[Eeglablist] Coherence & phase synchronization

[R.D. Pascual-Marqui]

Dear Colleagues,

I updated a technical report on coherence and phase synchronization
(I posted the first draft version about a month ago, 12-June-2007).

The changes, which are substantial, were made after many helpful
discussions with three colleagues, and I've acknowledged their help in
the paper.

Homepage with link to paper at:
http://arxiv.org/abs/0706.1776
Direct PDF download at:
http://arxiv.org/pdf/0706.1776

The title and abstract are at end of this message.

Hope this helps,
Cordially,
Roberto
--
R.D. Pascual-Marqui, PhD, PD
The KEY Institute for Brain-Mind Research
University Hospital of Psychiatry
Lenggstr. 31, CH-8032 Zurich, Switzerland
Tel:+41-44-3884934 ; Fax:+41-44-3803043
pascualm <at> key.uzh.ch
www.keyinst.uzh.ch/loreta

--------------------------------

RD Pascual-Marqui: Coherence and phase synchronization: generalization
to pairs of multivariate time series, and removal of zero-lag
contributions. arXiv:0706.1776v3 [stat.ME] 12 July 2007. (http://
arxiv.org/pdf/0706.1776)

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.