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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

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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.

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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.

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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?

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**METHOD General 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:

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**Data Acquisition 10-20 standard**

Five monopolar channels (O1, O2, P3, P4, Cz) out of the 14 recorded according to the 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.

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METHOD Procedure 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.

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**METHOD Time-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.

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**METHOD Connectivity 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:

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METHOD Datasets 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 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.

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**RESULTS Simulated data**

Adaptive DTF (left) and PDC (right) for the simulated model using the Kalman filtering approach.

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**Short-time DTF (left) and PDC (right) for the simulated model.**

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

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

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

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

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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

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