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

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  • 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.

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  • 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
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    References listed on IDEAS

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    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.
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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.

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