scholarly journals Asynchronous and Coherent Dynamics in Balanced Excitatory-Inhibitory Spiking Networks

2021 ◽  
Vol 15 ◽  
Author(s):  
Hongjie Bi ◽  
Matteo di Volo ◽  
Alessandro Torcini
Keyword(s):  
Spatial Scales ◽  
Spatial Coherence ◽  
Mean Field ◽  
Period Doubling ◽  
Structural Heterogeneity ◽  
Neural Mass Model ◽  
Current Fluctuations ◽  
Mass Model ◽  
Frequency Locking ◽  
Neural Mass

Dynamic excitatory-inhibitory (E-I) balance is a paradigmatic mechanism invoked to explain the irregular low firing activity observed in the cortex. However, we will show that the E-I balance can be at the origin of other regimes observable in the brain. The analysis is performed by combining extensive simulations of sparse E-I networks composed of N spiking neurons with analytical investigations of low dimensional neural mass models. The bifurcation diagrams, derived for the neural mass model, allow us to classify the possible asynchronous and coherent behaviors emerging in balanced E-I networks with structural heterogeneity for any finite in-degree K. Analytic mean-field (MF) results show that both supra and sub-threshold balanced asynchronous regimes are observable in our system in the limit N >> K >> 1. Due to the heterogeneity, the asynchronous states are characterized at the microscopic level by the splitting of the neurons in to three groups: silent, fluctuation, and mean driven. These features are consistent with experimental observations reported for heterogeneous neural circuits. The coherent rhythms observed in our system can range from periodic and quasi-periodic collective oscillations (COs) to coherent chaos. These rhythms are characterized by regular or irregular temporal fluctuations joined to spatial coherence somehow similar to coherent fluctuations observed in the cortex over multiple spatial scales. The COs can emerge due to two different mechanisms. A first mechanism analogous to the pyramidal-interneuron gamma (PING), usually invoked for the emergence of γ-oscillations. The second mechanism is intimately related to the presence of current fluctuations, which sustain COs characterized by an essentially simultaneous bursting of the two populations. We observe period-doubling cascades involving the PING-like COs finally leading to the appearance of coherent chaos. Fluctuation driven COs are usually observable in our system as quasi-periodic collective motions characterized by two incommensurate frequencies. However, for sufficiently strong current fluctuations these collective rhythms can lock. This represents a novel mechanism of frequency locking in neural populations promoted by intrinsic fluctuations. COs are observable for any finite in-degree K, however, their existence in the limit N >> K >> 1 appears as uncertain.

scholarly journals Asynchronous and coherent dynamics in balanced excitatory-inhibitory populations

2021 ◽  
Author(s):  
Hongjie Bi ◽  
Matteo di Volo ◽  
Alessandro Torcini
Keyword(s):  
Spatial Scales ◽  
Spatial Coherence ◽  
Period Doubling ◽  
Gamma Oscillations ◽  
Structural Heterogeneity ◽  
Neural Mass Model ◽  
Current Fluctuations ◽  
Mass Model ◽  
Frequency Locking ◽  
Neural Mass

Dynamic excitatory-inhibitory (E-I) balance is a paradigmatic mechanism invoked to explain the irregular low firing activity observed in the cortex. However, we will show that the E-I balance can be at the origin of other regimes observable in the brain. The analysis is performed by combining extensive simulations of sparse E-I networks composed of N spiking neurons with analytical investigations of low dimensional neural mass models. The bifurcation diagrams, derived for the neural mass model, allow to classify the possible asynchronous and coherent behaviours emerging in balanced E-I networks with structural heterogeneity for any finite in-degree K. In the limit N >> K >> 1 both supra and sub-threshold balanced asynchronous regimes can be observed in our system. Due to the heterogeneity the asynchronous states are characterized by the splitting of the neurons in three groups: silent, fluctuation and mean driven. These features are consistent with experimental observations reported for heterogeneous neural circuits. The coherent rhythms observed in our system can range from periodic and quasi-periodic collective oscillations (COs) to coherent chaos. These rhythms are characterized by regular or irregular temporal fluctuations joined to spatial coherence somehow similar to coherent fluctuations observed in the cortex over multiple spatial scales. The COs can emerge due to two different mechanisms. A first mechanism similar to the pyramidal-interneuron gamma (PING) one, usually invoked for the emergence of gamma-oscillations. The second mechanism is intimately related to the presence of current fluctuations, which sustain COs characterized by an essentially simultaneous bursting of the two populations. We observe period-doubling cascades involving the PING-like COs finally leading to the appearance of coherent chaos. Fluctuation driven COs are usually observable in our system as quasi-periodic collective motions characterized by two incommensurate frequencies. However, for sufficiently strong current fluctuations we report a novel mechanism of frequency locking among collective rhythms promoted by these intrinsic fluctuations. Our analysis suggest that despite PING-like or fluctuation driven COS are observable for any finite in-degree K, in the limit N >> K >> 1 these solutions finally result in two coexisting balanced regimes: an asynchronous and a fully synchronized one.

scholarly journals Mean-Field Models for EEG/MEG: From Oscillations to Waves

2021 ◽  
Author(s):  
Áine Byrne ◽  
James Ross ◽  
Rachel Nicks ◽  
Stephen Coombes
Keyword(s):  
Gap Junction ◽  
Large Scale ◽  
Mean Field ◽  
Coarse Grained ◽  
Neural Mass Model ◽  
Neuron Network ◽  
Mass Model ◽  
Mean Field Model ◽  
Neural Mass ◽  
The Rich

AbstractNeural mass models have been used since the 1970s to model the coarse-grained activity of large populations of neurons. They have proven especially fruitful for understanding brain rhythms. However, although motivated by neurobiological considerations they are phenomenological in nature, and cannot hope to recreate some of the rich repertoire of responses seen in real neuronal tissue. Here we consider a simple spiking neuron network model that has recently been shown to admit an exact mean-field description for both synaptic and gap-junction interactions. The mean-field model takes a similar form to a standard neural mass model, with an additional dynamical equation to describe the evolution of within-population synchrony. As well as reviewing the origins of this next generation mass model we discuss its extension to describe an idealised spatially extended planar cortex. To emphasise the usefulness of this model for EEG/MEG modelling we show how it can be used to uncover the role of local gap-junction coupling in shaping large scale synaptic waves.

scholarly journals Mean-field models for EEG/MEG: from oscillations to waves

2020 ◽  
Author(s):  
Á. Byrne ◽  
James Ross ◽  
Rachel Nicks ◽  
Stephen Coombes
Keyword(s):  
Gap Junction ◽  
Large Scale ◽  
Mean Field ◽  
Coarse Grained ◽  
Neural Mass Model ◽  
Neuron Network ◽  
Mass Model ◽  
Mean Field Model ◽  
Neural Mass ◽  
The Rich

AbstractNeural mass models have been actively used since the 1970s to model the coarse-grained activity of large populations of neurons. They have proven especially fruitful for understanding brain rhythms. However, although motivated by neurobiological considerations they are phenomeno-logical in nature, and cannot hope to recreate some of the rich repertoire of responses seen in real neuronal tissue. Here we consider a simple spiking neuron network model that has recently been shown to admit to an exact mean-field description for both synaptic and gap-junction interactions. The mean-field model takes a similar form to a standard neural mass model, with an additional dynamical equation to describe the evolution of population synchrony. As well as reviewing the origins of this next generation mass model we discuss its extension to describe an idealised spatially extended planar cortex. To emphasise the usefulness of this model for EEG/MEG modelling we show how it can be used to uncover the role of local gap-junction coupling in shaping large scale synaptic waves.

scholarly journals A novel density-based neural mass model for simulating neuronal network dynamics with conductance-based synapses and membrane current adaptation

2020 ◽  
Author(s):  
Chih-Hsu Huang ◽  
Chou-Ching K. Lin
Keyword(s):  
Large Scale ◽  
Network Dynamics ◽  
Mean Field ◽  
Critical Issue ◽  
Spike Frequency ◽  
Neural Mass Model ◽  
Spike Frequency Adaptation ◽  
Mass Model ◽  
Frequency Adaptation ◽  
Neural Mass

AbstractNowadays, building low-dimensional mean-field models of neuronal populations is still a critical issue in the computational neuroscience community, because their derivation is difficult for realistic networks of neurons with conductance-based interactions and spike-frequency adaptation that generate nonlinear properties of neurons. Here, based on a colored-noise population density method, we derived a novel neural mass model, termed density-based neural mass model (dNMM), as the mean-field description of network dynamics of adaptive exponential integrate-and-fire neurons. Our results showed that the dNMM was capable of correctly estimating firing rate responses under both steady- and dynamic-input conditions. Finally, it was also able to quantitatively describe the effect of spike-frequency adaptation on the generation of asynchronous irregular activity of excitatory-inhibitory cortical networks. We conclude that in terms of its biological reality and calculation efficiency, the dNMM is a suitable candidate to build very large-scale network models involving multiple brain areas.

scholarly journals Comparing average network signals and neural mass signals in systems with low-synchrony

2017 ◽  
Author(s):  
P. Tewarie ◽  
A. Daffertshofer ◽  
B.W. van Dijk
Keyword(s):  
Good Description ◽  
Mean Field ◽  
Neuronal Loss ◽  
Neuronal Population ◽  
Neural Mass Model ◽  
Test Statistic ◽  
Mass Model ◽  
Power Spectral ◽  
Neural Mass ◽  
The Mean

1AbstractNeural mass models are accepted as efficient modelling techniques to model empirical observations such as disturbed oscillations or neuronal synchronization. Neural mass models are based on the mean-field assumption, i.e. they capture the mean-activity of a neuronal population. However, it is unclear if neural mass models still describe the mean activity of a neuronal population when the underlying neural network topology is not homogenous. Here, we test whether the mean activity of a neuronal population can be described by neural mass models when there is neuronal loss and when the connections in the network become sparse. To this end, we derive two neural mass models from a conductance based leaky integrate-and-firing (LIF) model. We then compared the power spectral densities of the mean activity of a network of inhibitory and excitatory LIF neurons with that of neural mass models by computing the Kolmogorov-Smirnov test statistic. Firstly, we found that when the number of neurons in a fully connected LIF-network is larger than 300, the neural mass model is a good description of the mean activity. Secondly, if the connection density in the LIF-network does not exceed a crtical value, this leads to desynchronization of neurons within the LIF-network and to failure of neural mass description. Therefore we conclude that neural mass models can be used for analysing empirical observations if the neuronal network of interest is large enough and when neurons in this system synchronize.

Principal dynamic mode analysis of neural mass model for the identification of epileptic states

2016 ◽  
Vol 26 (11) ◽  
pp. 113118 ◽  
Author(s):  
Yuzhen Cao ◽  
Liu Jin ◽  
Fei Su ◽  
Jiang Wang ◽  
Bin Deng
Keyword(s):  
Mode Analysis ◽  
Neural Mass Model ◽  
Dynamic Mode ◽  
Mass Model ◽  
Neural Mass

scholarly journals Neural Mass Model-Based Different EEG Signal Generation and Analysis in Simulink Sheikh Md. Rabiul Islam1, Md. Shakibul Islam2

2021 ◽  
pp. 1-7
Author(s):  
Sheikh Md. Rabiul Islam ◽  
◽  
Md. Shakibul Islam ◽  
Keyword(s):  
Signal Generation ◽  
Neural Mass Model ◽  
Pathophysiological Mechanism ◽  
Eeg Signal ◽  
Eeg Signals ◽  
Mass Model ◽  
Detailed Model ◽  
Simulation Based ◽  
Neural Mass ◽  
The Brain

The electroencephalogram (EEG) is an electrophysiological monitoring strategy that records the spontaneous electrical movement of the brain coming about from ionic current inside the neurons of the brain. The importance of the EEG signal is mainly the diagnosis of different mental and brain neurodegenerative diseases and different abnormalities like seizure disorder, encephalopathy, dementia, memory problem, sleep disorder, stroke, etc. The EEG signal is very useful for someone in case of a coma to determine the level of brain activity. So, it is very important to study EEG generation and analysis. To reduce the complexity of understanding the pathophysiological mechanism of EEG signal generation and their changes, different simulation-based EEG modeling has been developed which are based on anatomical equivalent data. In this paper, Instead of a detailed model a neural mass model has been used to implement different simulation-based EEG models for EEG signal generation which refers to the simplified and straightforward method. This paper aims to introduce obtained EEG signals of own implementation of the Lopes da Silva model, Jansen-Rit model, and Wendling model in Simulink and to compare characteristic features with real EEG signals and better understanding the EEG abnormalities especially the seizure-like signal pattern.

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