Abstract

1
An EEG-based methodology for the study of
dynamical brain connectivity during cognitive
tasks  
Abstract   We present a method to obtain and
display the significant changes in EEG dynamical
connectivity (inferred from synchronization
patterns) relative to the pre-stimulus state in a
cognitive task. These changes are displayed as
detailed Time-Frequency-Topography maps where
specific synchronization patterns can be easily
located in time and frequency and interactive
segmentations may be performed. An analysis of
different synchronization measures shows that
most known synchrony measures can be classified
in one of two groups the first group matches the
criteria of strict phase synchrony, where
dynamical connections result in phase differences
smaller than 10 ms the second group consists of
measures which involve some type of
time-persistence and are highly correlated to the
variance of the apparent phase measured at each
electrode within a given time window, and thus,
they may not be measuring true long-range
synchrony. In our methodology, we avoid this
problem by handling time-persistence separately
by means of Bayesian estimation with a Markov
Random Field model. We also present a
mathematical model that explains many of these
observations, which is based on the idea that the
apparent phase measured at each electrode results
from contributions of several subjacent neural
subnetworks. Examples of the application of these
techniques to the analysis of dynamic
connectivity associated with specific cognitive
tasks are presented as well.
Alba F.A.1, Marroquin, J.L.1, Harmony T.2 1
Centro de Investigación en Matemáticas,
Guanajuato, Gto. (México) 2 Instituto de
Neurobiología, Campus UNAM Juriquilla, Querétaro,
Qro. (México)
Overview of Procedure 1.- Run the EEG signals
through bank of bandpass filters and extract
apparent phase information 2.- Estimate the
instantaneous mean phase-lock 3.- Estimate the
likelihoods and prior distributions for the
Markov Random Field (MRF) model using the
instantaneous phase-lock values 4.- Use Bayesian
estimation to find significant synchronization
patterns that are persistent 5.- Display
synchronization patterns as multitoposcopic
graphs and time-frequency-topography (TFT) maps
that can be interactively segmented.
2
Apparent phase for a population model
ERPA Phase-lock measure
We model the signal at each electrode e as the
sum of the contributions of a number of
oscillators whose phase takes values from fe,m
We have observed that measures which involve some
sort of time-persistence are seriously affected
by local phase scattering. Hence we decided to
treat phase-locking and persistence separtely.
Instantaneous synchrony measure
Instantaneous relative synchrony
The apparent amplitude and phase are those that
are obtained from the EEG observations by
band-pass filtering
Instantaneous mean relative synchrony
Bayesian classification of significant synchrony
changes
Example For a two-population model, there are
only two possible phase values per electrode.
Bayesian estimation with a prior Markov Random
Field (MRF) model Marroquin, 1987 is used to
classify significant changes in synchrony as
higher (c1), lower (c-1) or equal (c0), and
also to include a persistence constraint. The
posterior distribution of the class field c is
given by
A expif
(1 - a) expif2
a expif1
with
The product hr(k) of prior distributions and
likelihoods can be estimated from the data using
kernel density estimation.
Other common synchrony measures
Phase-LockingStatistic (PLS) Lachaux et al.,
1999
Single-Trial PLS (STPLS) Lachaux et al., 2000
This suggests fe1 (t) fe2(t) as synchrony
criterion. Thus synchrony is characterized
by 1.- Significant phase-lock changes 2.-
Persistence across a time window
Coherence Gardner, 1992 Bressler et al.,
1993, 1995
3
Visualization
Influence of Local Phase Dispersion (LPD)
If we take the STPLS measure and fix the phase of
one of the signals, we will be actually measuring
the variance of the other signals phase in the
given time window.
For a given point in the TF map we employ a
multitoposcopic view of the significant
synchronization patterns. Red point
Significantly higher synchrony (class c
1) Green point Significantly lower synchrony
(c -1) Example Words at 300 ms, 10 Hz.
We define LPD as
Time-Frequency-Topography Histograms
Marroquin et al., 2004
Coherence
STPLS
Significant changes in (1 LPD)
Correlation between pairs of measures
Interactively segmented maps
The Time-Frequency plane can be segmented in
areas which show an homogeneous synchrony pattern.
Conclusions
Synchrony changes for ERPA are characterized by
two properties 1) a significant change in
phase-lock, and 2) persistence of those changes
across time. When these factors are combined into
one measure, the results appear to be dominated
by Local Phase Dispersion. We propose handling
phase-locking and time-persistence separately.
Phase-locking is measured simply by the magnitude
of phase differences (as suggested by our
population model), while significancy and
persistence are taken into account using Bayesian
estimation with a Markov Random Field model. We
have also developed an user-friendly system with
powerful visualization tools that allow an easy
navigation of the TF plane, quick recognition of
areas with homogeneous synchrony patterns, and a
straightforward interactive segmentation of the
TF plane.
Example Experiment (Words) A word is displayed
onscreen and the subject is instructed to press
one button if the word corresponds to an animal
and starts with a consonant, and another button
otherwise.