scholarly journals Modeling mesoscopic cortical dynamics using a mean-field model of conductance-based networks of adaptive exponential integrate-and-fire neurons

2017 ◽  
Author(s):  
Yann Zerlaut∗ ◽  
Sandrine Chemla ◽  
Frederic Chavane ◽  
Alain Destexhe∗
Keyword(s):  
Time Course ◽  
Field Model ◽  
Mean Field ◽  
Temporal Patterns ◽  
Analytical Description ◽  
External Input ◽  
Inhibitory Neurons ◽  
Mean Field Model ◽  
Integrate And Fire ◽  
Spatio Temporal

AbstractVoltage-sensitive dye imaging (VSDi) has revealed fundamental properties of neocortical processing at macroscopic scales. Since for each pixel VSDi signals report the average membrane potential over hundreds of neurons, it seems natural to use a mean-field formalism to model such signals. Here, we present a mean-field model of networks of Adaptive Exponential (AdEx) integrate-and-fire neurons, with conductance-based synaptic interactions. We study here a network of regular-spiking (RS) excitatory neurons and fast-spiking (FS) inhibitory neurons. We use a Master Equation formalism, together with a semi-analytic approach to the transfer function of AdEx neurons to describe the average dynamics of the coupled populations. We compare the predictions of this mean-field model to simulated networks of RS-FS cells, first at the level of the spontaneous activity of the network, which is well predicted by the analytical description. Second, we investigate the response of the network to time-varying external input, and show that the mean-field model predicts the response time course of the population. Finally, to model VSDi signals, we consider a one-dimensional ring model made of interconnected RS-FS mean-field units. We found that this model can reproduce the spatio-temporal patterns seen in VSDi of awake monkey visual cortex as a response to local and transient visual stimuli. Conversely, we show that the model allows one to infer physiological parameters from the experimentally-recorded spatio-temporal patterns.

Period Focusing Induced by Network Feedback in Populations of Noisy Integrate-and-Fire Neurons

2001 ◽  
Vol 13 (11) ◽  
pp. 2495-2516 ◽  
Author(s):  
Francisco B. Rodríguez ◽  
Alberto Suárez ◽  
Vicente López
Keyword(s):  
Population Dynamics ◽  
Detailed Analysis ◽  
Field Model ◽  
Dominant Role ◽  
Mean Field ◽  
Progressive Decrease ◽  
Mean Field Model ◽  
Integrate And Fire ◽  
The Individual ◽  
Firing Period

The population dynamics of an ensemble of nonleaky integrate-and-fire stochastic neurons is studied. The model selected allows for a detailed analysis of situations where noise plays a dominant role. Simulations in a regime with weak to moderate interactions show that a mechanism of excitatory message interchange among the neurons leads to a decrease in the firing period dispersion of the individual units. The dispersion reduction observed is larger than what would be expected from the decrease in the period. This ‘period focusing’ is explained using a mean-field model. It is a dynamical effect that arises from the progressive decrease of the effective firing threshold as a result of the messages received by each unit from the rest of the population. A back-of-the-envelope formula to calculate this nontrivial dispersion reduction and a simple geometrical description of the effect are also provided.

scholarly journals Biologically realistic mean-field models of conductancebased networks of spiking neurons with adaptation

2018 ◽  
Author(s):  
Matteo di Volo ◽  
Alberto Romagnoni ◽  
Cristiano Capone ◽  
Alain Destexhe
Keyword(s):  
Large Scale ◽  
Field Model ◽  
Mean Field ◽  
Inhibitory Neurons ◽  
Activity Levels ◽  
Mean Field Model ◽  
Nonlinear Properties ◽  
Mean Field Models ◽  
The Mean

AbstractAccurate population models are needed to build very large scale neural models, but their derivation is difficult for realistic networks of neurons, in particular when nonlinear properties are involved such as conductance-based interactions and spike-frequency adaptation. Here, we consider such models based on networks of Adaptive exponential Integrate and fire excitatory and inhibitory neurons. Using a Master Equation formalism, we derive a mean-field model of such networks and compare it to the full network dynamics. The mean-field model is capable to correctly predict the average spontaneous activity levels in asynchronous irregular regimes similar to in vivo activity. It also captures the transient temporal response of the network to complex external inputs. Finally, the mean-field model is also able to quantitatively describe regimes where high and low activity states alternate (UP-DOWN state dynamics), leading to slow oscillations. We conclude that such mean-field models are “biologically realistic” in the sense that they can capture both spontaneous and evoked activity, and they naturally appear as candidates to build very large scale models involving multiple brain areas.

scholarly journals A mean-field approach to the dynamics of networks of complex neurons, from nonlinear Integrate-and-Fire to Hodgkin-Huxley models

2019 ◽  
Author(s):  
M. Carlu ◽  
O. Chehab ◽  
L. Dalla Porta ◽  
D. Depannemaecker ◽  
C. Héricé ◽  
...  
Keyword(s):  
Temporal Dynamics ◽  
Mean Field ◽  
Population Models ◽  
Inhibitory Neurons ◽  
Mathematical Tool ◽  
Mean Field Model ◽  
Integrate And Fire ◽  
Mean Field Models ◽  
Electrophysiological Recordings ◽  
Field Formalism

AbstractWe present a mean-field formalism able to predict the collective dynamics of large networks of conductance-based interacting spiking neurons. We apply this formalism to several neuronal models, from the simplest Adaptive Exponential Integrate-and-Fire model to the more complex Hodgkin-Huxley and Morris-Lecar models. We show that the resulting mean-field models are capable of predicting the correct spontaneous activity of both excitatory and inhibitory neurons in asynchronous irregular regimes, typical of cortical dynamics. Moreover, it is possible to quantitatively predict the populations response to external stimuli in the form of external spike trains. This mean-field formalism therefore provides a paradigm to bridge the scale between population dynamics and the microscopic complexity of the individual cells physiology.NEW & NOTEWORTHYPopulation models are a powerful mathematical tool to study the dynamics of neuronal networks and to simulate the brain at macroscopic scales. We present a mean-field model capable of quantitatively predicting the temporal dynamics of a network of complex spiking neuronal models, from Integrate-and-Fire to Hodgkin-Huxley, thus linking population models to neurons electrophysiology. This opens a perspective on generating biologically realistic mean-field models from electrophysiological recordings.

scholarly journals Dynamics of a Large-Scale Spiking Neural Network with Quadratic Integrate-and-Fire Neurons

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Weijie Ye
Keyword(s):  
Neural Network ◽  
Large Scale ◽  
Field Model ◽  
Network Dynamics ◽  
Mean Field ◽  
Spiking Neural Network ◽  
Stable Limit ◽  
Mean Field Model ◽  
Integrate And Fire ◽  
The Mean

Since the high dimension and complexity of the large-scale spiking neural network, it is difficult to research the network dynamics. In recent decades, the mean-field approximation has been a useful method to reduce the dimension of the network. In this study, we construct a large-scale spiking neural network with quadratic integrate-and-fire neurons and reduce it to a mean-field model to research the network dynamics. We find that the activity of the mean-field model is consistent with the network activity. Based on this agreement, a two-parameter bifurcation analysis is performed on the mean-field model to understand the network dynamics. The bifurcation scenario indicates that the network model has the quiescence state, the steady state with a relatively high firing rate, and the synchronization state which correspond to the stable node, stable focus, and stable limit cycle of the system, respectively. There exist several stable limit cycles with different periods, so we can observe the synchronization states with different periods. Additionally, the model shows bistability in some regions of the bifurcation diagram which suggests that two different activities coexist in the network. The mechanisms that how these states switch are also indicated by the bifurcation curves.

scholarly journals Optimal responsiveness and information flow in networks of heterogeneous neurons

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Matteo Di Volo ◽  
Alain Destexhe
Keyword(s):  
Information Flow ◽  
Heterogeneous Networks ◽  
Large Scale ◽  
Computational Models ◽  
Field Model ◽  
Mean Field ◽  
Network Models ◽  
Inhibitory Neurons ◽  
Mean Field Model ◽  
Optimal Responsiveness

AbstractCerebral cortex is characterized by a strong neuron-to-neuron heterogeneity, but it is unclear what consequences this may have for cortical computations, while most computational models consider networks of identical units. Here, we study network models of spiking neurons endowed with heterogeneity, that we treat independently for excitatory and inhibitory neurons. We find that heterogeneous networks are generally more responsive, with an optimal responsiveness occurring for levels of heterogeneity found experimentally in different published datasets, for both excitatory and inhibitory neurons. To investigate the underlying mechanisms, we introduce a mean-field model of heterogeneous networks. This mean-field model captures optimal responsiveness and suggests that it is related to the stability of the spontaneous asynchronous state. The mean-field model also predicts that new dynamical states can emerge from heterogeneity, a prediction which is confirmed by network simulations. Finally we show that heterogeneous networks maximise the information flow in large-scale networks, through recurrent connections. We conclude that neuronal heterogeneity confers different responsiveness to neural networks, which should be taken into account to investigate their information processing capabilities.

scholarly journals Resting State Networks in empirical and simulated dynamic functional connectivity

2016 ◽  
Author(s):  
Katharina Glomb ◽  
Adrián Ponce-Alvarez ◽  
Matthieu Gilson ◽  
Petra Ritter ◽  
Gustavo Deco
Keyword(s):  
Resting State ◽  
Field Model ◽  
Temporal Dynamics ◽  
Mean Field ◽  
Tensor Decomposition ◽  
Resting State Networks ◽  
Mean Field Model ◽  
Spatio Temporal ◽  
Time Courses ◽  
Over Time

AbstractIt is well-established that patterns of functional connectivity (FC) - measures of correlated activity between pairs of voxels or regions observed in the human brain using neuroimaging - are robustly expressed in spontaneous activity during rest. These patterns are not static, but exhibit complex spatio-temporal dynamics. Over the last years, a multitude of methods have been proposed to reveal these dynamics on the level of the whole brain. One finding is that the brain transitions through different FC configurations over time, and substantial effort has been put into characterizing these configurations. However, the dynamics governing these transitions are more elusive, specifically, the contribution of stationary vs. non-stationary dynamics is an active field of inquiry. In this study, we use a whole-brain approach, considering FC dynamics between 66 ROIs covering the entire cortex. We combine an innovative dimensionality reduction technique, tensor decomposition, with a mean field model which possesses stationary dynamics. It has been shown to explain resting state FC averaged over time and multiple subjects, however, this average FC summarizes the spatial distribution of correlations while hiding their temporal dynamics. First, we apply tensor decomposition to resting state scans from 24 healthy controls in order to characterize spatio-temporal dynamics present in the data. We simultaneously utilize temporal and spatial information by creating tensors that are subsequently decomposed into sets of brain regions (“communities”) that share similar temporal dynamics, and their associated time courses. The tensors contain pairwise FC computed inside of overlapping sliding windows. Communities are discovered by clustering features pooled from all subjects, thereby ensuring that they generalize. We find that, on the group level, the data give rise to four distinct communities that resemble known resting state networks (RSNs): default mode network, visual network, control networks, and somatomotor network. Second, we simulate data with our stationary mean field model whose nodes are connected according to results from DTI and fiber tracking. In this model, all spatio-temporal structure is due to noisy fluctuations around the average FC. We analyze the simulated data in the same way as the empirical data in order to determine whether stationary dynamics can explain the emergence of distinct FC patterns (RSNs) which have their own time courses. We find that this is the case for all four networks using the spatio-temporal information revealed by tensor decomposition if nodes in the simulation are connected according to model-based effective connectivity. Furthermore, we find that these results require only a small part of the FC values, namely the highest values that occur across time and ROI pair. Our findings show that stationary dynamics can account for the emergence of RSNs. We provide an innovative method that does not make strong assumptions about the underlying data and is generally applicable to resting state or task data from different subject populations.

scholarly journals Biologically Realistic Mean-Field Models of Conductance-Based Networks of Spiking Neurons with Adaptation

2019 ◽  
Vol 31 (4) ◽  
pp. 653-680 ◽  
Author(s):  
Matteo di Volo ◽  
Alberto Romagnoni ◽  
Cristiano Capone ◽  
Alain Destexhe
Keyword(s):  
Large Scale ◽  
Field Model ◽  
Mean Field ◽  
Inhibitory Neurons ◽  
Activity Levels ◽  
Mean Field Model ◽  
Nonlinear Properties ◽  
Mean Field Models ◽  
The Mean

Accurate population models are needed to build very large-scale neural models, but their derivation is difficult for realistic networks of neurons, in particular when nonlinear properties are involved, such as conductance-based interactions and spike-frequency adaptation. Here, we consider such models based on networks of adaptive exponential integrate-and-fire excitatory and inhibitory neurons. Using a master equation formalism, we derive a mean-field model of such networks and compare it to the full network dynamics. The mean-field model is capable of correctly predicting the average spontaneous activity levels in asynchronous irregular regimes similar to in vivo activity. It also captures the transient temporal response of the network to complex external inputs. Finally, the mean-field model is also able to quantitatively describe regimes where high- and low-activity states alternate (up-down state dynamics), leading to slow oscillations. We conclude that such mean-field models are biologically realistic in the sense that they can capture both spontaneous and evoked activity, and they naturally appear as candidates to build very large-scale models involving multiple brain areas.

scholarly journals Nonlinear collision between anisotropic propagating waves in mouse somatosensory cortex

2021 ◽  
Author(s):  
M. Di Volo ◽  
I. Férézou
Keyword(s):  
Somatosensory Cortex ◽  
Mean Field ◽  
Sensory Information ◽  
Temporal Patterns ◽  
Inversion Method ◽  
Model Parameters ◽  
Lower Sensitivity ◽  
Mean Field Model ◽  
Linear Interaction ◽  
Spatio Temporal

AbstractHow does cellular organization shape the spatio-temporal patterns of activity in the cortex while processing sensory information? After measuring the propagation of activity in the mouse primary somatosensory cortex (S1) in response to single whisker deflections with Voltage Sensitive Dye (VSD) imaging, we developed a two dimensional mean field model of S1. We observed that, for strong enough excitatory cortical interactions, whisker deflections generate a propagating wave in S1. We developed an inversion method that reconstructs model parameters from VSD data, revealing that a spatially heterogeneous organization of synaptic strengths between pyramidal neurons in S1 is likely to be responsible for the anisotropic spatio-temporal patterns of activity measured experimentally. Finally, we report that two consecutive stimuli activating different spatial locations in S1 generate two waves which collide sub-linearly. In the model, such sub-linear interaction is explained by a lower sensitivity to external perturbations of neural networks during activated states.

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