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Application of the nonlinear methods in pneumocardiogram signals

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Abstract

In this work, the pneumocardiogram signals of nine rats were analysed by scale index, Boltzmann Gibbs entropy and maximum Lyapunov exponents. The scale index method, based on wavelet transform, was proposed for determining the degree of aperiodicity and chaos. It means that the scale index parameter is close to zero when the signal is periodic and has a value between zero and one when the signal is aperiodic. A new entropy calculation method by normalized inner scalogram was suggested very recently. In this work, we also used this method for the first time in an empirical data. We compared the both methods with maximum Lyapunov exponents and observed that using together the scale index and the entropy calculation method by normalized inner scalogram increases the reliability of the pneumocardiogram signal analysis. Thus, the analysis of the pneumocardiogram signals by those methods enables to compare periodical and/or nonlinear aspects for further understanding of dynamics of cardiorespiratory system.

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References

  1. Strogatz, S.G.: Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry and Engineering. Addison-Wesley, Singapore (1994)

  2. Benitez, R., Bolos, V.J., Ramirez, M.E.: A wavelet-based tool for studying non-periodicity. Comput. Math. Appl. 60, 634–641 (2010)

    Article  MathSciNet  Google Scholar 

  3. Behnia, S., Ziaei, J., Ghiassi, M., Akhsani, A.: Nonlinear dynamic approach of heartbeats based on the Grudziński Zebrowski’s model. Chin. J. Phys. 53, 7 (2015)

  4. Piccirillo, V., Baltazar, J.M., Tusset, A., Bernardini, D., Rega, G.: Characterizing the nonlinear behavior of a pseudoelastic oscillator via the wavelet transform. J. Mech. Eng. Sci. 230(1), 120–132 (2016)

    Article  Google Scholar 

  5. Yılmaz, N., Canbaz, B., Akıllı, M., Önem, C.: Study of the stability of the fermionic instanton solutions by the scale index method. Phys. Lett. A 382(32), 2118–2121 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  6. Akıllı, M., Yılmaz, N.: Study of weak periodic signals in the EEG signals and their relationship with postsynaptic potentials. IEEE Trans. Neural Syst. Rehabil. Eng. 99(1), (2018). https://doi.org/10.1109/TNSRE.2018.2867515

  7. Akıllı, M., Yılmaz, N., Akdeniz, K.G.: Study of the q-Gaussian distribution with the scale index and calculating entropy by normalized inner scalogram. Phys. Lett. A, PLA-D-18-01463R2 (2019)

  8. Ivanov, P.C., et al.: Scaling behaviour of heartbeat intervals obtained by wavelet-based time-series analysis. Nature 383, 323–327 (1996)

  9. Ivanov, P.C., et al.: Scaling and universality in heart rate variability distributions. Phys. A 249, 587–593 (1998)

    Article  Google Scholar 

  10. Ivanov, P.C., et al.: Wavelets in medicine and physiology. In: van den Berg, J.C. (ed.) Wavelets in Physics. Cambridge University Press, Cambridge (1998)

    Google Scholar 

  11. Ivanov, P.C., et al.: From 1/f noise to multifractal cascades in heartbeat dynamics. Chaos 11(3), 641–652 (2001)

    Article  ADS  Google Scholar 

  12. Amaral, L.A.N., et al.: Behavioral-independent features of complex heartbeat dynamics. Phys. Rev. Lett. 86(26), 6026–6029 (2001)

    Article  ADS  Google Scholar 

  13. Zeren, T., Özbek, M., Ekerbiçer, N., Yalçın, G.C., Akdeniz, K.G.: Sensitively recorded breathing signals of rats and their nonlinear dynamics. J. Biochem. Biophys. Methods 70, 573–577 (2007)

    Article  Google Scholar 

  14. Zeren, T., Özbek, M., Kutlu, N., Akıllı, M.: Significance of using a nonlinear analysis technique, the Lyapunov exponent, on the understanding of the dynamics of the cardiorespiratory system in rats. Turkish J. Med. Sci. 46(1), 159–165 (2016)

    Article  Google Scholar 

  15. Mallat, S.A.: Wavelet Tour of Signal Processing. Academic Press, London (1999)

  16. Bolós, V.J., Benitez, R., Ferrer, R.: Quantifying non-periodicity of non-stationary time series through wavelets. arXiv, 1912.07299 (2019)

  17. Xiong, W., et al.: Entropy measures, entropy estimators, and their performance in quantifying complex dynamics: effects of artifacts, nonstationarity, and long-range correlations. Phys. Rev. E 95(6), 062114 (2017)

    Article  ADS  Google Scholar 

  18. Eckmann, J.P., Kamphorst, S.O., Ruelle, D., Ciliberto, S.: Liapunov exponents from time series. Phys. Rev. A 34, 4971–4979 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  19. Wolf, A., et al.: Determining Lyapunov exponents from a time series. Physica D 16, 285–317 (1985)

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

  21. Smith, N.T., Reitan, J.A.: The Pneumocardiogram: a potential monitor for the operating room. Anesth. Analg. 49(5), 781–790 (1970)

    Google Scholar 

  22. Reitan, J.A., Lim, A.: Automated measurement and frequency analysis of the pneumocardiogram. Anesth. Analg. 57(6), 647–652 (1978)

    Google Scholar 

  23. Kreit, J.W., Sciurba, F.C.: The accuracy of pneumotachograph measurements during mechanical ventilation. Am. J. Respir. Crit. Care Med. 154(4), 913–917 (1996)

  24. Heckman, J.L., Stewart, G.H., Tremblay, G., Lynch, P.R.: Relationship between stroke volume and pneumocardiogram. J. Appl. Physiol. 52(6), 1672–1677 (1982)

    Article  Google Scholar 

  25. Bijaoui, E., Bocannier, P.F., Bates, J.H.: Mechanical output impedance of the lung determined from cardiogenic oscillations. J. Appl. Physiol. 91, 859–865 (2001)

  26. Leondes, C.T.: Biomechanical Systems: Techniques and Applications, Volume II: Cardiovascular Techniques, 1st edn, (2000)

  27. Yoon, H., et al.: Sleep-dependent directional coupling of cardiorespiratory system in patients with obstructive sleep apnea. IEEE Trans. Biomed. Eng. 65(12), 2847–2854 (2018)

  28. Schulz, S., et al.: Cardiovascular and cardiorespiratory coupling analyses: a review. Philos. Trans. A Math. Phys. Eng. Sci. 2013(371), (1997)

  29. Ivanov, P., Nunes Amaral, L.A., Goldberger, A.L., Stanley, H.E.: Stochastic feedback and the regulation of biological rhythms. Europhys. Lett. 43, 363–368 (1998)

    Article  ADS  Google Scholar 

  30. Natarajan, K., Acharya, U.R., Alias, F., Tiboleng, T., Puthusserypady, S.K.: Nonlinear analysis of EEG signals at different mental states. Biomed. Eng. Online 3, 7 (2004)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Koç University, Istanbul, Turkey

    Nazmi Yılmaz

  2. Nonlinear Science Working Group, Istanbul, Turkey

    Mahmut Akıllı & K. Gediz Akdeniz

  3. Department of Physiology, Manisa Celal Bayar University Medical School, Manisa, Turkey

    Mustafa Özbek

  4. Department of Biophysics, Manisa Celal Bayar University Medical School, Manisa, Turkey

    Tamer Zeren

Authors
  1. Nazmi Yılmaz
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  2. Mahmut Akıllı
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  3. Mustafa Özbek
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  4. Tamer Zeren
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  5. K. Gediz Akdeniz
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Correspondence to Nazmi Yılmaz.

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The experimental process related with this work was approved by the regional animal ethics committee of Celal Bayar University (Turkey). The rats were treated in accordance with the Guidelines for the Care and Use of Laboratory Animals for Research designed by the National Association of Medical Research.

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Yılmaz, N., Akıllı, M., Özbek, M. et al. Application of the nonlinear methods in pneumocardiogram signals. J Biol Phys 46, 209–222 (2020). https://doi.org/10.1007/s10867-020-09549-2

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