Journal of Biological Physics

, Volume 36, Issue 2, pp 185–196 | Cite as

The dynamics of EEG entropy

  • Massimiliano IgnaccoloEmail author
  • Mirek Latka
  • Wojciech Jernajczyk
  • Paolo Grigolini
  • Bruce J. West
Original Paper


The scaling properties of human EEG have so far been analyzed predominantly in the framework of detrended fluctuation analysis (DFA). In particular, these studies suggested the existence of power-law correlations in EEG. In DFA, EEG time series are tacitly assumed to be made up of fluctuations, whose scaling behavior reflects neurophysiologically important information and polynomial trends. Even though these trends are physiologically irrelevant, they must be eliminated (detrended) to reliably estimate such measures as Hurst exponent or fractal dimension. Here, we employ the diffusion entropy method to study the scaling behavior of EEG. Unlike DFA, this method does not rely on the assumption of trends superposed on EEG fluctuations. We find that the growth of diffusion entropy of EEG increments of awake subjects with closed eyes is arrested only after approximately 0.5 s. We demonstrate that the salient features of diffusion entropy dynamics of EEG, such as the existence of short-term scaling, asymptotic saturation, and alpha wave modulation, may be faithfully reproduced using a dissipative, first-order, stochastic differential equation—an extension of the Langevin equation. The structure of such a model is utterly different from the “noise+trend” paradigm of DFA. Consequently, we argue that the existence of scaling properties for EEG dynamics is an open question that necessitates further studies.


EEG Entropy Statistical analysis 


  1. 1.
    Wiener, N.: Cybernetics. MIT, Cambridge (1948)Google Scholar
  2. 2.
    Watters, P.A., Matin, F.: A method for estimating long-range power law correlations from the electroencephalogram. Biol. Psychology 66, 79 (2004)CrossRefGoogle Scholar
  3. 3.
    Stead, M., Worrel, G.A., Litt, B.: Frequency and dependence of long range temporal correlations in human hippocampal energy fluctuations. Complexity 10(5), 35 (2005)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Yuan, J.W., Zheng, B., Pan, C.P., Wu, Y.Z., Trimper, S.: Dynamic scaling behavior of human brain electroencephalogram. Physica A 364, 315 (2006)CrossRefADSGoogle Scholar
  5. 5.
    Cai, S., Jiang, Z., Zhou, R., Shou, P., Yang, H., Wang, B.: Scale invariance of human electroencephalogram signals in sleep. Phys. Rev. E 76, 061903 (2007)CrossRefADSGoogle Scholar
  6. 6.
    Peng, C.K., Buldyrev, S.V., Havlin, S., Simons, M., Stanley, H.E., Golberger, A.L.: Mosaic organization of DNA nucleotides. Phys. Rev. E 49, 1685 (1994)CrossRefADSGoogle Scholar
  7. 7.
    West, B.J.: Where Medicine Went Wrong. World Scienitic, Singapore (2006)Google Scholar
  8. 8.
    West, B.J., Novaes, M.N., Kavcic, V.: In: Iannaccone, P.M., Khokha, M. (eds.) Fractal Geometry in Biological Systems. CRC, New York (1995)Google Scholar
  9. 9.
    Hwa, R.C., Ferree, T.C.: Scaling properties of fluctuations in the human electroencephalogram. Phys. Rev. E 66, 021901 (2002)CrossRefADSGoogle Scholar
  10. 10.
    Wiener, N.: Time Series. MIT, Cambridge (1949)zbMATHGoogle Scholar
  11. 11.
    Fox, M.D., Raichle, M.E.: Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging. Nat. Rev. Neurosci. 9, 700 (2007)CrossRefGoogle Scholar
  12. 12.
    Wiener, N.: Nonlinear Problems in Random Theory. MIT and Wiley, New York (1958)zbMATHGoogle Scholar
  13. 13.
    Linkenkaer-Hansen, K., Nikouline, V.V., Palva, J.M., Llmoniemi, R.J.: Long-range temporal correlations and scaling behavior in human brain oscillations. J. Neurosci. 21, 1370 (2001)Google Scholar
  14. 14.
    Inouye, T., Shinosaki, K., Sakamoto, H., Toi, S., Ukai, S., Iyama, A., Katzuda, Y., Hirano, M.: Quantification of EEG irregularity by the use of the entropy of the power spectrum. Electroencephalogr. Clin. Neurophysiol. 79, 204 (1991)CrossRefGoogle Scholar
  15. 15.
    Schlögl, A., Kemp, B., Penzel, T., Kunz, S., Himanen, S., Värri, A., Dorffner, G., Pfurtscheller, G.: Quality control of polysomnographic sleep data by histogram and entropy analysis. Clin. Neurophysiol. 110, 2165 (1999)CrossRefGoogle Scholar
  16. 16.
    Patel, P., Khosla, D., Al-Dayeh, L., Singh, M.: Distributed source imaging of alpha activity using a maximum entropy principle. Clin. Neurophysiol. 110, 538 (1999)CrossRefGoogle Scholar
  17. 17.
    Başar, E., Schürmann, M., Başar-Eroglu, C., Karakaş, S.: Alpha oscillations in brain functioning: an integrative theory. Int. J. Psychophysiol. 26, 5 (1997)CrossRefGoogle Scholar
  18. 18.
    Rosso, O.A., Blanco, S., Yordanova, J., Kolev, V., Figliola, A., Schürmann, M., Başar, E.: Wavelet entropy: a new tool for analysis of short duration brain electrical signals. J. Neurosci. Methods 105, 65 (2001)CrossRefGoogle Scholar
  19. 19.
    Rosso, O.A.: Entropy changes in brain function. Int. J. Psychophysiol. 64, 75 (2007)CrossRefGoogle Scholar
  20. 20.
    Scafetta, N., Hamilton, P., Grigolini, P.: The thermodynamics of social processes: the teen birt phenomenon. Fractals 9, 193 (2001)CrossRefGoogle Scholar
  21. 21.
    Grigolini, P., Palatella, L., Raffaelli, G.: Asymmetric anomalous diffusion: an efficient way to detect memory in time series. Fractals 9, 439 (2001)CrossRefGoogle Scholar
  22. 22.
    Ignaccolo, M., Allegrini, P., Grigolini, P., Hamilton, P., West, B.J.: Scaling in non-stationary time series. (II). Teen birth phenomenon. Physica A 336, 623 (2004)CrossRefADSGoogle Scholar
  23. 23.
    Scafetta, N., West, B.J.: Solar flare intermittency and the earth’s temperature anomalies. Phys. Rev. Lett. 90, 248701 (2003)CrossRefADSGoogle Scholar
  24. 24.
    Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423; Ibid 623–656 (1948)zbMATHMathSciNetGoogle Scholar
  25. 25.
    Allegrini, P., Benci, V., Grigolini, P., Hamilton, P., Ignaccolo, M., Menconi, G., Palatella, L., Raffaelli, G., Scafetta, N., Virgilio, M., Yang, J.: Compression and diffusion: a joint approach to detech complexity. Chaos Solitons & Fractals 15, 517, (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Ignaccolo, M., Latka, M., Jernajczyk, W., Grigolini, P., West, B.J.: Dynamics of EEG entropy: beyond signal plus noise. Phys. Rev. E. arXiv:0902.1113 (2009)
  27. 27.
    Robinson, P.A.: Interpretation of scaling properties of electroencephalographic fluctuations via spectral analysis and underlying physiology. Phys. Rev. E 67, 032902 (2003)CrossRefADSGoogle Scholar
  28. 28.
    Mallat, S.: A Wavelet Tour of Signal Processing, 2nd edn. Academic, San Diego (1999)zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Massimiliano Ignaccolo
    • 1
    Email author
  • Mirek Latka
    • 2
  • Wojciech Jernajczyk
    • 3
  • Paolo Grigolini
    • 4
  • Bruce J. West
    • 5
  1. 1.Physics DepartmentDuke UniversityDurhamUSA
  2. 2.Institute of Biomedical EngineeringWroclaw University of TechnologyWroclawPoland
  3. 3.Department of Clinical NeurophysiologyInstitute of Psychiatry and NeurologyWarsawPoland
  4. 4.Center for Nonlinear ScienceUniversity of North TexasDentonUSA
  5. 5.Mathematics and Information Science DirectorateArmy Research OfficeDurhamUSA

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