1. Kalman filter-based PDC and dDTF measures for time-varying cortical connectivity analysis of newborn EEG
A.H. Omidvarnia1, M. Mesbah1, M. S. Khlif1, J.M. O’Toole2,
P. Colditz1, B. Boashash1,3
1Centre for Clinical Research, The University of Queensland, Brisbane, Australia
2DeustoTech, University of Deusto, Bilbao, Spain
3Qatar University College of Engineering, Doha, Qatar

2. Outline
Motivation
Methodology
Results
Conclusion
References

3. Motivation
Significant difference between adult brain and newborn brain
Time-varying cortical connectivity analysis: a potential source localization approach for newborn brain
‘Partial’ and ‘direct’ information within the newborn brain
Track the seizure dynamics in newborn brain in terms of partiality and direction of the information flow

4. 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

5. Partiality and direction of the information flow
Indirect and Partial relationships from Ch1 to Ch2
Ch1
Ch2
Ch5
Ch3
Ch4

6. Time-varying Multivariate Autoregressive (MVAR) model
Time-varying MVAR model can be considered as a time- frozen multichannel FIR filter with the white noise as its input.

7. Dual Extended Kalman Filter (DEKF)
An adaptive way to estimate time-varying MVAR parameters
Two interlaced Kalman filters
Capable of dealing with nonlinearity and nonstationarity in dynamical systems.

8. Partial Directed Coherence (PDC)
Extraction of linearly ‘Partial’ and ‘directed’ relationships between channels
Transformation of the MVAR-based cross-correlation into the frequency domain.
Time-frequency version can be extended by time-varying MVAR parameter estimation.

9. direct Directed Transfer Function (dDTF)
A measure based on the transfer function matrix between channels.
Transfer function matrix: an SVD of the cross-spectral density matrix
A combination of partial coherence and directed transfer function

10. Results Simulated model b(n) and c(n): time-varying parameters Ch3 Ch2

11. PDC extracted from the simulated model using the DEKF

12. dDTF extracted from the simulated model using the DEKF

13. Simulated models - comparison
Two extra direct influences from channel 1 to channels 2 and 3 in the dDTF plots
No extra and incorrect information in the PDC plots
Very small values for the dDTF measure in contrast to the normalized values of the PDC measure

14. Newborn EEG data Time-varying PDC was applied to the EEG data.
10-sec of a 7-channel EEG epoch in presence of seizure was analyzed.
The optimum AR model order was evaluated by Schwarz’s Bayesian Criterion and fixed to 4 during the analysis.

15. PDC extracted from the simulated model using the DEKF

16. A screenshot of the directed graph

17. Conclusion
The results show the superiority of the DEKF-based PDC in terms of its ability to track fast parameter changes and at the same time, identify accurate interactions compared to the dDTF.
TV-PDC is useful for characterizing EEG abnormalities such as seizure in the newborn, during which the dynamics of the brain changes rapidly

18. References
[1] B. J. Fisch, Fisch & Spehlmann's EEG primer: Basic principles of digital and analog EEG, Amsterdam: Elsevier, 2005.
[2] G. L. Holmes, and C. T. Lombroso, “Prognostic Value of Background Patterns in the Neonatal EEG,” Journal of Clinical Neurophysiology, vol. 10, no. 3, pp , 1993.
[3] A. Aarabi, K. Kazemi, R. Grebe et al., “Detection of EEG transients in neonates and older children using a system based on dynamic time-warping template matching and spatial dipole clustering,” Neuroimage, vol. 48, no. 1, pp , Oct, 2009.
[4] L. A. Baccalá, and K. Sameshima, “Partial directed coherence: a new concept in neural structure determination,” Biological Cybernetics, vol. 84, no. 6, pp , 2001.

19. References (Cont.)
[5] M. Kaminski, and K. Blinowska, “A new method of the description of the information flow in the brain structures,” Biological Cybernetics, vol. 65, no. 3, pp , 1991.
[6] A. Korzeniewska, M. Manczak, M. Kaminski et al., “Determination of information flow direction among brain structures by a modified directed transfer function (dDTF) method,” Journal of Neuroscience Methods, vol. 125, no. 1-2, pp , 2003.
[7] R. Magjarevic, J. H. Nagel, Y. Ku et al., "Nonstationary EEG Analysis using random-walk model," World Congress on Medical Physics and Biomedical Engineering 2006, IFMBE Proceedings R. Magjarevic, ed., pp : Springer Berlin Heidelberg, 2007.

20. References (Cont.)
[8] B. Boashash, H. Carson, and M. Mesbah, “Detection of seizures in newborns using time-frequency analysis of EEG signals,” in Statistical Signal and Array Processing, Proceedings of the Tenth IEEE Workshop on, 2000, pp
[9] E. A. Wan, and A. T. Nelson, “Neural dual extended Kalman filtering: applications in speech enhancement and monaural blind signal separation,” in Neural Networks for Signal Processing [1997] VII. Proceedings of the IEEE Workshop, 1997, pp
[10] L. Sommerlade, K. Henschel, J. Wohlmuth et al., “Time-variant estimation of directed influences during Parkinsonian tremor,” Journal of Physiology-Paris, vol. 103, no. 6, pp , 2009.

21. References (Cont.)
[11] A. Neumaier, and T. Schneider, “Estimation of parameters and eigenmodes of multivariate autoregressive models,” ACM Trans. Math. Softw., vol. 27, no. 1, pp , 2001.
[12] W. Hesse, E. Möller, M. Arnold et al., “The use of time-variant EEG Granger causality for inspecting directed interdependencies of neural assemblies,” Journal of Neuroscience Methods, vol. 124, no. 1, pp , 2003.
[13] E. Niedermeyer, and F. Lopes da Silva, Electroencephalography: Basic Principles, Clinical Applications, and Related Fields 5th ed.: Lippincott Williams & Wilkins, 2004.

22. References (Cont.)
[14] I. Gath, C. Feuerstein, D. T. Pham et al., “On the tracking of rapid dynamic changes in seizure EEG,” Biomedical Engineering, IEEE Transactions on, vol. 39, no. 9, pp , 1992.
[15] N. Roche-Labarbe, A. Aarabi, G. Kongolo et al., “High-resolution Electroencephalography and source localization in neonates,” Human Brain Mapping, vol. 29, no. 2, pp , Feb, 2008.