Reentry near the percolation threshold in a heterogeneous discrete model for cardiac tissue.

Arrhythmias in cardiac tissue are related to irregular electrical wave propagation in the heart. Cardiac tissue is formed by a discrete cell network, which is often heterogeneous. A localized region with a fraction of nonconducting links surrounded by homogeneous conducting tissue can become a source of reentry and ectopic beats. Extensive simulations in a discrete model of cardiac tissue show that a wave crossing a heterogeneous region of cardiac tissue can disintegrate into irregular patterns, provided the fraction of nonconducting links is close to the percolation threshold of the cell network. The dependence of the reentry probability on this fraction, the system size, and the degree of excitability can be inferred from the size distribution of nonconducting clusters near the percolation threshold.

[1]  P. Hogeweg,et al.  Spiral breakup in a modified FitzHugh-Nagumo model , 1993 .

[2]  S. Torquato.  Random Heterogeneous Materials , 2002 .

[3]  F. Fenton,et al.  Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation. , 1998, Chaos.

[4]  Markus Bär,et al.  Effective medium theory for reaction rates and diffusion coefficients of heterogeneous systems. , 2009, Physical review letters.

[5]  K. Showalter,et al.  Dynamical Quorum Sensing and Synchronization in Large Populations of Chemical Oscillators , 2009, Science.

[6]  C. Henriquez,et al.  Incorporating Histology into a 3D Microscopic Computer Model of Myocardium to Study Propagation at a Cellular Level , 2010, Annals of Biomedical Engineering.

[7]  A. Garfinkel,et al.  Effects of Na(+) channel and cell coupling abnormalities on vulnerability to reentry: a simulation study. , 2004, American journal of physiology. Heart and circulatory physiology.

[8]  D. Stauffer.  Scaling Theory of Percolation Clusters , 1979, Complex Media and Percolation Theory.

[9]  Hideki Hayashi,et al.  The dynamics of cardiac fibrillation. , 2005, Circulation.

[10]  F. Fenton,et al.  Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity. , 2002, Chaos.

[11]  A. Garfinkel,et al.  Effects of fibroblast-myocyte coupling on cardiac conduction and vulnerability to reentry: A computational study. , 2009, Heart rhythm.

[12]  Elizabeth M Cherry,et al.  Pulmonary vein reentry--properties and size matter: insights from a computational analysis. , 2007, Heart rhythm.

[13]  K. Nademanee,et al.  A new approach for catheter ablation of atrial fibrillation: mapping of the electrophysiologic substrate. , 2004, Journal of the American College of Cardiology.

[14]  Kenneth Showalter,et al.  Regular and irregular spatial patterns in an immobilized-catalyst Belousov-Zhabotinskii reaction , 1989 .

[15]  Karma.  Spiral breakup in model equations of action potential propagation in cardiac tissue. , 1993, Physical review letters.

[16]  Alain Pumir,et al.  Low-energy Control of Electrical Turbulence in the Heart , 2011, Nature.

[17]  Alexander V Panfilov,et al.  Influence of diffuse fibrosis on wave propagation in human ventricular tissue. , 2007, Europace : European pacing, arrhythmias, and cardiac electrophysiology : journal of the working groups on cardiac pacing, arrhythmias, and cardiac cellular electrophysiology of the European Society of Cardiology.

[18]  M. Márquez,et al.  Target-wave to spiral-wave pattern transition in a discrete Belousov-Zhabotinsky reaction driven by inactive resin beads. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  A. Garfinkel,et al.  Mechanisms of Discordant Alternans and Induction of Reentry in Simulated Cardiac Tissue , 2000, Circulation.

[20]  Alvin Shrier,et al.  The role of heterogeneities and intercellular coupling in wave propagation in cardiac tissue , 2006, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[21]  Negative filament tension in the Luo-Rudy model of cardiac tissue. , 2007, Chaos.

[22]  J. Tyson,et al.  A cellular automation model of excitable media including curvature and dispersion. , 1990, Science.

[23]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[24]  Vladimir K. Vanag,et al.  Synchronization of Chemical Micro-oscillators , 2010 .

[25]  M. Eiswirth,et al.  Turbulence due to spiral breakup in a continuous excitable medium. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.