Skip to main content
SpringerLink
Log in

Extended detrended fluctuation analysis: effects of nonstationarity and application to sleep data

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

Extended detrended fluctuation analysis (EDFA) is a recently proposed modification of the conventional method, which provides a characterization of complex time series with varying nonstationarity. It evaluates two scaling exponents for a better quantification of inhomogeneous datasets. Here, we study the effect of different types of nonstationarity on these exponents, including trend, switching between processes with distinct statistical properties and energy variability. Using the simulated signals, we show that the first two types of nonstationarity have the strongest effect for anticorrelated processes and complicate their diagnosis. Nonstationarity in energy is more crucial for time series with positive long-range correlations. Next, we apply EDFA to rat experiments to study the activation of brain lymphatic drainage during sleep. Our analysis reveals significant distinctions in EDFA’s measures between the background electrical activity of the brain and the stage of sleep. The latter offers an indirect way to identify and characterize the nightly activation of the drainage and clearance of brain tissue.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. C.-K. Peng, S.V. Buldyrev, S. Havlin, M. Simons, H.E. Stanley, A.L. Goldberger, Phys. Rev. E 49, 1685 (1994)

    Article  ADS  Google Scholar 

  2. C.-K. Peng, S. Havlin, H.E. Stanley, A.L. Goldberger, Chaos 5, 82 (1995)

    Article  ADS  Google Scholar 

  3. K. Hu, PCh. Ivanov, Z. Chen, P. Carpena, H.E. Stanley, Phys. Rev. E 64, 011114 (2001)

    Article  ADS  Google Scholar 

  4. Z. Chen, PCh. Ivanov, K. Hu, H.E. Stanley, Phys. Rev. E 65, 041107 (2002)

    Article  ADS  Google Scholar 

  5. R.M. Bryce, K.B. Sprague, Sci. Rep. 2, 315 (2012)

    Article  ADS  Google Scholar 

  6. Y.H. Shao, G.F. Gu, Z.Q. Jiang, W.X. Zhou, D. Sornette, Sci. Rep. 2, 835 (2012)

    Article  Google Scholar 

  7. K. Ivanova, M. Ausloos, Physica A 274, 349 (1999)

    Article  ADS  Google Scholar 

  8. C. Heneghan, G. McDarby, Phys. Rev. E 62, 6103 (2000)

    Article  ADS  Google Scholar 

  9. P. Talkner, R.O. Weber, Phys. Rev. E 62, 150 (2000)

    Article  ADS  Google Scholar 

  10. J.W. Kantelhardt, E. Koscielny-Bunde, H.H.A. Rego, S. Havlin, A. Bunde, Physica A 295, 441 (2001)

    Article  ADS  Google Scholar 

  11. Q.D.Y. Ma, R.P. Bartsch, P. Bernaola-Galván, M. Yoneyama, PCh. Ivanov, Phys. Rev. E 81, 031101 (2010)

    Article  ADS  Google Scholar 

  12. O.N. Pavlova, A.S. Abdurashitov, M.V. Ulanova, N.A. Shushunova, A.N. Pavlov, Commun. Nonlinear Sci. Numer. Simul. 66, 31 (2019)

    Article  ADS  Google Scholar 

  13. N.S. Frolov, V.V. Grubov, V.A. Maksimenko, A. Lüttjohann, V.V. Makarov, A.N. Pavlov, E. Sitnikova, A.N. Pisarchik, J. Kurths, A.E. Hramov, Sci. Rep. 9, 7243 (2019)

    Article  ADS  Google Scholar 

  14. O.N. Pavlova, A.N. Pavlov, Physica A 536, 22586 (2019)

    Article  ADS  Google Scholar 

  15. A.N. Pavlov, A.S. Abdurashitov, A.A. Koronovskii Jr., O.N. Pavlova, O.V. Semyachkina-Glushkovskaya, J. Kurths, Commun. Nonlinear Sci. Numer. Simul. 85, 105232 (2020)

    Article  MathSciNet  Google Scholar 

  16. L. Xie, H. Kang, Q. Xu, M.J. Chen, Y. Liao, M. Thiyagarajan, J. O'Donnell, D.J. Christensen, C. Nicholson, J.J. Iliff, T. Takano, R. Deane, M. Nedergaard, Science 342, 373 (2013)

  17. S. Da Mesquita, Z. Fu, J. Kipnis, Neuron 100, 375 (2018)

    Article  Google Scholar 

  18. N.E. Fultz, G. Bonmassar, K. Setsompop, R.A. Stickgold, B.R. Rosen, J.R. Polimeni, L.D. Lewis, Science 366, 628 (2019)

    Article  ADS  Google Scholar 

  19. O. Semyachkina-Glushkovskaya, A. Abdurashitov, A. Dubrovsky, D. Bragin, O. Bragina, N. Shushunova, G. Maslyakova, N. Navolokin, A. Bucharskaya, V. Tuchin, J. Kurths, A. Shirokov, J. Biomed. Opt. 22, 121719 (2017)

    Article  ADS  Google Scholar 

  20. O. Semyachkina-Glushkovskaya, D. Postnov, J. Kurths, Int. J. Mol. Sci. 19, 3818 (2018)

    Article  Google Scholar 

  21. O. Semyachkina-Glushkovskaya, V. Chehonin, E. Borisova, I. Fedosov, A. Namykin, A. Abdurashitov, A. Shirokov, B. Khlebtsov, Y. Lyubun, N. Navolokin, M. Ulanova, N. Shushunova, A. Khorovodov, I. Agranovich, A. Bodrova, M. Sagatova, A.E. Shareef, E. Saranceva, T. Iskra, M. Dvoryatkina, E. Zhinchenko, O. Sindeeva, V. Tuchin, J. Kurths, J. Biophoton. 11, e201700287 (2018)

    Article  Google Scholar 

  22. N.P. Castellanos, V.A. Makarov, J. Neurosci. Methods 158, 300 (2006)

    Article  Google Scholar 

  23. A.N. Pavlov, A.I. Dubrovsky, A.A. Koronovskii Jr., O.N. Pavlova, O.V. Semyachkina-Glushkovskaya, J. Kurths, Chaos 30, 073138 (2020)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

Theoretical studies with simulated datasets were supported by the Russian Science Foundation (Agreement 19-12-00037). Analysis of experimental data in Sect. 3.4 was supported by the RF Government Grant No. 075-15-2019-1885.

Author information

Authors and Affiliations

  1. Saratov State University, Astrakhanskaya 83, Saratov, Russia, 410012

    A. N. Pavlov, O. N. Pavlova, O. V. Semyachkina-Glushkovskaya & J. Kurths

  2. Regional Scientific and Educational Mathematical Center “Mathematics of Future Technologies”, 23 Gagarina Avenue, Nizhny Novgorod, Russia, 603950

    A. N. Pavlov

  3. Potsdam Institute for Climate Impact Research, Telegraphenberg A 31, 14473, Potsdam, Germany

    J. Kurths

  4. Institute of Physics, Humboldt University Berlin, 12489, Berlin, Germany

    J. Kurths

Authors
  1. A. N. Pavlov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. N. Pavlova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. O. V. Semyachkina-Glushkovskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. Kurths
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. N. Pavlov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pavlov, A.N., Pavlova, O.N., Semyachkina-Glushkovskaya, O.V. et al. Extended detrended fluctuation analysis: effects of nonstationarity and application to sleep data. Eur. Phys. J. Plus 136, 10 (2021). https://doi.org/10.1140/epjp/s13360-020-00980-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-020-00980-x

Search

Navigation