Skip to main content
SpringerLink
Log in

Characterization of Epileptic EEG Time Series (I): Gabor Transform and Nonlinear Dynamics Methods

  • Chapter
Wavelet Theory and Harmonic Analysis in Applied Sciences

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

It has been well over a century since it was discovered that the mammalian brain generates a small but measurable electrical signal. The electroencephalogram ( EEG ) of small animals was measured by Caton in 1875, and in man by Berger in 1925. It had been thought by the mathematician N. Wiener, among others, that generalized harmonic analysis would provide the mathematical tools necessary to penetrate the mysterious relations between the EEG time series and the functioning of the brain. The progress along this path has been slow however, and the understanding and interpretation of EEG’s remain quite elusive.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Handbook of Electroencephalography and Clinical Neurophysiol-ogy, Vol. I: Methods of Analysis of Brain Electrical and Magnetic Signals. ( 1987 ) Gevins A., Rémond A. ( eds.), Elsevier, Amsterdam.

    Google Scholar 

  2. Handbook of Electroencephalography and Clinical Neurophysiology, Vol. II: Clinical Applications of Computer Analysis of EEG and Other Neurophysiological Signals. ( 1988 ) Lopes da Silva F. H., Storm van Leeuwen W., Rémond A. (eds.), Elsevier, Amsterdam.

    Google Scholar 

  3. Current Practice of Clinical Electroencephalography, 2nd. ed.(1990 ) Daly D. D., Pedley T. A. ( eds. ), Reven Press Ltd., New York.

    Google Scholar 

  4. Başar E. Dynamics of Sensory and Cognitive Processing by the Brain. Springer Series in Brain Dynamics, Vol. I. Springer-Verlag, Berlin, 1988.

    Google Scholar 

  5. Başar E. and Bullock T. H. Brain Dynamics. Springer Series in Brain Dynamics, Vol. II. Springer-Verlag, Berlin, 1989.

    Google Scholar 

  6. Başar E. Chaos in Brain Function. Springer-Verlag, Berlin, 1990.

    Google Scholar 

  7. West B. J. Fractal Physiology and Chaos in Medicine. Nonlinear Phenomena in Life Science, Vol 1.World Scientific, Singapore, 1990.

    Google Scholar 

  8. Gevins A. S. Overview of Computer Analysis. In Handbook of Electroencephalography and Clinical Neurophysiology, Vol. I: Methods of Analysis of Brain Electrical and Magnetic Signals.( Ref. [1] ), pp. 31–83, 1987.

    Google Scholar 

  9. Lopes da Silva F. a) EEG analysis: theory and practice, b) Computer-assisted EEG diagnosis: pattern recognition in EEG analysis, feature extraction and classification. In Electroen-cephalography: Basic Principles, Clinical Applications and Related Fields. Niedermeyer E. and Lopes da Silva F. ( eds. ), Urban & Schwarzenberg, Baltimore, (a) pp. 685–711, (b) pp. 713-732, 1982.

    Google Scholar 

  10. Gotman J. In Handbook of Electroencephalography and Clinical Neurophysiology, Vol. II: Clinical Applications of Computer Analysis of EEG and Other Neurophysiological Signals. (Ref. [2] ), pp. 546–597, 1988.

    Google Scholar 

  11. Dumermuth G. and Molinari L. Spectral Analysis of EEG Background Activity. In Handbook of Electroencephalography and Clinical Neurophysiology, Vol. I: Methods of Analysis of Brain Electrical and Magnetic Signals. ( Ref. [1] ), pp. 85–130, 1987.

    Google Scholar 

  12. Gotman J. The use of computers in analysis and display of EEG. In Current Practice of Clinical Electroencephalography. ( Ref. [3] ), pp. 51–83, 1990.

    Google Scholar 

  13. Mars N. J. I. and Lopes da Silva F. H. EEG analysis methods based on information theory. In Handbook of Electroencephalography and Clinical Neurophysiology, Vol. I: Methods of Analysis of Brain Electrical and Magnetic Signals.( Ref. [1] ), pp. 297–307, 1987.

    Google Scholar 

  14. Pijn J. P. M. Quantitative Evaluation of EEG Signals in Epilepsy: Nonlinear Associations, Time Delays and Nonlinear Dynamics. Ph.D. Thesis, Universiteit van Amsterdam, 1990.

    Google Scholar 

  15. Beldhis H. J. A., Suzuki T., Pijn J. P. M., Teisman M. and Lopes da Silva F. H. Propagation of epileptiform activity during development of amygdala kindling in rats: linear and non-linear association between ipsi-and contralateral sites. Eur. J. of Neu-roscience 5, 944–954, 1993.

    Article  Google Scholar 

  16. Pijn J. P. M. and Lopes da Silva F. H. Propagation of electrical activity: nonlinear associations and time delays between EEG signals. In Basic Mechanism of the EEG. Zschocke S., Speckmann E. J. ( eds. ), Bishäuser, Boston, 1993.

    Google Scholar 

  17. Babloyantz A. Evidence of chaotic dynamics of brain activity during the sleep cycle. In Dimensions and Entropies in Chaotic Systems. Meyer-Kress G. ( eds. ), Springer-Verlag, Berlin, pp. 241–245, 1986.

    Chapter  Google Scholar 

  18. Meyer-Kress G. and Layne S. C. Dimensionality of human electroencephalogram. In Perspectives in Biological Dynamics and Theoretical Medicine. Koslow S. H., Mandel A. J., Shlesinger M. F. ( eds. ), Ann. N. Y. Acad. Sci. 504, 1987.

    Google Scholar 

  19. Layne S. C., Meyer-Kress G. and Holzfuss J. Problems associated with dimensional analysis of electroencephalogram data. In Dimensions and Entropies in Chaotic Systems. Meyer-Kress G. ( eds. ), Springer-Verlag, Berlin, pp. 246–256, 1986.

    Chapter  Google Scholar 

  20. Frank G. W., Lookman T., Nerenberg N. A. H., Essex C., Lemieux J. and Blume W. Chaotic time series analysis of epileptic seizures. Physica D 46, 427–438, 1990.

    Article  MATH  Google Scholar 

  21. Gallez D. and Babloyantz A. Lyapunov exponents for nonuni-form attractors. Phys. Lett. 161, 247–254, 1991.

    Article  MathSciNet  Google Scholar 

  22. Gallez D. and Babloyantz A. Predictability of human EEG: a dynamical approach. Biol Cybern. 64, 381–391, 1991.

    Article  Google Scholar 

  23. Pijn J. P. N., Van Neerven J., Noest A. and Lopes da Silva F. Chaos or noise in EEG signals; dependence on state and brain site. Electroencephalog. Clin. Neurophysiol. 79, 371–381, 1991.

    Article  Google Scholar 

  24. Iasemidis L. D., Sackellares J. C, Zaveri H. P. and Williams W. J. Phase space topography and the Lyapunov exponent of electrocorticograms in partial seizures. Brain Topography 2, 187–201, 1990.

    Article  Google Scholar 

  25. Lehnetz K. and Elger C. E. Spatio-temporal dynamics of the primary epileptogenic area in temporal lobe epilepsy characterized by neuronal complexity loss. Elec. and Clinical Neurophys. 95, 108–117, 1995.

    Article  Google Scholar 

  26. Blanco S., Costa A., Jacovkis P. and Rosso O. A. Characterization of the dynamical evolution of an epileptic seizure. Proceedings of Primer Coloquio Latinoamericano de Matematica Aplicada a la Industria y la Medicina. ( in press ), 1996.

    Google Scholar 

  27. Blanco S., Kochen S., Quian Quiroga R., Rosso O. A. and Sal-gado P. Characterization of background electrical activity of brain structures by nonlinear dynamical parameters. ( to be published ), 1996

    Google Scholar 

  28. Gabor D. Theory of communication. J. Inst. Elec. Eng. 93, 429–459, 1946.

    Google Scholar 

  29. Blanco S., Quian Quiroga R., Rosso O. A. and Kochen S. Time-frequency analysis of electroencephalogram series. Phys. Rev. E 51 2624–2631, 1995.

    Article  Google Scholar 

  30. Blanco S., D’Attellis C, Isaacson S., Rosso O. A. and Sirne R. O. Time-frequency analysis of electroencephalogram series (II): Gabor and Wavelet Transform. Phys. Rev. E.Physical Rev. E 54, No. 5, 1996.

    Google Scholar 

  31. Blanco S., Kochen S., Rosso 0. A. and Salgado P. Application of the time-frequency analysis to seizure EEG activity in candidates for epileptic surgery. IEEE Eng. Med. Biol. Mag. ( in press ), 1996.

    Google Scholar 

  32. Blanco S., Kochen S., Rosso O. A. and Salgado P. Characterization of epileptic seizure using Gabor Transform. Proceedings of Primer Coloquio Latinoamericano de Matematica Aplicada a la Industria y la Medicina. ( in press ), 1996.

    Google Scholar 

  33. Blanco S., García H., Quian Quiroga R., Romanelli L. and Rosso O. A. Stationarity of the EEG series. IEEE Eng. Med. Biol. Mag. 14, 395–399, 1995.

    Article  Google Scholar 

  34. Caputo J. G. Practical remarks on the estimation of dimension and entropy from experimental data. In Measures of Complexity and Chaos. Abraham N. B., Albano A. M., Passamante A. and Rapp P. ( eds. ) NATO, Series B208, pp. 99–110, 1989.

    Google Scholar 

  35. Gasser T. General characteristic of the EEG as a signal. In EEG Informatics: a Didactic Review of Methods and Applications of EEG Data Processing. Remond A. ( eds. ), Elsevir, New York, pp. 37–55, 1977.

    Google Scholar 

  36. McEwen J. A. and Anderson G. B. Modeling the stationarity and gaussianity of spontaneous electroencephalographic activity. IEEE Trans. Biomed. Engng. 22, 361–369, 1975.

    Article  Google Scholar 

  37. Sugimoto H., Ishii N. and Suzumura N. Stationarity and normality test for biomédical data. Comput. Program. Biomed. 7, 293–304, 1977.

    Article  Google Scholar 

  38. Jenkins G. M. and Watts D. Spectral Analysis and Its Applications. Holden-Day, San Francisco, 1968.

    Google Scholar 

  39. Eckmann J. P. and Ruelle D. Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57, 617–656, 1985.

    Article  MathSciNet  Google Scholar 

  40. Abarbanel H. D. I., Brown R., Sidorowich J. J. and Tsimring L. S. The analysis of observed chaotic data in physical systems Rev. Mod. Phys. 65, 1331–1392, 1993.

    Article  MathSciNet  Google Scholar 

  41. Peitgen J. 0., Jürgens H. and Soupe D. Chaos and Fractals: New Frontiers of Science. Spring-Verlag, New York, 1992.

    Google Scholar 

  42. Packard N. H., Crutchfield J. P., Farmer J. D. and Shaw R. S. Geometry from a time series, Phys. Rev. Lett. 45, 712–716, 1980.

    Article  Google Scholar 

  43. Mañé R. On the dimension of compact invariant set of certain nonlinear maps. In Dynamical Systems and Turbulence, Warwick 1980. Lecture Notes in Mathematics 898, Springer-Verlag, pp. 230–242, 1981.

    Google Scholar 

  44. Takens F. Detecting strange attractors in turbulence. In Dynamical Systems and Turbulence, Warwick 1980. Lecture Notes in Mathematics 898, Springer-Verlag, pp. 366–381, 1981.

    Google Scholar 

  45. Rosenstein M. T., Collins J. J. and De Luca C. J. Reconstruction expansion as a geometry-based framework for choosing proper delay times. Physica D 73, 82–98, 1994.

    Article  MathSciNet  Google Scholar 

  46. Kennel M. B., Brawn R. and Abarbanel H. D. I. Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A 45, 3403–3411, 1992.

    Article  Google Scholar 

  47. Rosenstein M. T., Collins J. J. and De Luca C. J. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D 65, 117–134, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  48. Grassberger P. and Procaccia P. Characterization of strange attractors. Phys. Rev. Lett. 50, 346–349, 1983.

    Article  MathSciNet  Google Scholar 

  49. Grassberger P. and Procaccia P. Measuring the stragness of strange attractors. Phyica D 9, 189–208, 1983.

    Article  MathSciNet  MATH  Google Scholar 

  50. Eckmann J. P. and Ruelle D. Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems. Physica D 56, 185–187, 1992.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors
  1. Susana Blanco
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Silvia Kochen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rodrigo Quian Quiroga
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Luis Riquelme
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Osvaldo A. Rosso
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Pablo Salgado
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Buenos Aires, Paseo Colón 850, 1063, Buenos Aires, Argentina

    C. E. D’Attellis

  2. Instituto de Cálculo, Ciudad Universitaria — Pabellón II, 1428, Buenos Aires, Argentina

    E. M. Fernández-Berdaguer

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media New York

About this chapter

Cite this chapter

Blanco, S., Kochen, S., Quian Quiroga, R., Riquelme, L., Rosso, O.A., Salgado, P. (1997). Characterization of Epileptic EEG Time Series (I): Gabor Transform and Nonlinear Dynamics Methods. In: D’Attellis, C.E., Fernández-Berdaguer, E.M. (eds) Wavelet Theory and Harmonic Analysis in Applied Sciences. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-2010-7_9

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-2010-7_9

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7379-0

  • Online ISBN: 978-1-4612-2010-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation