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Courson J, Quoy M, Timofeeva Y, Manos T. An exploratory computational analysis in mice brain networks of widespread epileptic seizure onset locations along with potential strategies for effective intervention and propagation control. Front Comput Neurosci 2024; 18:1360009. [PMID: 38468870 PMCID: PMC10925689 DOI: 10.3389/fncom.2024.1360009] [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: 12/22/2023] [Accepted: 02/08/2024] [Indexed: 03/13/2024] Open
Abstract
Mean-field models have been developed to replicate key features of epileptic seizure dynamics. However, the precise mechanisms and the role of the brain area responsible for seizure onset and propagation remain incompletely understood. In this study, we employ computational methods within The Virtual Brain framework and the Epileptor model to explore how the location and connectivity of an Epileptogenic Zone (EZ) in a mouse brain are related to focal seizures (seizures that start in one brain area and may or may not remain localized), with a specific focus on the hippocampal region known for its association with epileptic seizures. We then devise computational strategies to confine seizures (prevent widespread propagation), simulating medical-like treatments such as tissue resection and the application of an anti-seizure drugs or neurostimulation to suppress hyperexcitability. Through selectively removing (blocking) specific connections informed by the structural connectome and graph network measurements or by locally reducing outgoing connection weights of EZ areas, we demonstrate that seizures can be kept constrained around the EZ region. We successfully identified the minimal connections necessary to prevent widespread seizures, with a particular focus on minimizing surgical or medical intervention while simultaneously preserving the original structural connectivity and maximizing brain functionality.
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Affiliation(s)
- Juliette Courson
- ETIS Lab, ENSEA, CNRS, UMR8051, CY Cergy-Paris University, Cergy, France
- Laboratoire de Physique Théorique et Modélisation, UMR 8089, CY Cergy Paris Université, CNRS, Cergy-Pontoise, France
- Department of Computer Science, University of Warwick, Coventry, United Kingdom
| | - Mathias Quoy
- ETIS Lab, ENSEA, CNRS, UMR8051, CY Cergy-Paris University, Cergy, France
- IPAL CNRS Singapore, Singapore, Singapore
| | - Yulia Timofeeva
- Department of Computer Science, University of Warwick, Coventry, United Kingdom
- Department of Clinical and Experimental Epilepsy, UCL Queen Square Institute of Neurology, University College London, London, United Kingdom
| | - Thanos Manos
- ETIS Lab, ENSEA, CNRS, UMR8051, CY Cergy-Paris University, Cergy, France
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2
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Zhang F, Wang J. Nonequilibrium indicator for the onset of epileptic seizure. Phys Rev E 2023; 108:044111. [PMID: 37978676 DOI: 10.1103/physreve.108.044111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2023] [Accepted: 08/17/2023] [Indexed: 11/19/2023]
Abstract
The occurrence of spontaneous bursts of uncontrolled electrical activity between neurons can disrupt normal brain function and lead to epileptic seizures. Despite extensive research, the mechanisms underlying seizure onset remain unclear. This study investigates the onset of seizures from the perspective of nonequilibrium statistical physics. By analyzing the probability flux within the framework of the nonequilibrium potential-flux landscape, we establish a connection between seizure dynamics and nonequilibrium. Our findings demonstrate that the degree of nonequilibrium is sensitive to the onset of epileptic seizures. This result offers an alternative perspective on assessing seizure onset in epilepsy.
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Affiliation(s)
- Feng Zhang
- State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin 130022, China
| | - Jin Wang
- Department of Chemistry and Physics, State University of New York at Stony Brook, Stony Brook, New York 11794-3400, USA
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3
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Brogin JAF, Faber J, Bueno DD. An Efficient Approach to Define the Input Stimuli to Suppress Epileptic Seizures Described by the Epileptor Model. Int J Neural Syst 2020; 30:2050062. [PMID: 32938259 DOI: 10.1142/s0129065720500628] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Epilepsy affects about 70 million people in the world. Every year, approximately 2.4 million people are diagnosed with epilepsy, two-thirds of them will not know the etiology of their disease, and 1% of these individuals will decease as a consequence of it. Due to the inherent complexity of predicting and explaining it, the mathematical model Epileptor was recently developed to reproduce seizure-like events, also providing insights to improve the understanding of the neural dynamics in the interictal and ictal periods, although the physics behind each parameter and variable of the model is not fully established in the literature. This paper introduces an approach to design a feedback-based controller for suppressing epileptic seizures described by Epileptor. Our work establishes how the nonlinear dynamics of this disorder can be written in terms of a combination of linear sub-models employing an exact solution. Additionally, we show how a feedback control gain can be computed to suppress seizures, as well as how specific shapes applied as input stimuli for this purpose can be obtained. The practical application of the approach is discussed and the results show that the proposed technique is promising for developing controllers in this field.
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Affiliation(s)
- João Angelo Ferres Brogin
- Department of Mechanical Engineering, São Paulo State University (UNESP), School of Engineering of Ilha Solteira, 56 Brasil Avenue, Ilha Solteira, São Paulo 15385-000, Brazil
| | - Jean Faber
- Department of Neurology and Neurosurgery, Federal University of São Paulo (UNIFESP), 667 Pedro de Toledo Street, São Paulo 04039-032, Brazil
| | - Douglas Domingues Bueno
- Department of Mathematics, São Paulo State University (UNESP), School of Engineering of Ilha Solteira, 56 Brasil Avenue, Ilha Solteira, São Paulo 15385-000, Brazil
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4
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Allegra Mascaro AL, Falotico E, Petkoski S, Pasquini M, Vannucci L, Tort-Colet N, Conti E, Resta F, Spalletti C, Ramalingasetty ST, von Arnim A, Formento E, Angelidis E, Blixhavn CH, Leergaard TB, Caleo M, Destexhe A, Ijspeert A, Micera S, Laschi C, Jirsa V, Gewaltig MO, Pavone FS. Experimental and Computational Study on Motor Control and Recovery After Stroke: Toward a Constructive Loop Between Experimental and Virtual Embodied Neuroscience. Front Syst Neurosci 2020; 14:31. [PMID: 32733210 PMCID: PMC7359878 DOI: 10.3389/fnsys.2020.00031] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2019] [Accepted: 05/08/2020] [Indexed: 01/22/2023] Open
Abstract
Being able to replicate real experiments with computational simulations is a unique opportunity to refine and validate models with experimental data and redesign the experiments based on simulations. However, since it is technically demanding to model all components of an experiment, traditional approaches to modeling reduce the experimental setups as much as possible. In this study, our goal is to replicate all the relevant features of an experiment on motor control and motor rehabilitation after stroke. To this aim, we propose an approach that allows continuous integration of new experimental data into a computational modeling framework. First, results show that we could reproduce experimental object displacement with high accuracy via the simulated embodiment in the virtual world by feeding a spinal cord model with experimental registration of the cortical activity. Second, by using computational models of multiple granularities, our preliminary results show the possibility of simulating several features of the brain after stroke, from the local alteration in neuronal activity to long-range connectivity remodeling. Finally, strategies are proposed to merge the two pipelines. We further suggest that additional models could be integrated into the framework thanks to the versatility of the proposed approach, thus allowing many researchers to achieve continuously improved experimental design.
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Affiliation(s)
- Anna Letizia Allegra Mascaro
- Neuroscience Institute, National Research Council, Pisa, Italy.,European Laboratory for Non-Linear Spectroscopy, Sesto Fiorentino, Italy
| | - Egidio Falotico
- Department of Excellence in Robotics & AI, The BioRobotics Institute, Scuola Superiore Sant'Anna, Pontedera, Italy
| | - Spase Petkoski
- Aix-Marseille Université, Inserm, INS UMR_S 1106, Marseille, France
| | - Maria Pasquini
- Department of Excellence in Robotics & AI, The BioRobotics Institute, Scuola Superiore Sant'Anna, Pontedera, Italy
| | - Lorenzo Vannucci
- Department of Excellence in Robotics & AI, The BioRobotics Institute, Scuola Superiore Sant'Anna, Pontedera, Italy
| | - Núria Tort-Colet
- Paris-Saclay University, Institute of Neuroscience, CNRS, Gif-sur-Yvette, France
| | - Emilia Conti
- European Laboratory for Non-Linear Spectroscopy, Sesto Fiorentino, Italy.,Department of Physics and Astronomy, University of Florence, Florence, Italy
| | - Francesco Resta
- European Laboratory for Non-Linear Spectroscopy, Sesto Fiorentino, Italy.,Department of Physics and Astronomy, University of Florence, Florence, Italy
| | | | | | | | - Emanuele Formento
- Bertarelli Foundation Chair in Translational NeuroEngineering, Institute of Bioengineering, Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland
| | - Emmanouil Angelidis
- Fortiss GmbH, Munich, Germany.,Chair of Robotics, Artificial Intelligence and Embedded Systems, Department of Informatics, Technical University of Munich, Munich, Germany
| | | | | | - Matteo Caleo
- Neuroscience Institute, National Research Council, Pisa, Italy.,Department of Biomedical Sciences, University of Padua, Padua, Italy
| | - Alain Destexhe
- Paris-Saclay University, Institute of Neuroscience, CNRS, Gif-sur-Yvette, France
| | - Auke Ijspeert
- Biorobotics Laboratory, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
| | - Silvestro Micera
- Department of Excellence in Robotics & AI, The BioRobotics Institute, Scuola Superiore Sant'Anna, Pontedera, Italy.,Bertarelli Foundation Chair in Translational NeuroEngineering, Institute of Bioengineering, Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland
| | - Cecilia Laschi
- Department of Excellence in Robotics & AI, The BioRobotics Institute, Scuola Superiore Sant'Anna, Pontedera, Italy
| | - Viktor Jirsa
- Aix-Marseille Université, Inserm, INS UMR_S 1106, Marseille, France
| | - Marc-Oliver Gewaltig
- Blue Brain Project (BBP), École Polytechnique Fédérale de Lausanne (EPFL), Geneva, Switzerland
| | - Francesco S Pavone
- European Laboratory for Non-Linear Spectroscopy, Sesto Fiorentino, Italy.,Department of Physics and Astronomy, University of Florence, Florence, Italy
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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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6
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Petkoski S, Spiegler A, Proix T, Aram P, Temprado JJ, Jirsa VK. Heterogeneity of time delays determines synchronization of coupled oscillators. Phys Rev E 2016; 94:012209. [PMID: 27575125 DOI: 10.1103/physreve.94.012209] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2015] [Indexed: 05/01/2023]
Abstract
Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial distribution of time delays with regard to synchronization, by decomposing it into patterns and therefore reducing the stability analysis into the tractable problem of a finite set of delay-coupled differential equations. We analyze delay-structured networks of phase oscillators and we find that, depending on the heterogeneity of the delays, the oscillators group in phase-shifted, anti-phase, steady, and non-stationary clusters, and analytically compute their stability boundaries. These results find direct application in the study of brain oscillations.
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Affiliation(s)
- Spase Petkoski
- Aix-Marseille Université, Inserm, INS UMR_S 1106, 13005, Marseille, France
- Aix-Marseille Université, CNRS, ISM UMR 7287, 13288, Marseille, France
| | - Andreas Spiegler
- Aix-Marseille Université, Inserm, INS UMR_S 1106, 13005, Marseille, France
| | - Timothée Proix
- Aix-Marseille Université, Inserm, INS UMR_S 1106, 13005, Marseille, France
| | - Parham Aram
- Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield S10 2TN, United Kingdom
| | | | - Viktor K Jirsa
- Aix-Marseille Université, Inserm, INS UMR_S 1106, 13005, Marseille, France
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7
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Proix T, Bartolomei F, Chauvel P, Bernard C, Jirsa VK. Permittivity coupling across brain regions determines seizure recruitment in partial epilepsy. J Neurosci 2014; 34:15009-21. [PMID: 25378166 PMCID: PMC6608363 DOI: 10.1523/jneurosci.1570-14.2014] [Citation(s) in RCA: 86] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2014] [Revised: 09/08/2014] [Accepted: 09/19/2014] [Indexed: 11/21/2022] Open
Abstract
Brain regions generating seizures in patients with refractory partial epilepsy are referred to as the epileptogenic zone (EZ). During a seizure, paroxysmal activity is not restricted to the EZ, but may recruit other brain regions and propagate activity through large brain networks, which comprise brain regions that are not necessarily epileptogenic. The identification of the EZ is crucial for candidates for neurosurgery and requires unambiguous criteria that evaluate the degree of epileptogenicity of brain regions. To obtain such criteria and investigate the mechanisms of seizure recruitment and propagation, we develop a mathematical framework of coupled neural populations, which can interact via signaling through a slow permittivity variable. The permittivity variable captures effects evolving on slow timescales, including extracellular ionic concentrations and energy metabolism, with time delays of up to seconds as observed clinically. Our analyses provide a set of indices quantifying the degree of epileptogenicity and predict conditions, under which seizures propagate to nonepileptogenic brain regions, explaining the responses to intracerebral electric stimulation in epileptogenic and nonepileptogenic areas. In conjunction, our results provide guidance in the presurgical evaluation of epileptogenicity based on electrographic signatures in intracerebral electroencephalograms.
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Affiliation(s)
- Timothée Proix
- Aix Marseille Université, Institut de Neurosciences des Systèmes, 13005 Marseille, France and INSERM, UMR 1106, 13005 Marseille, France and
| | - Fabrice Bartolomei
- Aix Marseille Université, Institut de Neurosciences des Systèmes, 13005 Marseille, France and INSERM, UMR 1106, 13005 Marseille, France and Assistance Publique-Hôpitaux de Marseille, Hôpital de la Timone, Service de Neurophysiologie Clinique, CHU, 13005 Marseille, France
| | - Patrick Chauvel
- Aix Marseille Université, Institut de Neurosciences des Systèmes, 13005 Marseille, France and INSERM, UMR 1106, 13005 Marseille, France and Assistance Publique-Hôpitaux de Marseille, Hôpital de la Timone, Service de Neurophysiologie Clinique, CHU, 13005 Marseille, France
| | - Christophe Bernard
- Aix Marseille Université, Institut de Neurosciences des Systèmes, 13005 Marseille, France and INSERM, UMR 1106, 13005 Marseille, France and
| | - Viktor K Jirsa
- Aix Marseille Université, Institut de Neurosciences des Systèmes, 13005 Marseille, France and INSERM, UMR 1106, 13005 Marseille, France and
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8
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Jirsa VK, Stacey WC, Quilichini PP, Ivanov AI, Bernard C. On the nature of seizure dynamics. ACTA ACUST UNITED AC 2014; 137:2210-30. [PMID: 24919973 DOI: 10.1093/brain/awu133] [Citation(s) in RCA: 384] [Impact Index Per Article: 38.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
Seizures can occur spontaneously and in a recurrent manner, which defines epilepsy; or they can be induced in a normal brain under a variety of conditions in most neuronal networks and species from flies to humans. Such universality raises the possibility that invariant properties exist that characterize seizures under different physiological and pathological conditions. Here, we analysed seizure dynamics mathematically and established a taxonomy of seizures based on first principles. For the predominant seizure class we developed a generic model called Epileptor. As an experimental model system, we used ictal-like discharges induced in vitro in mouse hippocampi. We show that only five state variables linked by integral-differential equations are sufficient to describe the onset, time course and offset of ictal-like discharges as well as their recurrence. Two state variables are responsible for generating rapid discharges (fast time scale), two for spike and wave events (intermediate time scale) and one for the control of time course, including the alternation between 'normal' and ictal periods (slow time scale). We propose that normal and ictal activities coexist: a separatrix acts as a barrier (or seizure threshold) between these states. Seizure onset is reached upon the collision of normal brain trajectories with the separatrix. We show theoretically and experimentally how a system can be pushed toward seizure under a wide variety of conditions. Within our experimental model, the onset and offset of ictal-like discharges are well-defined mathematical events: a saddle-node and homoclinic bifurcation, respectively. These bifurcations necessitate a baseline shift at onset and a logarithmic scaling of interspike intervals at offset. These predictions were not only confirmed in our in vitro experiments, but also for focal seizures recorded in different syndromes, brain regions and species (humans and zebrafish). Finally, we identified several possible biophysical parameters contributing to the five state variables in our model system. We show that these parameters apply to specific experimental conditions and propose that there exists a wide array of possible biophysical mechanisms for seizure genesis, while preserving central invariant properties. Epileptor and the seizure taxonomy will guide future modeling and translational research by identifying universal rules governing the initiation and termination of seizures and predicting the conditions necessary for those transitions.
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Affiliation(s)
- Viktor K Jirsa
- 1 Aix Marseille Université, Institut de Neurosciences des Systèmes, Marseille, France2 Inserm, UMR_S 1106, 27 Bd Jean Moulin, 13385 Marseille Cedex 5, France
| | - William C Stacey
- 3 Department of Neurology, Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
| | - Pascale P Quilichini
- 1 Aix Marseille Université, Institut de Neurosciences des Systèmes, Marseille, France2 Inserm, UMR_S 1106, 27 Bd Jean Moulin, 13385 Marseille Cedex 5, France
| | - Anton I Ivanov
- 1 Aix Marseille Université, Institut de Neurosciences des Systèmes, Marseille, France2 Inserm, UMR_S 1106, 27 Bd Jean Moulin, 13385 Marseille Cedex 5, France
| | - Christophe Bernard
- 1 Aix Marseille Université, Institut de Neurosciences des Systèmes, Marseille, France2 Inserm, UMR_S 1106, 27 Bd Jean Moulin, 13385 Marseille Cedex 5, France
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Woodman MM, Jirsa VK. Emergent dynamics from spiking neuron networks through symmetry breaking of connectivity. PLoS One 2013; 8:e64339. [PMID: 23691200 PMCID: PMC3656844 DOI: 10.1371/journal.pone.0064339] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2013] [Accepted: 04/03/2013] [Indexed: 11/18/2022] Open
Abstract
Low-dimensional attractive manifolds with flows prescribing the evolution of state variables are commonly used to capture the lawful behavior of behavioral and cognitive variables. Neural network dynamics underlie many of the mechanistic explanations of function and demonstrate the existence of such low-dimensional attractive manifolds. In this study, we focus on exploring the network mechanisms due to asymmetric couplings giving rise to the emergence of arbitrary flows in low dimensional spaces. Here we use a spiking neural network model, specifically the theta neuron model and simple synaptic dynamics, to show how a qualitatively identical set of basic behaviors arises from different combinations of couplings with broken symmetry, in fluctuations of both firing rate and spike timing. We further demonstrate how such network dynamics can be combined to create more complex processes. These results suggest that 1) asymmetric coupling is not always a variance to be averaged over, 2) different networks may produce the same dynamics by different dynamical routes and 3) complex dynamics may be formed by simpler dynamics through a combination of couplings.
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Affiliation(s)
- M. Marmaduke Woodman
- Institut de Neurosciences des Systèmes Inserm UMR1106 Aix-Marseille Université, Marseille, France
| | - Viktor K. Jirsa
- Institut de Neurosciences des Systèmes Inserm UMR1106 Aix-Marseille Université, Marseille, France
- * E-mail:
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10
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Roy D, Jirsa V. Inferring network properties of cortical neurons with synaptic coupling and parameter dispersion. Front Comput Neurosci 2013; 7:20. [PMID: 23533147 PMCID: PMC3607799 DOI: 10.3389/fncom.2013.00020] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2013] [Accepted: 03/05/2013] [Indexed: 11/13/2022] Open
Abstract
Computational models at different space-time scales allow us to understand the fundamental mechanisms that govern neural processes and relate uniquely these processes to neuroscience data. In this work, we propose a novel neurocomputational unit (a mesoscopic model which tell us about the interaction between local cortical nodes in a large scale neural mass model) of bursters that qualitatively captures the complex dynamics exhibited by a full network of parabolic bursting neurons. We observe that the temporal dynamics and fluctuation of mean synaptic action term exhibits a high degree of correlation with the spike/burst activity of our population. With heterogeneity in the applied drive and mean synaptic coupling derived from fast excitatory synapse approximations we observe long term behavior in our population dynamics such as partial oscillations, incoherence, and synchrony. In order to understand the origin of multistability at the population level as a function of mean synaptic coupling and heterogeneity in the firing rate threshold we employ a simple generative model for parabolic bursting recently proposed by Ghosh et al. (2009). Further, we use here a mean coupling formulated for fast spiking neurons for our analysis of generic model. Stability analysis of this mean field network allow us to identify all the relevant network states found in the detailed biophysical model. We derive here analytically several boundary solutions, a result which holds for any number of spikes per burst. These findings illustrate the role of oscillations occurring at slow time scales (bursts) on the global behavior of the network.
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Affiliation(s)
- Dipanjan Roy
- Theoretical Neuroscience Group, Faculté de Médecine, Institut de Neurosciences des Systèmes, Inserm UMR1106, Aix-Marseille Université Marseille, France ; Bernstein Center for Computational Neuroscience Berlin, Germany ; Department of Software Engineering and Theoretical Computer Science, Technische Universität Berlin Berlin, Germany
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