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

Abstract

Neural 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.

The effects of degree distributions in random networks of Type-I neurons

“…The quadratic integrate-andfire (QIF) neuron [39] with infinite firing threshold and reset to V = −∞ is equivalent under the transformation V = tan (θ/2) to a theta neuron [40], and since gap junction coupling is through voltage differences it is easier to start with a network of QIF neurons. Our analysis is similar to that in [31]; also see [41][42][43]. A theta neuron is an excitable system, so our results add to those on coupled excitable systems [44][45][46][47].…”

Collective states in a ring network of theta neurons

“…Byrne et al [16] considered a network of QIF neurons on a periodic domain, with synaptic dynamics and an inverted Mexican hat connectivity. They also included gap junctional coupling.…”

“…They also numerically followed a bump solution and found a scenario of the form shown in figure 7e. Byrne et al [16] considered a network of QIF neurons on a periodic domain, with synaptic dynamics and an inverted Mexican hat connectivity. They also included gap junctional coupling.…”

“…Our approach could easily be generalized to other forms of coupling such as synaptic coupling using reversal potentials [17] or gap junctional coupling [16,35], and different coupling kernels, as long as the form of the equations allows the use of the Ott/Antonsen ansatz.…”

“…A variety of model neurons have been considered when studying ring networks including leaky integrateand-fire [9,10], quadratic integrate-and-fire (QIF) [14][15][16][17], more realistic conductance-based models [5,18,19] and theta neurons [20,21]. Note that under a simple transformation, the quadratic integrate-and-fire neuron with infinite threshold and reset is exactly equivalent to a theta neuron.…”