  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.

Methodology;Applications