Estimation of the time-varying cortical connectivity patterns by the adaptive multivariate estimators in high resolution EEG studies

Abstract

The Directed Transfer Function (DTF) and the Partial Directed Coherence (PDC) are frequency-domain estimators, based on the multivariate autoregressive modelling (MVAR) of time series, that are able to describe interactions between cortical areas in terms of the concept of Granger causality. However, the classical estimation of these methods requires the stationary of the signals. In this way, transient pathways of information transfer remains hidden. The objective of this study is to test a time-varying multivariate method for the estimation of rapidly changing connectivity relationships between cortical areas of the human brain, based on DTF/PDC and on the use of adaptive MVAR modelling (AMVAR). This approach will allow the observation of transient influences between the cortical areas during the execution of a task. Time-varying DTF and PDC were obtained by the adaptive recursive fit of an MVAR model with time-dependent parameters, by means of a generalized recursive least-square (RLS) algorithm, taking into consideration a set of EEG epochs. Simulations were performed under different levels of Signal to Noise Ratio (SNR), number of trials (TRIALS) and frequency bands (BAND), and of different values of the RLS adaptation factor adopted (factor C). The results indicated that time-varying DTF and PDC are able to estimate correctly the imposed connectivity patterns under reasonable operative conditions of SNR ad number of trials. Moreover, the capability of follow the rapid changes in connectivity is highly increased by the number of trials at disposal, and by the right choice of the value adopted for the adaptation factor C. The results of the simulation study indicate that DTF and PDC computed on adaptive MVAR can be effectively used to estimate time-varying patterns of functional connectivity between cortical activations, under general conditions met in practical EEG recordings.