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Broadband Criticality of Human Brain Network Synchronization

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      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 (<0.5 Hz, measured using functional MRI) and at higher frequencies (1–125 Hz, measured using magnetoencephalography). We conclude that human brain functional networks demonstrate critical dynamics in all frequency intervals, a phenomenon we have described as broadband criticality.

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      Most cited references 57

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      Collective dynamics of 'small-world' networks.

      Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.
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        Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain.

        An anatomical parcellation of the spatially normalized single-subject high-resolution T1 volume provided by the Montreal Neurological Institute (MNI) (D. L. Collins et al., 1998, Trans. Med. Imag. 17, 463-468) was performed. The MNI single-subject main sulci were first delineated and further used as landmarks for the 3D definition of 45 anatomical volumes of interest (AVOI) in each hemisphere. This procedure was performed using a dedicated software which allowed a 3D following of the sulci course on the edited brain. Regions of interest were then drawn manually with the same software every 2 mm on the axial slices of the high-resolution MNI single subject. The 90 AVOI were reconstructed and assigned a label. Using this parcellation method, three procedures to perform the automated anatomical labeling of functional studies are proposed: (1) labeling of an extremum defined by a set of coordinates, (2) percentage of voxels belonging to each of the AVOI intersected by a sphere centered by a set of coordinates, and (3) percentage of voxels belonging to each of the AVOI intersected by an activated cluster. An interface with the Statistical Parametric Mapping package (SPM, J. Ashburner and K. J. Friston, 1999, Hum. Brain Mapp. 7, 254-266) is provided as a freeware to researchers of the neuroimaging community. We believe that this tool is an improvement for the macroscopical labeling of activated area compared to labeling assessed using the Talairach atlas brain in which deformations are well known. However, this tool does not alleviate the need for more sophisticated labeling strategies based on anatomical or cytoarchitectonic probabilistic maps.
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          Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition

           Lars Onsager (1944)
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            Author and article information

            Affiliations
            [1 ]Behavioural & Clinical Neurosciences Institute, Departments of Experimental Psychology and Psychiatry, University of Cambridge, Cambridge, United Kingdom
            [2 ]MRC Cognition and Brain Sciences Unit, Cambridge, United Kingdom
            [3 ]Clinical Unit Cambridge, GlaxoSmithKline, Addenbrooke's Hospital, Cambridge, United Kingdom
            John Radcliffe Hospital, United Kingdom
            Author notes

            Conceived and designed the experiments: SRC EB. Performed the experiments: MLS SRC. Analyzed the data: MGK MLS EB. Contributed reagents/materials/analysis tools: MGK EB. Wrote the paper: MGK MLS SRC EB.

            Contributors
            Role: Editor
            Journal
            PLoS Comput Biol
            plos
            ploscomp
            PLoS Computational Biology
            Public Library of Science (San Francisco, USA )
            1553-734X
            1553-7358
            March 2009
            March 2009
            20 March 2009
            : 5
            : 3
            2647739
            19300473
            08-PLCB-RA-0850R2
            10.1371/journal.pcbi.1000314
            (Editor)
            Kitzbichler et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
            Counts
            Pages: 13
            Categories
            Research Article
            Computational Biology/Computational Neuroscience
            Neuroscience/Theoretical Neuroscience
            Physics/Interdisciplinary Physics

            Quantitative & Systems biology

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