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

Áine Byrne,James Ross,Stephen Coombes,Rachel Nicks

doi:10.1007/s10548-021-00842-4

Áine Byrne, James Ross + Show 2 more

Open Access

https://doi.org/10.1007/s10548-021-00842-4

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Abstract

Neural 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.

Highlights

The use of mathematics has many historical successes, especially in the fields of physics and engineering, where mathematical concepts have been put to good use to address challenges far beyond the context in which they were originally developed
Many of the current models used to describe coarse-grained neural activity, such as the Wilson-Cowan (Wilson and Cowan 1972), Jansen-Rit (Jansen and Rit 1995), or Liley (Liley et al 2002) model are phenomenological in nature. They have been used extensively to study and explore the potential mechanisms that coordinate brain rhythms underlying cognitive processing and large scale neuronal communication (Fries 2005). Such neural mass models have recently been used to understand cross-frequency coupling between brain areas (Jedynak et al 2015), understand how patterns of functional connectivity may arise in brain imaging studies (Forrester et al 2020), and are a key ingredient of the Virtual Brain project that aims to deliver the first open simulation of the human brain based on individual large-scale connectivity (Sanz-Leon et al 2015)
Mean-field models have proven invaluable in understanding neural dynamics

Summary

Introduction

Keywords Neural mass · Neural field · Brain rhythms · Synchrony · Waves · Synaptic coupling · Gap-junction coupling In the “Neural Mass Model” section we introduce the mathematical description for the microscopic spiking cell dynamics as a network of QIF neurons with both synaptic and gap-junction coupling. We present the corresponding mean-field ordinary differential equation model with a focus on the bifurcation properties of the model under variation of key parameters, including the level of population excitability and the strength of gap-junction coupling.

Results

Conclusion