics
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
  • Social Sciences › Psychology › Experimental and Cognitive Psychology › Philosophy and Theoretical Science
Keywords
integrated information theory, network criticality, consciousness, level of consciousness, general anesthesia, brain networks, EEG, resting state, network models

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