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Design of an optimum Poincaré plane for extracting meaningful samples from EEG signals

Australasian Physical & Engineering Sciences in Medicine volume 41, pages 13–20 (2018)Cite this article

Abstract

Biosignals are considered as important sources of data for diagnosing and detecting abnormalities, and modeling dynamics in the body. These signals are usually analyzed using features taken from time and frequency domain. In theory‚ these dynamics can also be analyzed utilizing Poincaré plane that intersects system’s trajectory. However‚ selecting an appropriate Poincaré plane is a crucial part of extracting best Poincaré samples. There is no unique way to choose a Poincaré plane‚ because it is highly dependent to the system dynamics. In this study, a new algorithm is introduced that automatically selects an optimum Poincaré plane able to transfer maximum information from EEG time series to a set of Poincaré samples. In this algorithm‚ EEG time series are first embedded; then a parametric Poincaré plane is designed and finally the parameters of the plane are optimized using genetic algorithm. The presented algorithm is tested on EEG signals and the optimum Poincaré plane is obtained with more than 99% data information transferred. Results are compared with some typical method of creating Poinare samples and showed that the transferred information using with this method is higher. The generated samples can be used for feature extraction and further analysis.

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References

  1. Strumillo P, Ruta J (2002) Poincaré Mapping for Detecting Abnormal Dynamics of Cardiac Repolarization. IEEE Eng Med Biol Mag Jan/Feb:62–65

    Article  Google Scholar 

  2. Williams G (1997) Chaos theory. Joseph Henry Press‚ Washington

    Google Scholar 

  3. Hilborn R (2001) Chaos and Nonlinear Dynamics‚ An introduction for scientists and engineers‚ 2nd edn. Oxford University Press‚ Oxford

    Google Scholar 

  4. Yalcınkaya T, Lai Y (1997) Phase characterization of chaos. Phys Rev Lett 79(20):3885

    Article  Google Scholar 

  5. Tucker W (2002) Computing accurate Poincaré maps. Physica 171:127–137

    Google Scholar 

  6. Letellier C, Gilmore R (2009) Poincaré sections for a new three-dimensional toroidal attractor. Physics A 42:015101

    Article  Google Scholar 

  7. Garfinkel‚ A, Spano‚ M, Ditto W, Weiss J (1992) Controlling cardiac chaos. Science New Series 257:1230–1235

    Google Scholar 

  8. Yang S (2004) Nonlinear signal classification using geometric statistical features in state space. Electron Lett 40(12):780–781

    Article  Google Scholar 

  9. Magauer A, Banerjee S (2000) Bifurcations and chaos in the tolerance B and PWM technique. IEEE Trans Circ Syst 47(2):254–259

    Article  Google Scholar 

  10. Perez Velazquez‚ J, Khosravani‚ H, Lozano A, Berj B‚ CarleN P, Wennberg R (1999) Type III intermittency in human partial epilepsy. Eur J Neurosci 11(7):2571–2576

    Article  Google Scholar 

  11. Jalali‚ S, Lasseter R, Dobson I (1994) Dynamic response of a thyristor controlled switched capacitor. IEEE Trans Power Deliv 9(3):1609–1615

    Article  Google Scholar 

  12. Kabiri‚ K, Henschel S, Martí J, Dommel H (2005) A discrete state-space model for ssr stabilizing controller design for TCSC compensated systems. IEEE Trans Power Deliv 20(1):466–474

    Article  Google Scholar 

  13. Timmer J, Haussler S, Lauk M, Lucking C (2000) Pathological tremors: deterministic chaos or nonlinear stochastic oscillators. Chaos 10(1):278–288

    Article  PubMed  Google Scholar 

  14. Bodruzzaman‚ M, Devgan S, Kari S (1992) Chaotic classification of electromyographic (emg) signals via correlation dimension measurement. In: IEEE Southeastcon‚ Birmingham

  15. Janson‚ N, Balanov‚ A, Anishchenko VS, McClintock P (2001) Phase synchronization between several interacting processes from univariate data. Phys Rev Lett 86(9):1749

    CAS  Article  PubMed  Google Scholar 

  16. Morimoto J, Nakanishi J, Endo G, Cheng‚ G, Atkeson C, Zeglin G (2005) Poincaré-map-base reinforcement learning for biped walking. In: 2005 IEEE international conference on robotics and automation (ICRA)

  17. Tsankov T, Nishtala A, Gilmore R (2004) Embeddings of a strange attractor into R^3. Phys Rev E Stat Nonlin Soft Matter Phys 69:056215

    Article  PubMed  Google Scholar 

  18. Shen T, Kuo X, Hsin Y (2009) A novel seizure prediction method based on probability density distribution of poincaré chaos. In: IEEE TENCON‚ pp 4244–4547

  19. EEG Database‚ Seizure Prediction Project, University of Freiburg

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Acknowledgements

We sincerely thank Freiburg University in Germany for providing seizure prediction EEG database. This research has been supported by Tehran University of Medical Sciences & Health Services‚ Grant No. 20174 and Research Center for Biomedical Technologies and Robotics (RCBTR).

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Affiliations

  1. Medical Physics & Biomedical Engineering Department, Tehran University of Medical Sciences (TUMS), Tehran, Iran

    Babak Sharif & Amir Homayoun Jafari

  2. Research Center for Biomedical Technologies and Robotics (RCBTR), Tehran, Iran

    Babak Sharif & Amir Homayoun Jafari

Authors
  1. Babak Sharif
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  2. Amir Homayoun Jafari
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Correspondence to Amir Homayoun Jafari.

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The authors declare that they have no conflict of interest.

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This study does not contain any study with human participants or animals performed by any of authors.

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Sharif, B., Jafari, A.H. Design of an optimum Poincaré plane for extracting meaningful samples from EEG signals. Australas Phys Eng Sci Med 41, 13–20 (2018). https://doi.org/10.1007/s13246-017-0599-2

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  • DOI: https://doi.org/10.1007/s13246-017-0599-2

Keyword

  • Poincaré plane
  • Dynamical systems
  • Biosignals
  • Feature extraction