Modelling event-related responses in the brain

Abstract

The aim of this work was to investigate the mechanisms that shape evoked electroencephalographic (EEG) and magneto-encephalographic (MEG) responses. We used a neuronally plausible model to characterise the dependency of response components on the models parameters. This generative model was a neural mass model of hierarchically arranged areas using three kinds of inter-area connections (forward, backward and lateral). We investigated how responses, at each level of a cortical hierarchy, depended on the strength of connections or coupling. Our strategy was to systematically add connections and examine the responses of each successive architecture. We did this in the context of deterministic responses and then with stochastic spontaneous activity. Our aim was to show, in a simple way, how event-related dynamics depend on extrinsic connectivity. To emphasise the importance of nonlinear interactions, we tried to disambiguate the components of event-related potentials (ERPs) or event-related fields (ERFs) that can be explained by a linear superposition of trial-specific responses and those engendered nonlinearly (e.g., by phase-resetting). Our key conclusions were; (i) when forward connections, mediating bottom-up or extrinsic inputs, are sufficiently strong, nonlinear mechanisms cause a saturation of excitatory interneuron responses. This endows the system with an inherent stability that precludes nondissipative population dynamics. (ii) The duration of evoked transients increases with the hierarchical depth or level of processing. (iii) When backward connections are added, evoked transients become more protracted, exhibiting damped oscillations. These are formally identical to late or endogenous components seen empirically. This suggests that late components are mediated by reentrant dynamics within cortical hierarchies. (iv) Bilateral connections produce similar effects to backward connections but can also mediate zero-lag phase-locking among areas. (v) Finally, with spontaneous activity, ERPs/ERFs can arise from two distinct mechanisms: For low levels of (stimulus related and ongoing) activity, the systems response conforms to a quasi-linear superposition of separable responses to the fixed and stochastic inputs. This is consistent with classical assumptions that motivate trial averaging to suppress spontaneous activity and disclose the ERP/ERF. However, when activity is sufficiently high, there are nonlinear interactions between the fixed and stochastic inputs. This interaction is expressed as a phase-resetting and represents a qualitatively different explanation for the ERP/ERF.

Introduction

Classical event-related potentials (ERPs) and event-related fields (ERFs) have been used for decades as putative electrophysiological correlates of perceptual and cognitive operations. However, the exact neurobiological mechanisms underlying their generation are largely unknown. Recently, there has been a special interest in the distinction between evoked and induced responses. Evoked responses are disclosed by conventional averaging procedures, whereas the latter usually call for single-trial analyses of induced oscillations. In this paper, we used neuronal simulations to examine the mechanisms that underpin ERPs/ERFs. In a companion paper, we will examine induced responses using time–frequency analyses and other transforms of single-trial data.

The complexity of neural networks generating MEG/EEG signals (DeFelipe et al., 2002, Thomson and Deuchars, 1997) is considerable. This means that MEG/EEG observation models rely upon simplifying assumptions and empirical priors (David and Friston, 2003, Freeman, 1978, Lopes da Silva et al., 1974, Robinson et al., 2001, Stam et al., 1999, Valdes et al., 1999, Van Rotterdam et al., 1982, Wendling et al., 2000). The primary aim of this paper is to describe a candidate forward model and establish its face validity. This model was designed to reproduce responses seen empirically and enable mechanistic enquiries into the generation of evoked and induced responses. This is the focus of the current paper. However, we will also use this model in a forthcoming paper as an observation model, allowing its parameters to be inferred from real data (David et al., 2004b). In this context, face validity is especially important.

Neural mass models of MEG/EEG usually comprise cortical macro-columns, which can be treated as surrogates for cortical areas and, sometimes, thalamic nuclei. These models use a small number of state variables to represent a neuronal population mean state. This approach, referred to loosely as a mean-field approximation, is efficient when determining the steady-state behaviour of neuronal systems but its accuracy in a dynamic or nonstationary context is less established (Haskell et al., 2001). However, we will assume that the mean field approximation is sufficient for our purposes. The majority of neural mass models of MEG/EEG have been designed to generate alpha rhythms (Jansen and Rit, 1995, Lopes da Silva et al., 1974, Stam et al., 1999, Van Rotterdam et al., 1982). Recent studies have shown that it is possible to reproduce the whole spectrum of MEG/EEG oscillations, using appropriate values of model parameters (David and Friston, 2003, Robinson et al., 2001). In addition, these models have been used to test specific hypotheses about brain function, e.g., focal attention (Suffczynski et al., 2001). Pathological activity such as epilepsy can also be emulated. This means, in principle, that generative models of the sort employed above could be used to characterise the pathophysiological mechanisms underlying seizure activity (Robinson et al., 2002, Wendling et al., 2002).

To date, modelling event-related activity using neural mass models has received much less attention. An early attempt, in the context of visual ERPs, showed that it was possible to emulate ERP-like damped oscillations (Jansen and Rit, 1995). A more sophisticated thalamo–cortical model has been used to simulate event-related synchronisation (ERS) and event-related desynchronisation (ERD), commonly found in the alpha band (Suffczynski et al., 2001). Finally, it has been shown that model parameters can be adjusted to fit real ERPs (Rennie et al., 2002). These studies (Rennie et al., 2002, Suffczynski et al., 2001) emphasise the role of the thalamo–cortical interactions by modelling the cortex as a single compartment.

It is well-known that the cortex has a hierarchical organisation (Crick and Koch, 1998, Felleman and Van Essen, 1991), comprising bottom-up, top-down and lateral processes that can be understood from an anatomical and cognitive perspective (Engel et al., 2001). We have previously discussed the importance of hierarchical processes, in relation to perceptual inference in the brain, using the intimate relationship between hierarchical models and empirical Bayes (Friston, 2002). The current work was more physiologically motivated. Using a hierarchical neural mass model, we were primarily interested in the effects, on event-related MEG/EEG activity, of connections strengths, and how these effects were expressed at different hierarchical levels. In addition, we were interested in how nonlinearities in these connections might be expressed in observed responses.

The neuronal model described below embodies many neuroanatomic and physiological constraints which lend it a neuronal plausibility. It has been designed to (i) explore emergent behaviours that may help understand empirical phenomena and, critically, (ii) as the basis of dynamic observation models. Although the model comprises coupled systems, the coupling is highly asymmetric and heterogeneous. This contrasts with homogenous and symmetrically coupled map lattices (CML) and globally coupled maps (GCM) encountered in more analytic treatments. Using the concepts of chaotic dynamical systems, GCMs have motivated a view of neuronal dynamics that is cast in terms of high-dimensional transitory dynamics among ‘exotic’ attractors (Tsuda, 2001). Much of this work rests on uniform coupling, which induces a synchronisation manifold, around which the dynamics play. The ensuing chaotic itinerancy has many intriguing aspects that can be related to neuronal systems (Breakspear et al., 2003, Kaneko and Tsuda, 2003). However, the focus of this work is not chaotic itinerancy but chaotic transience (the transient dynamics evoked by perturbations to the systems state) in systems with asymmetric coupling. This focus precludes much of the analytic treatment available for GCMs (but see Jirsa and Kelso, 2000 for an analytical description of coherent pattern formation in a spatially continuous neural system with a heterogeneous connection topology). However, as we hope to show, simply integrating the model, to simulate responses, can be a revealing exercise.

It is generally held that an ERP/ERF is the result of averaging a set of discrete stimulus-evoked brain transients (Coles and Rugg, 1995). However, several groups (Jansen et al., 2003, Klimesch et al., 2004, Kolev and Yordanova, 1997, Makeig et al., 2002) have suggested that some ERP/ERF components might be generated by stimulus-induced changes in ongoing brain dynamics. This is consistent with views emerging from several neuroscientific fields, suggesting that phase-synchronisation, of ongoing rhythms, across different spatio–temporal scales mediates the functional integration necessary to perform higher cognitive tasks (Penny et al., 2002, Varela et al., 2001). In brief, a key issue is the distinction between processes that do and do not rely on phase-resetting of ongoing spontaneous activity. Both can lead to the expression of ERP/ERF components but their mechanisms are very different.

EEG and MEG signals are effectively ergodic and cancel when averaged over a sufficient number of randomly chosen epochs. The fact that ERPs/ERFs exhibit systematic waveforms, when the epochs are stimulus locked, suggests either a reproducible stimulus-dependent modulation of amplitude or phase-locking of ongoing MEG/EEG activity (Tass, 2003). The key distinction, between these two explanations, is whether the stimulus-related component interacts with ongoing or spontaneous activity. If there is no interaction, the spontaneous component will be averaged out, because it has no consistent phase relationship with stimulus onset. Conversely, if there is an interaction, dominant frequencies of the spontaneous activity must experience a phase-change, so that they acquire a degree of phase-locking to the stimulus. Note that phase-resetting is a stronger-requirement than induced oscillations. It requires any induced dynamics to be phase-locked in peristimulus time. In short, phase-resetting is explicitly nonlinear and implies an interaction between stimulus-related response and ongoing activity. Put simply, this means that the event-related response depends on ongoing activity. This dependency can be assessed with the difference between responses elicited with and without the stimulus (if we could reproduce exactly the same ongoing activity). In the absence of interactions, there will be no difference. Any difference implies nonlinear interactions. Clearly, this cannot be done empirically but it can be pursued using neuronal simulations.

The secondary aim of the current work was to use realistic neural mass models of hierarchically organised cortical areas to see whether phase-resetting is an emergent phenomenon and a plausible candidate for causing ERPs/ERFs. Phase-resetting is used in this paper as an interesting example of nonlinear responses that have been observed empirically. We use it to show that nonlinear mechanisms can be usefully explored with neuronal models of the sort developed here. In particular, static nonlinearities, in neuronal mass models, are sufficient to explain phase-resetting. Phase-resetting represents nonlinear behaviour because, in the absence of amplitude changes, phase-changes can only be mediated in a nonlinear way. This is why phase-synchronisation plays a central role in detecting nonlinear coupling among sources (Breakspear, 2002, Tass, 2003).

This paper is structured as follows. In the first section, we introduce the hierarchical neural mass model used in the remaining sections. It is based on previous neuroanatomic studies by Felleman and van Essen (Felleman and Van Essen, 1991) and work by Jansen and Rit on modelling MEG/EEG data (Jansen and Rit, 1995). In the second section, we demonstrate the basic behaviour of the model, by successive elaboration of a cortical hierarchy. We start with forward connections and then add backward and lateral connections. The goal of this approach was to provide an intuitive understanding of MEG/EEG like dynamics generated by coupled nonlinear systems. These simulations were performed in the absence of spontaneous activity. In the third section, we examine the interaction between evoked and spontaneous activity, using a representative hierarchical architecture established in the previous section. Finally, we discuss the potential benefits of this modelling approach, for the study of measured MEG/EEG activity.