Tracking the time-varying cortical connectivity patterns by adaptive multivariate estimators

Abstract

The directed transfer function (DTF) and the partial directed coherence (PDC) are frequency-domain estimators that are able to describe interactions between cortical areas in terms of the concept of Granger causality. However, the classical estimation of these methods is based on the multivariate autoregressive modelling (MVAR) of time series, which requires the stationarity 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) and to apply it to a set of real high resolution EEG data. This approach will allow the observation of rapidly changing influences between the cortical areas during the execution of a task. The simulation results indicated that time-varying DTF and PDC are able to estimate correctly the imposed connectivity patterns under reasonable operative conditions of signal-to-noise ratio (SNR) ad number of trials. An SNR of five and a number of trials of at least 20 provide a good accuracy in the estimation. After testing the method by the simulation study, we provide an application to the cortical estimations obtained from high resolution EEG data recorded from a group of healthy subject during a combined foot-lips movement and present the time-varying connectivity patterns resulting from the application of both DTF and PDC. Two different cortical networks were detected with the proposed methods, one constant across the task and the other evolving during the preparation of the joint movement.