scholarly journals On the Validity of Neural Mass Models

2021 ◽  
Vol 14 ◽  
Author(s):  
Nicolás Deschle ◽  
Juan Ignacio Gossn ◽  
Prejaas Tewarie ◽  
Björn Schelter ◽  
Andreas Daffertshofer
Keyword(s):  
Mean Field ◽  
Low Frequency ◽  
Inhibitory Neuron ◽  
Inhibitory Neurons ◽  
Neural Population ◽  
Mass Model ◽  
Time Scale Separation ◽  
Neural Mass ◽  
The Mean ◽  
Parameter Ranges

Modeling the dynamics of neural masses is a common approach in the study of neural populations. Various models have been proven useful to describe a plenitude of empirical observations including self-sustained local oscillations and patterns of distant synchronization. We discuss the extent to which mass models really resemble the mean dynamics of a neural population. In particular, we question the validity of neural mass models if the population under study comprises a mixture of excitatory and inhibitory neurons that are densely (inter-)connected. Starting from a network of noisy leaky integrate-and-fire neurons, we formulated two different population dynamics that both fall into the category of seminal Freeman neural mass models. The derivations contained several mean-field assumptions and time scale separation(s) between membrane and synapse dynamics. Our comparison of these neural mass models with the averaged dynamics of the population reveals bounds in the fraction of excitatory/inhibitory neuron as well as overall network degree for a mass model to provide adequate estimates. For substantial parameter ranges, our models fail to mimic the neural network's dynamics proper, be that in de-synchronized or in (high-frequency) synchronized states. Only around the onset of low-frequency synchronization our models provide proper estimates of the mean potential dynamics. While this shows their potential for, e.g., studying resting state dynamics obtained by encephalography with focus on the transition region, we must accept that predicting the more general dynamic outcome of a neural network via its mass dynamics requires great care.

scholarly journals Realistic alpha oscillations and transient responses in a cortical microcircuit model

2021 ◽  
Author(s):  
Andres A Kiani ◽  
Geoffrey M Ghose ◽  
Theoden I Netoff
Keyword(s):  
Electrical Stimulation ◽  
Cortical Neurons ◽  
Low Frequency ◽  
Population Data ◽  
Neural Mass Model ◽  
Neural Population ◽  
Brain State ◽  
Response Dynamics ◽  
Mass Model ◽  
Neural Mass

Neural-mass modeling of neural population data (EEG, ECoG, or LFPs) has shown promise both in elucidating the neural processes underlying cortical rhythms and changes in brain state, as well as offering a framework for testing the interplay between these rhythms and information processing. Models of cortical alpha rhythms (8 - 12 Hz) and their impact in visual sensory processing have been at the forefront of this effort, with the Jansen-Rit being one of the more popular models in this domain. The Jansen-Rit model, however, fails in reproducing key physiological observations including the level of inputs that cortical neurons receive and their responses to visual transients. To address these issues we generated a neural mass model that complies better with synaptic mediated dynamics, intrinsic alpha behavior, and produces realistic responses. The model is robust to many changes in parameter values but critically depends on the ratio of excitation to inhibition, producing response transients whose features are dependent on this ratio and alpha phase and power. The model is sufficiently flexible so as to be able to easily replicate the range of low frequency oscillations observed in different studies. Consistent with experimental observations, we find phase-dependent response dynamics to both visual and electrical stimulation using this model. The model suggests that stimulation facilitates alpha at particular phases and suppresses it in others due to a phase dependent lag in inhibitory responses. Hence, the model generates insight into the physiological parameters responsible for intrinsic oscillations and testable hypotheses regarding the interactions between visual and electrical stimulation on those oscillations.

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.

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 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.

A generalized mean-field model of the natural and high-frequency actuated flow around a high-lift configuration

2009 ◽  
Vol 623 ◽  
pp. 283-316 ◽  
Author(s):  
DIRK M. LUCHTENBURG ◽  
BERT GÜNTHER ◽  
BERND R. NOACK ◽  
RUDIBERT KING ◽  
GILEAD TADMOR
Keyword(s):  
High Frequency ◽  
Field Model ◽  
Mean Field ◽  
Low Frequency ◽  
Navier Stokes ◽  
Mean Field Model ◽  
High Lift ◽  
The Mean ◽  
Generalized Mean ◽  
Low Dimensional

A low-dimensional Galerkin model is proposed for the flow around a high-lift configuration, describing natural vortex shedding, the high-frequency actuated flow with increased lift and transients between both states. The form of the dynamical system has been derived from a generalized mean-field consideration. Steady state and transient URANS (unsteady Reynolds-averaged Navier–Stokes) simulation data are employed to derive the expansion modes and to calibrate the system parameters. The model identifies the mean field as the mediator between the high-frequency actuation and the low-frequency natural shedding instability.

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 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 Patient-Specific Network Connectivity Combined With a Next Generation Neural Mass Model to Test Clinical Hypothesis of Seizure Propagation

2021 ◽  
Vol 15 ◽  
Author(s):  
Moritz Gerster ◽  
Halgurd Taher ◽  
Antonín Škoch ◽  
Jaroslav Hlinka ◽  
Maxime Guye ◽  
...  
Keyword(s):  
Local Network ◽  
Neural Mass Model ◽  
Neural Population ◽  
Patient Specific ◽  
Epileptogenic Zone ◽  
Mass Model ◽  
Mean Field Equations ◽  
Neural Mass ◽  
Epileptic Patients ◽  
Emergent Dynamics

Dynamics underlying epileptic seizures span multiple scales in space and time, therefore, understanding seizure mechanisms requires identifying the relations between seizure components within and across these scales, together with the analysis of their dynamical repertoire. In this view, mathematical models have been developed, ranging from single neuron to neural population. In this study, we consider a neural mass model able to exactly reproduce the dynamics of heterogeneous spiking neural networks. We combine mathematical modeling with structural information from non invasive brain imaging, thus building large-scale brain network models to explore emergent dynamics and test the clinical hypothesis. We provide a comprehensive study on the effect of external drives on neuronal networks exhibiting multistability, in order to investigate the role played by the neuroanatomical connectivity matrices in shaping the emergent dynamics. In particular, we systematically investigate the conditions under which the network displays a transition from a low activity regime to a high activity state, which we identify with a seizure-like event. This approach allows us to study the biophysical parameters and variables leading to multiple recruitment events at the network level. We further exploit topological network measures in order to explain the differences and the analogies among the subjects and their brain regions, in showing recruitment events at different parameter values. We demonstrate, along with the example of diffusion-weighted magnetic resonance imaging (dMRI) connectomes of 20 healthy subjects and 15 epileptic patients, that individual variations in structural connectivity, when linked with mathematical dynamic models, have the capacity to explain changes in spatiotemporal organization of brain dynamics, as observed in network-based brain disorders. In particular, for epileptic patients, by means of the integration of the clinical hypotheses on the epileptogenic zone (EZ), i.e., the local network where highly synchronous seizures originate, we have identified the sequence of recruitment events and discussed their links with the topological properties of the specific connectomes. The predictions made on the basis of the implemented set of exact mean-field equations turn out to be in line with the clinical pre-surgical evaluation on recruited secondary networks.

scholarly journals Exact neural mass model for synaptic-based working memory

2020 ◽  
Vol 16 (12) ◽  
pp. e1008533
Author(s):  
Halgurd Taher ◽  
Alessandro Torcini ◽  
Simona Olmi
Keyword(s):  
Working Memory ◽  
Membrane Potential ◽  
Memory Load ◽  
Field Potential ◽  
Memory Capacity ◽  
Neural Mass Model ◽  
Cellular Mechanisms ◽  
Mass Model ◽  
Neural Mass ◽  
The Mean

A synaptic theory of Working Memory (WM) has been developed in the last decade as a possible alternative to the persistent spiking paradigm. In this context, we have developed a neural mass model able to reproduce exactly the dynamics of heterogeneous spiking neural networks encompassing realistic cellular mechanisms for short-term synaptic plasticity. This population model reproduces the macroscopic dynamics of the network in terms of the firing rate and the mean membrane potential. The latter quantity allows us to gain insight of the Local Field Potential and electroencephalographic signals measured during WM tasks to characterize the brain activity. More specifically synaptic facilitation and depression integrate each other to efficiently mimic WM operations via either synaptic reactivation or persistent activity. Memory access and loading are related to stimulus-locked transient oscillations followed by a steady-state activity in the β-γ band, thus resembling what is observed in the cortex during vibrotactile stimuli in humans and object recognition in monkeys. Memory juggling and competition emerge already by loading only two items. However more items can be stored in WM by considering neural architectures composed of multiple excitatory populations and a common inhibitory pool. Memory capacity depends strongly on the presentation rate of the items and it maximizes for an optimal frequency range. In particular we provide an analytic expression for the maximal memory capacity. Furthermore, the mean membrane potential turns out to be a suitable proxy to measure the memory load, analogously to event driven potentials in experiments on humans. Finally we show that the γ power increases with the number of loaded items, as reported in many experiments, while θ and β power reveal non monotonic behaviours. In particular, β and γ rhythms are crucially sustained by the inhibitory activity, while the θ rhythm is controlled by excitatory synapses.

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.

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