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Koller DP, Schirner M, Ritter P. Human connectome topology directs cortical traveling waves and shapes frequency gradients. Nat Commun 2024; 15:3570. [PMID: 38670965 PMCID: PMC11053146 DOI: 10.1038/s41467-024-47860-x] [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: 04/29/2023] [Accepted: 04/09/2024] [Indexed: 04/28/2024] Open
Abstract
Traveling waves and neural oscillation frequency gradients are pervasive in the human cortex. While the direction of traveling waves has been linked to brain function and dysfunction, the factors that determine this direction remain elusive. We hypothesized that structural connectivity instrength gradients - defined as the gradually varying sum of incoming connection strengths across the cortex - could shape both traveling wave direction and frequency gradients. We confirm the presence of instrength gradients in the human connectome across diverse cohorts and parcellations. Using a cortical network model, we demonstrate how these instrength gradients direct traveling waves and shape frequency gradients. Our model fits resting-state MEG functional connectivity best in a regime where instrength-directed traveling waves and frequency gradients emerge. We further show how structural subnetworks of the human connectome generate opposing wave directions and frequency gradients observed in the alpha and beta bands. Our findings suggest that structural connectivity instrength gradients affect both traveling wave direction and frequency gradients.
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Grants
- P.R. acknowledges funding from the following sources: Digital Europe Grant TEF-Health # 101100700, H2020 Research and Innovation Action Grant Human Brain Project SGA2 785907, H2020 Research and Innovation Action Grant Human Brain Project SGA3 945539, H2020 Research and Innovation Action Grant EOSC VirtualBrainCloud 826421, H2020 Research and Innovation Action Grant AISN 101057655, H2020 Research Infrastructures Grant EBRAINS-PREP 101079717, H2020 European Innovation Council PHRASE 101058240, H2020 Research Infrastructures Grant EBRAIN-Health 101058516, H2020 European Research Council Grant ERC BrainModes 683049, JPND ERA PerMed PatternCog 2522FSB904, Berlin Institute of Health & Foundation Charité, Johanna Quandt Excellence Initiative, German Research Foundation SFB 1436 (project ID 425899996), German Research Foundation SFB 1315 (project ID 327654276), German Research Foundation SFB 936 (project ID 178316478), German Research Foundation SFB-TRR 295 (project ID 424778381) German Research Foundation SPP Computational Connectomics RI 2073/6-1, RI 2073/10-2, RI 2073/9-1.
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Affiliation(s)
- Dominik P Koller
- Berlin Institute of Health (BIH) at Charité - Universitätsmedizin Berlin, Charitéplatz 1, 10117, Berlin, Germany.
- Department of Neurology with Experimental Neurology, Charité, Universitätsmedizin Berlin, Corporate member of Freie Universität Berlin and Humboldt Universität zu Berlin, Charitéplatz 1, 10117, Berlin, Germany.
| | - Michael Schirner
- Berlin Institute of Health (BIH) at Charité - Universitätsmedizin Berlin, Charitéplatz 1, 10117, Berlin, Germany
- Department of Neurology with Experimental Neurology, Charité, Universitätsmedizin Berlin, Corporate member of Freie Universität Berlin and Humboldt Universität zu Berlin, Charitéplatz 1, 10117, Berlin, Germany
- Bernstein Focus State Dependencies of Learning and Bernstein Center for Computational Neuroscience, 10115, Berlin, Germany
- Einstein Center for Neuroscience Berlin, Charitéplatz 1, 10117, Berlin, Germany
- Einstein Center Digital Future, Wilhelmstraße 67, 10117, Berlin, Germany
| | - Petra Ritter
- Berlin Institute of Health (BIH) at Charité - Universitätsmedizin Berlin, Charitéplatz 1, 10117, Berlin, Germany.
- Department of Neurology with Experimental Neurology, Charité, Universitätsmedizin Berlin, Corporate member of Freie Universität Berlin and Humboldt Universität zu Berlin, Charitéplatz 1, 10117, Berlin, Germany.
- Bernstein Focus State Dependencies of Learning and Bernstein Center for Computational Neuroscience, 10115, Berlin, Germany.
- Einstein Center for Neuroscience Berlin, Charitéplatz 1, 10117, Berlin, Germany.
- Einstein Center Digital Future, Wilhelmstraße 67, 10117, Berlin, Germany.
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Gil L. Self-adaptation of networks of nonidentical pulse-coupled excitatory and inhibitory oscillators in the presence of distance-related delays to achieve frequency synchronization. Phys Rev E 2023; 108:034211. [PMID: 37849137 DOI: 10.1103/physreve.108.034211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Accepted: 09/01/2023] [Indexed: 10/19/2023]
Abstract
We show that a network of nonidentical nodes, with excitable dynamics, pulse-coupled, with coupling delays depending on the Euclidean distance between nodes, is able to adapt the topology of its connections to obtain spike frequency synchronization. The adapted network exhibits remarkable properties: sparse, anticluster, necessary presence of a minimum of inhibitory nodes, predominance of connections from inhibitory nodes over those from excitatory nodes, and finally spontaneous spatial structuring of the inhibitory projections: the furthest are the most intense. In a second step, we discuss the possible implications of our findings to neural systems.
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Affiliation(s)
- L Gil
- Université Côte d'Azur, Institut de Physique de Nice, 17 rue Julien Lauprêtre, 06200 Nice, France
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Zhou S, Lin W. Eliminating synchronization of coupled neurons adaptively by using feedback coupling with heterogeneous delays. CHAOS (WOODBURY, N.Y.) 2021; 31:023114. [PMID: 33653064 DOI: 10.1063/5.0035327] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2020] [Accepted: 01/18/2021] [Indexed: 06/12/2023]
Abstract
In this paper, we present an adaptive scheme involving heterogeneous delay interactions to suppress synchronization in a large population of oscillators. We analytically investigate the incoherent state stability regions for several specific kinds of distributions for delays. Interestingly, we find that, among the distributions that we discuss, the exponential distribution may offer great convenience to the performance of our adaptive scheme because this distribution renders an unbounded stability region. Moreover, we demonstrate our scheme in the realization of synchronization elimination in some representative, realistic neuronal networks, which makes it possible to deepen the understanding and even refine the existing techniques of deep brain stimulation in the treatment of some synchronization-induced mental disorders.
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Affiliation(s)
- Shijie Zhou
- School of Mathematical Sciences, LMNS and SCMS, Fudan University, Shanghai 200433, China
| | - Wei Lin
- School of Mathematical Sciences, LMNS and SCMS, Fudan University, Shanghai 200433, China
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Petkoski S, Palva JM, Jirsa VK. Phase-lags in large scale brain synchronization: Methodological considerations and in-silico analysis. PLoS Comput Biol 2018; 14:e1006160. [PMID: 29990339 PMCID: PMC6039010 DOI: 10.1371/journal.pcbi.1006160] [Citation(s) in RCA: 44] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2017] [Accepted: 04/29/2018] [Indexed: 01/24/2023] Open
Abstract
Architecture of phase relationships among neural oscillations is central for their functional significance but has remained theoretically poorly understood. We use phenomenological model of delay-coupled oscillators with increasing degree of topological complexity to identify underlying principles by which the spatio-temporal structure of the brain governs the phase lags between oscillatory activity at distant regions. Phase relations and their regions of stability are derived and numerically confirmed for two oscillators and for networks with randomly distributed or clustered bimodal delays, as a first approximation for the brain structural connectivity. Besides in-phase, clustered delays can induce anti-phase synchronization for certain frequencies, while the sign of the lags is determined by the natural frequencies and by the inhomogeneous network interactions. For in-phase synchronization faster oscillators always phase lead, while stronger connected nodes lag behind the weaker during frequency depression, which consistently arises for in-silico results. If nodes are in anti-phase regime, then a distance π is added to the in-phase trends. The statistics of the phases is calculated from the phase locking values (PLV), as in many empirical studies, and we scrutinize the method’s impact. The choice of surrogates do not affects the mean of the observed phase lags, but higher significance levels that are generated by some surrogates, cause decreased variance and might fail to detect the generally weaker coherence of the interhemispheric links. These links are also affected by the non-stationary and intermittent synchronization, which causes multimodal phase lags that can be misleading if averaged. Taken together, the results describe quantitatively the impact of the spatio-temporal connectivity of the brain to the synchronization patterns between brain regions, and to uncover mechanisms through which the spatio-temporal structure of the brain renders phases to be distributed around 0 and π. Trial registration: South African Clinical Trials Register: http://www.sanctr.gov.za/SAClinicalbrnbspTrials/tabid/169/Default.aspx, then link to respiratory tract then link to tuberculosis, pulmonary; and TASK Applied Sciences Clinical Trials, AP-TB-201-16 (ALOPEXX): https://task.org.za/clinical-trials/. Functional connectivity, and in particular, phase coupling between distant brain regions may be fundamental in regulating neuronal processing and communication. However, phase relationships between the nodes of the brain and how they are confined by its spatio-temporal structure, have been mostly overlooked. We use a model of oscillatory dynamics superimposed on the space-time structure defined by the connectome, and we analyze the possible regimes of synchronization. Limitations of data analysis are also considered and we show that the choice of the significance threshold for coherence does not essentially impact the statistics of the observed phase lags, although it is crucial for the right detection of statistically significant coherence. Analytical insights are obtained for networks with heterogeneous time-delays, based on the empirical data from the connectome, and these are confirmed by numerical simulations, which show in- or anti-phase synchronization depending on the frequency and the distribution of time-delays. Phase lags are shown to result from inhomogeneous network interactions, so that stronger connected nodes generally phase lag behind the weaker.
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Affiliation(s)
- Spase Petkoski
- Aix-Marseille Université, Inserm, INS UMR_S 1106, Marseille, France
- * E-mail: (SP); (VKJ)
| | - J. Matias Palva
- Neuroscience Center, Helsinki Institute of Life Science, University of Helsinki, Helsinki, Finland
| | - Viktor K. Jirsa
- Aix-Marseille Université, Inserm, INS UMR_S 1106, Marseille, France
- * E-mail: (SP); (VKJ)
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Laing CR. Travelling waves in arrays of delay-coupled phase oscillators. CHAOS (WOODBURY, N.Y.) 2016; 26:094802. [PMID: 27781474 DOI: 10.1063/1.4953663] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
We consider the effects of several forms of delays on the existence and stability of travelling waves in non-locally coupled networks of Kuramoto-type phase oscillators and theta neurons. By passing to the continuum limit and using the Ott/Antonsen ansatz, we derive evolution equations for a spatially dependent order parameter. For phase oscillator networks, the travelling waves take the form of uniformly twisted waves, and these can often be characterised analytically. For networks of theta neurons, the waves are studied numerically.
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Affiliation(s)
- Carlo R Laing
- Institute of Natural and Mathematical Sciences, Massey University, Private Bag 102-904 NSMC, Auckland, New Zealand
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Timms L, English LQ. Synchronization in phase-coupled Kuramoto oscillator networks with axonal delay and synaptic plasticity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:032906. [PMID: 24730912 DOI: 10.1103/physreve.89.032906] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2013] [Indexed: 05/23/2023]
Abstract
We explore both analytically and numerically an ensemble of coupled phase oscillators governed by a Kuramoto-type system of differential equations. However, we have included the effects of time delay (due to finite signal-propagation speeds) and network plasticity (via dynamic coupling constants) inspired by the Hebbian learning rule in neuroscience. When time delay and learning effects combine, interesting synchronization phenomena are observed. We investigate the formation of spatiotemporal patterns in both one- and two-dimensional oscillator lattices with periodic boundary conditions and comment on the role of dimensionality.
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Affiliation(s)
- L Timms
- Department of Physics and Astronomy, Dickinson College, Carlisle, Pennsylvania 17013, USA
| | - L Q English
- Department of Physics and Astronomy, Dickinson College, Carlisle, Pennsylvania 17013, USA
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Nordenfelt A, Used J, Sanjuán MAF. Bursting frequency versus phase synchronization in time-delayed neuron networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:052903. [PMID: 23767594 DOI: 10.1103/physreve.87.052903] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2013] [Indexed: 06/02/2023]
Abstract
We investigate the dependence of the average bursting frequency on time delay for neuron networks with randomly distributed time-delayed chemical synapses. The result is compared with the corresponding curve for the phase synchronization and it turns out that, in some intervals, these have a very similar shape and appear as almost mirror images of each other. We have analyzed both the map-based chaotic Rulkov model and the continuous Hindmarsh-Rose model, yielding the same conclusions. In order to gain further insight, we also analyzed time-delayed Kuramoto models displaying an overall behavior similar to that observed on the neuron network models. For the Kuramoto models, we were able to derive analytical formulas providing an implicit functional relationship between the mean frequency and the phase synchronization. These formulas suggest a strong dependence between those two measures, which could explain the similarities in shape between the curves.
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Affiliation(s)
- Anders Nordenfelt
- Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, España
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Ermentrout B, Ko TW. Delays and weakly coupled neuronal oscillators. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2009; 367:1097-115. [PMID: 19218153 DOI: 10.1098/rsta.2008.0259] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
We use weakly coupled oscillator theory to study the effects of delays on coupled systems of neuronal oscillators. We explore, first, simple pairs with constant delays and then examine the role of distributed delays as would occur in systems with dendritic branches or in networks where there is a distance-dependent conductance delay. In the latter, we use mean field theory to show the emergence of travelling waves and the loss of synchronization. Next, we consider phase models with stronger coupling and delays in the state variables. We show that they have a richer dynamics but one that is still similar to the weakly coupled case.
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Affiliation(s)
- Bard Ermentrout
- Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA.
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Zhou J, Liu Z. Synchronized patterns induced by distributed time delays. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:056213. [PMID: 18643148 DOI: 10.1103/physreve.77.056213] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2008] [Indexed: 05/26/2023]
Abstract
Considering the fact that the distances between coupled oscillators may delay the receiving of signals, we study here the influence of uniformly distributed delays in an array of coupled pendulums instead of studying the influence of the coupling strength. We find that with an increase of the range of distributed delays, the chaotic behaviors of the coupled arrays may be controlled and different synchronized patterns can be induced. An analytic solution is given to confirm the numerical results. This finding may provide further insight into information processing in neurons.
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Affiliation(s)
- Jie Zhou
- Institute of Theoretical Physics and Department of Physics, East China Normal University, Shanghai 200062, China
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Ko TW, Ermentrout GB. Effects of axonal time delay on synchronization and wave formation in sparsely coupled neuronal oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:056206. [PMID: 18233738 DOI: 10.1103/physreve.76.056206] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2007] [Revised: 06/29/2007] [Indexed: 05/25/2023]
Abstract
We investigate the effects of axonal time delay when the neuronal oscillators are coupled by sparse and random connections. Using phase-reduced models with general coupling functions, we show that a small fraction of connections with time delay can destabilize synchronous states and induce near-regular wave states. An order parameter is introduced to characterize those states. We analyze the systems using mean-field-type approximation.
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Affiliation(s)
- Tae-Wook Ko
- Department of Mathematics, University of Pittsburgh, Pennsylvania 15260, USA.
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Ji L, Li QS. Turing pattern formation in coupled reaction-diffusion system with distributed delays. J Chem Phys 2005; 123:94509. [PMID: 16164355 DOI: 10.1063/1.2041427] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Turing pattern formation in coupled two-layer system with distributed delayed is investigated. Numerical simulations prove that, when the coupling is weak, it can apparently accelerate the formation process and enhance the spatial amplitude of the pattern. When it is strong, it will prolong the formation process or even inhibit the pattern and turn the whole system into bulk oscillatory state by its influence on the transient oscillatory state. If the coupling covers only part of the system, Turing pattern can be prominently oriented according to the shape of the coupling area at tiny coupling strength. However, if the coupling is too strong, the Turing pattern may also be destroyed. This means that in coupled systems, the delay effect in the cross-layer signal transfer may significantly influence the spatial character and/or the evolution dynamics in Turing pattern formation, even to destroy the pattern. This work is of practical significance in the study of Turing pattern in biosystems, where bilayer membranes or multilayer tissues are often found.
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Affiliation(s)
- Lin Ji
- The Institute for Chemical Physics, Beijing Institute of Technology, Beijing 100081, China
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12
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Masoller C, Martí AC. Random delays and the synchronization of chaotic maps. PHYSICAL REVIEW LETTERS 2005; 94:134102. [PMID: 15903993 DOI: 10.1103/physrevlett.94.134102] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2004] [Indexed: 05/02/2023]
Abstract
We investigate the dynamics of an array of chaotic logistic maps coupled with random delay times. We report that for adequate coupling strength the array is able to synchronize, in spite of the random delays. Specifically, we find that the synchronized state is a homogeneous steady state, where the chaotic dynamics of the individual maps is suppressed. This synchronization behavior is largely independent of the connection topology and depends mainly on the average number of links per node. We carry out a statistical linear stability analysis that confirms the numerical results and provides a better understanding of the nontrivial roles of random delayed interactions.
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Affiliation(s)
- C Masoller
- Instituto de Física, Facultad de Ciencias, Universidad de la República, Montevideo, Uruguay
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