Critical Brain Dynamics at Large Scale

Highly correlated brain dynamics produces synchronized states with no behavioral value, while weakly correlated dynamics prevent information flow. In between these states, the unique dynamical features of the critical state endow the brain with properties which are fundamental for adaptive behavior. We discuss the idea put forward two decades ago by Per Bak that the working brain stays at an intermediate (critical) regime characterized by power-law correlations. This proposal is now supported by a wide body of empirical evidence at different scales demonstrating that the spatiotemporal brain dynamics exhibit key signatures of critical dynamics, previously recognized in other complex systems. The rationale behind this program is discussed in these notes, followed by an account of the most recent results.

[1]  D. Chialvo.  Emergent complex neural dynamics , 2010, 1010.2530.

[2]  Dante R. Chialvo,et al.  What kind of noise is brain noise: anomalous scaling behavior of the resting brain activity fluctuations , 2010, Front. Physio..

[3]  J. David Neelin,et al.  Critical phenomena in atmospheric precipitation , 2006 .

[4]  D. Plenz,et al.  The organizing principles of neuronal avalanches: cell assemblies in the cortex? , 2007, Trends in Neurosciences.

[5]  C. Grady,et al.  The Importance of Being Variable , 2011, The Journal of Neuroscience.

[6]  G. Parisi,et al.  Scale-free correlations in starling flocks , 2009, Proceedings of the National Academy of Sciences.

[7]  G. Cecchi,et al.  Scale-free brain functional networks. , 2003, Physical review letters.

[8]  Olaf Sporns,et al.  The Human Connectome: A Structural Description of the Human Brain , 2005, PLoS Comput. Biol..

[9]  V. Haughton,et al.  Mapping functionally related regions of brain with functional connectivity MR imaging. , 2000, AJNR. American journal of neuroradiology.

[10]  P. Bak,et al.  Complexity, contingency, and criticality. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Stassinopoulos,et al.  Democratic reinforcement: A principle for brain function. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  Bak,et al.  Punctuated equilibrium and criticality in a simple model of evolution. , 1993, Physical review letters.

[13]  Per Bak,et al.  How Nature Works , 1996 .

[14]  M. Bellac,et al.  Nonequilibrium statistical mechanics , 2007, Physics Subject Headings (PhySH).

[15]  D. Turcotte,et al.  Self-organized criticality , 1999 .

[16]  Karl J. Friston.  Functional and effective connectivity in neuroimaging: A synthesis , 1994 .

[17]  N. Logothetis.  The neural basis of the blood-oxygen-level-dependent functional magnetic resonance imaging signal. , 2002, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[18]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

[19]  J Wakeling,et al.  Intelligent systems in the context of surrounding environment. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  I. Prigogine,et al.  Formative Processes. (Book Reviews: Self-Organization in Nonequilibrium Systems. From Dissipative Structures to Order through Fluctuations) , 1977 .

[21]  Justin L. Vincent,et al.  Intrinsic functional architecture in the anaesthetized monkey brain , 2007, Nature.

[22]  H. Stanley,et al.  Introduction to Phase Transitions and Critical Phenomena , 1972 .

[23]  Stephen M. Smith,et al.  Investigations into resting-state connectivity using independent component analysis , 2005, Philosophical Transactions of the Royal Society B: Biological Sciences.

[24]  D. Gilden.  Cognitive emissions of 1/f noise. , 2001, Psychological review.

[25]  P. Bak.  Life laws , 1998, Nature.

[26]  Pablo Balenzuela,et al.  Criticality in Large-Scale Brain fMRI Dynamics Unveiled by a Novel Point Process Analysis , 2012, Front. Physio..

[27]  Tang,et al.  Self-Organized Criticality: An Explanation of 1/f Noise , 2011 .

[28]  Per Bak,et al.  How Nature Works: The Science of Self‐Organized Criticality , 1997 .

[29]  Kim Christensen,et al.  A complexity view of rainfall. , 2002, Physical review letters.

[30]  M. Fox,et al.  Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging , 2007, Nature Reviews Neuroscience.

[31]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[32]  Stephen M Smith,et al.  Correspondence of the brain's functional architecture during activation and rest , 2009, Proceedings of the National Academy of Sciences.

[33]  M. Marchesi,et al.  Scaling and criticality in a stochastic multi-agent model of a financial market , 1999, Nature.

[34]  E. Bonabeau.  How nature works: The science of self-organized criticality (copernicus) , 1997 .

[35]  P. Bak,et al.  Adaptive learning by extremal dynamics and negative feedback. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Gordon D. A. Brown,et al.  Scale invariance in the retrieval of retrospective and prospective memories , 2001, Psychonomic bulletin & review.

[37]  C. Grady,et al.  Blood Oxygen Level-Dependent Signal Variability Is More than Just Noise , 2010, The Journal of Neuroscience.

[38]  A. Pérez-Villalba.  Rhythms of the Brain, G. Buzsáki. Oxford University Press, Madison Avenue, New York (2006), Price: GB £42.00, p. 448, ISBN: 0-19-530106-4 , 2008 .

[39]  P. Anderson.  More is different. , 1972, Science.

[40]  Henrik Jeldtoft Jensen,et al.  Self-Organized Criticality , 1998 .

[41]  K. Linkenkaer-Hansen,et al.  Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations , 2001, The Journal of Neuroscience.

[42]  Zbigniew R Struzik,et al.  Universal scaling law in human behavioral organization. , 2007, Physical review letters.

[43]  P. Bak,et al.  Learning from mistakes , 1997, Neuroscience.

[44]  C. Stam,et al.  Scale‐free dynamics of global functional connectivity in the human brain , 2004, Human brain mapping.

[45]  J. Schnakenberg,et al.  G. Nicolis und I. Prigogine: Self‐Organization in Nonequilibrium Systems. From Dissipative Structures to Order through Fluctuations. J. Wiley & Sons, New York, London, Sydney, Toronto 1977. 491 Seiten, Preis: £ 20.–, $ 34.– , 1978 .

[46]  Roel H. R. Deckers,et al.  Large-amplitude, spatially correlated fluctuations in BOLD fMRI signals during extended rest and early sleep stages. , 2006, Magnetic resonance imaging.

[47]  D. Chialvo,et al.  Pattern Formation and Functionality in Swarm Models , 1995, adap-org/9507003.

[48]  D. Sumpter,et al.  Phase transition between disordered and ordered foraging in Pharaoh's ants , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[49]  Dante R Chialvo,et al.  Brain organization into resting state networks emerges at criticality on a model of the human connectome. , 2012, Physical review letters.

[50]  J. T. Enright,et al.  Are the electroencephalograms mainly rhythmic? Assessment of periodicity in wide-band time series , 2003, Neuroscience.

[51]  Alison Abbott.  Letters to Leibniz in Berlin , 1998, Nature.

[52]  Kim Christensen,et al.  Rain: relaxations in the sky. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[53]  Annette Witt,et al.  Dynamic Effective Connectivity of Inter-Areal Brain Circuits , 2011, PLoS Comput. Biol..

[54]  D. R. Chialvo,et al.  Unraveling the fluctuations of animal motor activity. , 2009, Chaos.

[55]  L. Parsons,et al.  Interregional connectivity to primary motor cortex revealed using MRI resting state images , 1999, Human brain mapping.

[56]  R. Eckhorn,et al.  Oscillatory and non-oscillatory synchronizations in the visual cortex and their possible roles in associations of visual features. , 1994, Progress in brain research.

[57]  L Berthouze,et al.  Power-law distribution of phase-locking intervals does not imply critical interaction. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[58]  Jeffrey G. Ojemann,et al.  Power-Law Scaling in the Brain Surface Electric Potential , 2009, PLoS Comput. Biol..

[59]  Lawrence M. Ward,et al.  Dynamical Cognitive Science , 2001 .

[60]  D. Plenz,et al.  Criticality in neural systems , 2014 .

[61]  J. Deneubourg,et al.  Collective decision making through food recruitment , 1990, Insectes Sociaux.

[62]  O. Sporns,et al.  Mapping the Structural Core of Human Cerebral Cortex , 2008, PLoS biology.

[63]  H. Waelbroeck,et al.  Stable Criticality in a Feedforward Neural Network * , 2007 .

[64]  D. Chialvo,et al.  Self-similar correlation function in brain resting-state fMRI , 2010, 1003.3682.

[65]  Edward T. Bullmore,et al.  Broadband Criticality of Human Brain Network Synchronization , 2009, PLoS Comput. Biol..

[66]  Jeremy R. Manning,et al.  Broadband Shifts in Local Field Potential Power Spectra Are Correlated with Single-Neuron Spiking in Humans , 2009, The Journal of Neuroscience.

[67]  Barry Horwitz,et al.  The elusive concept of brain connectivity , 2003, NeuroImage.

[68]  H. Takayasu,et al.  Dynamic phase transition observed in the Internet traffic flow , 2000 .

[69]  D. Chialvo,et al.  Ising-like dynamics in large-scale functional brain networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[70]  D. Chialvo,et al.  Spontaneous BOLD event triggered averages for estimating functional connectivity at resting state , 2011, Neuroscience Letters.

[71]  D. Turcotte,et al.  Forest fires: An example of self-organized critical behavior , 1998, Science.

[72]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[73]  M. F.,et al.  Bibliography , 1985, Experimental Gerontology.

[74]  D. Chialvo,et al.  Self-similar correlation function in brain resting-state functional magnetic resonance imaging , 2010, Journal of The Royal Society Interface.