IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0045040.html
   My bibliography  Save this article

Nonequilibrium Arrhythmic States and Transitions in a Mathematical Model for Diffuse Fibrosis in Human Cardiac Tissue

Author

Listed:
  • Rupamanjari Majumder
  • Alok Ranjan Nayak
  • Rahul Pandit

Abstract

We present a comprehensive numerical study of spiral-and scroll-wave dynamics in a state-of-the-art mathematical model for human ventricular tissue with fiber rotation, transmural heterogeneity, myocytes, and fibroblasts. Our mathematical model introduces fibroblasts randomly, to mimic diffuse fibrosis, in the ten Tusscher-Noble-Noble-Panfilov (TNNP) model for human ventricular tissue; the passive fibroblasts in our model do not exhibit an action potential in the absence of coupling with myocytes; and we allow for a coupling between nearby myocytes and fibroblasts. Our study of a single myocyte-fibroblast (MF) composite, with a single myocyte coupled to fibroblasts via a gap-junctional conductance , reveals five qualitatively different responses for this composite. Our investigations of two-dimensional domains with a random distribution of fibroblasts in a myocyte background reveal that, as the percentage of fibroblasts increases, the conduction velocity of a plane wave decreases until there is conduction failure. If we consider spiral-wave dynamics in such a medium we find, in two dimensions, a variety of nonequilibrium states, temporally periodic, quasiperiodic, chaotic, and quiescent, and an intricate sequence of transitions between them; we also study the analogous sequence of transitions for three-dimensional scroll waves in a three-dimensional version of our mathematical model that includes both fiber rotation and transmural heterogeneity. We thus elucidate random-fibrosis-induced nonequilibrium transitions, which lead to conduction block for spiral waves in two dimensions and scroll waves in three dimensions. We explore possible experimental implications of our mathematical and numerical studies for plane-, spiral-, and scroll-wave dynamics in cardiac tissue with fibrosis.

Suggested Citation

  • Rupamanjari Majumder & Alok Ranjan Nayak & Rahul Pandit, 2012. "Nonequilibrium Arrhythmic States and Transitions in a Mathematical Model for Diffuse Fibrosis in Human Cardiac Tissue," PLOS ONE, Public Library of Science, vol. 7(10), pages 1-21, October.
    • Handle: RePEc:plo:pone00:0045040
    DOI: 10.1371/journal.pone.0045040
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0045040
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0045040&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0045040?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
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Rupamanjari Majumder & Alok Ranjan Nayak & Rahul Pandit, 2011. "Scroll-Wave Dynamics in Human Cardiac Tissue: Lessons from a Mathematical Model with Inhomogeneities and Fiber Architecture," PLOS ONE, Public Library of Science, vol. 6(4), pages 1-21, April.
    3. Richard A. Gray & Arkady M. Pertsov & José Jalife, 1998. "Erratum: Spatial and temporal organization during cardiac fibrillation," Nature, Nature, vol. 393(6681), pages 191-191, May.
    4. Richard A. Gray & Arkady M. Pertsov & José Jalife, 1998. "Spatial and temporal organization during cardiac fibrillation," Nature, Nature, vol. 392(6671), pages 75-78, March.
    5. T K Shajahan & Alok Ranjan Nayak & Rahul Pandit, 2009. "Spiral-Wave Turbulence and Its Control in the Presence of Inhomogeneities in Four Mathematical Models of Cardiac Tissue," PLOS ONE, Public Library of Science, vol. 4(3), pages 1-21, March.
    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. Alok Ranjan Nayak & T K Shajahan & A V Panfilov & Rahul Pandit, 2013. "Spiral-Wave Dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Fibroblasts," PLOS ONE, Public Library of Science, vol. 8(9), pages 1-25, September.

    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. Hu, Yipeng & Ding, Qianming & Wu, Yong & Jia, Ya, 2023. "Polarized electric field-induced drift of spiral waves in discontinuous cardiac media," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    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. Alok Ranjan Nayak & T K Shajahan & A V Panfilov & Rahul Pandit, 2013. "Spiral-Wave Dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Fibroblasts," PLOS ONE, Public Library of Science, vol. 8(9), pages 1-25, September.
    4. Yu, Yang F. & Fuller, Chase A. & McGuire, Margaret K. & Glaser, Rebecca & Smith, Nathaniel J. & Manz, Niklas & Lindner, John F., 2021. "Disruption and recovery of reaction–diffusion wavefronts interacting with concave, fractal, and soft obstacles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    5. Ding, Qianming & Wu, Yong & Hu, Yipeng & Liu, Chaoyue & Hu, Xueyan & Jia, Ya, 2023. "Tracing the elimination of reentry spiral waves in defibrillation: Temperature effects," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    6. Rupamanjari Majumder & Alok Ranjan Nayak & Rahul Pandit, 2011. "Scroll-Wave Dynamics in Human Cardiac Tissue: Lessons from a Mathematical Model with Inhomogeneities and Fiber Architecture," PLOS ONE, Public Library of Science, vol. 6(4), pages 1-21, April.
    7. Laura Martinez-Mateu & Lucia Romero & Ana Ferrer-Albero & Rafael Sebastian & José F Rodríguez Matas & José Jalife & Omer Berenfeld & Javier Saiz, 2018. "Factors affecting basket catheter detection of real and phantom rotors in the atria: A computational study," PLOS Computational Biology, Public Library of Science, vol. 14(3), pages 1-26, March.
    8. Young-Seon Lee & Jun-Seop Song & Minki Hwang & Byounghyun Lim & Boyoung Joung & Hui-Nam Pak, 2016. "A New Efficient Method for Detecting Phase Singularity in Cardiac Fibrillation," PLOS ONE, Public Library of Science, vol. 11(12), pages 1-14, December.
    9. Feng, Peihua & Fan, Qiang & Yuan, Zhixuan & Wu, Ying, 2021. "Transition from regular to labyrinth pattern in a neuronal network with fast inhibitory synapses," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    10. 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.
    11. 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.
    12. Xu, Binbin & Jacquir, Sabir & Laurent, Gabriel & Bilbault, Jean-Marie & Binczak, Stéphane, 2011. "A hybrid stimulation strategy for suppression of spiral waves in cardiac tissue," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 633-639.
    13. Xu, Ying & Ren, Guodong & Ma, Jun, 2023. "Patterns stability in cardiac tissue under spatial electromagnetic radiation," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    14. Smith, Nathaniel J. & Glaser, Rebecca & Hui, Vincent W.H. & Lindner, John F. & Manz, Niklas, 2019. "Disruption and recovery of reaction–diffusion wavefronts colliding with obstacles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 307-320.
    15. Soling Zimik & Rahul Pandit & Rupamanjari Majumder, 2020. "Anisotropic shortening in the wavelength of electrical waves promotes onset of electrical turbulence in cardiac tissue: An in silico study," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-14, March.
    16. Li, Fan & Liu, Shuai & Li, Xiaola, 2022. "Pattern selection in thermosensitive neuron network induced by noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    17. Yuangen Yao & Wei Cao & Qiming Pei & Chengzhang Ma & Ming Yi, 2018. "Breakup of Spiral Wave and Order-Disorder Spatial Pattern Transition Induced by Spatially Uniform Cross-Correlated Sine-Wiener Noises in a Regular Network of Hodgkin-Huxley Neurons," Complexity, Hindawi, vol. 2018, pages 1-10, April.
    18. Zhang, Yin & Wu, Fuqiang & Wang, Chunni & Ma, Jun, 2019. "Stability of target waves in excitable media under electromagnetic induction and radiation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 519-530.

    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:plo:pone00:0045040. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.