IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v41y2009i5p2553-2565.html
   My bibliography  Save this article

An analysis of heart rhythm dynamics using a three-coupled oscillator model

Author

Listed:
  • Gois, Sandra R.F.S.M.
  • Savi, Marcelo A.

Abstract

Rhythmic phenomena represent one of the most striking manifestations of the dynamic behavior in biological systems. Understanding the mechanisms responsible for biological rhythms is crucial for the comprehension of the dynamics of life. Natural rhythms could be either regular or irregular over time and space. Each kind of dynamical behavior may be related to both normal and pathological physiological functioning. The cardiac conducting system can be treated as a network of self-excitatory elements and, since these elements exhibit oscillatory behavior, they can be modeled as nonlinear oscillators. This paper proposes a mathematical model to describe heart rhythms considering three modified Van der Pol oscillators connected with time delay couplings. Therefore, the heart dynamics is represented by a system of differential difference equations. Numerical simulations are carried out presenting qualitative agreement with the general heart rhythm behavior. Normal and pathological rhythms represented by the ECG signals are reproduced. Pathological rhythms are generated by either the coupling alterations that represents communications aspects in the heart electric system or forcing excitation representing external pacemaker excitation.

Suggested Citation

  • Gois, Sandra R.F.S.M. & Savi, Marcelo A., 2009. "An analysis of heart rhythm dynamics using a three-coupled oscillator model," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2553-2565.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:5:p:2553-2565
    DOI: 10.1016/j.chaos.2008.09.040
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077908004517
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2008.09.040?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Boucekkine, Raouf & Licandro, Omar & Paul, Christopher, 1997. "Differential-difference equations in economics: On the numerical solution of vintage capital growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 347-362.
    2. Francis X. Witkowski & L. Joshua Leon & Patricia A. Penkoske & Wayne R. Giles & Mark L. Spano & William L. Ditto & Arthur T. Winfree, 1998. "Spatiotemporal evolution of ventricular fibrillation," Nature, Nature, vol. 392(6671), pages 78-82, March.
    3. de Paula, Aline Souza & Savi, Marcelo Amorim, 2009. "Controlling chaos in a nonlinear pendulum using an extended time-delayed feedback control method," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2981-2988.
    4. dos Santos, Angela M. & Lopes, Sergio R. & Viana, R.L.Ricardo L., 2004. "Rhythm synchronization and chaotic modulation of coupled Van der Pol oscillators in a model for the heartbeat," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(3), pages 335-355.
    5. de Paula, Aline Souza & Savi, Marcelo Amorim, 2009. "A multiparameter chaos control method based on OGY approach," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1376-1390.
    6. Leon Glass, 2001. "Synchronization and rhythmic processes in physiology," Nature, Nature, vol. 410(6825), pages 277-284, March.
    7. Grudziński, Krzysztof & Żebrowski, Jan J, 2004. "Modeling cardiac pacemakers with relaxation oscillators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 153-162.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lounis, Fatima & Boukabou, Abdelkrim & Soukkou, Ammar, 2020. "Implementing high-order chaos control scheme for cardiac conduction model with pathological rhythms," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    2. Templos-Hernández, Diana J. & Quezada-Téllez, Luis A. & González-Hernández, Brian M. & Rojas-Vite, Gerardo & Pineda-Sánchez, José E. & Fernández-Anaya, Guillermo & Rodriguez-Torres, Erika E., 2021. "A fractional-order approach to cardiac rhythm analysis," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    3. Isao Shoji & Masahiro Nozawa, 2020. "A geometric analysis of nonlinear dynamics and its application to financial time series," Papers 2012.11825, arXiv.org.
    4. Shoji, Isao & Nozawa, Masahiro, 2022. "Geometric analysis of nonlinear dynamics in application to financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    5. Ferreira, Bianca Borem & de Paula, Aline Souza & Savi, Marcelo Amorim, 2011. "Chaos control applied to heart rhythm dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 587-599.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ferreira, Bianca Borem & de Paula, Aline Souza & Savi, Marcelo Amorim, 2011. "Chaos control applied to heart rhythm dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 587-599.
    2. Acosta, A. & Gallo, R. & García, P. & Peluffo-Ordóñez, D., 2023. "Positive invariant regions for a modified Van Der Pol equation modeling heart action," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    3. Lounis, Fatima & Boukabou, Abdelkrim & Soukkou, Ammar, 2020. "Implementing high-order chaos control scheme for cardiac conduction model with pathological rhythms," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    4. Ulrich Brandt-Pollmann & Ralph Winkler & Sebastian Sager & Ulf Moslener & Johannes Schlöder, 2008. "Numerical Solution of Optimal Control Problems with Constant Control Delays," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 181-206, March.
    5. Ricardo Bioni Liberalquino & Maurizio Monge & Stefano Galatolo & Luigi Marangio, 2018. "Chaotic Itinerancy in Random Dynamical System Related to Associative Memory Models," Mathematics, MDPI, vol. 6(3), pages 1-10, March.
    6. YATSENKO, Yuri & BOUCEKKINE, Raouf & HRITONENKO, Natali, 2008. "Estimating the dynamics of R&D-based growth models," LIDAM Discussion Papers CORE 2008052, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Robert G. Sacco, 2019. "The Predictability of Synchronicity Experience: Results from a Survey of Jungian Analysts," International Journal of Psychological Studies, Canadian Center of Science and Education, vol. 11(3), pages 1-46, September.
    8. David de la Croix & Omar Licandro, 2013. "The Child is Father Of the Man: Implications for the Demographic Transition," Economic Journal, Royal Economic Society, vol. 123(567), pages 236-261, March.
    9. Alexey V. Rusakov & Dmitry A. Tikhonov & Nailya I. Nurieva & Alexander B. Medvinsky, 2021. "Emergence of Self-Organized Dynamical Domains in a Ring of Coupled Population Oscillators," Mathematics, MDPI, vol. 9(6), pages 1-13, March.
    10. Jiang, Wei & Chen, Zhong & Hu, Ning & Song, Haiyang & Yang, Zhaohong, 2020. "Multi-scale orthogonal basis method for nonlinear fractional equations with fractional integral boundary value conditions," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    11. Boucekkine, Raouf & Germain, Marc & Licandro, Omar, 1997. "Replacement Echoes in the Vintage Capital Growth Model," Journal of Economic Theory, Elsevier, vol. 74(2), pages 333-348, June.
    12. Meo, Marcos M. & Iaconis, Francisco R. & Del Punta, Jessica A. & Delrieux, Claudio A. & Gasaneo, Gustavo, 2024. "Multifractal information on reading eye tracking data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 638(C).
    13. Vivek H. Dehejia & Douglas W. Dwyer, 1998. "Output and Unemployment Dynamics in Transition," William Davidson Institute Working Papers Series 178, William Davidson Institute at the University of Michigan.
    14. Arnott, Richard, 2013. "A bathtub model of downtown traffic congestion," Journal of Urban Economics, Elsevier, vol. 76(C), pages 110-121.
    15. Luo, Hao-jie & Xue, Yu & Huang, Mu-yang & Zhang, Qiang & Zhang, Kun, 2024. "Pattern and waves on 2D-Kuramoto model with many-body interactions," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    16. dos Santos, A.M. & Lopes, S.R. & Viana, R.L., 2008. "Synchronization regimes for two coupled noisy Liénard-type driven oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 901-910.
    17. David, DE LA CROIX & Bo, MALMBERG, 2006. "Growth and Longevity from the Industrial Revolution to the Future of an Aging Society," Discussion Papers (ECON - Département des Sciences Economiques) 2006037, Université catholique de Louvain, Département des Sciences Economiques.
    18. Marc Germain, 2022. "Limits to growth and creative destruction in the framework of a vintage capital model [Limites à la croissance et destruction créatrice dans le cadre d'un modèle à générations de capital]," Working Papers hal-03849759, HAL.
    19. Reis, A.S. & Brugnago, E.L. & Viana, R.L. & Batista, A.M. & Iarosz, K.C. & Ferrari, F.A.S. & Caldas, I.L., 2023. "The role of the fitness model in the suppression of neuronal synchronous behavior with three-stage switching control in clustered networks," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    20. David de la Croix & Thomas Lindh & Bo Malmberg, 2008. "Swedish economic growth and education since 1800," Canadian Journal of Economics, Canadian Economics Association, vol. 41(1), pages 166-185, February.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:41:y:2009:i:5:p:2553-2565. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.