The use of time-variant EEG Granger causality for inspecting directed interdependencies of neural assemblies

Abstract

Understanding of brain functioning requires the investigation of activated cortical networks, in particular the detection of interactions between different cortical sites. Commonly, coherence and correlation are used to describe interrelations between EEG signals. However, on this basis, no statements on causality or the direction of their interrelations are possible. Causality between two signals may be expressed in terms of upgrading the predictability of one signal by the knowledge of the immediate past of the other signal. The best-established approach in this context is the so-called Granger causality. The classical estimation of Granger causality requires the stationarity of the signals. In this way, transient pathways of information transfer stay hidden. The study presents an adaptive estimation of Granger causality. Simulations demonstrate the usefulness of the time-variant Granger causality for detecting dynamic causal relations within time intervals of less than 100 ms. The time-variant Granger causality is applied to EEG data from the Stroop task. It was shown that conflict situations generate dense webs of interactions directed from posterior to anterior cortical sites. The web of directed interactions occurs mainly 400 ms after the stimulus onset and lasts up to the end of the task.

Introduction

In cognitive operations large cortical networks are engaged, the investigation of which is usually carried out by correlation and coherence measures (cf. Bressler and Kelso, 2001) or phase synchronisation measures (cf. Varela et al., 2001) of the EEG data. These measures tell about the strengths of interactions between groups of neurons. But, these measures provide no insight into the directionality of information flow. Several recent works based on the structural analysis of signal deal with this problem. Causal relations between different components of a multi-dimensional signal can be analysed in the context of multivariate autoregressive modelling. The parameter matrices and transfer matrix of fitted vector autoregressive (VAR) models are mostly not symmetrical and thus are suitable for the detection of the direction of information transfer. The best-established approach in this context is the so-called Granger causality (Granger, 1969). The general idea of causality may be expressed in terms of predictability. If a signal X causes a signal Y, the knowledge of the past of both X and Y should improve the prediction of the presence of Y in comparison with the knowledge of the past of Y alone. Within this concept of predictability, Geweke (1982) developed measures of linear feedback and proposed their decomposition by frequency. Bernasconi and König (1999) and Bernasconi et al. (2000) used these measures for the investigation of directional interactions between different areas of the cat visual system. Several further measures for the description of directed information transfer within the frequency domain were developed currently. Baccala et al. (1998) and Sameshima and Baccala (1999) introduced directed coherence and partial directed coherence and applied them to the analysis of electrophysiological signals. Kaminski and Blinowska (1991) proposed the so-called directed transfer function (DTF). Kaminski et al. (2001) compared the properties of Granger causality and DTF. All these measures are based on the transfer matrix of a fitted VAR model and presuppose the stationarity of the signals in the time interval to be investigated. Ding et al. (2000) and Liang et al. (2000) developed the fit of VAR models for short-time windows using the information of multiple trials. This approach is used for constructing a short-time directed transfer function (STDTF) with a time resolution up to 100 ms. Ginter et al. (2001) used the STDTF for investigating short-time changes in the direction and spectral content of the propagation of EEG activity. Freiwald et al. (1999) generalised the Granger causality by applying local linear autoregressive models. In this study, the generalised Granger causality was used to detect both linear and nonlinear directed interactions between neural groups in the macaque inferotemporal cortex.

The present paper focuses on the recursive time-variant estimation of the Granger causality. Our approach overcomes the requirement of stationarity of the signals and thus permits the observation of transient directed neural networks. Ding et al. (2000) used a short-time windows technique, which require the stationarity of the signal within short-time windows only, and also enables the construction of a time-variant Granger causality. Our method is based on the adaptive recursive fit of a VAR model with time-dependent parameters by means of a generalised recursive least-square (RLS) algorithm, which also takes into consideration a set of EEG epochs as a whole. In contrast to short-window techniques, the multi-trial RLS algorithm involves the information of the actual past of the signal, whereby the influence of the past decreases exponentially with the time distance to the actual samples. Thus, adaptive filter algorithms enable the fit of VAR models with an arbitrary order. Properties of the time-variant Granger causality are demonstrated for simulated signals.

The applicability of the time-variant Granger causality is demonstrated on data from the Stroop task. In the standard color-word Stroop task, subjects must identify the color in which a word is written, while inhibiting the more automatic response of reading the word. The need for attentional selection is high in the so-called ‘incongruent condition’ in which the meaning of the word conflicts with the color in which it is written. This task is commonly employed in studies of selective attention and has been found to be sensitive to damages in prefrontal regions (see, e.g. Vendrell et al., 1995). For incongruent conditions, PET and fMRI studies have shown an increased activation of a widespread network of anterior brain regions. Most studies report on activation of the anterior cingulate cortex (ACC) and the frontal polar cortex (see, e.g. Pardo et al., 1990, Bench et al., 1993, Taylor et al., 1994, Carter et al., 1995, Carter et al., 2000, Banich et al., 2000, MacDonald et al., 2000). MacDonald et al. (2000) succeeded in discriminating the role of different areas of the frontal cortex in a network serving cognitive control. They found that the dorsolateral prefrontal cortex (DLPFC) was selectively engaged during the preparatory period for color naming in particular and assigned the DLPFC a role in implementation of control. On the other hand, ACC was found to be selectively activated during the response period, more for incongruent color-naming tasks. This later activation speaks for the role of ACC in conflict monitoring. Several authors hint at changes of the regional cerebral blood flow (rCFB) in posterior cingulate and other posterior regions (see, e.g. Bench et al., 1993, Carter et al., 1995). In an EEG study, West and Bell (1997) have shown not only increased Alpha1 power (8–10 Hz) for medial (F3, F4) and lateral (F7, F8) frontal sites, but also for parietal regions (P3, P4). They suppose that greater activation of the parietal cortex may have resulted from the interaction between prefrontal and parietal regions during the suppression of the influence of the irrelevant word dimension of the stimulus. Ilan and Polich (1999) found in another EEG study that P300 latency did not vary across color/word congruence conditions. They reasoned that the reaction time difference between congruence conditions is originated after stimulus evaluation by the translation of stimulus code into response code. In our own previous EEG coherence study (Schack et al., 1999a, Schack et al., 1999b), the authors ascertained increased fronto-parietal interactions beside increased coherences within the frontal area in the time interval from 400 ms up to the end of the task.

Based on our time-variant Granger causality approach, new aspects of the Stroop effect are detected pertaining to the role of the frontal areas of the cortex and the temporal interactions with posterior areas. The evaluation of the existence of temporal directed interdependencies is performed by the construction of temporal thresholds using surrogate data.