A neural mass model for MEG/EEG:

Abstract

Although MEG/EEG signals are highly variable, systematic changes in distinct frequency bands are commonly encountered. These frequency-specific changes represent robust neural correlates of cognitive or perceptual processes (for example, alpha rhythms emerge on closing the eyes). However, their functional significance remains a matter of debate. Some of the mechanisms that generate these signals are known at the cellular level and rest on a balance of excitatory and inhibitory interactions within and between populations of neurons. The kinetics of the ensuing population dynamics determine the frequency of oscillations. In this work we extended the classical nonlinear lumped-parameter model of alpha rhythms, initially developed by Lopes da Silva and colleagues [Kybernetik 15 (1974) 27], to generate more complex dynamics. We show that the whole spectrum of MEG/EEG signals can be reproduced within the oscillatory regime of this model by simply changing the population kinetics. We used the model to examine the influence of coupling strength and propagation delay on the rhythms generated by coupled cortical areas. The main findings were that (1) coupling induces phase-locked activity, with a phase shift of 0 or π when the coupling is bidirectional, and (2) both coupling and propagation delay are critical determinants of the MEG/EEG spectrum. In forthcoming articles, we will use this model to (1) estimate how neuronal interactions are expressed in MEG/EEG oscillations and establish the construct validity of various indices of nonlinear coupling, and (2) generate event-related transients to derive physiologically informed basis functions for statistical modelling of average evoked responses.

Introduction

It is generally assumed that the signals measured in magnetoencephalography (MEG) and electroencephalography (EEG) can be decomposed into distinct frequency bands (delta: 1–4 Hz, theta: 4–8 Hz, alpha: 8–12 Hz, beta: 12–30 Hz, gamma: 30–70 Hz) (Nunez, 1981). These rhythms sometimes exhibit robust correlates of behavioural states but often with no obvious functional role. It is clear that MEG/EEG signals result mainly from extracellular current flow, associated with massively summed postsynaptic potentials in synchronously activated and vertically oriented neurons (dendritic activity of macro-columns of pyramidal cells in the cortical sheet). The exact neurophysiological mechanisms, which constrain this synchronisation to a given frequency band, remain obscure. However, the generation of oscillations appears to depend on interactions between inhibitory and excitatory populations, whose kinetics determine their oscillation frequency. This dependency suggests a modelling strategy could help to disclose the causes of different MEG/EEG rhythms and to characterise the neuronal processes underlying MEG/EEG activity.

There are several ways to model neural signals (Whittington et al., 2000a): either using a detailed model, in which it is difficult to determine the influence of each model parameter, or a simplified one, in which realism is sacrificed for a more parsimonious description of key mechanisms. The complexity of neural networks generating MEG/EEG signals is such that the second approach is usually more viable. This involves modelling neuronal activity with simplifying assumptions and empirical priors to emulate realistic signals. Neural mass models Freeman, 1978, Lopes da Silva et al., 1974, Robinson et al., 2001, Stam et al., 1999, Valdes et al., 1999, Wendling et al., 2000 are based upon this approach. These models comprise macro-columns, or even cortical areas, using only one or two state variables to represent the mean activity of the whole population. This procedure, sometimes referred to as a “mean-field approximation,” is very efficient for determining the steady-state behaviour of neuronal systems, but its utility in a dynamic or nonstationary context is less established (Haskell et al., 2001). The majority of neural mass models of EEG responses have been designed to model alpha rhythms Jansen and Rit, 1995, Lopes da Silva et al., 1974, Stam et al., 1999. Recent studies have emphasised that the kinetics of inhibitory populations have a key influence on the signals generated (Wendling et al., 2002). Specifically, it has been suggested that fast inhibition kinetics are needed to produce gamma-like activity (Jefferys et al., 1996). In fact, MEG/EEG signals depend upon the kinetics of both inhibitory and excitatory neural populations, and exhibit very complex dynamics because of the huge diversity and connectivity of cortical areas.

In this study we describe a simple neural mass model that can produce various rhythms ranging from delta to gamma, depending on the kinetics of the populations modelled. We start from the model of Jansen and Rit, (1995) using standard parameters to produce alpha activity in a single area. We then show that variation of excitatory and inhibitory kinetics, within a physiologically plausible range, can generate oscillatory activity in the delta, theta, alpha, beta, and gamma bands using the same model. Next, we assume that a cortical area comprises several resonant neuronal populations, characterised by different kinetics. We describe the particular case of two populations that underlie intrinsic alpha and gamma rhythms. In this dual-kinetic model, a single parameter controls the relative contribution of fast and slow populations, leading to a modulation of the rhythms produced. Finally, we address the coupling of two areas, with a particular focus on the dependence of cortical rhythms upon the strength of the coupling and upon the distance between cortical areas (modelled as a propagation delay). Using several sets of parameters, we show that this model can generate a wide variety of oscillations in the alpha, beta, and gamma bands that are characteristic of MEG/EEG signals.

The goal of this study is to introduce and characterise the behaviour of the model. This is the first component of a broader program that aims to (1) quantify the sensitivity of linear and nonlinear methods for the detection of long-range cortical interactions using MEG/EEG signals, and (2) model event-related dynamics and derive basis functions for statistical models of averaged evoked potentials/fields.