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Chaotic Algorithms of Analysis of Cardiovascular Systems and Artificial Intelligence

  • Ivan V. StepanyanEmail author
  • Alexey A. Mekler
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1126)

Abstract

Despite the intensive development of the dynamical systems theory and artificial intelligence, which is quite a powerful theoretical apparatus, an adequate description of chaotic processes at cardiovascular systems is a rather complicated problem. In this paper, the dynamical systems theory is applied to cardiovascular studies by processing the recorded signals with stochastic neural networks as well as dynamic chaos methods. The method of investigation is the reconstruction of dynamic systems attractor. Phase-temporal characteristics of human pulse waves were discussed, the new concept of the stochastic-graph of the pulse wave was shown. The attractor of heart pulse waves was reconstructed and its correlation dimension was estimated.

Keywords

Chaotic dynamics Quasi-neural network Clusterization Chaotic attractor Sphygmograph Pulse waves 

Notes

Acknowledgments

The authors wish to sincerely thank Igor Yavelov for devices used in this research.

References

  1. 1.
    Dumas, H.S.: The KAM Story – A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov–Arnold–Moser Theory. World Scientific Publishing (2014). ISBN 978-981-4556-58-3. Chapter 1: IntroductionGoogle Scholar
  2. 2.
    Kac, M., Logan, J., Montroll, E.W., Lebowitz, J.L. (eds.): Fluctuation Phenomena. North-Holland, Amsterdam (1976)Google Scholar
  3. 3.
    Nelson, E.: Quantum Fluctuations. Princeton University Press, Princeton (1985)zbMATHGoogle Scholar
  4. 4.
    Nichols, W.W.: Clinical measurement of arterial stiffness obtained from noninvasive pressure waveforms. Am. J. Hypertens. 18(1 Pt 2), 3S–10S (2005).  https://doi.org/10.1016/j.amjhyper.2004.10.009. PMID 15683725CrossRefGoogle Scholar
  5. 5.
    Khazaee, A.: Heart beat classification using particle swarm optimization. Int. J. Intell. Syst. Appl. (IJISA) 5(6), 25–33 (2013)CrossRefGoogle Scholar
  6. 6.
    Queyam, A.B., Pahuja, S.K., Singh, D.: Doppler ultrasound based non-invasive heart rate telemonitoring system for wellbeing assessment. Int. J. Intell. Syst. Appl. (IJISA) 10(12), 69–79 (2018)CrossRefGoogle Scholar
  7. 7.
    Yavelov, I.S, Rochagov, A.V.: “Pulse” pulse diagnosis and computer analyzer. Moscow-Izhevsk: Research Center “Regular and chaotic dynamics” (2006)Google Scholar
  8. 8.
    Kurama, V., Alla, S., Rohith, V.K.: Image semantic segmentation using deep learning. Int. J. Image Graph. Sig. Process. (IJIGSP) 10(12), 1–10 (2018).  https://doi.org/10.5815/ijigsp.2018.12.01CrossRefGoogle Scholar
  9. 9.
    Anthony, M., Wang, K., Hu, B.: Qualitative Theory of Dynamical Systems. Taylor & Francis (2001). ISBN 978-0-8247-0526-8. OCLC 45873628Google Scholar
  10. 10.
    Stepanyan, I.V., Yavelov, I.S., Saveliev, A.V., Do, O.K., Svirin, V.I., Pleshakov, K.V.: Phase-impulse analysis of the pulse wave and biopotentials of the human brain. Biomed. Radio Electron. 4, 81–83 (2015)Google Scholar
  11. 11.
    Sassi, R., Cerutti, S., Lombardi, F., Malik, M., Huikuri, H.V., Peng, C.K., Schmidt, G., Yamamoto, Y., Document Reviewers, Gorenek, B., Lip, G.Y., Grassi, G., Kudaiberdieva, G., Fisher, J.P., Zabel, M., Macfadyen, R.: Advances in heart rate variability signal analysis: joint position statement by the e-Cardiology and the ESC Working Group Europ Heart Rhythm Association co-endorsed by the Asia Pacific Heart Rhythm Society. Europace. http://dx.doi.org/10.1093/europace/euv015. First published online: 15 July 2015
  12. 12.
    Huikuri, H.V., Makikällio, T.H., Perkiomaki, J.: Measurement of heart rate variability by methods based on nonlinear dynamics. J. Electrocardiol. 36(Suppl), 95–99 (2003)CrossRefGoogle Scholar
  13. 13.
    Melillo, P., Bracale, M., Pecchia, L.: Nonlinear Heart Rate Variability features for real-life stress detection. Case study: students under stress due to university examination Biomed. Eng. Online 10, 96 (2011). Published online 7 Nov 2011.  https://doi.org/10.1186/1475-925x-10-96CrossRefGoogle Scholar
  14. 14.
    Wu, G.Q., Arzeno, N.M., Shen, L.L., et al.: Chaotic signatures of heart rate variability and its power spectrum in health, aging and heart failure. PLoS ONE 4(2), e4323 (2009).  https://doi.org/10.1371/journal.pone.0004323CrossRefGoogle Scholar
  15. 15.
    Krstacic, G., Krstacic, A., Smalcelj, A., Milicic, D., Jembrek-gostovic, M.: The, “Chaos Theory” and nonlinear dynamics in heart rate variability analysis: does it work in short-time series in patients with coronary heart disease? Ann. Noninvasive Electrocardiol. 12(2), 130–136 (2007)CrossRefGoogle Scholar
  16. 16.
    Korolj, A., Wu, H.T., Radisic, M.: A healthy dose of chaos: using fractal frameworks for engineering higher-fidelity biomedical systems. Biomaterials 219, 119363 (2019)CrossRefGoogle Scholar
  17. 17.
    Nasrolahzadeh, M., Mohammadpoory, Z., Haddadnia, J.: Analysis of heart rate signals during meditation using visibility graph complexity. Cogn. Neurodyn. 13(1), 45–52 (2019)CrossRefGoogle Scholar
  18. 18.
    Ziabari, M.T., Sahab, A.R., Fakhari, S.N.S.: Synchronization new 3D chaotic system using brain emotional learning based intelligent controller. Int. J. Inf. Technol. Comput. Sci. (IJITCS) 7(2), 80–87 (2015).  https://doi.org/10.5815/ijitcs.2015.02.10CrossRefGoogle Scholar
  19. 19.
    Çetinel, G., Çerkezi, L.L.: Robust chaotic digital image watermarking scheme based on RDWT and SVD. Int. J. Image Graph. Sig. Process. (IJIGSP) 8(8), 58–67 (2016).  https://doi.org/10.5815/ijigsp.2016.08.08CrossRefGoogle Scholar
  20. 20.
    Ziabari, M.T., Moarefianpur, A., Morvarid, M.: Fuzzy stability and synchronization of new 3D chaotic systems. Int. J. Inf. Eng. Electron. Bus. (IJIEEB) 6(5), 53–62 (2014).  https://doi.org/10.5815/ijieeb.2014.05.08CrossRefGoogle Scholar
  21. 21.
    Tyagi, T., Dubey, H.M., Pandit, M.: Multi-objective optimal dispatch solution of solar-wind-thermal system using improved stochastic fractal search algorithm. Int. J. Inf. Technol. Comput. Sci. (IJITCS) 8(11), 61–73 (2016).  https://doi.org/10.5815/ijitcs.2016.11.08CrossRefGoogle Scholar
  22. 22.
    Nakamori, S.: New RLS wiener smoother for colored observation noise in linear discrete-time stochastic systems. Int. J. Inf. Technol. Comput. Sci. (IJITCS) 6(1), 13–24 (2014).  https://doi.org/10.5815/ijitcs.2014.01.02CrossRefGoogle Scholar
  23. 23.
    Akimov, N.N., Buhnin, A.V., Milov, V.R., Koltsov, V.A.: Kuranov AAA method of verification models based technical systems mining processes. Inf. Measur. Oper. Syst. 11, 19–25 (2015)Google Scholar
  24. 24.
    Grassberger, P., Procaccia, I.: Characterization of strange attractors. Phys. Rev. Lett. 50, 346–349 (1983)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Goshvarpour, A., Goshvarpour, A.: Classification of electroencephalographic changes in meditation and rest: using correlation dimension and wavelet coefficients. Int. J. Inf. Technol. Comput. Sci. (IJITCS) 4(3), 24–30 (2012)CrossRefGoogle Scholar
  26. 26.
    Mekler, A.: Calculation of EEG correlation dimension: Large massifs of experimental data. Comput. Methods Programs Biomed. 92, 154–160 (2008)CrossRefGoogle Scholar
  27. 27.
    Tsonis, A.A., Elsner, J.B.: The weather attractor over short timescales. Nature 333, 545–547 (1988)CrossRefGoogle Scholar
  28. 28.
    Kennel, M.B., Brown, R., Abarbanel, H.D.I.: Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A 45, 3403 (1992)CrossRefGoogle Scholar
  29. 29.
    Hegger, R., Kantz, H., Schreiber, T.: Practical implementation of nonlinear time series methods: the TISEAN package. CHAOS 9, 413 (1999)CrossRefGoogle Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Mechanical Engineering Research Institute of the Russian Academy of SciencesMoscowRussian Federation
  2. 2.Saint Petersburg State Pediatric Medical UniversitySt. PetersburgRussian Federation

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