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Fontenele AJ, Sooter JS, Norman VK, Gautam SH, Shew WL. Low-dimensional criticality embedded in high-dimensional awake brain dynamics. SCIENCE ADVANCES 2024; 10:eadj9303. [PMID: 38669340 PMCID: PMC11051676 DOI: 10.1126/sciadv.adj9303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Accepted: 03/26/2024] [Indexed: 04/28/2024]
Abstract
Whether cortical neurons operate in a strongly or weakly correlated dynamical regime determines fundamental information processing capabilities and has fueled decades of debate. We offer a resolution of this debate; we show that two important dynamical regimes, typically considered incompatible, can coexist in the same local cortical circuit by separating them into two different subspaces. In awake mouse motor cortex, we find a low-dimensional subspace with large fluctuations consistent with criticality-a dynamical regime with moderate correlations and multi-scale information capacity and transmission. Orthogonal to this critical subspace, we find a high-dimensional subspace containing a desynchronized dynamical regime, which may optimize input discrimination. The critical subspace is apparent only at long timescales, which explains discrepancies among some previous studies. Using a computational model, we show that the emergence of a low-dimensional critical subspace at large timescales agrees with established theory of critical dynamics. Our results suggest that the cortex leverages its high dimensionality to multiplex dynamical regimes across different subspaces.
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2
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Papo D, Buldú JM. Does the brain behave like a (complex) network? I. Dynamics. Phys Life Rev 2024; 48:47-98. [PMID: 38145591 DOI: 10.1016/j.plrev.2023.12.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Accepted: 12/10/2023] [Indexed: 12/27/2023]
Abstract
Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.
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Affiliation(s)
- D Papo
- Department of Neuroscience and Rehabilitation, Section of Physiology, University of Ferrara, Ferrara, Italy; Center for Translational Neurophysiology, Fondazione Istituto Italiano di Tecnologia, Ferrara, Italy.
| | - J M Buldú
- Complex Systems Group & G.I.S.C., Universidad Rey Juan Carlos, Madrid, Spain
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3
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Lombardi F, Herrmann HJ, Parrino L, Plenz D, Scarpetta S, Vaudano AE, de Arcangelis L, Shriki O. Beyond pulsed inhibition: Alpha oscillations modulate attenuation and amplification of neural activity in the awake resting state. Cell Rep 2023; 42:113162. [PMID: 37777965 PMCID: PMC10842118 DOI: 10.1016/j.celrep.2023.113162] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2022] [Revised: 06/07/2023] [Accepted: 09/07/2023] [Indexed: 10/03/2023] Open
Abstract
Alpha oscillations are a distinctive feature of the awake resting state of the human brain. However, their functional role in resting-state neuronal dynamics remains poorly understood. Here we show that, during resting wakefulness, alpha oscillations drive an alternation of attenuation and amplification bouts in neural activity. Our analysis indicates that inhibition is activated in pulses that last for a single alpha cycle and gradually suppress neural activity, while excitation is successively enhanced over a few alpha cycles to amplify neural activity. Furthermore, we show that long-term alpha amplitude fluctuations-the "waxing and waning" phenomenon-are an attenuation-amplification mechanism described by a power-law decay of the activity rate in the "waning" phase. Importantly, we do not observe such dynamics during non-rapid eye movement (NREM) sleep with marginal alpha oscillations. The results suggest that alpha oscillations modulate neural activity not only through pulses of inhibition (pulsed inhibition hypothesis) but also by timely enhancement of excitation (or disinhibition).
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Affiliation(s)
- Fabrizio Lombardi
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria; Department of Biomedical Sciences, University of Padova, Via Ugo Bassi 58B, 35131 Padova, Italy.
| | - Hans J Herrmann
- Departamento de Fisica, Universitade Federal do Ceara, Fortaleza 60451-970, Ceara, Brazil; PMMH, ESPCI, 7 quai St. Bernard, 75005 Paris, France
| | - Liborio Parrino
- Sleep Disorders Center, Department of Neurosciences, University of Parma, 43121 Parma, Italy
| | - Dietmar Plenz
- Section on Critical Brain Dynamics, NIH, Bethesda, MD 20892, USA
| | - Silvia Scarpetta
- Department of Physics, University of Salerno, 84084 Fisciano, Italy; INFN sez, Napoli Gr. Coll, 84084 Fisciano, Italy
| | - Anna Elisabetta Vaudano
- Neurology Unit, Azienda Ospedaliero-Universitaria of Modena, OCB Hospital, 41125 Modena, Italy; Department of Biomedical, Metabolic, and Neural Sciences, University of Modena and Reggio Emilia, 41125 Modena, Italy
| | - Lucilla de Arcangelis
- Department of Mathematics and Physics, University of Campania "Luigi Vanvitelli", Viale Lincoln 5, 81100 Caserta, Italy.
| | - Oren Shriki
- Department of Cognitive and Brain Sciences, Ben-Gurion University of the Negev, Beer-sheva, Israel.
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4
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González J, Cavelli M, Tort ABL, Torterolo P, Rubido N. Sleep disrupts complex spiking dynamics in the neocortex and hippocampus. PLoS One 2023; 18:e0290146. [PMID: 37590234 PMCID: PMC10434889 DOI: 10.1371/journal.pone.0290146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Accepted: 08/02/2023] [Indexed: 08/19/2023] Open
Abstract
Neuronal interactions give rise to complex dynamics in cortical networks, often described in terms of the diversity of activity patterns observed in a neural signal. Interestingly, the complexity of spontaneous electroencephalographic signals decreases during slow-wave sleep (SWS); however, the underlying neural mechanisms remain elusive. Here, we analyse in-vivo recordings from neocortical and hippocampal neuronal populations in rats and show that the complexity decrease is due to the emergence of synchronous neuronal DOWN states. Namely, we find that DOWN states during SWS force the population activity to be more recurrent, deterministic, and less random than during REM sleep or wakefulness, which, in turn, leads to less complex field recordings. Importantly, when we exclude DOWN states from the analysis, the recordings during wakefulness and sleep become indistinguishable: the spiking activity in all the states collapses to a common scaling. We complement these results by implementing a critical branching model of the cortex, which shows that inducing DOWN states to only a percentage of neurons is enough to generate a decrease in complexity that replicates SWS.
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Affiliation(s)
- Joaquín González
- Departamento de Fisiología de Facultad de Medicina, Universidad de la República, Montevideo, Uruguay
- Brain Institute, Federal University of Rio Grande do Norte, Natal, Brazil
| | - Matias Cavelli
- Department of Psychiatry, University of Wisconsin, Madison, Wisconsin, United States of America
| | - Adriano B. L. Tort
- Brain Institute, Federal University of Rio Grande do Norte, Natal, Brazil
| | - Pablo Torterolo
- Departamento de Fisiología de Facultad de Medicina, Universidad de la República, Montevideo, Uruguay
| | - Nicolás Rubido
- University of Aberdeen, King’s College, Institute for Complex Systems and Mathematical Biology, Aberdeen, United Kingdom
- Instituto de Física, Facultad de Ciencias, Universidad de la República, Montevideo, Uruguay
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5
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Fontenele AJ, Sooter JS, Norman VK, Gautam SH, Shew WL. Low dimensional criticality embedded in high dimensional awake brain dynamics. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.01.05.522896. [PMID: 37546833 PMCID: PMC10401950 DOI: 10.1101/2023.01.05.522896] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/08/2023]
Abstract
Whether cortical neurons operate in a strongly or weakly correlated dynamical regime determines fundamental information processing capabilities and has fueled decades of debate. Here we offer a resolution of this debate; we show that two important dynamical regimes, typically considered incompatible, can coexist in the same local cortical circuit by separating them into two different subspaces. In awake mouse motor cortex, we find a low-dimensional subspace with large fluctuations consistent with criticality - a dynamical regime with moderate correlations and multi-scale information capacity and transmission. Orthogonal to this critical subspace, we find a high-dimensional subspace containing a desynchronized dynamical regime, which may optimize input discrimination. The critical subspace is apparent only at long timescales, which explains discrepancies among some previous studies. Using a computational model, we show that the emergence of a low-dimensional critical subspace at large timescale agrees with established theory of critical dynamics. Our results suggest that cortex leverages its high dimensionality to multiplex dynamical regimes across different subspaces.
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Affiliation(s)
- Antonio J. Fontenele
- UA Integrative Systems Neuroscience Group, Department of Physics, University of Arkansas, Fayetteville, AR, USA, 72701
| | - J. Samuel Sooter
- UA Integrative Systems Neuroscience Group, Department of Physics, University of Arkansas, Fayetteville, AR, USA, 72701
| | - V. Kindler Norman
- UA Integrative Systems Neuroscience Group, Department of Physics, University of Arkansas, Fayetteville, AR, USA, 72701
| | - Shree Hari Gautam
- UA Integrative Systems Neuroscience Group, Department of Physics, University of Arkansas, Fayetteville, AR, USA, 72701
| | - Woodrow L. Shew
- UA Integrative Systems Neuroscience Group, Department of Physics, University of Arkansas, Fayetteville, AR, USA, 72701
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6
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Ponce-Alvarez A, Kringelbach ML, Deco G. Critical scaling of whole-brain resting-state dynamics. Commun Biol 2023; 6:627. [PMID: 37301936 PMCID: PMC10257708 DOI: 10.1038/s42003-023-05001-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2022] [Accepted: 05/31/2023] [Indexed: 06/12/2023] Open
Abstract
Scale invariance is a characteristic of neural activity. How this property emerges from neural interactions remains a fundamental question. Here, we studied the relation between scale-invariant brain dynamics and structural connectivity by analyzing human resting-state (rs-) fMRI signals, together with diffusion MRI (dMRI) connectivity and its approximation as an exponentially decaying function of the distance between brain regions. We analyzed the rs-fMRI dynamics using functional connectivity and a recently proposed phenomenological renormalization group (PRG) method that tracks the change of collective activity after successive coarse-graining at different scales. We found that brain dynamics display power-law correlations and power-law scaling as a function of PRG coarse-graining based on functional or structural connectivity. Moreover, we modeled the brain activity using a network of spins interacting through large-scale connectivity and presenting a phase transition between ordered and disordered phases. Within this simple model, we found that the observed scaling features were likely to emerge from critical dynamics and connections exponentially decaying with distance. In conclusion, our study tests the PRG method using large-scale brain activity and theoretical models and suggests that scaling of rs-fMRI activity relates to criticality.
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Affiliation(s)
- Adrián Ponce-Alvarez
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, 08005, Spain.
- Departament de Matemàtiques, Universitat Politècnica de Catalunya, Barcelona, Spain.
| | - Morten L Kringelbach
- Department of Psychiatry, University of Oxford, Oxford, OX3 7JX, UK
- Center for Music in the Brain, Department of Clinical Medicine, Aarhus University, Aarhus, 8000, Denmark
- Centre for Eudaimonia and Human Flourishing, Linacre College, University of Oxford, Oxford, UK
| | - Gustavo Deco
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, 08005, Spain
- Institució Catalana de la Recerca i Estudis Avançats (ICREA), Barcelona, 08010, Spain
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7
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Nattagh-Najafi M, Nabil M, Mridha RH, Nabavizadeh SA. Anomalous Self-Organization in Active Piles. ENTROPY (BASEL, SWITZERLAND) 2023; 25:861. [PMID: 37372205 DOI: 10.3390/e25060861] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2023] [Revised: 05/16/2023] [Accepted: 05/17/2023] [Indexed: 06/29/2023]
Abstract
Inspired by recent observations on active self-organized critical (SOC) systems, we designed an active pile (or ant pile) model with two ingredients: beyond-threshold toppling and under-threshold active motions. By including the latter component, we were able to replace the typical power-law distribution for geometric observables with a stretched exponential fat-tailed distribution, where the exponent and decay rate are dependent on the activity's strength (ζ). This observation helped us to uncover a hidden connection between active SOC systems and α-stable Levy systems. We demonstrate that one can partially sweep α-stable Levy distributions by changing ζ. The system undergoes a crossover towards Bak-Tang-Weisenfeld (BTW) sandpiles with a power-law behavior (SOC fixed point) below a crossover point ζ<ζ*≈0.1.
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Affiliation(s)
| | - Mohammad Nabil
- Department of Mechanical Engineering, University of Akron, Akron, OH 44325, USA
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8
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Gervais C, Boucher LP, Villar GM, Lee U, Duclos C. A scoping review for building a criticality-based conceptual framework of altered states of consciousness. Front Syst Neurosci 2023; 17:1085902. [PMID: 37304151 PMCID: PMC10248073 DOI: 10.3389/fnsys.2023.1085902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2022] [Accepted: 05/08/2023] [Indexed: 06/13/2023] Open
Abstract
The healthy conscious brain is thought to operate near a critical state, reflecting optimal information processing and high susceptibility to external stimuli. Conversely, deviations from the critical state are hypothesized to give rise to altered states of consciousness (ASC). Measures of criticality could therefore be an effective way of establishing the conscious state of an individual. Furthermore, characterizing the direction of a deviation from criticality may enable the development of treatment strategies for pathological ASC. The aim of this scoping review is to assess the current evidence supporting the criticality hypothesis, and the use of criticality as a conceptual framework for ASC. Using the PRISMA guidelines, Web of Science and PubMed were searched from inception to February 7th 2022 to find articles relating to measures of criticality across ASC. N = 427 independent papers were initially found on the subject. N = 378 were excluded because they were either: not related to criticality; not related to consciousness; not presenting results from a primary study; presenting model data. N = 49 independent papers were included in the present research, separated in 7 sub-categories of ASC: disorders of consciousness (DOC) (n = 5); sleep (n = 13); anesthesia (n = 18); epilepsy (n = 12); psychedelics and shamanic state of consciousness (n = 4); delirium (n = 1); meditative state (n = 2). Each category included articles suggesting a deviation of the critical state. While most studies were only able to identify a deviation from criticality without being certain of its direction, the preliminary consensus arising from the literature is that non-rapid eye movement (NREM) sleep reflects a subcritical state, epileptic seizures reflect a supercritical state, and psychedelics are closer to the critical state than normal consciousness. This scoping review suggests that, though the literature is limited and methodologically inhomogeneous, ASC are characterized by a deviation from criticality, though its direction is not clearly reported in a majority of studies. Criticality could become, with more extensive research, an effective and objective way to characterize ASC, and help identify therapeutic avenues to improve criticality in pathological brain states. Furthermore, we suggest how anesthesia and psychedelics could potentially be used as neuromodulation techniques to restore criticality in DOC.
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Affiliation(s)
- Charles Gervais
- Department of Psychology, Université de Montréal, Montréal, QC, Canada
- Centre for Advanced Research in Sleep Medicine & Integrated Trauma Centre, Centre Intégré Universitaire de Santé et de Services Sociaux du Nord-de-l’île-de-Montréal, Montréal, QC, Canada
| | - Louis-Philippe Boucher
- Centre for Advanced Research in Sleep Medicine & Integrated Trauma Centre, Centre Intégré Universitaire de Santé et de Services Sociaux du Nord-de-l’île-de-Montréal, Montréal, QC, Canada
- Department of Neuroscience, Université de Montréal, Montréal, QC, Canada
| | - Guillermo Martinez Villar
- Department of Psychology, Université de Montréal, Montréal, QC, Canada
- Centre for Advanced Research in Sleep Medicine & Integrated Trauma Centre, Centre Intégré Universitaire de Santé et de Services Sociaux du Nord-de-l’île-de-Montréal, Montréal, QC, Canada
- Department of Biomedical Sciences, Université de Montréal, Montréal, QC, Canada
| | - UnCheol Lee
- Department of Anesthesiology, University of Michigan Medical School, Ann Arbor, MI, United States
- Center for Consciousness Science, University of Michigan Medical School, Ann Arbor, MI, United States
| | - Catherine Duclos
- Centre for Advanced Research in Sleep Medicine & Integrated Trauma Centre, Centre Intégré Universitaire de Santé et de Services Sociaux du Nord-de-l’île-de-Montréal, Montréal, QC, Canada
- Department of Neuroscience, Université de Montréal, Montréal, QC, Canada
- Department of Anesthesiology and Pain Medicine, Université de Montréal, Montréal, QC, Canada
- CIFAR Azrieli Global Scholars Program, Toronto, ON, Canada
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9
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Müller PM, Meisel C. Spatial and temporal correlations in human cortex are inherently linked and predicted by functional hierarchy, vigilance state as well as antiepileptic drug load. PLoS Comput Biol 2023; 19:e1010919. [PMID: 36867652 PMCID: PMC10027224 DOI: 10.1371/journal.pcbi.1010919] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2022] [Revised: 03/20/2023] [Accepted: 02/03/2023] [Indexed: 03/04/2023] Open
Abstract
The ability of neural circuits to integrate information over time and across different cortical areas is believed an essential ingredient for information processing in the brain. Temporal and spatial correlations in cortex dynamics have independently been shown to capture these integration properties in task-dependent ways. A fundamental question remains if temporal and spatial integration properties are linked and what internal and external factors shape these correlations. Previous research on spatio-temporal correlations has been limited in duration and coverage, thus providing only an incomplete picture of their interdependence and variability. Here, we use long-term invasive EEG data to comprehensively map temporal and spatial correlations according to cortical topography, vigilance state and drug dependence over extended periods of time. We show that temporal and spatial correlations in cortical networks are intimately linked, decline under antiepileptic drug action, and break down during slow-wave sleep. Further, we report temporal correlations in human electrophysiology signals to increase with the functional hierarchy in cortex. Systematic investigation of a neural network model suggests that these dynamical features may arise when dynamics are poised near a critical point. Our results provide mechanistic and functional links between specific measurable changes in the network dynamics relevant for characterizing the brain's changing information processing capabilities.
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Affiliation(s)
- Paul Manuel Müller
- Computational Neurology Lab, Department of Neurology, Charité-Universitätsmedizin Berlin, Berlin, Germany
- Berlin Institute of Health, Berlin, Germany
- NeuroCure Cluster of Excellence, Charité-Universitätsmedizin Berlin, Berlin, Germany
| | - Christian Meisel
- Computational Neurology Lab, Department of Neurology, Charité-Universitätsmedizin Berlin, Berlin, Germany
- Berlin Institute of Health, Berlin, Germany
- NeuroCure Cluster of Excellence, Charité-Universitätsmedizin Berlin, Berlin, Germany
- Center for Stroke Research Berlin, Berlin, Germany
- Bernstein Center for Computational Neuroscience, Berlin, Germany
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10
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Alvankar Golpayegan H, de Candia A. Bistability and criticality in the stochastic Wilson-Cowan model. Phys Rev E 2023; 107:034404. [PMID: 37073019 DOI: 10.1103/physreve.107.034404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2022] [Accepted: 02/17/2023] [Indexed: 04/20/2023]
Abstract
We study a stochastic version of the Wilson-Cowan model of neural dynamics, where the response function of neurons grows faster than linearly above the threshold. The model shows a region of parameters where two attractive fixed points of the dynamics exist simultaneously. One fixed point is characterized by lower activity and scale-free critical behavior, while the second fixed point corresponds to a higher (supercritical) persistent activity, with small fluctuations around a mean value. When the number of neurons is not too large, the system can switch between these two different states with a probability depending on the parameters of the network. Along with alternation of states, the model displays a bimodal distribution of the avalanches of activity, with a power-law behavior corresponding to the critical state, and a bump of very large avalanches due to the high-activity supercritical state. The bistability is due to the presence of a first-order (discontinuous) transition in the phase diagram, and the observed critical behavior is connected with the line where the low-activity state becomes unstable (spinodal line).
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Affiliation(s)
- Hanieh Alvankar Golpayegan
- Dipartimento di Neuroscienze, Scienze Riproduttive e Odontostomatologiche, Università di Napoli Federico II, Via S. Pansini 5, 80131 Napoli, Italy
| | - Antonio de Candia
- Dipartimento di Fisica "E. Pancini", Università di Napoli Federico II, Complesso Universitario di Monte Sant'Angelo, via Cintia, 80126 Napoli, Italy
- INFN, Sezione di Napoli, Gruppo collegato di Salerno, 84084 Fisciano (SA), Italy
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11
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Scale free avalanches in excitatory-inhibitory populations of spiking neurons with conductance based synaptic currents. J Comput Neurosci 2023; 51:149-172. [PMID: 36280652 PMCID: PMC9840601 DOI: 10.1007/s10827-022-00838-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2022] [Revised: 09/19/2022] [Accepted: 10/04/2022] [Indexed: 01/18/2023]
Abstract
We investigate spontaneous critical dynamics of excitatory and inhibitory (EI) sparsely connected populations of spiking leaky integrate-and-fire neurons with conductance-based synapses. We use a bottom-up approach to derive a single neuron gain function and a linear Poisson neuron approximation which we use to study mean-field dynamics of the EI population and its bifurcations. In the low firing rate regime, the quiescent state loses stability due to saddle-node or Hopf bifurcations. In particular, at the Bogdanov-Takens (BT) bifurcation point which is the intersection of the Hopf bifurcation and the saddle-node bifurcation lines of the 2D dynamical system, the network shows avalanche dynamics with power-law avalanche size and duration distributions. This matches the characteristics of low firing spontaneous activity in the cortex. By linearizing gain functions and excitatory and inhibitory nullclines, we can approximate the location of the BT bifurcation point. This point in the control parameter phase space corresponds to the internal balance of excitation and inhibition and a slight excess of external excitatory input to the excitatory population. Due to the tight balance of average excitation and inhibition currents, the firing of the individual cells is fluctuation-driven. Around the BT point, the spiking of neurons is a Poisson process and the population average membrane potential of neurons is approximately at the middle of the operating interval [Formula: see text]. Moreover, the EI network is close to both oscillatory and active-inactive phase transition regimes.
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12
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Neto JP, Spitzner FP, Priesemann V. Sampling effects and measurement overlap can bias the inference of neuronal avalanches. PLoS Comput Biol 2022; 18:e1010678. [PMID: 36445932 PMCID: PMC9733887 DOI: 10.1371/journal.pcbi.1010678] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2020] [Revised: 12/09/2022] [Accepted: 10/24/2022] [Indexed: 12/02/2022] Open
Abstract
To date, it is still impossible to sample the entire mammalian brain with single-neuron precision. This forces one to either use spikes (focusing on few neurons) or to use coarse-sampled activity (averaging over many neurons, e.g. LFP). Naturally, the sampling technique impacts inference about collective properties. Here, we emulate both sampling techniques on a simple spiking model to quantify how they alter observed correlations and signatures of criticality. We describe a general effect: when the inter-electrode distance is small, electrodes sample overlapping regions in space, which increases the correlation between the signals. For coarse-sampled activity, this can produce power-law distributions even for non-critical systems. In contrast, spike recordings do not suffer this particular bias and underlying dynamics can be identified. This may resolve why coarse measures and spikes have produced contradicting results in the past.
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Affiliation(s)
- Joao Pinheiro Neto
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
| | - F. Paul Spitzner
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
| | - Viola Priesemann
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Bernstein Center for Computational Neuroscience, Göttingen, Germany
- Georg-August University Göttingen, Göttingen, Germany
- * E-mail:
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13
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Ehsani M, Jost J. Self-organized criticality in a mesoscopic model of excitatory-inhibitory neuronal populations by short-term and long-term synaptic plasticity. Front Comput Neurosci 2022; 16:910735. [PMID: 36299476 PMCID: PMC9588946 DOI: 10.3389/fncom.2022.910735] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2022] [Accepted: 09/16/2022] [Indexed: 09/19/2023] Open
Abstract
Dynamics of an interconnected population of excitatory and inhibitory spiking neurons wandering around a Bogdanov-Takens (BT) bifurcation point can generate the observed scale-free avalanches at the population level and the highly variable spike patterns of individual neurons. These characteristics match experimental findings for spontaneous intrinsic activity in the brain. In this paper, we address the mechanisms causing the system to get and remain near this BT point. We propose an effective stochastic neural field model which captures the dynamics of the mean-field model. We show how the network tunes itself through local long-term synaptic plasticity by STDP and short-term synaptic depression to be close to this bifurcation point. The mesoscopic model that we derive matches the directed percolation model at the absorbing state phase transition.
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Affiliation(s)
- Masud Ehsani
- Max Planck Institute for Mathematics in Sciences, Leipzig, Germany
| | - Jürgen Jost
- Max Planck Institute for Mathematics in Sciences, Leipzig, Germany
- Santa Fe Institute, Santa Fe, NM, United States
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14
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Tian Y, Tan Z, Hou H, Li G, Cheng A, Qiu Y, Weng K, Chen C, Sun P. Theoretical foundations of studying criticality in the brain. Netw Neurosci 2022; 6:1148-1185. [PMID: 38800464 PMCID: PMC11117095 DOI: 10.1162/netn_a_00269] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2022] [Accepted: 07/12/2022] [Indexed: 05/29/2024] Open
Abstract
Criticality is hypothesized as a physical mechanism underlying efficient transitions between cortical states and remarkable information-processing capacities in the brain. While considerable evidence generally supports this hypothesis, nonnegligible controversies persist regarding the ubiquity of criticality in neural dynamics and its role in information processing. Validity issues frequently arise during identifying potential brain criticality from empirical data. Moreover, the functional benefits implied by brain criticality are frequently misconceived or unduly generalized. These problems stem from the nontriviality and immaturity of the physical theories that analytically derive brain criticality and the statistic techniques that estimate brain criticality from empirical data. To help solve these problems, we present a systematic review and reformulate the foundations of studying brain criticality, that is, ordinary criticality (OC), quasi-criticality (qC), self-organized criticality (SOC), and self-organized quasi-criticality (SOqC), using the terminology of neuroscience. We offer accessible explanations of the physical theories and statistical techniques of brain criticality, providing step-by-step derivations to characterize neural dynamics as a physical system with avalanches. We summarize error-prone details and existing limitations in brain criticality analysis and suggest possible solutions. Moreover, we present a forward-looking perspective on how optimizing the foundations of studying brain criticality can deepen our understanding of various neuroscience questions.
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Affiliation(s)
- Yang Tian
- Department of Psychology & Tsinghua Laboratory of Brain and Intelligence, Tsinghua University, Beijing, China
- Laboratory of Advanced Computing and Storage, Central Research Institute, 2012 Laboratories, Huawei Technologies Co. Ltd., Beijing, China
| | - Zeren Tan
- Institute for Interdisciplinary Information Science, Tsinghua University, Beijing, China
| | - Hedong Hou
- UFR de Mathématiques, Université de Paris, Paris, France
| | - Guoqi Li
- Institute of Automation, Chinese Academy of Science, Beijing, China
- University of Chinese Academy of Science, Beijing, China
| | - Aohua Cheng
- Tsien Excellence in Engineering Program, School of Aerospace Engineering, Tsinghua University, Beijing, China
| | - Yike Qiu
- Tsien Excellence in Engineering Program, School of Aerospace Engineering, Tsinghua University, Beijing, China
| | - Kangyu Weng
- Tsien Excellence in Engineering Program, School of Aerospace Engineering, Tsinghua University, Beijing, China
| | - Chun Chen
- Department of Psychology & Tsinghua Laboratory of Brain and Intelligence, Tsinghua University, Beijing, China
| | - Pei Sun
- Department of Psychology & Tsinghua Laboratory of Brain and Intelligence, Tsinghua University, Beijing, China
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15
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Yu C, Zhai J. Scale-free avalanche dynamics possibly generated by randomly jumping among many stable states. CHAOS (WOODBURY, N.Y.) 2022; 32:103116. [PMID: 36319307 DOI: 10.1063/5.0104853] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2022] [Accepted: 09/21/2022] [Indexed: 06/16/2023]
Abstract
A large amount of research has used the scale-free statistics of neuronal avalanches as a signature of the criticality of neural systems, which bears criticisms. For instance, the work of Touboul and Destexhe demonstrated that non-critical systems could also display such scale-free dynamics, which passed their rigorous statistical analyses. In this paper, we show that a fully connected stochastic neural network may also generate scale-free dynamics simply by jumping among many stable states.
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Affiliation(s)
- Chaojun Yu
- School of Mathematical Sciences, Zhejiang University, Hangzhou 310058, China
| | - Jian Zhai
- School of Mathematical Sciences, Zhejiang University, Hangzhou 310058, China
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16
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O'Byrne J, Jerbi K. How critical is brain criticality? Trends Neurosci 2022; 45:820-837. [PMID: 36096888 DOI: 10.1016/j.tins.2022.08.007] [Citation(s) in RCA: 49] [Impact Index Per Article: 24.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2022] [Revised: 07/27/2022] [Accepted: 08/10/2022] [Indexed: 10/31/2022]
Abstract
Criticality is the singular state of complex systems poised at the brink of a phase transition between order and randomness. Such systems display remarkable information-processing capabilities, evoking the compelling hypothesis that the brain may itself be critical. This foundational idea is now drawing renewed interest thanks to high-density data and converging cross-disciplinary knowledge. Together, these lines of inquiry have shed light on the intimate link between criticality, computation, and cognition. Here, we review these emerging trends in criticality neuroscience, highlighting new data pertaining to the edge of chaos and near-criticality, and making a case for the distance to criticality as a useful metric for probing cognitive states and mental illness. This unfolding progress in the field contributes to establishing criticality theory as a powerful mechanistic framework for studying emergent function and its efficiency in both biological and artificial neural networks.
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Affiliation(s)
- Jordan O'Byrne
- Cognitive and Computational Neuroscience Lab, Psychology Department, University of Montreal, Montreal, Quebec, Canada
| | - Karim Jerbi
- Cognitive and Computational Neuroscience Lab, Psychology Department, University of Montreal, Montreal, Quebec, Canada; MILA (Quebec Artificial Intelligence Institute), Montreal, Quebec, Canada; UNIQUE Center (Quebec Neuro-AI Research Center), Montreal, Quebec, Canada.
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17
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Walter N, Hinterberger T. Self-organized criticality as a framework for consciousness: A review study. Front Psychol 2022; 13:911620. [PMID: 35911009 PMCID: PMC9336647 DOI: 10.3389/fpsyg.2022.911620] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2022] [Accepted: 06/29/2022] [Indexed: 01/04/2023] Open
Abstract
Objective No current model of consciousness is univocally accepted on either theoretical or empirical grounds, and the need for a solid unifying framework is evident. Special attention has been given to the premise that self-organized criticality (SOC) is a fundamental property of neural system. SOC provides a competitive model to describe the physical mechanisms underlying spontaneous brain activity, and thus, critical dynamics were proposed as general gauges of information processing representing a strong candidate for a surrogate measure of consciousness. As SOC could be a neurodynamical framework, which may be able to bring together existing theories and experimental evidence, the purpose of this work was to provide a comprehensive overview of progress of research on SOC in association with consciousness. Methods A comprehensive search of publications on consciousness and SOC published between 1998 and 2021 was conducted. The Web of Science database was searched, and annual number of publications and citations, type of articles, and applied methods were determined. Results A total of 71 publications were identified. The annual number of citations steadily increased over the years. Original articles comprised 50.7% and reviews/theoretical articles 43.6%. Sixteen studies reported on human data and in seven studies data were recorded in animals. Computational models were utilized in n = 12 studies. EcoG data were assessed in n = 4 articles, fMRI in n = 4 studies, and EEG/MEG in n = 10 studies. Notably, different analytical tools were applied in the EEG/MEG studies to assess a surrogate measure of criticality such as the detrended fluctuation analysis, the pair correlation function, parameters from the neuronal avalanche analysis and the spectral exponent. Conclusion Recent studies pointed out agreements of critical dynamics with the current most influencing theories in the field of consciousness research, the global workspace theory and the integrated information theory. Thus, the framework of SOC as a neurodynamical parameter for consciousness seems promising. However, identified experimental work was small in numbers, and a heterogeneity of applied analytical tools as a surrogate measure of criticality was observable, which limits the generalizability of findings.
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18
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Sawicki J, Hartmann L, Bader R, Schöll E. Modelling the perception of music in brain network dynamics. FRONTIERS IN NETWORK PHYSIOLOGY 2022; 2:910920. [PMID: 36926090 PMCID: PMC10013054 DOI: 10.3389/fnetp.2022.910920] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2022] [Accepted: 07/11/2022] [Indexed: 11/13/2022]
Abstract
We analyze the influence of music in a network of FitzHugh-Nagumo oscillators with empirical structural connectivity measured in healthy human subjects. We report an increase of coherence between the global dynamics in our network and the input signal induced by a specific music song. We show that the level of coherence depends crucially on the frequency band. We compare our results with experimental data, which also describe global neural synchronization between different brain regions in the gamma-band range in a time-dependent manner correlated with musical large-scale form, showing increased synchronization just before transitions between different parts in a musical piece (musical high-level events). The results also suggest a separation in musical form-related brain synchronization between high brain frequencies, associated with neocortical activity, and low frequencies in the range of dance movements, associated with interactivity between cortical and subcortical regions.
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Affiliation(s)
- Jakub Sawicki
- Potsdam Institute for Climate Impact Research, Potsdam, Germany.,Institut für Musikpädagogik, Universität der Künste Berlin, Berlin, Germany.,Fachhochschule Nordwestschweiz FHNW, Basel, Switzerland.,Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany
| | - Lenz Hartmann
- Institute of Systematic Musicology, University of Hamburg, Hamburg, Germany
| | - Rolf Bader
- Institute of Systematic Musicology, University of Hamburg, Hamburg, Germany
| | - Eckehard Schöll
- Potsdam Institute for Climate Impact Research, Potsdam, Germany.,Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany.,Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität, Berlin, Germany
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19
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Johansson B. Challenges and Controversies in COVID-19: Masking the General Population may Attenuate This Pandemic's Outbreak. Front Public Health 2021; 9:643991. [PMID: 34568248 PMCID: PMC8455895 DOI: 10.3389/fpubh.2021.643991] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2020] [Accepted: 06/22/2021] [Indexed: 11/13/2022] Open
Abstract
SARS-CoV-2, the virus that causes COVID-19, spreads i. a., by respiratory droplets. The use of masks in preventing spread is controversial; masks are considered useless by many, while being mandated in some locations. Here, the effect of masking the general population on a COVID-19-like epidemic is estimated by computer simulation using three separate types of software. The main questions are whether mask use by the general population can limit the spread of SARS-CoV-2 in a country and how to identify opportunities when mask use is cost-effective and safe. To address these questions, the protective effects of different types of masks, the side-effects of masks, and avenues for improvements of masks and masking are addressed. Main results: (i) Any type of mask, even simple home-made ones, may be of value, even if the protective effect of each mask (here dubbed "one mask-protection") is low. Strict adherence to mask use does not appear to be critical but increasing one mask-protection to >50% was found to be advantageous. (ii) Masks do seem to reduce the number of new cases even if introduced at a late stage in an epidemic, but early implementation helps reduce the cumulative and total number of cases. (iii) The simulations suggest that it might be possible to eliminate a COVID-19 outbreak by widespread mask use during a limited period. There is a brief discussion of why the reported effect size of masking varies widely, and is expected to do so, because of different filtration abilities of different masks, differences in compliance and fitting, other routes of transmission, pre-existing immunity, and because a system of interconnected, disease-prone individuals has non-linear properties. A software solution to visualize infection spread is presented. The results from these simulations are encouraging, but do not necessarily represent the real-life situation, so it is suggested that clinical trials of masks are now carried out while continuously monitoring effects and side-effects. As mask use is not without risks and costs, it is suggested that governments and scientists have an important role in advising the public about the sensible use of masks.
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Affiliation(s)
- Björn Johansson
- Theme Aging, Karolinska University Hospital, Stockholm, Sweden
- Department of Clinical Neuroscience, Karolinska Institutet, Stockholm, Sweden
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20
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Mariani B, Nicoletti G, Bisio M, Maschietto M, Oboe R, Leparulo A, Suweis S, Vassanelli S. Neuronal Avalanches Across the Rat Somatosensory Barrel Cortex and the Effect of Single Whisker Stimulation. Front Syst Neurosci 2021; 15:709677. [PMID: 34526881 PMCID: PMC8435673 DOI: 10.3389/fnsys.2021.709677] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2021] [Accepted: 08/02/2021] [Indexed: 11/13/2022] Open
Abstract
Since its first experimental signatures, the so called "critical brain hypothesis" has been extensively studied. Yet, its actual foundations remain elusive. According to a widely accepted teleological reasoning, the brain would be poised to a critical state to optimize the mapping of the noisy and ever changing real-world inputs, thus suggesting that primary sensory cortical areas should be critical. We investigated whether a single barrel column of the somatosensory cortex of the anesthetized rat displays a critical behavior. Neuronal avalanches were recorded across all cortical layers in terms of both multi-unit activities and population local field potentials, and their behavior during spontaneous activity compared to the one evoked by a controlled single whisker deflection. By applying a maximum likelihood statistical method based on timeseries undersampling to fit the avalanches distributions, we show that neuronal avalanches are power law distributed for both multi-unit activities and local field potentials during spontaneous activity, with exponents that are spread along a scaling line. Instead, after the tactile stimulus, activity switches to a transient across-layers synchronization mode that appears to dominate the cortical representation of the single sensory input.
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Affiliation(s)
- Benedetta Mariani
- Laboratory of Interdisciplinary Physics, Department of Physics and Astronomy, University of Padova, Padova, Italy
- Padova Neuroscience Center, University of Padova, Padova, Italy
| | - Giorgio Nicoletti
- Laboratory of Interdisciplinary Physics, Department of Physics and Astronomy, University of Padova, Padova, Italy
| | - Marta Bisio
- Padova Neuroscience Center, University of Padova, Padova, Italy
- Department of Biomedical Science, University of Padova, Padova, Italy
| | - Marta Maschietto
- Department of Biomedical Science, University of Padova, Padova, Italy
| | - Roberto Oboe
- Department of Management and Engineering, University of Padova, Padova, Italy
| | | | - Samir Suweis
- Laboratory of Interdisciplinary Physics, Department of Physics and Astronomy, University of Padova, Padova, Italy
- Padova Neuroscience Center, University of Padova, Padova, Italy
| | - Stefano Vassanelli
- Padova Neuroscience Center, University of Padova, Padova, Italy
- Department of Biomedical Science, University of Padova, Padova, Italy
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21
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de Heuvel J, Wilting J, Becker M, Priesemann V, Zierenberg J. Characterizing spreading dynamics of subsampled systems with nonstationary external input. Phys Rev E 2021; 102:040301. [PMID: 33212575 DOI: 10.1103/physreve.102.040301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2019] [Accepted: 09/21/2020] [Indexed: 11/07/2022]
Abstract
Many systems with propagation dynamics, such as spike propagation in neural networks and spreading of infectious diseases, can be approximated by autoregressive models. The estimation of model parameters can be complicated by the experimental limitation that one observes only a fraction of the system (subsampling) and potentially time-dependent parameters, leading to incorrect estimates. We show analytically how to overcome the subsampling bias when estimating the propagation rate for systems with certain nonstationary external input. This approach is readily applicable to trial-based experimental setups and seasonal fluctuations as demonstrated on spike recordings from monkey prefrontal cortex and spreading of norovirus and measles.
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Affiliation(s)
- Jorge de Heuvel
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
| | - Jens Wilting
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
| | - Moritz Becker
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany.,Department of Computational Neuroscience, Third Institute of Physics-Biophysics, Georg-August-University, 37077 Göttingen, Germany
| | - Viola Priesemann
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
| | - Johannes Zierenberg
- Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
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22
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Lotfi N, Fontenele AJ, Feliciano T, Aguiar LAA, de Vasconcelos NAP, Soares-Cunha C, Coimbra B, Rodrigues AJ, Sousa N, Copelli M, Carelli PV. Signatures of brain criticality unveiled by maximum entropy analysis across cortical states. Phys Rev E 2021; 102:012408. [PMID: 32795006 DOI: 10.1103/physreve.102.012408] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2020] [Accepted: 07/01/2020] [Indexed: 11/07/2022]
Abstract
It has recently been reported that statistical signatures of brain criticality, obtained from distributions of neuronal avalanches, can depend on the cortical state. We revisit these claims with a completely different and independent approach, employing a maximum entropy model to test whether signatures of criticality appear in urethane-anesthetized rats. To account for the spontaneous variation of cortical states, we parse the time series and perform the maximum entropy analysis as a function of the variability of the population spiking activity. To compare data sets with different numbers of neurons, we define a normalized distance to criticality that takes into account the peak and width of the specific heat curve. We found a universal collapse of the normalized distance to criticality dependence on the cortical state, on an animal by animal basis. This indicates a universal dynamics and a critical point at an intermediate value of spiking variability.
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Affiliation(s)
- Nastaran Lotfi
- Departamento de Física, Universidade Federal de Pernambuco, Recife, PE 50670-901, Brazil
| | - Antonio J Fontenele
- Departamento de Física, Universidade Federal de Pernambuco, Recife, PE 50670-901, Brazil
| | - Thaís Feliciano
- Departamento de Física, Universidade Federal de Pernambuco, Recife, PE 50670-901, Brazil
| | - Leandro A A Aguiar
- Departamento de Física, Universidade Federal de Pernambuco, Recife, PE 50670-901, Brazil
| | - Nivaldo A P de Vasconcelos
- Life and Health Sciences Research Institute (ICVS), School of Medicine, University of Minho, Braga, 4710-057, Portugal.,ICVS/3B's-PT Government Associate Laboratory, Braga/Guimarães, 4806-909, Portugal
| | - Carina Soares-Cunha
- Life and Health Sciences Research Institute (ICVS), School of Medicine, University of Minho, Braga, 4710-057, Portugal.,ICVS/3B's-PT Government Associate Laboratory, Braga/Guimarães, 4806-909, Portugal
| | - Bárbara Coimbra
- Life and Health Sciences Research Institute (ICVS), School of Medicine, University of Minho, Braga, 4710-057, Portugal.,ICVS/3B's-PT Government Associate Laboratory, Braga/Guimarães, 4806-909, Portugal
| | - Ana João Rodrigues
- Life and Health Sciences Research Institute (ICVS), School of Medicine, University of Minho, Braga, 4710-057, Portugal.,ICVS/3B's-PT Government Associate Laboratory, Braga/Guimarães, 4806-909, Portugal
| | - Nuno Sousa
- Life and Health Sciences Research Institute (ICVS), School of Medicine, University of Minho, Braga, 4710-057, Portugal.,ICVS/3B's-PT Government Associate Laboratory, Braga/Guimarães, 4806-909, Portugal
| | - Mauro Copelli
- Departamento de Física, Universidade Federal de Pernambuco, Recife, PE 50670-901, Brazil
| | - Pedro V Carelli
- Departamento de Física, Universidade Federal de Pernambuco, Recife, PE 50670-901, Brazil
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23
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Miller SR, Yu S, Pajevic S, Plenz D. Long-term stability of avalanche scaling and integrative network organization in prefrontal and premotor cortex. Netw Neurosci 2021; 5:505-526. [PMID: 34189375 PMCID: PMC8233112 DOI: 10.1162/netn_a_00188] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2020] [Accepted: 02/11/2021] [Indexed: 11/29/2022] Open
Abstract
Ongoing neuronal activity in the brain establishes functional networks that reflect normal and pathological brain function. Most estimates of these functional networks suffer from low spatiotemporal resolution and indirect measures of neuronal population activity, limiting the accuracy and reliability in their reconstruction over time. Here, we studied the stability of neuronal avalanche dynamics and corresponding reconstructed functional networks in the adult brain. Using chronically implanted high-density microelectrode arrays, the local field potential (LFP) of resting-state activity was recorded in prefrontal and premotor cortex of awake nonhuman primates. Avalanche dynamics revealed stable scaling exhibiting an inverted parabolic profile and collapse exponent of 2 in line with a critical branching process over many days and weeks. Functional networks were based on a Bayesian-derived estimator and demonstrated stable integrative properties characterized by nontrivial high neighborhood overlap between strongly connected nodes and robustness to weak-link pruning. Entropy-based mixing analysis revealed significant changes in strong link weights over weeks. The long-term stability in avalanche scaling and integrative network organization in the face of individual link weight changes should support the development of noninvasive biomarkers to characterize normal and abnormal brain states in the adult brain. The brain is spontaneously active even in the absence of specific sensations or movements. This ongoing activity arises from the interactions among hundreds of thousands of neurons, which has been captured by a variety of distinct functional networks predictive of healthy and pathological brain functions. The global dynamical states and overarching network principles that underlie such ongoing brain activity are not well understood. Here we identify avalanche dynamics and “friendship” networks as two major features of ongoing activity in the frontal cortex of nonhuman primates. We demonstrate their stability over weeks in the face of local network changes. Deviation from avalanche dynamics and “friendship” organization might provide robust biomarkers to identify normal and pathological brain states.
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Affiliation(s)
- Stephanie R Miller
- Section on Critical Brain Dynamics, National Institute of Mental Health, Bethesda, MD, USA
| | - Shan Yu
- Section on Critical Brain Dynamics, National Institute of Mental Health, Bethesda, MD, USA
| | - Sinisa Pajevic
- Section on Quantitative Imaging and Tissue Sciences, National Institute of Child Health and Development, NIH, Bethesda, MD, USA
| | - Dietmar Plenz
- Section on Critical Brain Dynamics, National Institute of Mental Health, Bethesda, MD, USA
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24
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Zhou X, Ma N, Song B, Wu Z, Liu G, Liu L, Yu L, Feng J. Optimal Organization of Functional Connectivity Networks for Segregation and Integration With Large-Scale Critical Dynamics in Human Brains. Front Comput Neurosci 2021; 15:641335. [PMID: 33867963 PMCID: PMC8044315 DOI: 10.3389/fncom.2021.641335] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2020] [Accepted: 02/23/2021] [Indexed: 12/04/2022] Open
Abstract
The optimal organization for functional segregation and integration in brain is made evident by the “small-world” feature of functional connectivity (FC) networks and is further supported by the loss of this feature that has been described in many types of brain disease. However, it remains unknown how such optimally organized FC networks arise from the brain's structural constrains. On the other hand, an emerging literature suggests that brain function may be supported by critical neural dynamics, which is believed to facilitate information processing in brain. Though previous investigations have shown that the critical dynamics plays an important role in understanding the relation between whole brain structural connectivity and functional connectivity, it is not clear if the critical dynamics could be responsible for the optimal FC network configuration in human brains. Here, we show that the long-range temporal correlations (LRTCs) in the resting state fMRI blood-oxygen-level-dependent (BOLD) signals are significantly correlated with the topological matrices of the FC brain network. Using structure-dynamics-function modeling approach that incorporates diffusion tensor imaging (DTI) data and simple cellular automata dynamics, we showed that the critical dynamics could optimize the whole brain FC network organization by, e.g., maximizing the clustering coefficient while minimizing the characteristic path length. We also demonstrated with a more detailed excitation-inhibition neuronal network model that loss of local excitation-inhibition (E/I) balance causes failure of critical dynamics, therefore disrupting the optimal FC network organization. The results highlighted the crucial role of the critical dynamics in forming an optimal organization of FC networks in the brain and have potential application to the understanding and modeling of abnormal FC configurations in neuropsychiatric disorders.
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Affiliation(s)
- Xinchun Zhou
- Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou Center for Theoretical Physics, Lanzhou University, Lanzhou, China
| | - Ningning Ma
- School of Mathematical Sciences and Centre for Computational Systems Biology, Fudan University, Shanghai, China
| | - Benseng Song
- Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou Center for Theoretical Physics, Lanzhou University, Lanzhou, China
| | - Zhixi Wu
- Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou Center for Theoretical Physics, Lanzhou University, Lanzhou, China
| | - Guangyao Liu
- Department of Magnetic Resonance, Lanzhou University Second Hospital, Lanzhou, China
| | - Liwei Liu
- College of Electrical Engineering, Northwest University for Nationalities, Lanzhou, China
| | - Lianchun Yu
- Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou Center for Theoretical Physics, Lanzhou University, Lanzhou, China
| | - Jianfeng Feng
- School of Mathematical Sciences and Centre for Computational Systems Biology, Fudan University, Shanghai, China.,School of Mathematical Sciences, School of Life Science and the Collaborative Innovation Center for Brain Science, Fudan University, Shanghai, China
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25
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Shiromani PJ, Blanco-Centurion C, Vidal-Ortiz A. Mapping Network Activity in Sleep. Front Neurosci 2021; 15:646468. [PMID: 33828453 PMCID: PMC8019804 DOI: 10.3389/fnins.2021.646468] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2020] [Accepted: 03/04/2021] [Indexed: 11/22/2022] Open
Abstract
It was in the influenza pandemic of 1918 that von Economo identified specific brain regions regulating sleep and wake. Since then researchers have used a variety of tools to determine how the brain shifts between states of consciousness. In every enterprise new tools have validated existing data, corrected errors and made new discoveries to advance science. The brain is a challenge but new tools can disentangle the brain network. We summarize the newest tool, a miniature microscope, that provides unprecedented view of activity of glia and neurons in freely behaving mice. With this tool we have observed that the activity of a majority of GABA and MCH neurons in the lateral hypothalamus is heavily biased toward sleep. We suggest that miniscope data identifies activity at the cellular level in normal versus diseased brains, and also in response to specific hypnotics. Shifts in activity in small networks across the brain will help identify point of criticality that switches the brain from wake to sleep.
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Affiliation(s)
- Priyattam J Shiromani
- Ralph H. Johnson VA Medical Center, Charleston, SC, United States.,Department of Psychiatry and Biobehavioral Science, Medical University of South Carolina, Charleston, SC, United States
| | - Carlos Blanco-Centurion
- Department of Psychiatry and Biobehavioral Science, Medical University of South Carolina, Charleston, SC, United States
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26
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Hagemann A, Wilting J, Samimizad B, Mormann F, Priesemann V. Assessing criticality in pre-seizure single-neuron activity of human epileptic cortex. PLoS Comput Biol 2021; 17:e1008773. [PMID: 33684101 PMCID: PMC7971851 DOI: 10.1371/journal.pcbi.1008773] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2020] [Revised: 03/18/2021] [Accepted: 02/04/2021] [Indexed: 11/18/2022] Open
Abstract
Epileptic seizures are characterized by abnormal and excessive neural activity, where cortical network dynamics seem to become unstable. However, most of the time, during seizure-free periods, cortex of epilepsy patients shows perfectly stable dynamics. This raises the question of how recurring instability can arise in the light of this stable default state. In this work, we examine two potential scenarios of seizure generation: (i) epileptic cortical areas might generally operate closer to instability, which would make epilepsy patients generally more susceptible to seizures, or (ii) epileptic cortical areas might drift systematically towards instability before seizure onset. We analyzed single-unit spike recordings from both the epileptogenic (focal) and the nonfocal cortical hemispheres of 20 epilepsy patients. We quantified the distance to instability in the framework of criticality, using a novel estimator, which enables an unbiased inference from a small set of recorded neurons. Surprisingly, we found no evidence for either scenario: Neither did focal areas generally operate closer to instability, nor were seizures preceded by a drift towards instability. In fact, our results from both pre-seizure and seizure-free intervals suggest that despite epilepsy, human cortex operates in the stable, slightly subcritical regime, just like cortex of other healthy mammalians.
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Affiliation(s)
- Annika Hagemann
- Max-Planck-Institute for Dynamics and Self-Organization, Göttingen, Germany
| | - Jens Wilting
- Max-Planck-Institute for Dynamics and Self-Organization, Göttingen, Germany
| | - Bita Samimizad
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
| | - Florian Mormann
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
| | - Viola Priesemann
- Max-Planck-Institute for Dynamics and Self-Organization, Göttingen, Germany
- Bernstein Center for Computational Neuroscience (BCCN) Göttingen, Germany
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27
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Carvalho TTA, Fontenele AJ, Girardi-Schappo M, Feliciano T, Aguiar LAA, Silva TPL, de Vasconcelos NAP, Carelli PV, Copelli M. Subsampled Directed-Percolation Models Explain Scaling Relations Experimentally Observed in the Brain. Front Neural Circuits 2021; 14:576727. [PMID: 33519388 PMCID: PMC7843423 DOI: 10.3389/fncir.2020.576727] [Citation(s) in RCA: 25] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2020] [Accepted: 11/30/2002] [Indexed: 12/14/2022] Open
Abstract
Recent experimental results on spike avalanches measured in the urethane-anesthetized rat cortex have revealed scaling relations that indicate a phase transition at a specific level of cortical firing rate variability. The scaling relations point to critical exponents whose values differ from those of a branching process, which has been the canonical model employed to understand brain criticality. This suggested that a different model, with a different phase transition, might be required to explain the data. Here we show that this is not necessarily the case. By employing two different models belonging to the same universality class as the branching process (mean-field directed percolation) and treating the simulation data exactly like experimental data, we reproduce most of the experimental results. We find that subsampling the model and adjusting the time bin used to define avalanches (as done with experimental data) are sufficient ingredients to change the apparent exponents of the critical point. Moreover, experimental data is only reproduced within a very narrow range in parameter space around the phase transition.
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Affiliation(s)
- Tawan T A Carvalho
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Brazil
| | | | - Mauricio Girardi-Schappo
- Department of Physics, University of Ottawa, Ottawa, ON, Canada.,Departamento de Física, Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Ribeirão Preto, Brazil
| | - Thaís Feliciano
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Brazil
| | - Leandro A A Aguiar
- Departamento de Ciências Fundamentais e Sociais, Universidade Federal da Paraíba, Areia, Brazil
| | - Thais P L Silva
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Brazil
| | - Nivaldo A P de Vasconcelos
- Life and Health Sciences Research Institute (ICVS), School of Medicine, University of Minho, Braga, Portugal.,Life and Health Sciences Research Institute/Biomaterials, Biodegradables and Biomimetics, Braga, Portugal
| | - Pedro V Carelli
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Brazil
| | - Mauro Copelli
- Departamento de Física, Universidade Federal de Pernambuco, Recife, Brazil
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28
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Li J, Shew WL. Tuning network dynamics from criticality to an asynchronous state. PLoS Comput Biol 2020; 16:e1008268. [PMID: 32986705 PMCID: PMC7544040 DOI: 10.1371/journal.pcbi.1008268] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2020] [Revised: 10/08/2020] [Accepted: 08/17/2020] [Indexed: 01/03/2023] Open
Abstract
According to many experimental observations, neurons in cerebral cortex tend to operate in an asynchronous regime, firing independently of each other. In contrast, many other experimental observations reveal cortical population firing dynamics that are relatively coordinated and occasionally synchronous. These discrepant observations have naturally led to competing hypotheses. A commonly hypothesized explanation of asynchronous firing is that excitatory and inhibitory synaptic inputs are precisely correlated, nearly canceling each other, sometimes referred to as 'balanced' excitation and inhibition. On the other hand, the 'criticality' hypothesis posits an explanation of the more coordinated state that also requires a certain balance of excitatory and inhibitory interactions. Both hypotheses claim the same qualitative mechanism-properly balanced excitation and inhibition. Thus, a natural question arises: how are asynchronous population dynamics and critical dynamics related, how do they differ? Here we propose an answer to this question based on investigation of a simple, network-level computational model. We show that the strength of inhibitory synapses relative to excitatory synapses can be tuned from weak to strong to generate a family of models that spans a continuum from critical dynamics to asynchronous dynamics. Our results demonstrate that the coordinated dynamics of criticality and asynchronous dynamics can be generated by the same neural system if excitatory and inhibitory synapses are tuned appropriately.
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Affiliation(s)
- Jingwen Li
- Department of Physics, University of Arkansas, Fayetteville, Arkansas, United States of America
| | - Woodrow L. Shew
- Department of Physics, University of Arkansas, Fayetteville, Arkansas, United States of America
- * E-mail:
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29
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Wilting J, Priesemann V. Between Perfectly Critical and Fully Irregular: A Reverberating Model Captures and Predicts Cortical Spike Propagation. Cereb Cortex 2020; 29:2759-2770. [PMID: 31008508 PMCID: PMC6519697 DOI: 10.1093/cercor/bhz049] [Citation(s) in RCA: 34] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2018] [Revised: 01/20/2019] [Indexed: 12/11/2022] Open
Abstract
Knowledge about the collective dynamics of cortical spiking is very informative about the underlying coding principles. However, even most basic properties are not known with certainty, because their assessment is hampered by spatial subsampling, i.e., the limitation that only a tiny fraction of all neurons can be recorded simultaneously with millisecond precision. Building on a novel, subsampling-invariant estimator, we fit and carefully validate a minimal model for cortical spike propagation. The model interpolates between two prominent states: asynchronous and critical. We find neither of them in cortical spike recordings across various species, but instead identify a narrow "reverberating" regime. This approach enables us to predict yet unknown properties from very short recordings and for every circuit individually, including responses to minimal perturbations, intrinsic network timescales, and the strength of external input compared to recurrent activation "thereby informing about the underlying coding principles for each circuit, area, state and task.
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Affiliation(s)
- J Wilting
- Max-Planck-Institute for Dynamics and Self-Organization, Am Faß berg 17, Göttingen, Germany
| | - V Priesemann
- Max-Planck-Institute for Dynamics and Self-Organization, Am Faß berg 17, Göttingen, Germany.,Bernstein-Center for Computational Neuroscience, Göttingen, Germany
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30
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Ma Z, Liu H, Komiyama T, Wessel R. Stability of motor cortex network states during learning-associated neural reorganizations. J Neurophysiol 2020; 124:1327-1342. [PMID: 32937084 DOI: 10.1152/jn.00061.2020] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
A substantial reorganization of neural activity and neuron-to-movement relationship in motor cortical circuits accompanies the emergence of reproducible movement patterns during motor learning. Little is known about how this tempest of neural activity restructuring impacts the stability of network states in recurrent cortical circuits. To investigate this issue, we reanalyzed data in which we recorded for 14 days via population calcium imaging the activity of the same neural populations of pyramidal neurons in layer 2/3 and layer 5 of forelimb motor and premotor cortex in mice during the daily learning of a lever-press task. We found that motor cortex network states remained stable with respect to the critical network state during the extensive reorganization of both neural population activity and its relation to lever movement throughout learning. Specifically, layer 2/3 cortical circuits unceasingly displayed robust evidence for operating at the critical network state, a regime that maximizes information capacity and transmission and provides a balance between network robustness and flexibility. In contrast, layer 5 circuits operated away from the critical network state for all 14 days of recording and learning. In conclusion, this result indicates that the wide-ranging malleability of synapses, neurons, and neural connectivity during learning operates within the constraint of a stable and layer-specific network state regarding dynamic criticality, and suggests that different cortical layers operate under distinct constraints because of their specialized goals.NEW & NOTEWORTHY The neural activity reorganizes throughout motor learning, but how this reorganization impacts the stability of network states is unclear. We used two-photon calcium imaging to investigate how the network states in layer 2/3 and layer 5 of forelimb motor and premotor cortex are modulated by motor learning. We show that motor cortex network states are layer-specific and constant regarding criticality during neural activity reorganization, and suggests that layer-specific constraints could be motivated by different functions.
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Affiliation(s)
- Zhengyu Ma
- Department of Physics, Washington University in St. Louis, Saint Louis, Missouri
| | - Haixin Liu
- Neurobiology Section and Department of Neuroscience, University of California San Diego, La Jolla, California
| | - Takaki Komiyama
- Neurobiology Section and Department of Neuroscience, University of California San Diego, La Jolla, California
| | - Ralf Wessel
- Department of Physics, Washington University in St. Louis, Saint Louis, Missouri
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31
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Zimmern V. Why Brain Criticality Is Clinically Relevant: A Scoping Review. Front Neural Circuits 2020; 14:54. [PMID: 32982698 PMCID: PMC7479292 DOI: 10.3389/fncir.2020.00054] [Citation(s) in RCA: 56] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2020] [Accepted: 07/23/2020] [Indexed: 12/13/2022] Open
Abstract
The past 25 years have seen a strong increase in the number of publications related to criticality in different areas of neuroscience. The potential of criticality to explain various brain properties, including optimal information processing, has made it an increasingly exciting area of investigation for neuroscientists. Recent reviews on this topic, sometimes termed brain criticality, make brief mention of clinical applications of these findings to several neurological disorders such as epilepsy, neurodegenerative disease, and neonatal hypoxia. Other clinicallyrelevant domains - including anesthesia, sleep medicine, developmental-behavioral pediatrics, and psychiatry - are seldom discussed in review papers of brain criticality. Thorough assessments of these application areas and their relevance for clinicians have also yet to be published. In this scoping review, studies of brain criticality involving human data of all ages are evaluated for their current and future clinical relevance. To make the results of these studies understandable to a more clinical audience, a review of the key concepts behind criticality (e.g., phase transitions, long-range temporal correlation, self-organized criticality, power laws, branching processes) precedes the discussion of human clinical studies. Open questions and forthcoming areas of investigation are also considered.
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Affiliation(s)
- Vincent Zimmern
- Division of Child Neurology, The University of Texas Southwestern Medical Center, Dallas, TX, United States
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32
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Duncan NW, Hsu TY, Cheng PZ, Wang HY, Lee HC, Lane TJ. Intrinsic activity temporal structure reactivity to behavioural state change is correlated with depressive symptoms. Eur J Neurosci 2020; 52:4840-4850. [PMID: 32524682 DOI: 10.1111/ejn.14858] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2019] [Revised: 06/01/2020] [Accepted: 06/02/2020] [Indexed: 01/24/2023]
Abstract
The brain's intrinsic activity plays a fundamental role in its function. In normal conditions this activity is responsive to behavioural context, changing as an individual switches between directed tasks and task-free conditions. A key feature of such changes is the movement of the brain between corresponding critical and sub-critical states, with these dynamics supporting efficient cognitive processing. Breakdowns in processing efficiency can occur, however, in brain disorders such as depression. It was therefore hypothesised that depressive symptoms would be related to reduced intrinsic activity responsiveness to changes in behavioural state. This was tested in a mixed group of major depressive disorder patients (n = 26) and healthy participants (n = 37) by measuring intrinsic EEG activity temporal structure, quantified with detrended fluctuation analysis (DFA), in eyes-closed (EC) and eyes-open task-free states and contrasting between the conditions. The degree to which DFA values changed between the states was found to correlate negatively with depressive symptoms. DFA values did not differ between states in those with higher symptom levels, meaning that the brain remained in a less flexible sub-critical condition. This sub-critical condition in the EC state was further found to correlate with levels of maladaptive rumination. This may reflect a general cognitive inflexibility resulting from a lack in neural activity reactivity that may predispose people to overly engage in self-directed attention. These results provide an initial link between intrinsic activity reactivity and psychological features found in psychiatric disorders.
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Affiliation(s)
- Niall W Duncan
- Graduate Institute of Mind, Brain and Consciousness, Taipei Medical University, Taipei, Taiwan.,Brain and Consciousness Research Centre, TMU Shuang-Ho Hospital, New Taipei City, Taiwan
| | - Tzu-Yu Hsu
- Graduate Institute of Mind, Brain and Consciousness, Taipei Medical University, Taipei, Taiwan.,Brain and Consciousness Research Centre, TMU Shuang-Ho Hospital, New Taipei City, Taiwan
| | - Paul Z Cheng
- Graduate Institute of Mind, Brain and Consciousness, Taipei Medical University, Taipei, Taiwan.,Brain and Consciousness Research Centre, TMU Shuang-Ho Hospital, New Taipei City, Taiwan
| | - Hsin-Yi Wang
- Graduate Institute of Mind, Brain and Consciousness, Taipei Medical University, Taipei, Taiwan.,Brain and Consciousness Research Centre, TMU Shuang-Ho Hospital, New Taipei City, Taiwan
| | - Hsin-Chien Lee
- Department of Psychiatry, School of Medicine, College of Medicine, Taipei Medical University, Taipei, Taiwan.,Department of Psychiatry, TMU Shuang-Ho Hospital, New Taipei City, Taiwan
| | - Timothy J Lane
- Graduate Institute of Mind, Brain and Consciousness, Taipei Medical University, Taipei, Taiwan.,Brain and Consciousness Research Centre, TMU Shuang-Ho Hospital, New Taipei City, Taiwan.,College of Humanities and Social Science, Taipei Medical University, Taipei, Taiwan
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33
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Faqeeh A, Osat S, Radicchi F, Gleeson JP. Emergence of power laws in noncritical neuronal systems. Phys Rev E 2020; 100:010401. [PMID: 31499795 PMCID: PMC7217540 DOI: 10.1103/physreve.100.010401] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2019] [Indexed: 11/07/2022]
Abstract
Experimental and computational studies provide compelling evidence that neuronal systems are characterized by power-law distributions of neuronal avalanche sizes. This fact is interpreted as an indication that these systems are operating near criticality, and, in turn, typical properties of critical dynamical processes, such as optimal information transmission and stability, are attributed to neuronal systems. The purpose of this Rapid Communication is to show that the presence of power-law distributions for the size of neuronal avalanches is not a sufficient condition for the system to operate near criticality. Specifically, we consider a simplistic model of neuronal dynamics on networks and show that the degree distribution of the underlying neuronal network may trigger power-law distributions for neuronal avalanches even when the system is not in its critical regime. To certify and explain our findings we develop an analytical approach based on percolation theory and branching processes techniques.
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Affiliation(s)
- Ali Faqeeh
- Mathematics Consortium for Science and Industry, Department of Mathematics and Statistics, University of Limerick, Limerick V94 T9PX, Ireland.,Center for Complex Networks and Systems Research, School of Informatics, Computing, and Engineering, Indiana University, Bloomington, Indiana 47408, USA
| | - Saeed Osat
- Deep Quantum Labs, Skolkovo Institute of Science and Technology, Moscow 143026, Russia
| | - Filippo Radicchi
- Center for Complex Networks and Systems Research, School of Informatics, Computing, and Engineering, Indiana University, Bloomington, Indiana 47408, USA
| | - James P Gleeson
- Mathematics Consortium for Science and Industry, Department of Mathematics and Statistics, University of Limerick, Limerick V94 T9PX, Ireland
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34
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Lima Dias Pinto I, Copelli M. Oscillations and collective excitability in a model of stochastic neurons under excitatory and inhibitory coupling. Phys Rev E 2019; 100:062416. [PMID: 31962449 DOI: 10.1103/physreve.100.062416] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2019] [Indexed: 06/10/2023]
Abstract
We study a model with excitable neurons modeled as stochastic units with three states, representing quiescence, firing, and refractoriness. The transition rates between quiescence and firing depend exponentially on the number of firing neighbors, whereas all other rates are kept constant. This model class was shown to exhibit collective oscillations (synchronization) if neurons are spiking autonomously, but not if neurons are in the excitable regime. In both cases, neurons were restricted to interact through excitatory coupling. Here we show that a plethora of collective phenomena appear if inhibitory coupling is added. Besides the usual transition between an absorbing and an active phase, the model with excitatory and inhibitory neurons can also undergo reentrant transitions to an oscillatory phase. In the mean-field description, oscillations can emerge through supercritical or subcritical Hopf bifurcations, as well as through infinite period bifurcations. The model has bistability between active and oscillating behavior, as well as collective excitability, a regime where the system can display a peak of global activity when subject to a sufficiently strong perturbation. We employ a variant of the Shinomoto-Kuramoto order parameter to characterize the phase transitions and their system-size dependence.
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Affiliation(s)
| | - Mauro Copelli
- Physics Department, Federal University of Pernambuco (UFPE), Recife, PE 50670-901, Brazil
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35
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Critical Dynamics and Coupling in Bursts of Cortical Rhythms Indicate Non-Homeostatic Mechanism for Sleep-Stage Transitions and Dual Role of VLPO Neurons in Both Sleep and Wake. J Neurosci 2019; 40:171-190. [PMID: 31694962 DOI: 10.1523/jneurosci.1278-19.2019] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2019] [Revised: 09/07/2019] [Accepted: 10/07/2019] [Indexed: 11/21/2022] Open
Abstract
Origin and functions of intermittent transitions among sleep stages, including brief awakenings and arousals, constitute a challenge to the current homeostatic framework for sleep regulation, focusing on factors modulating sleep over large time scales. Here we propose that the complex micro-architecture characterizing sleep on scales of seconds and minutes results from intrinsic non-equilibrium critical dynamics. We investigate θ- and δ-wave dynamics in control rats and in rats where the sleep-promoting ventrolateral preoptic nucleus (VLPO) is lesioned (male Sprague-Dawley rats). We demonstrate that bursts in θ and δ cortical rhythms exhibit complex temporal organization, with long-range correlations and robust duality of power-law (θ-bursts, active phase) and exponential-like (δ-bursts, quiescent phase) duration distributions, features typical of non-equilibrium systems self-organizing at criticality. We show that such non-equilibrium behavior relates to anti-correlated coupling between θ- and δ-bursts, persists across a range of time scales, and is independent of the dominant physiologic state; indications of a basic principle in sleep regulation. Further, we find that VLPO lesions lead to a modulation of cortical dynamics resulting in altered dynamical parameters of θ- and δ-bursts and significant reduction in θ-δ coupling. Our empirical findings and model simulations demonstrate that θ-δ coupling is essential for the emerging non-equilibrium critical dynamics observed across the sleep-wake cycle, and indicate that VLPO neurons may have dual role for both sleep and arousal/brief wake activation. The uncovered critical behavior in sleep- and wake-related cortical rhythms indicates a mechanism essential for the micro-architecture of spontaneous sleep-stage and arousal transitions within a novel, non-homeostatic paradigm of sleep regulation.SIGNIFICANCE STATEMENT We show that the complex micro-architecture of sleep-stage/arousal transitions arises from intrinsic non-equilibrium critical dynamics, connecting the temporal organization of dominant cortical rhythms with empirical observations across scales. We link such behavior to sleep-promoting neuronal population, and demonstrate that VLPO lesion (model of insomnia) alters dynamical features of θ and δ rhythms, and leads to significant reduction in θ-δ coupling. This indicates that VLPO neurons may have dual role for both sleep and arousal/brief wake control. The reported empirical findings and modeling simulations constitute first evidences of a neurophysiological fingerprint of self-organization and criticality in sleep- and wake-related cortical rhythms; a mechanism essential for spontaneous sleep-stage and arousal transitions that lays the bases for a novel, non-homeostatic paradigm of sleep regulation.
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36
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Wang JWJL, Lombardi F, Zhang X, Anaclet C, Ivanov PC. Non-equilibrium critical dynamics of bursts in θ and δ rhythms as fundamental characteristic of sleep and wake micro-architecture. PLoS Comput Biol 2019; 15:e1007268. [PMID: 31725712 PMCID: PMC6855414 DOI: 10.1371/journal.pcbi.1007268] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2019] [Accepted: 07/11/2019] [Indexed: 01/08/2023] Open
Abstract
Origin and functions of intermittent transitions among sleep stages, including short awakenings and arousals, constitute a challenge to the current homeostatic framework for sleep regulation, focusing on factors modulating sleep over large time scales. Here we propose that the complex micro-architecture characterizing the sleep-wake cycle results from an underlying non-equilibrium critical dynamics, bridging collective behaviors across spatio-temporal scales. We investigate θ and δ wave dynamics in control rats and in rats with lesions of sleep-promoting neurons in the parafacial zone. We demonstrate that intermittent bursts in θ and δ rhythms exhibit a complex temporal organization, with long-range power-law correlations and a robust duality of power law (θ-bursts, active phase) and exponential-like (δ-bursts, quiescent phase) duration distributions, typical features of non-equilibrium systems self-organizing at criticality. Crucially, such temporal organization relates to anti-correlated coupling between θ- and δ-bursts, and is independent of the dominant physiologic state and lesions, a solid indication of a basic principle in sleep dynamics.
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Affiliation(s)
- Jilin W. J. L. Wang
- Keck Laboratory for Network Physiology, Department of Physics, Boston University, Boston, Massachusetts, United States of America
| | - Fabrizio Lombardi
- Keck Laboratory for Network Physiology, Department of Physics, Boston University, Boston, Massachusetts, United States of America
- Institute of Science and Technology Austria, A-3400 Klosterneuburg, Austria
| | - Xiyun Zhang
- Keck Laboratory for Network Physiology, Department of Physics, Boston University, Boston, Massachusetts, United States of America
| | - Christelle Anaclet
- Department of Neurobiology, University of Massachusetts Medical School, Worcester, Massachusetts, United States of America
- Department of Neurology, Division of Sleep Medicine, Harvard Medical School and Beth Israel Deaconess Medical Center, Boston, Massachusetts, United States of America
| | - Plamen Ch. Ivanov
- Keck Laboratory for Network Physiology, Department of Physics, Boston University, Boston, Massachusetts, United States of America
- Department of Neurology, Division of Sleep Medicine, Harvard Medical School and Beth Israel Deaconess Medical Center, Boston, Massachusetts, United States of America
- Harvard Medical School and Division of Sleep Medicine, Brigham and Women’s Hospital, Boston, Massachusetts, United States of America
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37
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Ma Z, Turrigiano GG, Wessel R, Hengen KB. Cortical Circuit Dynamics Are Homeostatically Tuned to Criticality In Vivo. Neuron 2019; 104:655-664.e4. [PMID: 31601510 DOI: 10.1016/j.neuron.2019.08.031] [Citation(s) in RCA: 105] [Impact Index Per Article: 21.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2019] [Revised: 06/26/2019] [Accepted: 08/19/2019] [Indexed: 11/26/2022]
Abstract
Homeostatic mechanisms stabilize neuronal activity in vivo, but whether this process gives rise to balanced network dynamics is unknown. Here, we continuously monitored the statistics of network spiking in visual cortical circuits in freely behaving rats for 9 days. Under control conditions in light and dark, networks were robustly organized around criticality, a regime that maximizes information capacity and transmission. When input was perturbed by visual deprivation, network criticality was severely disrupted and subsequently restored to criticality over 48 h. Unexpectedly, the recovery of excitatory dynamics preceded homeostatic plasticity of firing rates by >30 h. We utilized model investigations to manipulate firing rate homeostasis in a cell-type-specific manner at the onset of visual deprivation. Our results suggest that criticality in excitatory networks is established by inhibitory plasticity and architecture. These data establish that criticality is consistent with a homeostatic set point for visual cortical dynamics and suggest a key role for homeostatic regulation of inhibition.
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Affiliation(s)
- Zhengyu Ma
- Department of Physics, Washington University in St. Louis, St. Louis, MO 63130, USA
| | | | - Ralf Wessel
- Department of Physics, Washington University in St. Louis, St. Louis, MO 63130, USA
| | - Keith B Hengen
- Department of Biology, Washington University in St. Louis, St. Louis, MO 63130, USA.
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38
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Bocaccio H, Pallavicini C, Castro MN, Sánchez SM, De Pino G, Laufs H, Villarreal MF, Tagliazucchi E. The avalanche-like behaviour of large-scale haemodynamic activity from wakefulness to deep sleep. J R Soc Interface 2019; 16:20190262. [PMID: 31506046 PMCID: PMC6769314 DOI: 10.1098/rsif.2019.0262] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2019] [Accepted: 08/08/2019] [Indexed: 02/02/2023] Open
Abstract
Increasing evidence suggests that responsiveness is associated with critical or near-critical cortical dynamics, which exhibit scale-free cascades of spatio-temporal activity. These cascades, or 'avalanches', have been detected at multiple scales, from in vitro and in vivo microcircuits to voltage imaging and brain-wide functional magnetic resonance imaging (fMRI) recordings. Criticality endows the cortex with certain information-processing capacities postulated as necessary for conscious wakefulness, yet it remains unknown how unresponsiveness impacts on the avalanche-like behaviour of large-scale human haemodynamic activity. We observed a scale-free hierarchy of co-activated connected clusters by applying a point-process transformation to fMRI data recorded during wakefulness and non-rapid eye movement (NREM) sleep. Maximum-likelihood estimates revealed a significant effect of sleep stage on the scaling parameters of the cluster size power-law distributions. Post hoc statistical tests showed that differences were maximal between wakefulness and N2 sleep. These results were robust against spatial coarse graining, fitting alternative statistical models and different point-process thresholds, and disappeared upon phase shuffling the fMRI time series. Evoked neural bistabilities preventing arousals during N2 sleep do not suffice to explain these differences, which point towards changes in the intrinsic dynamics of the brain that could be necessary to consolidate a state of deep unresponsiveness.
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Affiliation(s)
- H. Bocaccio
- Grupo de Investigación en Neurociencias Aplicadas a las Alteraciones de la Conducta, Instituto de Neurociencias FLENI-CONICET, Buenos Aires, Argentina
- National Scientific and Technical Research Council (CONICET), Buenos Aires, Argentina
- Departamento de Física, FCEyN, UBA, e Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
| | - C. Pallavicini
- Grupo de Investigación en Neurociencias Aplicadas a las Alteraciones de la Conducta, Instituto de Neurociencias FLENI-CONICET, Buenos Aires, Argentina
- National Scientific and Technical Research Council (CONICET), Buenos Aires, Argentina
- Departamento de Física, FCEyN, UBA, e Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
| | - M. N. Castro
- Grupo de Investigación en Neurociencias Aplicadas a las Alteraciones de la Conducta, Instituto de Neurociencias FLENI-CONICET, Buenos Aires, Argentina
- National Scientific and Technical Research Council (CONICET), Buenos Aires, Argentina
- Departamento de Fisiología, Facultad de Medicina, UBA, Buenos Aires, Argentina
- Departamento Salud Mental, Unidad Docente FLENI, Facultad de Medicina, UBA, Buenos Aires, Argentina
| | - S. M. Sánchez
- Grupo de Investigación en Neurociencias Aplicadas a las Alteraciones de la Conducta, Instituto de Neurociencias FLENI-CONICET, Buenos Aires, Argentina
- National Scientific and Technical Research Council (CONICET), Buenos Aires, Argentina
- Departamento de Física, FCEyN, UBA, e Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
| | - G. De Pino
- Grupo de Investigación en Neurociencias Aplicadas a las Alteraciones de la Conducta, Instituto de Neurociencias FLENI-CONICET, Buenos Aires, Argentina
- Laboratorio de Neuroimágenes, Departamento de Imágenes, FLENI, Buenos Aires, Argentina
- Escuela de Ciencia y Tecnología (ECyT), Universidad Nacional de San Martín, Argentina
| | - H. Laufs
- Department of Neurology, Christian-Albrechts-University, Kiel, Germany
| | - M. F. Villarreal
- Grupo de Investigación en Neurociencias Aplicadas a las Alteraciones de la Conducta, Instituto de Neurociencias FLENI-CONICET, Buenos Aires, Argentina
- National Scientific and Technical Research Council (CONICET), Buenos Aires, Argentina
- Departamento de Física, FCEyN, UBA, e Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
| | - E. Tagliazucchi
- National Scientific and Technical Research Council (CONICET), Buenos Aires, Argentina
- Departamento de Física, FCEyN, UBA, e Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
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39
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Wilting J, Priesemann V. 25 years of criticality in neuroscience - established results, open controversies, novel concepts. Curr Opin Neurobiol 2019; 58:105-111. [PMID: 31546053 DOI: 10.1016/j.conb.2019.08.002] [Citation(s) in RCA: 61] [Impact Index Per Article: 12.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2019] [Accepted: 08/25/2019] [Indexed: 12/19/2022]
Abstract
Twenty-five years ago, Dunkelmann and Radons (1994) showed that neural networks can self-organize to a critical state. In models, the critical state offers a number of computational advantages. Thus this hypothesis, and in particular the experimental work by Beggs and Plenz (2003), has triggered an avalanche of research, with thousands of studies referring to it. Nonetheless, experimental results are still contradictory. How is it possible, that a hypothesis has attracted active research for decades, but nonetheless remains controversial? We discuss the experimental and conceptual controversy, and then present a parsimonious solution that (i) unifies the contradictory experimental results, (ii) avoids disadvantages of a critical state, and (iii) enables rapid, adaptive tuning of network properties to task requirements.
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Affiliation(s)
- J Wilting
- Max-Planck-Institute for Dynamics and Self-Organization, Göttingen, Germany
| | - V Priesemann
- Max-Planck-Institute for Dynamics and Self-Organization, Göttingen, Germany; Bernstein-Center for Computational Neuroscience, Göttingen, Germany
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40
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Bowen Z, Winkowski DE, Seshadri S, Plenz D, Kanold PO. Neuronal Avalanches in Input and Associative Layers of Auditory Cortex. Front Syst Neurosci 2019; 13:45. [PMID: 31551721 PMCID: PMC6737089 DOI: 10.3389/fnsys.2019.00045] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2019] [Accepted: 08/16/2019] [Indexed: 12/26/2022] Open
Abstract
The primary auditory cortex processes acoustic sequences for the perception of behaviorally meaningful sounds such as speech. Sound information arrives at its input layer four from where activity propagates to associative layer 2/3. It is currently not known whether there is a characteristic organization of neuronal population activity across layers and sound levels during sound processing. Here, we identify neuronal avalanches, which in theory and experiments have been shown to maximize dynamic range and optimize information transfer within and across networks, in primary auditory cortex. We used in vivo 2-photon imaging of pyramidal neurons in cortical layers L4 and L2/3 of mouse A1 to characterize the populations of neurons that were active spontaneously, i.e., in the absence of a sound stimulus, and those recruited by single-frequency tonal stimuli at different sound levels. Single-frequency sounds recruited neurons of widely ranging frequency selectivity in both layers. We defined neuronal ensembles as neurons being active within or during successive temporal windows at the temporal resolution of our imaging. For both layers, neuronal ensembles were highly variable in size during spontaneous activity as well as during sound presentation. Ensemble sizes distributed according to power laws, the hallmark of neuronal avalanches, and were similar across sound levels. Avalanches activated by sound were composed of neurons with diverse tuning preference, yet with selectivity independent of avalanche size. Our results suggest that optimization principles identified for avalanches guide population activity in L4 and L2/3 of auditory cortex during and in-between stimulus processing.
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Affiliation(s)
- Zac Bowen
- Department of Biology, University of Maryland, College Park, College Park, MD, United States
| | - Daniel E Winkowski
- Department of Biology, University of Maryland, College Park, College Park, MD, United States.,Institute for Systems Research, University of Maryland, College Park, College Park, MD, United States
| | - Saurav Seshadri
- Section on Critical Brain Dynamics, National Institute of Mental Health, Bethesda, MD, United States
| | - Dietmar Plenz
- Section on Critical Brain Dynamics, National Institute of Mental Health, Bethesda, MD, United States
| | - Patrick O Kanold
- Department of Biology, University of Maryland, College Park, College Park, MD, United States.,Institute for Systems Research, University of Maryland, College Park, College Park, MD, United States
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41
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Ramlow L, Sawicki J, Zakharova A, Hlinka J, Claussen JC, Schöll E. Partial synchronization in empirical brain networks as a model for unihemispheric sleep. ACTA ACUST UNITED AC 2019. [DOI: 10.1209/0295-5075/126/50007] [Citation(s) in RCA: 32] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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42
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Fontenele AJ, de Vasconcelos NAP, Feliciano T, Aguiar LAA, Soares-Cunha C, Coimbra B, Dalla Porta L, Ribeiro S, Rodrigues AJ, Sousa N, Carelli PV, Copelli M. Criticality between Cortical States. PHYSICAL REVIEW LETTERS 2019; 122:208101. [PMID: 31172737 DOI: 10.1103/physrevlett.122.208101] [Citation(s) in RCA: 97] [Impact Index Per Article: 19.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2018] [Revised: 02/18/2019] [Indexed: 05/21/2023]
Abstract
Since the first measurements of neuronal avalanches, the critical brain hypothesis has gained traction. However, if the brain is critical, what is the phase transition? For several decades, it has been known that the cerebral cortex operates in a diversity of regimes, ranging from highly synchronous states (with higher spiking variability) to desynchronized states (with lower spiking variability). Here, using both new and publicly available data, we test independent signatures of criticality and show that a phase transition occurs in an intermediate value of spiking variability, in both anesthetized and freely moving animals. The critical exponents point to a universality class different from mean-field directed percolation. Importantly, as the cortex hovers around this critical point, the avalanche exponents follow a linear relation that encompasses previous experimental results from different setups and is reproduced by a model.
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Affiliation(s)
- Antonio J Fontenele
- Physics Department, Federal University of Pernambuco (UFPE), Recife, PE 50670-901, Brazil
| | - Nivaldo A P de Vasconcelos
- Physics Department, Federal University of Pernambuco (UFPE), Recife, PE 50670-901, Brazil
- Department of Biomedical Engineering, Federal University of Pernambuco, Recife, PE 50670-901, Brazil
- Life and Health Sciences Research Institute (ICVS), School of Medicine, University of Minho, Braga 4710-057, Portugal
- ICVS/3Bs-PT Government Associate Laboratory, 4806-909, Braga/Guimarães, Portugal
| | - Thaís Feliciano
- Physics Department, Federal University of Pernambuco (UFPE), Recife, PE 50670-901, Brazil
| | - Leandro A A Aguiar
- Physics Department, Federal University of Pernambuco (UFPE), Recife, PE 50670-901, Brazil
- Departamento de Morfologia e Fisiologia Animal, Universidade Federal Rural de Pernambuco (UFRPE), Recife, PE 52171-900, Brazil
| | - Carina Soares-Cunha
- Life and Health Sciences Research Institute (ICVS), School of Medicine, University of Minho, Braga 4710-057, Portugal
- ICVS/3Bs-PT Government Associate Laboratory, 4806-909, Braga/Guimarães, Portugal
| | - Bárbara Coimbra
- Life and Health Sciences Research Institute (ICVS), School of Medicine, University of Minho, Braga 4710-057, Portugal
- ICVS/3Bs-PT Government Associate Laboratory, 4806-909, Braga/Guimarães, Portugal
| | - Leonardo Dalla Porta
- Physics Department, Federal University of Pernambuco (UFPE), Recife, PE 50670-901, Brazil
- Systems Neuroscience, Institut dInvestigacions Biomèdiques August Pi i Sunyer (IDIBAPS), 08036, Barcelona, Spain
| | - Sidarta Ribeiro
- Brain Institute, Federal University of Rio Grande do Norte (UFRN), Natal, RN 59056-450, Brazil
| | - Ana João Rodrigues
- Life and Health Sciences Research Institute (ICVS), School of Medicine, University of Minho, Braga 4710-057, Portugal
- ICVS/3Bs-PT Government Associate Laboratory, 4806-909, Braga/Guimarães, Portugal
| | - Nuno Sousa
- Life and Health Sciences Research Institute (ICVS), School of Medicine, University of Minho, Braga 4710-057, Portugal
- ICVS/3Bs-PT Government Associate Laboratory, 4806-909, Braga/Guimarães, Portugal
| | - Pedro V Carelli
- Physics Department, Federal University of Pernambuco (UFPE), Recife, PE 50670-901, Brazil
| | - Mauro Copelli
- Physics Department, Federal University of Pernambuco (UFPE), Recife, PE 50670-901, Brazil
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43
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Single-Cell Membrane Potential Fluctuations Evince Network Scale-Freeness and Quasicriticality. J Neurosci 2019; 39:4738-4759. [PMID: 30952810 DOI: 10.1523/jneurosci.3163-18.2019] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2018] [Revised: 03/01/2019] [Accepted: 03/25/2019] [Indexed: 11/21/2022] Open
Abstract
What information single neurons receive about general neural circuit activity is a fundamental question for neuroscience. Somatic membrane potential (V m) fluctuations are driven by the convergence of synaptic inputs from a diverse cross-section of upstream neurons. Furthermore, neural activity is often scale-free, implying that some measurements should be the same, whether taken at large or small scales. Together, convergence and scale-freeness support the hypothesis that single V m recordings carry useful information about high-dimensional cortical activity. Conveniently, the theory of "critical branching networks" (one purported explanation for scale-freeness) provides testable predictions about scale-free measurements that are readily applied to V m fluctuations. To investigate, we obtained whole-cell current-clamp recordings of pyramidal neurons in visual cortex of turtles with unknown genders. We isolated fluctuations in V m below the firing threshold and analyzed them by adapting the definition of "neuronal avalanches" (i.e., spurts of population spiking). The V m fluctuations which we analyzed were scale-free and consistent with critical branching. These findings recapitulated results from large-scale cortical population data obtained separately in complementary experiments using microelectrode arrays described previously (Shew et al., 2015). Simultaneously recorded single-unit local field potential did not provide a good match, demonstrating the specific utility of V m Modeling shows that estimation of dynamical network properties from neuronal inputs is most accurate when networks are structured as critical branching networks. In conclusion, these findings extend evidence of critical phenomena while also establishing subthreshold pyramidal neuron V m fluctuations as an informative gauge of high-dimensional cortical population activity.SIGNIFICANCE STATEMENT The relationship between membrane potential (V m) dynamics of single neurons and population dynamics is indispensable to understanding cortical circuits. Just as important to the biophysics of computation are emergent properties such as scale-freeness, where critical branching networks offer insight. This report makes progress on both fronts by comparing statistics from single-neuron whole-cell recordings with population statistics obtained with microelectrode arrays. Not only are fluctuations of somatic V m scale-free, they match fluctuations of population activity. Thus, our results demonstrate appropriation of the brain's own subsampling method (convergence of synaptic inputs) while extending the range of fundamental evidence for critical phenomena in neural systems from the previously observed mesoscale (fMRI, LFP, population spiking) to the microscale, namely, V m fluctuations.
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44
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Dalla Porta L, Copelli M. Modeling neuronal avalanches and long-range temporal correlations at the emergence of collective oscillations: Continuously varying exponents mimic M/EEG results. PLoS Comput Biol 2019; 15:e1006924. [PMID: 30951525 PMCID: PMC6469813 DOI: 10.1371/journal.pcbi.1006924] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2018] [Revised: 04/17/2019] [Accepted: 03/06/2019] [Indexed: 01/17/2023] Open
Abstract
We revisit the CROS ("CRitical OScillations") model which was recently proposed as an attempt to reproduce both scale-invariant neuronal avalanches and long-range temporal correlations. With excitatory and inhibitory stochastic neurons locally connected in a two-dimensional disordered network, the model exhibits a transition where alpha-band oscillations emerge. Precisely at the transition, the fluctuations of the network activity have nontrivial detrended fluctuation analysis (DFA) exponents, and avalanches (defined as supra-threshold activity) have power law distributions of size and duration. We show that, differently from previous results, the exponents governing the distributions of avalanche size and duration are not necessarily those of the mean-field directed percolation universality class (3/2 and 2, respectively). Instead, in a narrow region of parameter space, avalanche exponents obtained via a maximum-likelihood estimator vary continuously and follow a linear relation, in good agreement with results obtained from M/EEG data. In that region, moreover, the values of avalanche and DFA exponents display a spread with positive correlations, reproducing human MEG results.
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Affiliation(s)
- Leonardo Dalla Porta
- Departamento de Física, Universidade Federal de Pernambuco (UFPE), Recife, PE, Brazil
| | - Mauro Copelli
- Departamento de Física, Universidade Federal de Pernambuco (UFPE), Recife, PE, Brazil
- * E-mail:
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45
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Alonso LM, Solovey G, Yanagawa T, Proekt A, Cecchi GA, Magnasco MO. Single-trial classification of awareness state during anesthesia by measuring critical dynamics of global brain activity. Sci Rep 2019; 9:4927. [PMID: 30894626 PMCID: PMC6426977 DOI: 10.1038/s41598-019-41345-4] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2018] [Accepted: 03/01/2019] [Indexed: 11/09/2022] Open
Abstract
In daily life, in the operating room and in the laboratory, the operational way to assess wakefulness and consciousness is through responsiveness. A number of studies suggest that the awake, conscious state is not the default behavior of an assembly of neurons, but rather a very special state of activity that has to be actively maintained and curated to support its functional properties. Thus responsiveness is a feature that requires active maintenance, such as a homeostatic mechanism to balance excitation and inhibition. In this work we developed a method for monitoring such maintenance processes, focusing on a specific signature of their behavior derived from the theory of dynamical systems: stability analysis of dynamical modes. When such mechanisms are at work, their modes of activity are at marginal stability, neither damped (stable) nor exponentially growing (unstable) but rather hovering in between. We have previously shown that, conversely, under induction of anesthesia those modes become more stable and thus less responsive, then reversed upon emergence to wakefulness. We take advantage of this effect to build a single-trial classifier which detects whether a subject is awake or unconscious achieving high performance. We show that our approach can be developed into a means for intra-operative monitoring of the depth of anesthesia, an application of fundamental importance to modern clinical practice.
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Affiliation(s)
- Leandro M Alonso
- Laboratory of integrative neuroscience, The Rockefeller University, New York, NY, 10065, USA. .,Volen Center for Complex Systems, Department of Biology, Brandeis University, Waltham, MA, 02454, USA.
| | - Guillermo Solovey
- Instituto del Cálculo, FCEyN, Universidad de Buenos Aires, (C1428EGA), Buenos Aires, Argentina.
| | - Toru Yanagawa
- Laboratory for Adaptive Intelligence, Brain Science Institute, RIKEN, Saitama, 351-0198, Japan
| | - Alex Proekt
- Anesthesiology and Critical Care, University of Pennsylvania, Philadelphia, PA, 19104, USA
| | | | - Marcelo O Magnasco
- Laboratory of integrative neuroscience, The Rockefeller University, New York, NY, 10065, USA.,Volen Center for Complex Systems, Department of Biology, Brandeis University, Waltham, MA, 02454, USA
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46
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Deco G, Cruzat J, Kringelbach ML. Brain songs framework used for discovering the relevant timescale of the human brain. Nat Commun 2019; 10:583. [PMID: 30718478 PMCID: PMC6361902 DOI: 10.1038/s41467-018-08186-7] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2018] [Accepted: 12/12/2018] [Indexed: 01/18/2023] Open
Abstract
A key unresolved problem in neuroscience is to determine the relevant timescale for understanding spatiotemporal dynamics across the whole brain. While resting state fMRI reveals networks at an ultraslow timescale (below 0.1 Hz), other neuroimaging modalities such as MEG and EEG suggest that much faster timescales may be equally or more relevant for discovering spatiotemporal structure. Here, we introduce a novel way to generate whole-brain neural dynamical activity at the millisecond scale from fMRI signals. This method allows us to study the different timescales through binning the output of the model. These timescales can then be investigated using a method (poetically named brain songs) to extract the spacetime motifs at a given timescale. Using independent measures of entropy and hierarchy to characterize the richness of the dynamical repertoire, we show that both methods find a similar optimum at a timescale of around 200 ms in resting state and in task data.
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Affiliation(s)
- Gustavo Deco
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Roc Boronat 138, Barcelona, 08018, Spain.
- Institució Catalana de la Recerca i Estudis Avançats (ICREA), Passeig Lluís Companys 23, Barcelona, 08010, Spain.
- Department of Neuropsychology, Max Planck Institute for Human Cognitive and Brain Sciences, 04103, Leipzig, Germany.
- School of Psychological Sciences, Monash University, Melbourne, Clayton, VIC, 3800, Australia.
| | - Josephine Cruzat
- Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, Universitat Pompeu Fabra, Roc Boronat 138, Barcelona, 08018, Spain
- Department of Psychiatry, University of Oxford, Oxford, OX3 7JX, UK
| | - Morten L Kringelbach
- Department of Psychiatry, University of Oxford, Oxford, OX3 7JX, UK.
- Center for Music in the Brain, Department of Clinical Medicine, Aarhus University, Aarhus, DK-8000, Denmark.
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47
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Wu S, Zhang Y, Cui Y, Li H, Wang J, Guo L, Xia Y, Yao D, Xu P, Guo D. Heterogeneity of synaptic input connectivity regulates spike-based neuronal avalanches. Neural Netw 2018; 110:91-103. [PMID: 30508808 DOI: 10.1016/j.neunet.2018.10.017] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2018] [Revised: 09/26/2018] [Accepted: 10/30/2018] [Indexed: 10/27/2022]
Abstract
Our mysterious brain is believed to operate near a non-equilibrium point and generate critical self-organized avalanches in neuronal activity. A central topic in neuroscience is to elucidate the underlying circuitry mechanisms of neuronal avalanches in the brain. Recent experimental evidence has revealed significant heterogeneity in both synaptic input and output connectivity, but whether the structural heterogeneity participates in the regulation of neuronal avalanches remains poorly understood. By computational modeling, we predict that different types of structural heterogeneity contribute distinct effects on avalanche neurodynamics. In particular, neuronal avalanches can be triggered at an intermediate level of input heterogeneity, but heterogeneous output connectivity cannot evoke avalanche dynamics. In the criticality region, the co-emergence of multi-scale cortical activities is observed, and both the avalanche dynamics and neuronal oscillations are modulated by the input heterogeneity. Remarkably, we show similar results can be reproduced in networks with various types of in- and out-degree distributions. Overall, these findings not only provide details on the underlying circuitry mechanisms of nonrandom synaptic connectivity in the regulation of neuronal avalanches, but also inspire testable hypotheses for future experimental studies.
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Affiliation(s)
- Shengdun Wu
- The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China
| | - Yangsong Zhang
- The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China; School of Life Science and Technology, Center for Information in Medicine, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China
| | - Yan Cui
- The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China
| | - Heng Li
- The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China
| | - Jiakang Wang
- The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China
| | - Lijun Guo
- The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China
| | - Yang Xia
- The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China; School of Life Science and Technology, Center for Information in Medicine, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China
| | - Dezhong Yao
- The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China; School of Life Science and Technology, Center for Information in Medicine, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China
| | - Peng Xu
- The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China; School of Life Science and Technology, Center for Information in Medicine, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China
| | - Daqing Guo
- The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China; School of Life Science and Technology, Center for Information in Medicine, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China.
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48
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Girardi-Schappo M, Tragtenberg MHR. Measuring neuronal avalanches in disordered systems with absorbing states. Phys Rev E 2018; 97:042415. [PMID: 29758702 DOI: 10.1103/physreve.97.042415] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2017] [Indexed: 11/07/2022]
Abstract
Power-law-shaped avalanche-size distributions are widely used to probe for critical behavior in many different systems, particularly in neural networks. The definition of avalanche is ambiguous. Usually, theoretical avalanches are defined as the activity between a stimulus and the relaxation to an inactive absorbing state. On the other hand, experimental neuronal avalanches are defined by the activity between consecutive silent states. We claim that the latter definition may be extended to some theoretical models to characterize their power-law avalanches and critical behavior. We study a system in which the separation of driving and relaxation time scales emerges from its structure. We apply both definitions of avalanche to our model. Both yield power-law-distributed avalanches that scale with system size in the critical point as expected. Nevertheless, we find restricted power-law-distributed avalanches outside of the critical region within the experimental procedure, which is not expected by the standard theoretical definition. We remark that these results are dependent on the model details.
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Affiliation(s)
- M Girardi-Schappo
- Neuroimaging of Epilepsy Laboratory, McConnell Brain Imaging Center, McGill University, Montreal Neurological Institute and Hospital, H3A 2B4, Montreal, Quebec, Canada.,Departamento de Física, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil
| | - M H R Tragtenberg
- Departamento de Física, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil
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49
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Inferring collective dynamical states from widely unobserved systems. Nat Commun 2018; 9:2325. [PMID: 29899335 PMCID: PMC5998151 DOI: 10.1038/s41467-018-04725-4] [Citation(s) in RCA: 54] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2017] [Accepted: 05/09/2018] [Indexed: 12/02/2022] Open
Abstract
When assessing spatially extended complex systems, one can rarely sample the states of all components. We show that this spatial subsampling typically leads to severe underestimation of the risk of instability in systems with propagating events. We derive a subsampling-invariant estimator, and demonstrate that it correctly infers the infectiousness of various diseases under subsampling, making it particularly useful in countries with unreliable case reports. In neuroscience, recordings are strongly limited by subsampling. Here, the subsampling-invariant estimator allows to revisit two prominent hypotheses about the brain’s collective spiking dynamics: asynchronous-irregular or critical. We identify consistently for rat, cat, and monkey a state that combines features of both and allows input to reverberate in the network for hundreds of milliseconds. Overall, owing to its ready applicability, the novel estimator paves the way to novel insight for the study of spatially extended dynamical systems. From infectious diseases to brain activity, complex systems can be approximated using autoregressive models. Here, the authors show that incomplete sampling can bias estimates of the stability of such systems, and introduce a novel, unbiased metric for use in such situations.
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50
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Wang DJJ, Jann K, Fan C, Qiao Y, Zang YF, Lu H, Yang Y. Neurophysiological Basis of Multi-Scale Entropy of Brain Complexity and Its Relationship With Functional Connectivity. Front Neurosci 2018; 12:352. [PMID: 29896081 PMCID: PMC5986880 DOI: 10.3389/fnins.2018.00352] [Citation(s) in RCA: 69] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2018] [Accepted: 05/07/2018] [Indexed: 01/06/2023] Open
Abstract
Recently, non-linear statistical measures such as multi-scale entropy (MSE) have been introduced as indices of the complexity of electrophysiology and fMRI time-series across multiple time scales. In this work, we investigated the neurophysiological underpinnings of complexity (MSE) of electrophysiology and fMRI signals and their relations to functional connectivity (FC). MSE and FC analyses were performed on simulated data using neural mass model based brain network model with the Brain Dynamics Toolbox, on animal models with concurrent recording of fMRI and electrophysiology in conjunction with pharmacological manipulations, and on resting-state fMRI data from the Human Connectome Project. Our results show that the complexity of regional electrophysiology and fMRI signals is positively correlated with network FC. The associations between MSE and FC are dependent on the temporal scales or frequencies, with higher associations between MSE and FC at lower temporal frequencies. Our results from theoretical modeling, animal experiment and human fMRI indicate that (1) Regional neural complexity and network FC may be two related aspects of brain's information processing: the more complex regional neural activity, the higher FC this region has with other brain regions; (2) MSE at high and low frequencies may represent local and distributed information processing across brain regions. Based on literature and our data, we propose that the complexity of regional neural signals may serve as an index of the brain's capacity of information processing—increased complexity may indicate greater transition or exploration between different states of brain networks, thereby a greater propensity for information processing.
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Affiliation(s)
- Danny J J Wang
- Laboratory of FMRI Technology, Stevens Neuroimaging and Informatics Institute, Keck School of Medicine, University of Southern California, Los Angeles, CA, United States
| | - Kay Jann
- Laboratory of FMRI Technology, Stevens Neuroimaging and Informatics Institute, Keck School of Medicine, University of Southern California, Los Angeles, CA, United States
| | - Chang Fan
- Laboratory of FMRI Technology, Stevens Neuroimaging and Informatics Institute, Keck School of Medicine, University of Southern California, Los Angeles, CA, United States
| | - Yang Qiao
- Department of Psychology, Center for Cognition and Brain Disorders, Hangzhou Normal University, Hangzhou, China.,Neuroimaging Research Branch, National Institute on Drug Abuse, National Institutes of Health, Baltimore, MD, United States
| | - Yu-Feng Zang
- Department of Psychology, Center for Cognition and Brain Disorders, Hangzhou Normal University, Hangzhou, China
| | - Hanbing Lu
- Neuroimaging Research Branch, National Institute on Drug Abuse, National Institutes of Health, Baltimore, MD, United States
| | - Yihong Yang
- Neuroimaging Research Branch, National Institute on Drug Abuse, National Institutes of Health, Baltimore, MD, United States
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