IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v175y2023ip2s0960077923008846.html
   My bibliography  Save this article

Cardiac behaviors and chaotic arrhythmias in the Hindmarsh–Rose model

Author

Listed:
  • Stenzinger, R.V.
  • Scalvin, T.E.
  • Morelo, P.A.
  • Tragtenberg, M.H.R.

Abstract

The Hindmarsh–Rose is one of the best-known models of computational neuroscience. Despite its popularity as a neuron model, we demonstrate that it is also a complete cardiac model. We employ a method based on bifurcations of the interspike interval to redraw its phase diagram and reveal a cardiac region. This diagram bears great resemblance to that of the map-based model for neurons and cardiac cells, the KTz model. Both phase diagrams are compared, showing a very similar placement of behaviors in the parameter space. Adjusting the Hindmarsh–Rose parameters allows us to obtain behaviors similar to atrial, ventricular and pacemaker cells. We also report the neuronal behavior of sustained subthreshold oscillations in the diagram, also unknown in the model. We demonstrate the existence of periodic and chaotic early afterdepolarizations, a behavior linked to life-threatening arrhythmias. In a second phase diagram, we find a chaotic region with early afterdepolarizations and self-organized periodic structures known as shrimps. We also propose a new and simple method to calculate the electrocardiogram using the membrane potential of a point cell and demonstrate its use for the study of QT syndromes using the Hindmarsh–Rose model. Given the smaller number of equations and parameters than detailed conductance models and richer dynamics than other general models, this work presents the Hindmarsh–Rose as a promising alternative for computational cardiology studies.

Suggested Citation

  • Stenzinger, R.V. & Scalvin, T.E. & Morelo, P.A. & Tragtenberg, M.H.R., 2023. "Cardiac behaviors and chaotic arrhythmias in the Hindmarsh–Rose model," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
  • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p2:s0960077923008846
    DOI: 10.1016/j.chaos.2023.113983
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923008846
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2023.113983?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. Huaguang Gu & Baobao Pan & Jian Xu, 2013. "Bifurcation Scenarios of Neural Firing Patterns across Two Separated Chaotic Regions as Indicated by Theoretical and Biological Experimental Models," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, November.
    2. Nele Vandersickel & Ivan V Kazbanov & Anita Nuitermans & Louis D Weise & Rahul Pandit & Alexander V Panfilov, 2014. "A Study of Early Afterdepolarizations in a Model for Human Ventricular Tissue," PLOS ONE, Public Library of Science, vol. 9(1), pages 1-19, January.
    3. Copelli, M. & Tragtenberg, M.H.R. & Kinouchi, O., 2004. "Stability diagrams for bursting neurons modeled by three-variable maps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 263-269.
    Full references (including those not matched with items on IDEAS)

    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. Soling Zimik & Nele Vandersickel & Alok Ranjan Nayak & Alexander V Panfilov & Rahul Pandit, 2015. "A Comparative Study of Early Afterdepolarization-Mediated Fibrillation in Two Mathematical Models for Human Ventricular Cells," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-20, June.
    2. Roman Rokeakh & Tatiana Nesterova & Konstantin Ushenin & Ekaterina Polyakova & Dmitry Sonin & Michael Galagudza & Tim De Coster & Alexander Panfilov & Olga Solovyova, 2021. "Anatomical Model of Rat Ventricles to Study Cardiac Arrhythmias under Infarction Injury," Mathematics, MDPI, vol. 9(20), pages 1-27, October.
    3. Arsenii Dokuchaev & Alexander V. Panfilov & Olga Solovyova, 2020. "Myocardial Fibrosis in a 3D Model: Effect of Texture on Wave Propagation," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
    4. Daria Mangileva & Pavel Konovalov & Arsenii Dokuchaev & Olga Solovyova & Alexander V. Panfilov, 2021. "Period of Arrhythmia Anchored around an Infarction Scar in an Anatomical Model of the Human Ventricles," Mathematics, MDPI, vol. 9(22), pages 1-15, November.
    5. Bashkirtseva, Irina A. & Ryashko, Lev B. & Pisarchik, Alexander N., 2020. "Ring of map-based neural oscillators: From order to chaos and back," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    6. Pavel Konovalov & Daria Mangileva & Arsenii Dokuchaev & Olga Solovyova & Alexander V. Panfilov, 2021. "Rotational Activity around an Obstacle in 2D Cardiac Tissue in Presence of Cellular Heterogeneity," Mathematics, MDPI, vol. 9(23), pages 1-15, November.
    7. Enid Van Nieuwenhuyse & Gunnar Seemann & Alexander V Panfilov & Nele Vandersickel, 2017. "Effects of early afterdepolarizations on excitation patterns in an accurate model of the human ventricles," PLOS ONE, Public Library of Science, vol. 12(12), pages 1-19, December.
    8. Pravdin, Sergei F. & Panfilov, Alexander V., 2022. "Doppler shift during overdrive pacing of spiral waves. Prediction of the annihilation site," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

    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:175:y:2023:i:p2:s0960077923008846. 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.