Analysis of Multichannel EEG Recordings Based on Generalized Phase Synchronization and Cointegrated VAR

  • Alla R. KammerdinerEmail author
  • Panos M. PardalosEmail author
Part of the Springer Optimization and Its Applications book series (SOIA, volume 38)


Synchronization is shown to be a characteristic feature of electroencephalogram data collected from patients affected by neurological diseases, such as epilepsy. Phase synchronization has been applied successfully to investigate synchrony in neurophysiological signal. The classical approach to phase synchronization is inherently bivariate. We propose a novel multivariate approach to phase synchronization, by extending the bivariate case via cointegrated vector autoregression, and then apply the new concept to absence epilepsy data.


Electroencephalogram Phase synchronization Cointegrated vector autoregressive processes 


  1. 1.
    Bressler, S.L., Coppola, R., Nakamura, R. Episodic multiregional cortical coherence at multiple frequencies during visual task performance. Nature 366, 153–156 (1993)CrossRefGoogle Scholar
  2. 2.
    Bullock, T.H., McClune, M.C. Lateral coherence of the electrocorticogram: A new measure of brain synchrony. Electroencephalogr Clin Neurophysiol 73, 479–498 (1989)CrossRefGoogle Scholar
  3. 3.
    Carroll, T.L., Pecora, L.M. Cascading synchronized chaotic systems. Physica D 67, 126 (1993)zbMATHCrossRefGoogle Scholar
  4. 4.
    Carter, G.C. Coherence and time delay estimation. Proc IEEE 75, 236–255 (1987)CrossRefGoogle Scholar
  5. 5.
    Cheung, Y.W., Lai, K.S. Lag order and critical values of the augmented dickey-fuller test. J Bus Econ Stat 13(3), 277–280 (1995)Google Scholar
  6. 6.
    Damasio, A.R. Synchronous activation in multiple cortical regions: A mechanism for recall. Semin Neurosci 2, 287–296 (1990)Google Scholar
  7. 7.
    Dickey, D.A., Fuller, W.A. Distribution of the estimators for autoregressive time series with a unit root. J Am Stat Assoc 74, 427–431 (1979)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Fabiny, L., Colet, P., Roy, R. Coherence and phase dynamics of spatially coupled solid-state lasers. Phys Rev A 47, 4287 (1993)CrossRefGoogle Scholar
  9. 9.
    Freeman, W.J. Spatial properties of an EEG event in the olfactory bulb and cortex. Electroencephalogr Clin Neurophysiol 44, 586–605 (1978)CrossRefGoogle Scholar
  10. 10.
    Fuller, W.A. Introduction to Statistical Time Series, 2nd edn. John Wiley, New York (1996)Google Scholar
  11. 11.
    Gabor, D. Theory of communication. Proc IEEE Lond 93, 429 (1946)Google Scholar
  12. 12.
    Huygens, C. Horoloquium Oscilatorium. Parisiis, Paris (1673)Google Scholar
  13. 13.
    Johansen, S., Juselius, K. Maximum likelihood estimation and inference on cointegration – with applications to the demand for money. Oxford Bulletin of Economics and Statistics 52, 169–210 (1990)CrossRefGoogle Scholar
  14. 14.
    Kreuz, T. Measuring synchronization in model systems and electroencephalographic time series from epilepsy patients. Ph.D. thesis. Dissertation NIC Series, Vol. 21 (2001)Google Scholar
  15. 15.
    Lachaux, J.P., Rodriguez, E., Martinerie, J., Adam, C., Hasboun, D., Varela, F.J. Gamma-band activity in human intracortical recordings triggered by cognitive tasks. Eur J Neurosci 12, 2608–2622 (2000)CrossRefGoogle Scholar
  16. 16.
    Lachaux, J.P., Rodriguez, E., Martinerie, J., Varela, F.J. Measuring phase synchrony in brain signals. Hum Brain Mapp 8, 194 (1999)CrossRefGoogle Scholar
  17. 17.
    Lütkepohl, H. Introduction to Multiple Time Series Analysis. Springer-Verlag, Berlin, Heidelberg (1991)Google Scholar
  18. 18.
    MacKinnon, J.G. Critical values for cointegration tests. In: Long-Run Economic Relationships: Readings in Cointegration, pp. 266–276. Oxford University Press, New York (1991)Google Scholar
  19. 19.
    MacKinnon, J.G. Approximate asymptotic distribution functions for unit-root and cointegration tests. J Bus Econ Stat 12, 167–176 (1994)MathSciNetGoogle Scholar
  20. 20.
    Mormann, F., Lehnertz, K., David, P., Elger, C.E. Mean phase coherence as a measure for phase synchronization and its application to the EEG of epileptic patients. Physica D 144, 358–369 (2000)zbMATHCrossRefGoogle Scholar
  21. 21.
    Murray, M.P. A drunk and her dog: An illustration of cointegration and error correction. Am Stat 48(1), 37–39 (1994)Google Scholar
  22. 22.
    Parlitz, U., Junge, L., Lauterborn, W., Kocarev, L. Experimental observation of phase synchronization. Phys Rev E 54, 2115 (1996)CrossRefGoogle Scholar
  23. 23.
    Patten, J.B. Neurological Differential Diagnosis, 2nd edn. Springer-Verlag, New York (1996)CrossRefGoogle Scholar
  24. 24.
    Peterman, D.W., Ye, M., Wigen, P.E. High frequency synchronization of chaos. Phys Rev Lett 74, 1740 (1995)CrossRefGoogle Scholar
  25. 25.
    Phillips, P.C.B. Time series regression with a unit root. Econometrica 55, 277–301 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Phillips, P.C.B., Ouliaris, S. Asymptotic properties of residual based tests for cointegration. Econometrica 58, 165–193 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Pikovsky, A.S. Phase synchronization of chaotic oscillations by a periodic external field. Sov J Commun Technol Electron 30, 85 (1985)Google Scholar
  28. 28.
    Pikovsky, A.S., Rosenblum, M.G., Kurths, J. Synchronization. A universal concept in nonlinear sciences. Cambridge University Press, Cambridge (2001)CrossRefGoogle Scholar
  29. 29.
    van der Pol, B., van der Mark, J. The heartbeat considered as a relaxation oscillation, and an electrical model of the heart. Phil Mag 6, 763 (1928)Google Scholar
  30. 30.
    Pyragas, K. Continuous control of chaos by self-controlling feedback. Phys Lett A 170, 421 (1992)CrossRefGoogle Scholar
  31. 31.
    Quyen, M.L.V., Foucher, J., Lachaux, J.P., Rodriguez, E., Lutz, A., Martinerie, J., Varela, F.J. Comparison of Hilbert transform and wavelet methods for the analysis of neuronal synchrony. J Neurosci Methods 111, 83–98 (2001)CrossRefGoogle Scholar
  32. 32.
    Rodriguez, E., George, N., Lachaux, J.P., Martinerie, J., Varela, F.J. Perceptions shadow: Long-distance synchronization in the human brain. Nature 397, 340–343 (1999)Google Scholar
  33. 33.
    Roelfsema, P.R., Engel, A.K., König, P., Singer, W. Visuomotor integration is associated with zero time-lag synchronization among cortical areas. Nature 385, 157–161 (1997)CrossRefGoogle Scholar
  34. 34.
    Rosa, E., Jr. Pardo, W.B., Ticos, C.M., Walkenstein, J.A., Monti, M. Phase synchronization of chaos in a plasma discharge tube. Int J Bifurc Chaos 10, 2551 (2000)zbMATHGoogle Scholar
  35. 35.
    Rosenblum, M.G., Pikovsky, A.S., Schäfer, C., Tass, P., Kurths, J. Phase synchronization: From theory to data analysis. In: Handbook of Biological Physics, Neuro-informatics, Vol. 4. Elsevier Science, Amsterdam (1999)Google Scholar
  36. 36.
    Roy, R., Thornburg, K.S. Experimental synchronization on chaotic lasers. Phys Rev Lett 72, 2009 (1994)CrossRefGoogle Scholar
  37. 37.
    Rulkov, N.F., Tsimring, L.S., Abarbanel, H.D.I. Tracking unstable orbits in chaos using dissipative feedback control. Phys Rev E 50, 314 (1994)CrossRefGoogle Scholar
  38. 38.
    Singer, W., Gray, C.M. Visual feature integration and the temporal correlation hypothesis. Annu Rev Neurosci 18, 555–586 (1995)CrossRefGoogle Scholar
  39. 39.
    Tang, D.Y., Dykstra, R., Hamilton, M.W., Heckenberg, N.R. Experimental evidence of frequency entrainment between coupled chaotic oscillations. Phys Rev E 57(3), 3649 (1998)CrossRefGoogle Scholar
  40. 40.
    Tass, P., Rosenblum, M.G., Weule, J., Kurths, J., Pikovsky, A., Volkmann, J., et al. Detection of n:m phase locking from noisy data: Application to magnetoencephalography. Phys Rev Lett 81, 3291–3294 (1998)CrossRefGoogle Scholar
  41. 41.
    Tononi, G., Edelman, G. Consciousness and complexity. Science 282, 1846–1851 (1998)CrossRefGoogle Scholar
  42. 42.
    Varela, F.J. Resonant cell assemblies: A new approach to cognitive functions and neuronal synchrony. Biol Res 28, 81–95 (1995)Google Scholar
  43. 43.
    Varela, F.J., Lachaux, J.P., Rodriguez, E., Martinerie, J. The brain web: Phase synchronization and large-scale integration. Nat Rev Neurosci 2, 229–239 (2001)CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Industrial and Systems, EngineeringUniversity of FloridaGainesvilleUSA
  2. 2.Department of Industrial and System Engineering, Center for Applied OptimizationUniversity of FloridaGainesvilleUSA

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