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

Carlu, Mallory; Chehab, Omar; Porta, Leonardo Dalla; Depannemaecker, Damien; Héricé, Charlotte; Jedynak, Maciej; Ersöz, Elif Köksal; Muratore, Paolo; Souihel, Selma; Capone, Cristiano; Zerlaut, Yann; Destexhe, Alain; Volo, Matteo di

doi:10.1152/jn.00399.2019

Cited by 41 publications

(52 citation statements)

References 53 publications

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“…Mean-Field models describe the activity of a large group of neurons using average values of their activity, such as the mean membrane potential or, more often, the firing rate of the population. Some studies have derived these descriptors of the activity from single neuron models [41,42]. Another method is to consider that a neuron can represent the mean activity of a population of neurons.…”

Section: From Mean-field To Large Scale Modelsmentioning

confidence: 99%

Modeling seizures: From single neurons to networks

Depannemaecker

Destexhe

Jirsa

et al. 2021

Seizure

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Dynamical systems tools offer a complementary approach to detailed biophysical seizure modeling, with high potential for clinical applications. This review describes the theoretical framework, allowing theorizing certain properties of seizures and their classifications according to their dynamics properties at onset and offset. We describe various modeling approaches spanning different scales, from single neurons to large-scale networks. We try to offer a large accessible overview through nonexhaustive examples of recent important works.

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Section: From Mean-field To Large Scale Modelsmentioning

confidence: 99%

Modeling seizures: From single neurons to networks

Depannemaecker

Destexhe

Jirsa

et al. 2021

Seizure

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show abstract

“…So called population density techniques (PDTs) have been used for many years (Knight, 1972 ; Knight et al, 1996 ; Omurtag et al, 2000 ) to describe a population of neurons in terms of a probability density function. The transfer function of a neuron model or even an experimental neural recording can be used to approximate the response from a population using this technique (Wilson and Cowan, 1972 ; El Boustani and Destexhe, 2009 ; Carlu et al, 2020 ). However, analytical solutions are often limited to regular spiking behaviour with constant or slowly changing input.…”

Section: Introductionmentioning

confidence: 99%

MIIND : A Model-Agnostic Simulator of Neural Populations

Osborne

Lai

Lepperød

et al. 2021

Front. Neuroinform.

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MIIND is a software platform for easily and efficiently simulating the behaviour of interacting populations of point neurons governed by any 1D or 2D dynamical system. The simulator is entirely agnostic to the underlying neuron model of each population and provides an intuitive method for controlling the amount of noise which can significantly affect the overall behaviour. A network of populations can be set up quickly and easily using MIIND's XML-style simulation file format describing simulation parameters such as how populations interact, transmission delays, post-synaptic potentials, and what output to record. During simulation, a visual display of each population's state is provided for immediate feedback of the behaviour and population activity can be output to a file or passed to a Python script for further processing. The Python support also means that MIIND can be integrated into other software such as The Virtual Brain. MIIND's population density technique is a geometric and visual method for describing the activity of each neuron population which encourages a deep consideration of the dynamics of the neuron model and provides insight into how the behaviour of each population is affected by the behaviour of its neighbours in the network. For 1D neuron models, MIIND performs far better than direct simulation solutions for large populations. For 2D models, performance comparison is more nuanced but the population density approach still confers certain advantages over direct simulation. MIIND can be used to build neural systems that bridge the scales between an individual neuron model and a population network. This allows researchers to maintain a plausible path back from mesoscopic to microscopic scales while minimising the complexity of managing large numbers of interconnected neurons. In this paper, we introduce the MIIND system, its usage, and provide implementation details where appropriate.

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“…Yet, we have to admit that -when it comes to biological plausibility-this choice might be considered unrealistic: the homogeneity between neurons of the same type can be challenged (Reyes et al, 1998;Jinno et al, 2007;Ávila-Åkerberg et al, 2010) and the uniform distribution of connectivity might be replaced by, e.g., smallworld topologies (Bettencourt et al, 2007;van den Heuvel et al, 2016;Bassett and Bullmore, 2017). Here we would like to add that using the current modeling approach the cell-tocell heterogeneity including their role in neural coding has been explored elsewhere (Boustani and Destexhe, 2009;Longtin, 2012, 2014;Carlu et al, 2020) while the modeling of small-world, modular and more realistic topologies remains future work.…”

Section: Discussionmentioning

confidence: 99%

On the Validity of Neural Mass Models

Deschle

Gossn

Tewarie

et al. 2021

Front. Comput. Neurosci.

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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.

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

Cited by 41 publications

References 53 publications

Modeling seizures: From single neurons to networks

Modeling seizures: From single neurons to networks

MIIND : A Model-Agnostic Simulator of Neural Populations

On the Validity of Neural Mass Models

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