GMPC has clearly marked synchronous time periods within the simulated bivariate/multivariate signal. Considering

the multivariate binary masks, the majority of variables present a trend-stationary phase during the marked intervals.

Synchrony of spatially segregated brain activities is an important feature that mediates their functional connections. Inter-hemispheric asynchrony of EEG bursts in full-term neonates is an indication of brain abnormality.

A bivariate measure is unlikely to capture the key feature of asynchrony seen in the sick neonatal brain, which is characterized by a global disruption of synchrony.

Different approaches including Evolution Map Approach ,

Instantaneous Period Approach, Mutual Prediction Approach, General Field Synchronization and Stochastic Event Synchrony have also been proposed for phase synchrony computation within bivariate and multivariate data.

The concept of cointegration, introduced in econometrics, has been used to develop a parametric multivariate phase synchrony measure for EEG data.

The present study uses the concept of cointegration to generalize the bivariate Mean Phase Coherence (MPC) to the multivariate case which is suitable for analysis of newborn EEG asynchrony.

Concept of cointegrationA one-dimensional stochastic process is said to be integrated of order d (I(d)) if the reverse characteristic polynomial

of its fitted multivariate autoregressive (MVAR) model has d roots on the unit circle in the complex plane. Two or

more integrated signals can be in a long-term relation with each other if there is linear combination of these signals

that results in a stationary process. In such case, these signals are referred to as cointegrated signals.

Generalized Phase Synchrony (GePS)Two signals x1(t) and x2(t) are said to be in a generalized phase synchrony if the following equation is satisfied:

where z(t)~N(m,σ) is a normal stationary stochastic process. Such relationship is generalized to a multivariate cointegrating relationship among K phase signals extracted from a multivariate signal x(t) as

x(t) is said to be phase synchronized of rank r, if there are r cointegrating relationships within the phases extracted

from the signals variables. A higher rank implies a larger number of interconnected phase signals and therefore, higher

synchrony within channels.

Generalized Mean Phase Coherence (GMPC)A. The signals are divided into short duration segments using a sliding window with an optional overlap.

B. The multivariate phase signal is computed from each segment using the analytic signal approach.

C. The multivariate Johansen test is applied on the extracted phase signals to obtain all coefficients of r cointegrating

relationships.

D. The Generalized Mean Phase Coherence (GMPC) is defined as:

where the residual noise zi(t) represents the fluctuation around zero and is related to the strength of the i'th

cointegrating relationship (i=1,…,r).

E. A surrogate data method (here, shuffling over the segments) is then applied to determine the significance threshold

for the measure.

Mean Phase Coherence (MPC)Let zx(t) and zy(t) be the analytic signals associated with two one-

dimensional stochastic real-valued signals x(t) and y(t), respectively; that is:

where and are the Hilbert transforms of x(t) and y(t), respectively. The two signals x(t) and y(t) are said to be phase-locked of order (m,n) if

The ratio m/n is assumed to be rational. In the case of discrete signals and for the case m = n = 1, the MPC is used as a measure of phase synchrony:

where ∆t is the sampling period and N the length of the two signals in samples. R can be re-written in a simpler form as:

INTRODUCTION

BACKGROUND

METHOD

CONCLUSIONS

Generalized Mean Phase Coherence for Asynchrony Abnormality Detection in Multichannel Newborn EEG

Amir Omidvarnia, Sampsa Vanhatalo, Mostefa Mesbah, Ghasem Azemi, Paul Colditz, Boualem Boashash The University of Queensland, Australia

Centre for Clinical Research (UQCCR)

RESULTS – NEWBORN EEG DATA

The very low variation of the thresholds with time suggests a consistent probability

distribution of the null hypothesis (the state of asynchrony) for all time segments.

The findings suggest that a consistent time shift may exist between the EEG bursts

recorded from the left and right hemispheres of an abnormal newborn brain.

The results obtained from simulated signals and newborn EEG show the performance of

the GMPC measure in detecting phase synchrony.

This approach is able to extract phase interdependencies of a multivariate signal

independent of the signal amplitude.

Ratio of the synchronous periods detected by the GMPC measure comparing to the asynchronous ones in the multichannel EEG can be used as a quantitative measure of EEG inter-hemispheric asynchrony.

Figure 2: Binary phase masks for the simulated multivariate data (left). The GMPC measure

extracted from the simulated multivariate data (right). Shadowed areas emphasis on the synchronous

intervals detected by the GMPC.

Figure 3: A 19-channel cap adjusted for the newborn EEG recordings according to

the 10-20 standard. Dashed areas represent the selected left and right groups

of electrodes.

Figure 4: The GMPC measures and their

corresponding binary masks extracted from the left and right groups of electrodes. The lowest

panel illustrates the point-wise AND operator of the left and right hemisphere binary masks. Circles and

arrows demonstrate a correspondence between the left and right binary

masks.

RESULTS – SIMULATED DATA

Figure 1: Binary phase masks for the simulated bivariate data (left). MPC

versus GMPC extracted from the simulated bivariate data (right).