Model of Cardiac Tissue as a conductive System with Interacting pacemakers and Refractory Time

The model of the cardiac tissue as a conductive system with two interacting pacemakers and a refractory time is proposed. In the parametric space of the model the phase locking areas are investigated in detail. The obtained results make possible to predict the behavior of excitable systems with two pacemakers, depending on the type and intensity of their interaction and the initial phase. Comparison of the described phenomena with intrinsic pathologies of cardiac rhythms is given.

[1]  D. Bernardo,et al.  Simulation of heartbeat dynamics: a nonlinear model , 1998 .

[2]  James P. Keener,et al.  On cardiac arrythmias: AV conduction block , 1981 .

[3]  D. Salem,et al.  Disorders of cardiac rhythm. , 1978, The Orthopedic clinics of North America.

[4]  Ary L. Goldberger Nonlinear dynamics, fractals and chaos: Applications to cardiac electrophysiology , 2006, Annals of Biomedical Engineering.

[5]  Simulated sinoatrial exit blocks explained by circle map analysis. , 2001, Journal of theoretical biology.

[6]  L Glass,et al.  Global bifurcations of a periodically forced nonlinear oscillator , 1984, Journal of mathematical biology.

[7]  T Sato,et al.  Difference equation model of ventricular parasystole as an interaction between cardiac pacemakers based on the phase response curve. , 1983, Journal of theoretical biology.

[8]  A V Holden,et al.  Reentrant waves and their elimination in a model of mammalian ventricular tissue. , 1998, Chaos.

[9]  L Glass,et al.  Phase locking, period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: A theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias , 1982, Journal of mathematical biology.

[10]  J. Keener,et al.  Phase locking of biological clocks , 1982, Journal of mathematical biology.

[11]  José Jalife,et al.  Cardiac electrophysiology and arrhythmias , 1985 .

[12]  L. Glass,et al.  From Clocks to Chaos: The Rhythms of Life , 1988 .

[13]  L Glass,et al.  Phase resetting of spontaneously beating embryonic ventricular heart cell aggregates. , 1986, The American journal of physiology.

[14]  C Antzelevitch,et al.  The Case for Modulated Parasystole , 1982, Pacing and clinical electrophysiology : PACE.

[15]  B. A.,et al.  Sudden Death , 1855, Developments in Cardiovascular Medicine.

[16]  James P. Keener,et al.  Stability conditions for the traveling pulse: Modifying the restitution hypothesis. , 2002, Chaos.

[17]  R. Pérez,et al.  Bifurcation and chaos in a periodically stimulated cardiac oscillator , 1983 .

[18]  Leon Glass,et al.  Predicting the entrainment of reentrant cardiac waves using phase resetting curves. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Bruce J. West,et al.  Nonlinear dynamics of the heartbeat: I. The AV junction: Passive conduit or active oscillator? , 1985 .

[20]  Balth van der Pol Jun Docts. Sc.,et al.  LXXII. The heartbeat considered as a relaxation oscillation, and an electrical model of the heart , 1928 .

[21]  Yu-Ao He,et al.  Lyapunov exponents of the circle map in human hearts , 1992 .

[22]  V. Krinsky,et al.  Deexcitation of cardiac cells. , 1998, Biophysical journal.

[23]  J. Jalife,et al.  Cardiac Electrophysiology: From Cell to Bedside , 1990 .

[24]  James P. Keener,et al.  Re-entry in three-dimensional Fitzhugh-Nagumo medium with rotational anisotropy , 1995 .

[25]  T. Cochrane,et al.  When Time Breaks Down : The Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias , 1987 .

[26]  S C Müller,et al.  Elimination of spiral waves in cardiac tissue by multiple electrical shocks. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[27]  A Garfinkel,et al.  From local to global spatiotemporal chaos in a cardiac tissue model. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  Anastasios Bezerianos,et al.  REPRESENTATION OF SINO-ATRIAL NODE DYNAMICS BY CIRCLE MAPS , 1996 .

[29]  V. Krinsky,et al.  Models of defibrillation of cardiac tissue. , 1998, Chaos.

[30]  Leon Glass,et al.  BIFURCATIONS IN A DISCONTINUOUS CIRCLE MAP: A THEORY FOR A CHAOTIC CARDIAC ARRHYTHMIA , 1995 .

[31]  A Garfinkel,et al.  Controlling cardiac chaos. , 1992, Science.

[32]  S. Weidmann,et al.  Effect of current flow on the membrane potential of cardiac muscle , 1951, The Journal of physiology.

[33]  D. Zipes,et al.  Cardiac Electrophysiology: From Cell to Bedside, 6th Edition , 2013 .

[34]  James P. Keener,et al.  Propagation of Waves in an Excitable Medium with Discrete Release Sites , 2000, SIAM J. Appl. Math..

[35]  J Jalife,et al.  A Mathematical Model of Parasystole and its Application to Clinical Arrhythmias , 1977, Circulation.

[36]  Alan Garfinkel,et al.  Spatiotemporal Chaos in a Simulated Ring of Cardiac Cells , 1997 .

[37]  Richard H. Rand,et al.  1∶1 and 2∶1 phase entrainment in a system of two coupled limit cycle oscillators , 1984 .

[38]  L. Glass,et al.  A circle map in a human heart , 1990 .

[39]  G. Scoles,et al.  Viscosity and thermal conductivity of polar gases in an electric field , 1970 .

[40]  D. Bernardo,et al.  A Model of Two Nonlinear Coupled Oscillators for the Study of Heartbeat Dynamics , 1998 .

[41]  J Honerkamp,et al.  The heart as a system of coupled nonlinear oscillators , 1983, Journal of mathematical biology.

[42]  From Clocks to Chaos: The Rhythms of Life , 1988 .

[43]  Michael F. Shlesinger,et al.  Dynamic patterns in complex systems , 1988 .

[44]  James P. Keener,et al.  Wave-Block in Excitable Media Due to Regions of Depressed Excitability , 2000, SIAM J. Appl. Math..

[45]  J Jalife,et al.  Effect of Electrotonic Potentials on Pacemaker Activity of Canine Purkinje Fibers in Relation to Parasystole , 1976, Circulation research.