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MVAR-based EEG Connectivity

MVAR-based EEG Connectivity. Amir Omidvarnia 4 March 2011. Outline. A linear model for EEG signals Causality between EEG channels Partial Directed Coherence: Connectivity within cortical areas Time-varying connectivity Two examples: Simulated model and neonatal EEG data Pros and Cons

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MVAR-based EEG Connectivity

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  1. MVAR-based EEG Connectivity Amir Omidvarnia 4 March 2011

  2. Outline • A linear model for EEG signals • Causality between EEG channels • Partial Directed Coherence: Connectivity within cortical areas • Time-varying connectivity • Two examples: Simulated model and neonatal EEG data • Pros and Cons • Conclusion

  3. A linear model for EEG signals • Multivariate Autoregressive model: • In this model, the current values of a channel are estimated by using its previous values as well as the previous values of the other channels. • The input of the model is considered as Gaussian white noise.

  4. A linear model for EEG signals • An example of a bivariate AR model: Bivariate AR model Ch1(n) n1(n) n2(n) Ch2(n)

  5. A linear model for EEG signals • Model coefficients and delays are sufficient for estimation of the outputs.

  6. Causality between EEG channels • Now, suppose we want to estimate Ch1(n) and Ch2(n) using the model below: instead of the original model:

  7. Causality between EEG channels • The first model results in erroneous outputs, as we have ignored the effect of the channel 1 on channel 2. Granger causality • Ch1 is said to Granger-cause Ch2, if information of the past of process Ch1 enhances the prediction of the process Ch2 compared to the knowledge of the past of process Ch2 alone. Ch1 Ch2

  8. Causality between EEG channels By quantifying Granger causality, one can detect the direction of the information flow between channels.

  9. Partial Directed Coherence: Connectivity within cortical areas • AR coefficients reflect the causality between channels. • Partial Directed Coherence function quantifies the Granger causality in the frequency domain. Time domain AR model FFT(AR model) Ch1(n) CH1(f) n1(n) N1(f) n2(n) N2(f) Ch2(n) CH2(f) Frequency domain

  10. Partial Directed Coherence: Connectivity within cortical areas • Indirect and Partial relationships from Ch1 to Ch2 Ch4 Ch5 Ch3 Ch1 Ch2

  11. Partial Directed Coherence: Connectivity within cortical areas • Example of the simulated data: a 5-channel dataset with time-invariant interactions Affecting channels Affected channels Ref. of the images: L. A. Baccalá, and K. Sameshima, “Partial directed coherence: a new concept in neural structure determination,” Biological Cybernetics, vol. 84, no. 6, pp. 463-474, 2001.

  12. Partial Directed Coherence: Connectivity within cortical areas • The procedure of extracting partial directed information from the EEG data: • Fit a multivariate AR model onto the channels 2. Extract the connectivity measures using the fitted model. 3. Extract the directed graph based on the connectivity measures.

  13. Partial Directed Coherence: Connectivity within cortical areas AR model PDC Ref. Of the brain image: L. Astolfi, F. Cincotti, D. Mattia et al., “Tracking the Time-Varying Cortical Connectivity Patterns by Adaptive Multivariate Estimators,” IEEE Transactions on Biomedical Engineering, vol. 55, no. 3, pp. 902-913, 2008.

  14. Time-varying connectivity • The interrelations within the EEG channels are not time-invariant. • Time-invariant connectivity measures can be modified to time-varying versions using time-varying MVAR estimation algorithms.

  15. Time-varying connectivity • Example: a 3-channel simulated model Ch1 Ch2 Ch3

  16. Time-varying connectivity • Example: neonatal seizure EEG Beforehand, the seizure source has been localized by a seizure detection algorithm. Seizure mask

  17. Time-varying connectivity • Example: neonatal seizure EEG

  18. Pros and Cons • Pros • Direction of the information flow can be extracted. • Direct and indirect influences can be differentiated. • The problems of ordinary coherence function is solved. • Cons • Performance strongly depends on the goodness of fit of the AR model. • For multichannel data and long segments, the computational load increases drastically.

  19. Conclusion • Time-varying connectivity measures can be helpful for neonatal seizure characterization. • Partial directed information may lead to a seizure detection approach for neonatal EEG signals.

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