Supernormal conduction in cardiac tissue promotes concordant alternans and action potential bunching.

Supernormal conduction (SNC) in excitable cardiac tissue refers to an increase of pulse (or action potential) velocity with decreasing distance to the preceding pulse. Here we employ a simple ionic model to study the effect of SNC on the propagation of action potentials (APs) and the phenomenology of alternans in excitable cardiac tissue. We use bifurcation analysis and simulations to study attraction between propagating APs caused by SNC that leads to AP pairs and bunching. It is shown that SNC stabilizes concordant alternans in arbitrarily long paced one-dimensional cables. As a consequence, spiral waves in two-dimensional tissue simulations exhibit straight nodal lines for SNC in contrast to spiraling ones in the case of normal conduction.

[1]  J. Keener,et al.  Singular perturbation theory of traveling waves in excitable media (a review) , 1988 .

[2]  C. Luo,et al.  A model of the ventricular cardiac action potential. Depolarization, repolarization, and their interaction. , 1991, Circulation research.

[3]  P. Kam,et al.  : 4 , 1898, You Can Cross the Massacre on Foot.

[4]  O. Steinbock,et al.  Anomalous dispersion in the Belousov–Zhabotinsky reaction: Experiments and modeling , 2010 .

[5]  G. W. Beeler,et al.  Reconstruction of the action potential of ventricular myocardial fibres , 1977, The Journal of physiology.

[6]  Elizabeth M Cherry,et al.  Suppression of alternans and conduction blocks despite steep APD restitution: electrotonic, memory, and conduction velocity restitution effects. , 2004, American journal of physiology. Heart and circulatory physiology.

[7]  Björn Sandstede,et al.  Period-Doubling of Spiral Waves and Defects , 2007, SIAM J. Appl. Dyn. Syst..

[8]  Raymond Kapral,et al.  SPIRAL WAVES IN MEDIA WITH COMPLEX-EXCITABLE DYNAMICS , 1999, chao-dyn/9901024.

[9]  Blas Echebarria,et al.  Instability and spatiotemporal dynamics of alternans in paced cardiac tissue. , 2001, Physical review letters.

[10]  From ballistic to brownian vortex motion in complex oscillatory media. , 2004, Physical review letters.

[11]  Jin Hee Hong,et al.  Cardiac beat-to-beat alternations driven by unusual spiral waves , 2007, Proceedings of the National Academy of Sciences.

[12]  Okyu Kwon,et al.  Period-2 spiral waves supported by nonmonotonic wave dispersion. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  F A Roberge,et al.  Revised formulation of the Hodgkin-Huxley representation of the sodium current in cardiac cells. , 1987, Computers and biomedical research, an international journal.

[14]  Excitation waves in reaction-diffusion media with non-monotonic dispersion relations , 2003 .

[15]  James P. Keener,et al.  A Delay Equation Representation of Pulse Circulation on a Ring in Excitable Media , 1996, SIAM J. Appl. Math..

[16]  Okyu Kwon,et al.  Nucleation, drift, and decay of phase bubbles in period-2 oscillatory wave trains in a reaction-diffusion system. , 2008, Physical review letters.

[17]  F. Fenton,et al.  Minimal model for human ventricular action potentials in tissue. , 2008, Journal of theoretical biology.

[18]  Markus Bär,et al.  ANOMALOUS DISPERSION AND PULSE INTERACTION IN AN EXCITABLE SURFACE REACTION , 1999 .

[19]  J. Spear,et al.  Supernormal Excitability and Conduction in the His‐Purkinje System of the Dog , 1974, Circulation research.

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

[21]  Enno de Lange,et al.  The transfer functions of cardiac tissue during stochastic pacing. , 2009, Biophysical journal.

[22]  A. Wear.  CIRCULATION , 1964, The Lancet.

[23]  Enno de Lange,et al.  Alternans resonance and propagation block during supernormal conduction in cardiac tissue with decreased [K(+)](o). , 2010, Biophysical journal.

[24]  H M Hastings,et al.  Mechanisms for Discordant Alternans , 2001, Journal of cardiovascular electrophysiology.

[25]  L. Glass,et al.  Instabilities of a propagating pulse in a ring of excitable media. , 1993, Physical review letters.

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

[27]  Jin Sung Park,et al.  Complex Periodic Spirals and Line-Defect Turbulence in a Chemical System , 1999 .

[28]  M. Bär,et al.  Alternans and the influence of ionic channel modifications: Cardiac three-dimensional simulations and one-dimensional numerical bifurcation analysis. , 2007, Chaos.

[29]  Oliver Steinbock,et al.  Anomalous Dispersion and Attractive Pulse Interaction in the 1,4-Cyclohexanedione Belousov-Zhabotinsky Reaction † , 2001 .

[30]  Shuichi Maeda,et al.  Wavelength-Doubled Spiral Fragments in Photosensitive Monolayers , 1995 .

[31]  E. Meron.  Pattern formation in excitable media , 1992 .

[32]  Raymond Kapral,et al.  Synchronization Defect Lines , 2000, Int. J. Bifurc. Chaos.

[33]  Markus Bär,et al.  Stable bound states of pulses in an excitable medium , 2000 .

[34]  D. Rosenbaum,et al.  Mechanism linking T-wave alternans to the genesis of cardiac fibrillation. , 1999, Circulation.

[35]  Blas Echebarria,et al.  Amplitude equation approach to spatiotemporal dynamics of cardiac alternans. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  J. Restrepo,et al.  Line-defect patterns of unstable spiral waves in cardiac tissue. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  R. Winslow,et al.  A computational model of the human left-ventricular epicardial myocyte. , 2004, Biophysical journal.