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Wang CY, Zhang JQ, Wu ZX, Guan JY. Collective firing patterns of neuronal networks with short-term synaptic plasticity. Phys Rev E 2021; 103:022312. [PMID: 33735974 DOI: 10.1103/physreve.103.022312] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2020] [Accepted: 01/28/2021] [Indexed: 12/31/2022]
Abstract
We investigate the occurrence of synchronous population activities in a neuronal network composed of both excitatory and inhibitory neurons and equipped with short-term synaptic plasticity. The collective firing patterns with different macroscopic properties emerge visually with the change of system parameters, and most long-time collective evolution also shows periodic-like characteristics. We systematically discuss the pattern-formation dynamics on a microscopic level and find a lot of hidden features of the population activities. The bursty phase with power-law distributed avalanches is observed in which the population activity can be either entire or local periodic-like. In the purely spike-to-spike synchronous regime, the periodic-like phase emerges from the synchronous chaos after the backward period-doubling transition. The local periodic-like population activity and the synchronous chaotic activity show substantial trial-to-trial variability, which is unfavorable for neural code, while they are contrary to the stable periodic-like phases. We also show that the inhibitory neurons can promote the generation of cluster firing behavior and strong bursty collective firing activity by depressing the activities of postsynaptic neurons partially or wholly.
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Affiliation(s)
- Chong-Yang Wang
- Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Ji-Qiang Zhang
- Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing 100191, China
- School of Physics and Electronic-Electrical Engineering, Ningxia University, Yinchuan 750021, China
| | - Zhi-Xi Wu
- Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Jian-Yue Guan
- Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, Gansu 730000, China
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Jung N, Le QA, Lee KE, Lee JW. Avalanche size distribution of an integrate-and-fire neural model on complex networks. CHAOS (WOODBURY, N.Y.) 2020; 30:063118. [PMID: 32611110 DOI: 10.1063/5.0008767] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2020] [Accepted: 05/07/2020] [Indexed: 06/11/2023]
Abstract
We considered the neural avalanche dynamics of a modified integrate-and-fire model on complex networks, as well as the neural dynamics in a fully connected network, random network, small-world network, and scale-free network. We observed the self-organized criticality of the neural model on complex networks. The probability distribution of the avalanche size and lifetime follow the power law at the critical synaptic strength. Neuronal dynamics on a complex network are not universal. The critical exponents of the avalanche dynamics depend on the structure of the complex network. We observed that the critical exponents deviate from the mean-field value.
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Affiliation(s)
- Nam Jung
- Department of Physics, Inha University, Incheon 22212, Korea
| | - Quang Anh Le
- Department of Physics, Inha University, Incheon 22212, Korea
| | - Kyoung-Eun Lee
- Ecology and Future Research Institute, 45 Dusilo, Geumjeong-gu, Busan 46228, Korea
| | - Jae Woo Lee
- Department of Physics, Inha University, Incheon 22212, Korea
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Schmutz V, Gerstner W, Schwalger T. Mesoscopic population equations for spiking neural networks with synaptic short-term plasticity. JOURNAL OF MATHEMATICAL NEUROSCIENCE 2020; 10:5. [PMID: 32253526 PMCID: PMC7136387 DOI: 10.1186/s13408-020-00082-z] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2019] [Accepted: 03/25/2020] [Indexed: 06/07/2023]
Abstract
Coarse-graining microscopic models of biological neural networks to obtain mesoscopic models of neural activities is an essential step towards multi-scale models of the brain. Here, we extend a recent theory for mesoscopic population dynamics with static synapses to the case of dynamic synapses exhibiting short-term plasticity (STP). The extended theory offers an approximate mean-field dynamics for the synaptic input currents arising from populations of spiking neurons and synapses undergoing Tsodyks-Markram STP. The approximate mean-field dynamics accounts for both finite number of synapses and correlation between the two synaptic variables of the model (utilization and available resources) and its numerical implementation is simple. Comparisons with Monte Carlo simulations of the microscopic model show that in both feedforward and recurrent networks, the mesoscopic mean-field model accurately reproduces the first- and second-order statistics of the total synaptic input into a postsynaptic neuron and accounts for stochastic switches between Up and Down states and for population spikes. The extended mesoscopic population theory of spiking neural networks with STP may be useful for a systematic reduction of detailed biophysical models of cortical microcircuits to numerically efficient and mathematically tractable mean-field models.
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Affiliation(s)
- Valentin Schmutz
- Brain Mind Institute, École Polytechnique Féderale de Lausanne (EPFL), Lausanne, Switzerland.
| | - Wulfram Gerstner
- Brain Mind Institute, École Polytechnique Féderale de Lausanne (EPFL), Lausanne, Switzerland
| | - Tilo Schwalger
- Brain Mind Institute, École Polytechnique Féderale de Lausanne (EPFL), Lausanne, Switzerland
- Bernstein Center for Computational Neuroscience, Institut für Mathematik, Technische Universität Berlin, Berlin, Germany
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Shirzhiyan Z, Keihani A, Farahi M, Shamsi E, GolMohammadi M, Mahnam A, Haidari MR, Jafari AH. Introducing chaotic codes for the modulation of code modulated visual evoked potentials (c-VEP) in normal adults for visual fatigue reduction. PLoS One 2019; 14:e0213197. [PMID: 30840671 PMCID: PMC6402685 DOI: 10.1371/journal.pone.0213197] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2018] [Accepted: 02/16/2019] [Indexed: 11/19/2022] Open
Abstract
Code modulated Visual Evoked Potentials (c-VEP) based BCI studies usually employ m-sequences as a modulating codes for their broadband spectrum and correlation property. However, subjective fatigue of the presented codes has been a problem. In this study, we introduce chaotic codes containing broadband spectrum and similar correlation property. We examined whether the introduced chaotic codes could be decoded from EEG signals and also compared the subjective fatigue level with m-sequence codes in normal subjects. We generated chaotic code from one-dimensional logistic map and used it with conventional 31-bit m-sequence code. In a c-VEP based study in normal subjects (n = 44, 21 females) we presented these codes visually and recorded EEG signals from the corresponding codes for their four lagged versions. Canonical correlation analysis (CCA) and spatiotemporal beamforming (STB) methods were used for target identification and comparison of responses. Additionally, we compared the subjective self-declared fatigue using VAS caused by presented m-sequence and chaotic codes. The introduced chaotic code was decoded from EEG responses with CCA and STB methods. The maximum total accuracy values of 93.6 ± 11.9% and 94 ± 14.4% were achieved with STB method for chaotic and m-sequence codes for all subjects respectively. The achieved accuracies in all subjects were not significantly different in m-sequence and chaotic codes. There was significant reduction in subjective fatigue caused by chaotic codes compared to the m-sequence codes. Both m-sequence and chaotic codes were similar in their accuracies as evaluated by CCA and STB methods. The chaotic codes significantly reduced subjective fatigue compared to the m-sequence codes.
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Affiliation(s)
- Zahra Shirzhiyan
- Medical Physics & Biomedical Engineering Department, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran
- Research Center for Biomedical Technologies and Robotics (RCBTR), Tehran University of Medical Sciences, Tehran, Iran
| | - Ahmadreza Keihani
- Medical Physics & Biomedical Engineering Department, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran
- Research Center for Biomedical Technologies and Robotics (RCBTR), Tehran University of Medical Sciences, Tehran, Iran
| | - Morteza Farahi
- Medical Physics & Biomedical Engineering Department, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran
- Research Center for Biomedical Technologies and Robotics (RCBTR), Tehran University of Medical Sciences, Tehran, Iran
| | - Elham Shamsi
- Medical Physics & Biomedical Engineering Department, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran
- Research Center for Biomedical Technologies and Robotics (RCBTR), Tehran University of Medical Sciences, Tehran, Iran
| | - Mina GolMohammadi
- Research Center for Biomedical Technologies and Robotics (RCBTR), Tehran University of Medical Sciences, Tehran, Iran
| | - Amin Mahnam
- Department of Biomedical Engineering, Faculty of Engineering, University of Isfahan, Isfahan, Iran
| | - Mohsen Reza Haidari
- Section of Neuroscience, Department of Neurology, Faculty of Medicine, Baqiyatallah University of Medical Sciences, Tehran, Iran
| | - Amir Homayoun Jafari
- Medical Physics & Biomedical Engineering Department, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran
- Research Center for Biomedical Technologies and Robotics (RCBTR), Tehran University of Medical Sciences, Tehran, Iran
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Michiels van Kessenich L, Berger D, de Arcangelis L, Herrmann HJ. Pattern recognition with neuronal avalanche dynamics. Phys Rev E 2019; 99:010302. [PMID: 30780306 DOI: 10.1103/physreve.99.010302] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2018] [Indexed: 11/07/2022]
Abstract
Pattern recognition is a fundamental neuronal process which enables a cortical system to interpret visual stimuli. How the brain learns to recognize patterns is, however, an unsolved problem. The frequently employed method of back propagation excels at this task but has been found to be unbiological in many aspects. In this Rapid Communication we achieve pattern recognition tasks in a biologically, fully consistent framework. We consider a neuronal network exhibiting avalanche dynamics, as observed experimentally, and implement negative feedback signals. These are chemical signals, such as dopamine, which mediate synaptic plasticity and sculpt the network to achieve certain tasks. The system is able to distinguish horizontal and vertical lines with high accuracy, as well as to perform well at the more complicated task of handwritten digit recognition. Resulting from the learning mechanism, spatially separate activity regions emerge, as observed in the primary visual cortex using functional magnetic resonance imaging techniques. The results therefore suggest that negative feedback signals offer an explanation for the emergence of distinct activity areas in the visual cortex.
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Affiliation(s)
| | - D Berger
- Computational Physics for Engineering Materials, IfB, ETH Zürich, 8093 Zürich, Switzerland
| | - L de Arcangelis
- Department of Engineering, University of Campania "Luigi Vanvitelli," I-81031 Aversa (CE), Italy and INFN Sezione Naples, Gruppo Collegato Salerno, Salerno, Italy
| | - H J Herrmann
- Computational Physics for Engineering Materials, IfB, ETH Zürich, 8093 Zürich, Switzerland and Departamento de Fisica, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil
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Landau-Ginzburg theory of cortex dynamics: Scale-free avalanches emerge at the edge of synchronization. Proc Natl Acad Sci U S A 2018; 115:E1356-E1365. [PMID: 29378970 DOI: 10.1073/pnas.1712989115] [Citation(s) in RCA: 76] [Impact Index Per Article: 12.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Understanding the origin, nature, and functional significance of complex patterns of neural activity, as recorded by diverse electrophysiological and neuroimaging techniques, is a central challenge in neuroscience. Such patterns include collective oscillations emerging out of neural synchronization as well as highly heterogeneous outbursts of activity interspersed by periods of quiescence, called "neuronal avalanches." Much debate has been generated about the possible scale invariance or criticality of such avalanches and its relevance for brain function. Aimed at shedding light onto this, here we analyze the large-scale collective properties of the cortex by using a mesoscopic approach following the principle of parsimony of Landau-Ginzburg. Our model is similar to that of Wilson-Cowan for neural dynamics but crucially, includes stochasticity and space; synaptic plasticity and inhibition are considered as possible regulatory mechanisms. Detailed analyses uncover a phase diagram including down-state, synchronous, asynchronous, and up-state phases and reveal that empirical findings for neuronal avalanches are consistently reproduced by tuning our model to the edge of synchronization. This reveals that the putative criticality of cortical dynamics does not correspond to a quiescent-to-active phase transition as usually assumed in theoretical approaches but to a synchronization phase transition, at which incipient oscillations and scale-free avalanches coexist. Furthermore, our model also accounts for up and down states as they occur (e.g., during deep sleep). This approach constitutes a framework to rationalize the possible collective phases and phase transitions of cortical networks in simple terms, thus helping to shed light on basic aspects of brain functioning from a very broad perspective.
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