IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v517y2019icp307-320.html
   My bibliography  Save this article

Disruption and recovery of reaction–diffusion wavefronts colliding with obstacles

Author

Listed:
  • Smith, Nathaniel J.
  • Glaser, Rebecca
  • Hui, Vincent W.H.
  • Lindner, John F.
  • Manz, Niklas

Abstract

We study the damage to and restoration of planar reaction–diffusion wavefronts colliding with convex obstacles in narrow two-dimensional channels using finite-difference numerical integration of the Tyson–Fife reduction of the Oregonator model of the Belousov–Zhabotinsky reaction. We characterize the obstacles’ effects on the wavefront shape by plotting wavefront delay versus time. Due to the curvature dependent wavefront velocities, the initial planar wavefront (or iso-concentration line) is restored after a relaxation period that can be characterized by a power-law. We find that recovery times are insensitive to obstacle concatenation or to the upstream obstacle shape but are sensitive to the downstream shape, with a vertical back side causing the longest disruption. Delays vary cyclically with obstacle orientations. The relaxation power-laws confirm that larger obstacles produce larger wavefront delays and longer recovery times, and for a given area larger obstacle width-to-length ratios produce longer delays. Possible applications include elucidating the effect of inhomogeneities on wavefront recovery in cardiac tissue.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:517:y:2019:i:c:p:307-320
    DOI: 10.1016/j.physa.2018.11.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118314407
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.11.024?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. 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.
    2. Rostami, Zahra & Rajagopal, Karthikeyan & Khalaf, Abdul Jalil M. & Jafari, Sajad & Perc, Matjaž & Slavinec, Mitja, 2018. "Wavefront-obstacle interactions and the initiation of reentry in excitable media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 1162-1173.
    3. Wang, Cheng & Tan, Jiale & Lou, Bendong, 2015. "Influence of obstacles on the propagation speeds of nonlinear waves driven by curvature," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 425(C), pages 41-49.
    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. 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).
    2. Kim, Sangkwon & Park, Jintae & Lee, Chaeyoung & Jeong, Darae & Choi, Yongho & Kwak, Soobin & Kim, Junseok, 2020. "Periodic travelling wave solutions for a reaction-diffusion system on landscape fitted domains," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).

    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. 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).
    2. 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).
    3. Rajagopal, Karthikeyan & Hussain, Iqtadar & Rostami, Zahra & Li, Chunbiao & Pham, Viet-Thanh & Jafari, Sajad, 2021. "Magnetic induction can control the effect of external electrical stimuli on the spiral wave," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    4. Panahi, Shirin & Shirzadian, Touraj & Jalili, Mahdi & Jafari, Sajad, 2019. "A new chaotic network model for epilepsy," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 395-407.
    5. Rajagopal, Karthikeyan & Nezhad Hajian, Dorsa & Natiq, Hayder & Peng, Yuexi & Parastesh, Fatemeh & Jafari, Sajad, 2024. "Effect of Gaussian gradient in the medium's action potential morphology on spiral waves," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    6. 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.
    7. 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).
    8. Wang, Zhen & Rostami, Zahra & Jafari, Sajad & Alsaadi, Fawaz E. & Slavinec, Mitja & Perc, Matjaž, 2019. "Suppression of spiral wave turbulence by means of periodic plane waves in two-layer excitable media," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 229-233.
    9. Parastesh, Fatemeh & Rajagopal, Karthikeyan & Alsaadi, Fawaz E. & Hayat, Tasawar & Pham, V.-T. & Hussain, Iqtadar, 2019. "Birth and death of spiral waves in a network of Hindmarsh–Rose neurons with exponential magnetic flux and excitable media," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 377-384.
    10. 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.
    11. 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.
    12. 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).

    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:phsmap:v:517:y:2019:i:c:p:307-320. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.