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Myocardial Fibrosis in a 3D Model: Effect of Texture on Wave Propagation

Author

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  • Arsenii Dokuchaev

    (Institute of Immunology and Physiology, Ural Branch of Russian Academy of Sciences, Ekaterinburg 620049, Russia)

  • Alexander V. Panfilov

    (Department of Physics and Astronomy, Ghent University, Krijgslaan 281, 9000 Gent, Belgium
    Laboratory of Computational Biology and Medicine, Ural Federal University, Ekaterinburg 620075, Russia)

  • Olga Solovyova

    (Institute of Immunology and Physiology, Ural Branch of Russian Academy of Sciences, Ekaterinburg 620049, Russia
    Laboratory of Computational Biology and Medicine, Ural Federal University, Ekaterinburg 620075, Russia)

Abstract

Non-linear electrical waves propagate through the heart and control cardiac contraction. Abnormal wave propagation causes various forms of the heart disease and can be lethal. One of the main causes of abnormality is a condition of cardiac fibrosis, which, from mathematical point of view, is the presence of multiple non-conducting obstacles for wave propagation. The fibrosis can have different texture which varies from diffuse (e.g., small randomly distributed obstacles), patchy (e.g., elongated interstitional stria), and focal (e.g., post-infarct scars) forms. Recently, Nezlobinsky et al. (2020) used 2D biophysical models to quantify the effects of elongation of obstacles (fibrosis texture) and showed that longitudinal and transversal propagation differently depends on the obstacle length resulting in anisotropy for wave propagation. In this paper, we extend these studies to 3D tissue models. We show that 3D consideration brings essential new effects; for the same obstacle length in 3D systems, anisotropy is about two times smaller compared to 2D, however, wave propagation is more stable with percolation threshold of about 60% (compared to 35% in 2D). The percolation threshold increases with the obstacle length for the longitudinal propagation, while it decreases for the transversal propagation. Further, in 3D, the dependency of velocity on the obstacle length for the transversal propagation disappears.

Suggested Citation

  • 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.
  • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1352-:d:398161
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    References listed on IDEAS

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    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.
    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. Hermenegild J. Arevalo & Fijoy Vadakkumpadan & Eliseo Guallar & Alexander Jebb & Peter Malamas & Katherine C. Wu & Natalia A. Trayanova, 2016. "Arrhythmia risk stratification of patients after myocardial infarction using personalized heart models," Nature Communications, Nature, vol. 7(1), pages 1-8, September.
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