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Fractal Analysis of Electroencephalographic Time Series (EEG Signals)

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The Fractal Geometry of the Brain

Part of the book series: Springer Series in Computational Neuroscience ((NEUROSCI))

Abstract

Nonlinear methods are better suited for analysis of EEG signals than so-called linear methods like fast Fourier transform (FFT). In this chapter, we illustrate the use of the Higuchi’s fractal dimension method. We present several examples of the usefulness of this method in application to sleep-EEG analysis, revealing influence of electromagnetic fields, monitoring anesthesia, and assessing bright light therapy (BLT) and electroconvulsive therapy (ECT). We conclude that Higuchi’s fractal dimension method is very useful in the analysis of EEG signals.

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References

  1. Acardo A, et al. Use of the fractal dimension for the analysis of electroencephalographic time series. Biol Cybern. 1997;77:339–50.

    Article  Google Scholar 

  2. Ahmadi B, Amirfattahi R. Comparison of correlation dimension and fractal dimension in estimating BIS index. Wirel Sens Netw. 2010;2:67–73.

    Google Scholar 

  3. Beck A. Die Bestimmung der Localisation des Gehirn- und Rückenmarks-functionen Vermittelst der Electrischen Erscheinungen [The determination of the localisation of the brain and spinal cord functions by way of electrical appearances]. Zentralblatt Physiol. 1890;4:473–6.

    Google Scholar 

  4. Berger H. Ueber das Elektroenkephalogramm des Menschen. Arch Psychiatr Nervenkr. 1929;87:527–70.

    Article  Google Scholar 

  5. Caton R. The electric currents of the brain. Br Med J. 1875;2:278.

    Google Scholar 

  6. Ciszewski J, et al. Application of chaos theory for EEG-signal analysis in patients with seasonal affective disorder. Med Biol Eng Comput. 1999;37:359–60.

    Article  Google Scholar 

  7. Coenen A, Zayachkivska O. Adolf Beck: a pioneer in electroencephalography in between Richard Caton and Hans Berger. Adv Cogn Psychol. 2013;9:216–21.

    Article  PubMed  PubMed Central  Google Scholar 

  8. Di Ieva A, et al. Fractals in the neurosciences, part II: clinical applications and future perspectives. Neuroscientist. 2015;21:30–43.

    Article  PubMed  Google Scholar 

  9. Georgiev S, et al. EEG fractal dimension measurement before and after human auditory stimulation. Biogeosciences. 2009;12:70–81.

    Google Scholar 

  10. Haas LF. Neurological stamp. Hans Berger (1873–1941), Richard Caton (1842–1926), and electroencephalography. J Neurol Neurosurg Psychiatry. 2003;74:9.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  11. Hameroff S, Penrose R. Consciousness in the universe: a review of the ‘Orch OR’ theory. Phys Life Rev. 2013.

    Google Scholar 

  12. Higuchi T. Approach to an irregular time series on the basis of the fractal theory. Phys D. 1988;31:277–83.

    Article  Google Scholar 

  13. Higuchi T. Relationship between the fractal dimension and the power law index for a time series: a numerical investigation. Phys D. 1990;46:254–64.

    Article  Google Scholar 

  14. Klonowski W, et al. Nonlinear dynamics from conformons to human brain. Technol Health Care. 2001;9:88–9.

    Google Scholar 

  15. Klonowski W, et al. Nonlinear dynamics algorithms for time series analysis: implementation in EEG-data acquisition/analysis system. In: Klonowski W, editor. Attractor, signals, and synergetics, pp. 553–560, proceedings of the 1st European Interdisciplinary School on Nonlinear Dynamics for System and Signal Analysis EUROATTRACTOR2000. Lengerich: Pabst Science Publishers; 2002.

    Google Scholar 

  16. Klonowski W, et al. Complexity of EEG-signal in time domain: possible biomedical application. In: Boccaletti S et al., editors. Experimental Chaos, AIP conference proceedings, vol. 622. New York: Melville; 2002. p. 155–60.

    Google Scholar 

  17. Klonowski W. Chaotic dynamics applied to signal complexity in phase space and in time domain. Chaos Solitons Fractals. 2002;14:1379–87.

    Article  Google Scholar 

  18. Klonowski W et al. Sleep-EEG analysis using Higuchi’s fractal dimension. Proceedings of the International Symposium on Nonlinear Theory and its Applications NOLTA 2005, Bruges, Belgium, 18–21 Oct, pp. 222–225. http://www.ieice.org/proceedings/NOLTA2005/HTMLS/paper/5025.pdf.

  19. Klonowski W, et al. Monitoring the depth of anaesthesia using fractal complexity method. In: Novak MN, editor. Complexus mundi. Emergent patterns in nature. New Jersey: World Scientific; 2006. p. 333–42.

    Chapter  Google Scholar 

  20. Klonowski W. From conformons to human brains: an informal overview of nonlinear dynamics and its applications in biomedicine. Nonlinear Biomed Phys. 2007;1:5. http://www.nonlinearbiomedphys.com/content/pdf/1753-4631-1-5.pdf.

    Article  PubMed  PubMed Central  Google Scholar 

  21. Klonowski W. Nonlinear EEG-signal analysis reveals hypersensitivity to electromagnetic fields generated by cellular phones. IFMBE Proc. 2007;14:1056–8.

    Article  Google Scholar 

  22. Klonowski W. Neuroscience and nonlinear dynamics. IFMBE Proc. 2009;22:1236–40.

    Article  Google Scholar 

  23. Klonowski W. Everything you wanted to ask about EEG but were afraid to get the right answer. Nonlinear Biomed Phys. 2009;3:2. http://www.nonlinearbiomedphys.com/content/pdf/1753-4631-3-2.pdf.

    Article  PubMed  PubMed Central  Google Scholar 

  24. Klonowski W. Informational interactions and the brain: nonlinear dynamics reveals individual (hyper)sensitivity to EMF. Far East J Dyn Sys. 2010;13:129–37.

    Google Scholar 

  25. Klonowski W, et al. Complexity measures of brain electrophysiological activity: in consciousness, under anesthesia, during epileptic seizure, and in physiological sleep. J Psychophysiol. 2010;24:131–5.

    Article  Google Scholar 

  26. Losa GA. The fractal geometry of life. Riv Biol. 2009;102:29–59.

    PubMed  Google Scholar 

  27. Lutzenberger W, et al. Dimensional analysis of the human EEG and intelligence. Neurosci Lett. 1992;143(1–2):10–4.

    Google Scholar 

  28. Lutzenberger W, et al. Fractal dimension of electroencephalographic time series and underlying brain processes. Biol Cybern. 1995;73:477–82.

    Article  CAS  PubMed  Google Scholar 

  29. Niedermeyer E, Da Silva FL, Editors. Electroencephalography. Basic principles, clinical application, and related fields. 5th ed. Philadelphia: Lippincott, Williams & Wilkins (Wolter Kluwer Co); 2005.

    Google Scholar 

  30. Penzel T, et al. Reliability of visual evaluation of sleep stages according to Rechtschaffen and Kales from eight polysomnographs by nine sleep centres [in German]. Somnology. 2003;7:49–58.

    Article  Google Scholar 

  31. Phothisonothai M, et al. A comparison of actual and artifactual features based on fractal analyses: resting-state MEG data. Adv Intell Sys Comput. 2013;212:1257–65.

    Article  Google Scholar 

  32. Pritchard WS, Duke DW. Dimensional analysis of no-task human EEG using the Grassberger-Procaccia method. Psychophysiology. 1992;29:182–92.

    Google Scholar 

  33. Rechtschaffen A, Kales A. A manual of standardized terminology, techniques, and scoring for sleep stages in human subjects. Washington, DC: GPO; 1968.

    Google Scholar 

  34. Schwartz BE. The advantages of digital over analog recording techniques. Electroencephalogr Clin Neurophysiol. 1998;106:1113–7.

    Google Scholar 

  35. Stam CJ. Nonlinear dynamical analysis of EEG and MEG: review of an emerging field. Clin Neurophysiol. 2005;116:2266–301.

    Article  CAS  PubMed  Google Scholar 

  36. Wahlund B, et al. EEG data, fractal dimension and multivariate statistics. J Comput Sci Eng. 2010;3:10–6.

    Google Scholar 

  37. Watt RC, Hameroff SR. Phase space electroencephalography (EEG): a new mode of intraoperative EEG analysis. Int J Clin Monit Comput. 1988;5:3–13.

    Article  CAS  PubMed  Google Scholar 

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Acknowledgments

W. Klonowski acknowledges the support of Nalecz Institute of Biocybernetics and Biomedical Engineering of the Polish Academy of Sciences, Warsaw, through statutory activities.

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Authors and Affiliations

  1. Nalecz Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Warsaw, Poland

    Wlodzimierz Klonowski PhD, DSc

Authors
  1. Wlodzimierz Klonowski PhD, DSc
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Correspondence to Wlodzimierz Klonowski PhD, DSc .

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Editors and Affiliations

  1. Department of Surgery Division of Neurosurgery, University of Toronto St. Michael's Hospital, Toronto, Ontario, Canada

    Antonio Di Ieva

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Klonowski, W. (2016). Fractal Analysis of Electroencephalographic Time Series (EEG Signals). In: Di Ieva, A. (eds) The Fractal Geometry of the Brain. Springer Series in Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3995-4_25

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