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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

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slide1

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

background
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.
background1
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.
research questions
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?
method general form of the time varying mvar models
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:

data acquisition 10 20 standard
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.

method procedure
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.
method time varying mvar estimation methods
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.
method connectivity measures
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:
method datasets
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.
results
RESULTS
  • Simulated data

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

results1
RESULTS
  • Simulated data

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

results2
RESULTS
  • EEG data

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

results3
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.

conclusions
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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