Amir Omidvarnia, Mostefa Mesbah, John M. O’Toole, Paul Colditz, Boualem Boashash

1. Analysis of the time-varying cortical neural connectivity in the newborn EEG: a time-frequency approach Amir Omidvarnia, Mostefa Mesbah, John M. O’Toole, Paul Colditz, Boualem Boashash The University of Queensland Qatar University Centre for Clinical Research (UQCCR) College of Engineering

2. BACKGROUND • The ability of the brain to conduct high level sensory and cognitive functions depends strongly on underlying interactions between different brain regions. • Insights into the inter-relations across the brain provide a basis for understanding high level mechanisms of both healthy and pathological brain function. • The mutual influence of brain regions and, therefore, of EEG channels doesn’t necessarily show a time-invariant behavior.

3. BACKGROUND • Multivariate autoregressive (MVAR) models are able to represent time-varying interactions between EEG signals in the form of linear difference equations. • Directed Coherence, Partial Directed Coherence, Generalized Partial Directed Coherence, Directed Transfer Function, direct Directed Transfer Function and Granger Causality Index are MVAR-based criteria which have been introduced to determine time-invariant directional influence in multivariate systems. • Short time approaches, linear Kalman filtering and Dual Kalman Filtering have been suggested to account for the problem of time-varying directional interactions between EEG channels.

4. RESEARCH QUESTIONS 1. Which MVAR estimation method is able to present the time-varying interactions between neonatal EEG channels during the seizure? • Does Partial Directed Coherence (PDC) outperform Directed Transfer Function (DTF) on the neonatal multichannel EEG data, as being suggested for adult EEG studies? • Is there any significant difference between short time-based causality measures and Kalman filter-based ones?

5. METHODGeneral form of the time-varying MVAR models • A time-varying N-variate AR process of order p can be represented as: where w is a vector white noise, the matrices Ar are given by:

6. Data Acquisition10-20 standard Five monopolar channels (O1, O2, P3, P4, Cz) out of the 14 recorded according to the 10-20 standard [21] modified for newborns were selected from a newborn EEG dataset to investigate the time-varying interhemispheric and intrahemispheric interactions during an EEG seizure period.

7. METHODProcedure • Time-varying connectivity measures were computed based on the time-varying MVAR model fitted to both simulated and real EEG data. • The time-varying MVAR parameters were estimated using a linear Kalman filter based algorithm (AAR) as well as the windowing approach. • A surrogate data method with 50 realizations was then used to select the most significant values of the measures at 99% confidence level. Surrogates were obtained by randomizing all samples of the signal to remove all causal relationships between them.

8. METHODTime-varying MVAR estimation methods • Adaptive AR modeling: MVAR equations are reformulated in the form of state space equations by re-arranging all matrix parameters into a state vector of the dynamical system and considering the non-stationary signal as the observation. Then, a linear Kalman filter is utilized to estimate the parameters vector. • Short time-based approach: The entire signal is divided into short overlapping time intervals using a Hamming window. Then, connectivity measures are computed for each interval and finally, time-frequency maps of the information flow are plotted for each combination of channels.

9. METHODConnectivity measures • Partial Directed Coherence (PDC): The time-varying version of partial directed coherence (PDC) is defined as: aj(n,f) is the j’th column of the matrix A(n,f). • Directed Transfer Function (DTF): The time-varying version of directed transfer function (DTF) is defined as:

10. METHODDatasets • Simulated data: A 3-dimensional MVAR(2)-process was simulated with two time-variant parameters, namely, a step function and a positive triangular function. This process has previously been used to evaluate non-stationary directed interactions in multivariate neural data. • EEG data: Five monopolar channels (O1, O2, P3, P4, Cz) out of the 14 recorded according to the 10-20 standard [21] modified for newborns were selected from a newborn EEG dataset to investigate the time-varying interhemispheric and intrahemispheric interactions during an EEG seizure period.

11. RESULTS • Simulated data Adaptive DTF (left) and PDC (right) for the simulated model using the Kalman filtering approach.

12. RESULTS • Simulated data Short-time DTF (left) and PDC (right) for the simulated model.

13. RESULTS • EEG data Short-time DTF (left) and PDC (right) of the newborn EEG data.

14. RESULTS • EEG data Cz Cz P3 P4 P3 P4 O1 O2 O2 O1 Suggested directed graphs based on ST-DTF (left) and ST-PDC (right) measures for the newborn EEG data.

15. CONCLUSIONS • Results show the advantage of using the PDC measure in terms of the ability of tracking fast parameter changes compared to the DTF measure using the simulated data. • The results imply that the windowing (short-time) based PDC is more appropriate for the newborn EEG analysis, as the Kalman filter based AR estimation method discussed here has limitations in tracking fast parameter changes. • Further improvements in the estimation of the functional connectivity between cortical brain regions could be obtained by investigating a non-parametric approach that is based on the use of a selected quadratic TFD and instantaneous frequency estimation