Coherence and phase synchronization: generalization to pairs of multivariate time series, and removal of zero-lag contributions

TL;DR

This paper extends coherence and phase synchronization measures to multivariate time series from brain signals, addressing zero-lag artifacts and introducing new generalizations, with applications in neurophysiology.

Contribution

It presents novel methods for analyzing connectivity in multivariate brain signals, including solutions for zero-lag artifacts and generalizations to conditional and non-stationary analyses.

Findings

New measures for multivariate coherence and phase synchronization

Effective removal of zero-lag contributions in EEG/MEG data

Applicable to both invasive and non-invasive brain recordings

Abstract

Coherence and phase synchronization between time series corresponding to different spatial locations are usually interpreted as indicators of the connectivity between locations. In neurophysiology, time series of electric neuronal activity are essential for studying brain interconnectivity. Such signals can either be invasively measured from depth electrodes, or computed from very high time resolution, non-invasive, extracranial recordings of scalp electric potential differences (EEG: electroencephalogram) and magnetic fields (MEG: magnetoencephalogram) by means of a tomography such as sLORETA (standardized low resolution brain electromagnetic tomography). There are two problems in this case. First, in the usual situation of unknown cortical geometry, the estimated signal at each brain location is a vector with three components (i.e. a current density vector), which means that coherence and phase synchronization must be generalized to pairs of multivariate time series. Second, the inherent low spatial resolution of the EEG/MEG tomography introduces artificially high zero-lag coherence and phase synchronization. In this report, solutions to both problems are presented. Two additional generalizations are briefly mentioned: (1) conditional coherence and phase synchronization; and (2) non-stationary time-frequency analysis. Finally, a non-parametric randomization method for connectivity significance testing is outlined. The new connectivity measures proposed here can be applied to pairs of univariate EEG/MEG signals, as is traditional in the published literature. However, these calculations cannot be interpreted as connectivity, since it is in general incorrect to associate an extracranial electrode or sensor to the underlying cortex.