Skip to main content
SpringerLink
Log in

Biochaos in cardiac rhythms

  • Review
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

Biological rhythm is an essential characteristic of natural systems that can present regular or irregular dynamics, which can be associated with normal or pathological functioning. In this regard, nonlinear dynamics perspective is able to connect biorhythm with functioning characteristics. This paper investigates the heart dynamics by considering a mathematical model that is built from three coupled nonlinear oscillators. The main strategy is to investigate natural pacemaker behavior, establishing its influence on the electrical activity of the heart represented by electrocardiograms (ECGs). Different kinds of pacemaker behaviors are treated, dedicating special attention to chaotic rhythms.

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
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. M.A. Savi, J. Braz. Soc. Mech. Sci. Eng. 27, 157–169 (2005)

    Article  Google Scholar 

  2. R. Pool, Science 243, 604–607 (1989)

    Article  ADS  Google Scholar 

  3. A.L. Goldberger, D.R. Rigney, B.J. West, Sci. Am. 262, 42–49 (1990)

    Article  Google Scholar 

  4. J.E. Skinner, A.L. Goldberger, G. Mayer-Kress, R.E. Ideker, Nat. Biotechnol. 8, 1018–1024 (1990)

    Article  Google Scholar 

  5. J.N. Herbschleb, R.M. Heethaar, I. Tweel, F.L. Meijler, Comput. Cardiol. 365–368 (1980)

  6. P.S. Chen, A. Garfinkel, J.N. Weiss, H.S. Karagueuzian, Chaos: Interdiscip. J. Nonlinear Sci. 8, 127–136 (1998)

    Article  Google Scholar 

  7. A.C. Skanes, R. Mandapati, O. Berenfeld, J.M. Davidenko, J. Jalife, Circulation 98, 1236–1248 (1998)

    Article  Google Scholar 

  8. L. Glass, M.C. Mackey, From Clocks to Chaos: The Rhythms of Life (Princeton University Press, Princeton, 1988)

    Book  MATH  Google Scholar 

  9. P.E. Rapp, Biologist 40, 89–94 (1993)

    Google Scholar 

  10. S.R.S.M. Gois, M.A. Savi, Chaos Sol. Fract. 41, 2553–2565 (2009)

    Article  ADS  Google Scholar 

  11. L. Glass, Chaos 19, 028501 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  12. D. Dubin, Interpretacao Rapida Do ECG (EPUB, Rio de Janeiro, 1996)

    Google Scholar 

  13. M. Malik, A.J. Camm, Heart Rate Variability (Futura, New York, 1995)

    Google Scholar 

  14. A.L. Goldberger, E. Goldberger, Clinical Electrocardiography (Mosby, 1977)

  15. D.T. Kaplan, R.J. Cohen, Circul. Res. 67, 886–892 (1990)

    Article  Google Scholar 

  16. J. Pan, W.J. Tompkins, IEEE. Trans. Biomed. Eng. 3, 220–236 (1985)

    Google Scholar 

  17. G.B. Moody, R.G. Mark, A. Zoccola, S. Mantero, Comput. Cardiol. 12, 113–116 (1985)

    Google Scholar 

  18. H. Kantz, T. Schreiber, Nonlinear Time Series Analysis, Ser. 7. (Cambridge Nonlinear Science, USA 2002)

  19. F.X. Witkowski, L.J. Leon, P.A. Penkoske, W.R. Giles, M.L. Spano, W.L. Ditto, A.T. Winfree, Nature 392, 78–82 (1998)

    Article  ADS  Google Scholar 

  20. R.K.A. Radhakrishna, D.N. Dutt, V.K. Yeragani, Auton. Neurosci. Basic Clin. 83, 148–158 (2000)

    Article  Google Scholar 

  21. P.V. Bayly, B.H. Kenknight, J.M. Rogers, E.E. Johnson, R.E. Ideker, W.M. Smith, Chaos 8, 103–115 (1998)

    Article  ADS  Google Scholar 

  22. J.Q. Zhang, A.V. Holden, O. Monfredi, M.R. Boyett, H. Zhang, Chaos 19, 028509 (2009)

    Article  ADS  Google Scholar 

  23. H.D.I. Abarbanel, R. Brown, J.B. Kadtke, Phys. Rev. A 41, 1782–1807 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  24. J.D. Farmer, J.J. Sidorowich, Phys. Rev. Lett 59, 845–848 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  25. G. Sugihara, R. May, Nature 344, 734–741 (1990)

    Article  ADS  Google Scholar 

  26. M.E.D. Gomes, A.V.P. Souza, H.N. Guimaraes, L.A. Aguirre, Chaos 10, 398–410 (2000)

    Article  ADS  Google Scholar 

  27. J.H. Lefebvre, D.A. Goodings, M.V. Kamath, E.L. Fallen, Chaos 3, 267–276 (1993)

    Article  ADS  Google Scholar 

  28. R.B. Govindan, K. Narayanan, M.S. Gopinathan, Chaos 8, 495–502 (1998)

    Article  ADS  Google Scholar 

  29. M. Barahona, C.S. Poon, Nature 381, 215–217 (1996)

    Article  ADS  Google Scholar 

  30. C.S. Poon, M. Barahona, Proc. Natl. Acad. Sci. USA 98, 7107–7112 (2001)

    Article  ADS  Google Scholar 

  31. G.Q. Wu, N.M. Arzeno, L.L. Shen, D.K. Tang, D.A. Zheng, N.Q. Zhao, D.L. Eckberg, C.S. Poon, PLoS One 4, e423 (2009)

    Google Scholar 

  32. A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Physica D 16, 285–317 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  33. C.K. Peng, S. Havlin, H.E. Stanley, A.L. Goldberger, Chaos 5, 82–87 (1995)

    Article  ADS  Google Scholar 

  34. J. Alvarez-Ramirez, E. Rodriguez, J.C. Echeverría, Chaos 19, 028502 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  35. M.D. Costa, C.K. Peng, A.L. Goldberger, Cardiovasc. Eng. 8, 88–93 (2009)

    Article  Google Scholar 

  36. B. van Der Pol, J. van Der Mark, Philos. Mag. 6, 763–775 (1928)

    Article  Google Scholar 

  37. G.K. Moe, W.C. Rheinboldt, J.A. Abildskov, Am. Heart J. 67, 200–220 (1964)

    Article  Google Scholar 

  38. J. Jalife, O. Berenfeld, A. Skanes, R. Mandapati, J. Cardiovasc. Electrophysiol. 9 (1998)

  39. V.I. Krinsky, Pharmacol. Thera. Part B General Syst. Pharmacol. 3, 539–555 (1978)

    Google Scholar 

  40. F. Fenton, A. Karma, Chaos 8, 20–47 (1998)

    Article  ADS  Google Scholar 

  41. F.H. Fenton, E.M. Cherry, H.M. Hastings, S.J. Evans, Chaos Interdiscip. J. Nonlinear Sci. 12, 852–892 (2002)

    Article  Google Scholar 

  42. J. Jalife, Ann. Rev. Physiol. 62, 25–50 (2000)

    Article  Google Scholar 

  43. M.P. Nash, A.V. Panfilov, Prog. Biophys. Mol. Biol. 85, 501–522 (2004)

    Article  Google Scholar 

  44. K. Grudzinski, J.J. Zebrowski, Physica A 336, 153–162 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  45. A.M. Dos Santos, S.R. Lopes, R.R.L. Viana, Physica A 338, 335–355 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  46. A. Cheffer, M.A. Savi, T.L. Pereira, A.S. de Paula, Appl. Math. Model. 96, 152–176 (2021)

    Article  MathSciNet  Google Scholar 

  47. E. Ryzhii, M. Ryzhii, International Conference on Biomedical Informatics and Technology (Springer, Berlin, Heidelberg, 2013), pp. 67–75

    Google Scholar 

  48. E. Ryzhii, M. Ryzhii, Comput. Methods Prog. Biomed. 117, 40–49 (2014)

    Article  Google Scholar 

  49. G.C. Cardarilli, L. Di Nunzio, R. Fazzolari, M. Re, F. Silvestri, Appl. Sci. 9, 3653 (2019)

    Article  Google Scholar 

  50. A. Garfinkel, M.L. Spano, W.L. Ditto, J.N. Weiss, Science 257, 1230–1235 (1992)

    Article  ADS  Google Scholar 

  51. A. Garfinkel, J.N. Weiss, W.L. Ditto, M.L. Spano, Trends Cardiovasc. Med. 5, 76–80 (1995)

    Article  Google Scholar 

  52. E. Ott, C. Grebogi, J.A. Yorke, Phys. Rev. Lett. 64, 1196–1199 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  53. B.B. Ferreira, A.S. De Paula, M.A. Savi, Chaos Sol. Fract. 44, 587–599 (2011)

    Article  ADS  Google Scholar 

  54. B.B. Ferreira, M.A. Savi, A.S. De Paula, Physica Scripta 89, 105203 (2014)

    Article  ADS  Google Scholar 

  55. F. Lounis, A. Boukabou, A. Soukkou, Chaos Sol. Fract. 132, 109581 (2020)

    Article  Google Scholar 

  56. M.A. Quiroz-Juárez, O. Jiménez-Ramírez, R. Vázquez-Medina, V. Breña-Medina, J.L. Aragón, R.A. Barrio, Sci. Rep. 9, 1–10 (2019)

    Article  Google Scholar 

  57. A. Khan, U. Nigar, Int. J. Appl. Comput. Math. 6, 1–22 (2020)

    Article  Google Scholar 

  58. F.E. Yates, L.A. Benton, Math. Comput. Model. 19, 161–170 (1994)

    Article  Google Scholar 

  59. A. Cheffer, M.A. Savi, Biosystems 196, 104177 (2020)

    Article  Google Scholar 

  60. A. Cheffer, T.G. Ritto, M.A. Savi, Int. J. Non Linear Mech. 129, 103653 (2021)

    Article  ADS  Google Scholar 

  61. B. Mensour, A. Longtin, Physica D 113, 1–25 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  62. W.J. Cunningham, Proc. Natl. Acad. Sci. 40, 708–713 (1954)

    Article  ADS  Google Scholar 

  63. P. Brugada, J. Brugada, L. Mont, J. Smeets, E.W. Andries, Circulation 83, 1649–1659 (1991)

    Article  Google Scholar 

  64. P.R.B. Barbosa, J. BarbosaFilho, A.D.S. Bonfim, E.C. Barbosa, S.H.C. Boghossian, R.L. Ribeiro, P. Ginefra, Revista da SOCERJ 17, 227–242 (2004)

    Google Scholar 

Download references

Acknowledgements

The authors would like to acknowledge the support of the Brazilian Research Agencies CNPq, CAPES and FAPERJ.

Author information

Authors and Affiliations

  1. Center for Nonlinear Mechanics, COPPE - Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, P.O. Box 68.503, Rio de Janeiro, RJ, Brazil

    Augusto Cheffer & Marcelo A. Savi

Authors
  1. Augusto Cheffer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marcelo A. Savi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marcelo A. Savi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cheffer, A., Savi, M.A. Biochaos in cardiac rhythms. Eur. Phys. J. Spec. Top. 231, 833–845 (2022). https://doi.org/10.1140/epjs/s11734-021-00314-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjs/s11734-021-00314-7

Search

Navigation