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      Neuronal Avalanches Differ from Wakefulness to Deep Sleep – Evidence from Intracranial Depth Recordings in Humans

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          Abstract

          Neuronal activity differs between wakefulness and sleep states. In contrast, an attractor state, called self-organized critical (SOC), was proposed to govern brain dynamics because it allows for optimal information coding. But is the human brain SOC for each vigilance state despite the variations in neuronal dynamics? We characterized neuronal avalanches – spatiotemporal waves of enhanced activity - from dense intracranial depth recordings in humans. We showed that avalanche distributions closely follow a power law – the hallmark feature of SOC - for each vigilance state. However, avalanches clearly differ with vigilance states: slow wave sleep (SWS) shows large avalanches, wakefulness intermediate, and rapid eye movement (REM) sleep small ones. Our SOC model, together with the data, suggested first that the differences are mediated by global but tiny changes in synaptic strength, and second, that the changes with vigilance states reflect small deviations from criticality to the subcritical regime, implying that the human brain does not operate at criticality proper but close to SOC. Independent of criticality, the analysis confirms that SWS shows increased correlations between cortical areas, and reveals that REM sleep shows more fragmented cortical dynamics.

          Author Summary

          Brain activity shows complex dynamics, even in the absence of external stimulation. In fact, most brain activity is generated internally. Therefore, it is crucial to understand the generation principles of internal activity. One hypothesis is that complex brain dynamics emerges from simple local interactions if the network is in a specific state, called “self-organized critical” (SOC). SOC indeed can account for dynamics in slices of brain tissue. However, we lack evidence that human brain dynamics is SOC. In addition, we wondered whether SOC can account for brain activity from wakefulness to deep sleep, despite clear changes in brain dynamics with vigilances states. To answer these questions, we analyzed intracranial depth recordings in humans. We found evidence that the human brain indeed operates close to criticality from wakefulness to deep sleep. However, we found deviations from criticality with vigilance states. These deviations, together with our modelling results, indicated that the human brain is close to SOC, but in a subcritical regime. In the subcritical regime complex dynamics still emerges from purely local interactions, but are more stable than the SOC state. In fact, operation the subcritical regime allows for a safety margin to supercriticality, which was linked to epilepsy.

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          Crackling Noise

          Crackling noise arises when a system responds to changing external conditions through discrete, impulsive events spanning a broad range of sizes. A wide variety of physical systems exhibiting crackling noise have been studied, from earthquakes on faults to paper crumpling. Because these systems exhibit regular behavior over many decades of sizes, their behavior is likely independent of microscopic and macroscopic details, and progress can be made by the use of very simple models. The fact that simple models and real systems can share the same behavior on a wide range of scales is called universality. We illustrate these ideas using results for our model of crackling noise in magnets, explaining the use of the renormalization group and scaling collapses. This field is still developing: we describe a number of continuing challenges.
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            Real-time computation at the edge of chaos in recurrent neural networks.

            Depending on the connectivity, recurrent networks of simple computational units can show very different types of dynamics, ranging from totally ordered to chaotic. We analyze how the type of dynamics (ordered or chaotic) exhibited by randomly connected networks of threshold gates driven by a time-varying input signal depends on the parameters describing the distribution of the connectivity matrix. In particular, we calculate the critical boundary in parameter space where the transition from ordered to chaotic dynamics takes place. Employing a recently developed framework for analyzing real-time computations, we show that only near the critical boundary can such networks perform complex computations on time series. Hence, this result strongly supports conjectures that dynamical systems that are capable of doing complex computational tasks should operate near the edge of chaos, that is, the transition from ordered to chaotic dynamics.
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              Spontaneous cortical activity in awake monkeys composed of neuronal avalanches.

              Spontaneous neuronal activity is an important property of the cerebral cortex but its spatiotemporal organization and dynamical framework remain poorly understood. Studies in reduced systems--tissue cultures, acute slices, and anesthetized rats--show that spontaneous activity forms characteristic clusters in space and time, called neuronal avalanches. Modeling studies suggest that networks with this property are poised at a critical state that optimizes input processing, information storage, and transfer, but the relevance of avalanches for fully functional cerebral systems has been controversial. Here we show that ongoing cortical synchronization in awake rhesus monkeys carries the signature of neuronal avalanches. Negative LFP deflections (nLFPs) correlate with neuronal spiking and increase in amplitude with increases in local population spike rate and synchrony. These nLFPs form neuronal avalanches that are scale-invariant in space and time and with respect to the threshold of nLFP detection. This dimension, threshold invariance, describes a fractal organization: smaller nLFPs are embedded in clusters of larger ones without destroying the spatial and temporal scale-invariance of the dynamics. These findings suggest an organization of ongoing cortical synchronization that is scale-invariant in its three fundamental dimensions--time, space, and local neuronal group size. Such scale-invariance has ontogenetic and phylogenetic implications because it allows large increases in network capacity without a fundamental reorganization of the system.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS Comput Biol
                PLoS Comput. Biol
                plos
                ploscomp
                PLoS Computational Biology
                Public Library of Science (San Francisco, USA )
                1553-734X
                1553-7358
                March 2013
                March 2013
                21 March 2013
                : 9
                : 3
                : e1002985
                Affiliations
                [1 ]Max Planck Institute for Brain Research, Department of Neural Systems and Coding, Frankfurt, Germany
                [2 ]University of Los Andes, Bogotá, Colombia
                [3 ]Johann Wolfgang Goethe University, Magnetoencephalography Unit, Brain Imaging Center, Frankfurt am Main, Germany
                [4 ]Hôpital de la Pitié-Salpêtrière, Centre de Recherche de l'Institut du Cerveau et de la Moelle épinière (CRICM), INSERM UMRS 975 - CNRS UMR 7225-UPMC, Paris, France
                Indiana University, United States of America
                Author notes

                The authors have declared that no competing interests exist.

                Conceived the study: VP. Conceived and designed the experiments: VP. Performed the experiments: MV MLVQ. Analyzed the data: VP. Contributed reagents/materials/analysis tools: MV MW. Wrote the paper: VP MW MV MLVQ.

                Article
                PCOMPBIOL-D-12-01510
                10.1371/journal.pcbi.1002985
                3605058
                23555220
                dcbace9a-1ebc-4e7a-b486-23ebd4fa16ee
                Copyright @ 2013

                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.

                History
                : 23 September 2012
                : 25 January 2013
                Page count
                Pages: 14
                Funding
                VP received support from the Max Planck Society. VP and MW received support from LOEWE Grant Neuronale Koordination Forschungsschwerpunkt Frankfurt (NeFF). MV and MLVQ received support from the European Union-FP7 Project EPILEPSIAE (Evolving Platform for Improving Living Expectation of Subjects Suffering from IctAl Events, Grant No 211713). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Categories
                Research Article
                Biology
                Neuroscience
                Computational Neuroscience
                Neural Networks
                Neurophysiology
                Physics
                Biophysics
                Biophysics Simulations
                Interdisciplinary Physics

                Quantitative & Systems biology
                Quantitative & Systems biology

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