Nonlinear dynamics of periodically paced cardiac tissue

This manuscript reviews various experimental methods and mathematical approaches for nonlinear dynamics of paced cardiac tissue. A particular focus is on cardiac alternans. Several mapping models are introduced to predict alternans at the cellular level. Experimental observations and modeling approaches are introduced to understand mechanisms of alternans formation in extended heart tissue. In addition, potential bifurcation mechanisms of alternans and the underlying interplay between calcium and voltage dynamics are discussed.

[1]  A. Panfilov,et al.  Spiral breakup as a model of ventricular fibrillation. , 1998, Chaos.

[2]  Mari A. Watanabe,et al.  Mathematical analysis of dynamics of cardiac memory and accommodation: theory and experiment. , 2002, American journal of physiology. Heart and circulatory physiology.

[3]  Xiaopeng Zhao.  Indeterminacy of spatiotemporal cardiac alternans. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  D. G. Schaeffer,et al.  Analysis of the Fenton-Karma model through an approximation by a one-dimensional map. , 2002, Chaos.

[5]  H. Hellerstein,et al.  Electrical alternation in experimental coronary artery occlusion. , 1950, The American journal of physiology.

[6]  David S Rosenbaum,et al.  Importance of spatiotemporal heterogeneity of cellular restitution in mechanism of arrhythmogenic discordant alternans. , 2006, Heart rhythm.

[7]  M. Rosen.  What is Cardiac Memory? , 2000, Journal of cardiovascular electrophysiology.

[8]  E. Caref,et al.  Mechanism of Discordant T Wave Alternans in the In Vivo Heart , 2003, Journal of cardiovascular electrophysiology.

[9]  Elizabeth M Cherry,et al.  Dynamics of human atrial cell models: restitution, memory, and intracellular calcium dynamics in single cells. , 2008, Progress in biophysics and molecular biology.

[10]  Eberhard Bodenschatz,et al.  Period-doubling instability and memory in cardiac tissue. , 2002, Physical review letters.

[11]  Alain Karma,et al.  Coupled dynamics of voltage and calcium in paced cardiac cells. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Erik Mosekilde,et al.  Bifurcations and Chaos in Piecewise-Smooth Dynamical Systems: Applications to Power Converters, Relay and Pulse-Width Modulated Control Systems, and Human Decision-Making Behavior , 2003 .

[13]  Elena G Tolkacheva,et al.  The Rate- and Species-Dependence of Short-Term Memory in Cardiac Myocytes , 2007, Journal of biological physics.

[14]  Daniel J Gauthier,et al.  Restitution in mapping models with an arbitrary amount of memory. , 2005, Chaos.

[15]  Joshua I. Goldhaber,et al.  Action Potential Duration Restitution and Alternans in Rabbit Ventricular Myocytes: The Key Role of Intracellular Calcium Cycling , 2005, Circulation research.

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

[17]  José Jalife,et al.  Role of Conduction Velocity Restitution and Short-Term Memory in the Development of Action Potential Duration Alternans in Isolated Rabbit Hearts , 2008, Circulation.

[18]  J J Heger,et al.  Sudden cardiac death. , 1998, Circulation.

[19]  Y. Rudy,et al.  Determinants of excitability in cardiac myocytes: mechanistic investigation of memory effect. , 2000, Biophysical journal.

[20]  Alternate pacing of border-collision period-doubling bifurcations , 2006, Nonlinear dynamics.

[21]  A. Garfinkel,et al.  Dynamic origin of spatially discordant alternans in cardiac tissue , 2007 .

[22]  Richard A Gray,et al.  Effect of Action Potential Duration and Conduction Velocity Restitution and Their Spatial Dispersion on Alternans and the Stability of Arrhythmias , 2002, Journal of cardiovascular electrophysiology.

[23]  D. Chialvo,et al.  Electrical Restitution, Critical Mass, and the Riddle of Fibrillation , 1999, Journal of cardiovascular electrophysiology.

[24]  Steven H. Strogatz,et al.  Nonlinear Dynamics and Chaos , 2024 .

[25]  Daniel J Gauthier,et al.  The Restitution Portrait: , 2004, Journal of cardiovascular electrophysiology.

[26]  R. Myerburg.  Cardiac arrest and sudden cardiac death , 2005 .

[27]  Daniel J Gauthier,et al.  Condition for alternans and its control in a two-dimensional mapping model of paced cardiac dynamics. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  J Thomas Bigger,et al.  Microvolt T-wave alternans and the risk of death or sustained ventricular arrhythmias in patients with left ventricular dysfunction. , 2006, Journal of the American College of Cardiology.

[29]  M. Franz.  The Electrical Restitution Curve Revisited: , 2003, Journal of cardiovascular electrophysiology.

[30]  Erik Mosekilde,et al.  Bifurcations and chaos in piecewise-smooth dynamical systems , 2003 .

[31]  R. Gilmour,et al.  Electrical restitution and spatiotemporal organization during ventricular fibrillation. , 1999, Circulation research.

[32]  R. Gilmour,et al.  Conduction block in one-dimensional heart fibers. , 2002, Physical review letters.

[33]  Eberhard Bodenschatz,et al.  Spatiotemporal Transition to Conduction Block in Canine Ventricle , 2002, Circulation research.

[34]  A. Garfinkel,et al.  Nonlinear Dynamics of Paced Cardiac Cells , 2006, Annals of the New York Academy of Sciences.

[35]  R. Gilmour,et al.  Biphasic restitution of action potential duration and complex dynamics in ventricular myocardium. , 1995, Circulation research.

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

[37]  Peter N. Jordan,et al.  Determining the effects of memory and action potential duration alternans on cardiac restitution using a constant-memory restitution protocol. , 2004, Physiological measurement.

[38]  A. Karma.  Electrical alternans and spiral wave breakup in cardiac tissue. , 1994, Chaos.

[39]  D. Schaeffer,et al.  A two-current model for the dynamics of cardiac membrane , 2003, Bulletin of mathematical biology.

[40]  M. Franz,et al.  Cycle length dependence of human action potential duration in vivo. Effects of single extrastimuli, sudden sustained rate acceleration and deceleration, and different steady-state frequencies. , 1988, The Journal of clinical investigation.

[41]  Michael R. Guevara,et al.  Hysteresis and bistability in the direct transition from 1:1 to 2:1 rhythm in periodically driven single ventricular cells. , 1999, Chaos.

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

[43]  Donald M. Bers,et al.  Excitation-Contraction Coupling and Cardiac Contractile Force , 1991, Developments in Cardiovascular Medicine.

[44]  Alan Garfinkel,et al.  Spatially Discordant Alternans in Cardiac Tissue: Role of Calcium Cycling , 2006 .

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

[46]  D. Gauthier,et al.  Small-signal amplification of period-doubling bifurcations in smooth iterated maps , 2006, Nonlinear dynamics.

[47]  Daniel J. Gauthier,et al.  Cardiac Alternans Arising From an Unfolded Border-Collision Bifurcation , 2007, 0712.3336.

[48]  C. Luo,et al.  A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. , 1994, Circulation research.

[49]  Vladimir Shusterman,et al.  Upsurge in T-Wave Alternans and Nonalternating Repolarization Instability Precedes Spontaneous Initiation of Ventricular Tachyarrhythmias in Humans , 2006 .

[50]  Daniel J. Gauthier,et al.  Prevalence of Rate-Dependent Behaviors in Cardiac Muscle , 1999 .

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

[52]  A Malliani,et al.  Electrical alternation of the T-wave: clinical and experimental evidence of its relationship with the sympathetic nervous system and with the long Q-T syndrome. , 1975, American heart journal.

[53]  M. Endo,et al.  Calcium release from the sarcoplasmic reticulum. , 1977, Physiological reviews.

[54]  D. Rubenstein,et al.  Premature beats elicit a phase reversal of mechanoelectrical alternans in cat ventricular myocytes. A possible mechanism for reentrant arrhythmias. , 1995, Circulation.

[55]  Thomas Lewis,et al.  NOTES UPON ALTERNATION OF THE HEART , 1911 .

[56]  Alain Karma,et al.  Turing instability mediated by voltage and calcium diffusion in paced cardiac cells. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[57]  R. Gilmour,et al.  Memory and complex dynamics in cardiac Purkinje fibers. , 1997, The American journal of physiology.

[58]  R. Gilmour.  Electrical Restitution and Ventricular Fibrillation: Negotiating a Slippery Slope , 2002, Journal of cardiovascular electrophysiology.

[59]  E. Braunwald.  Heart Disease: A Textbook of Cardiovascular Medicine , 1992, Annals of Internal Medicine.

[60]  Friedberg Ck.  Computers in cardiology. , 1970 .

[61]  Elena G Tolkacheva,et al.  Toward prediction of the local onset of alternans in the heart. , 2011, Biophysical journal.

[62]  P. Spooner,et al.  Opportunities for sudden death prevention: directions for new clinical and basic research. , 2001, Cardiovascular research.

[63]  J. Clark,et al.  Mathematical model of an adult human atrial cell: the role of K+ currents in repolarization. , 1998, Circulation research.

[64]  D. Rosenbaum,et al.  Cellular basis for dispersion of repolarization underlying reentrant arrhythmias. , 2000, Journal of electrocardiology.

[65]  A. Garfinkel,et al.  From Pulsus to Pulseless: The Saga of Cardiac Alternans , 2006, Circulation research.

[66]  Isao Kubota,et al.  Discordant S-T alternans contributes to formation of reentry: a possible mechanism of reperfusion arrhythmia. , 1998, American journal of physiology. Heart and circulatory physiology.

[67]  Hui-Nam Pak,et al.  Spatial Dispersion of Action Potential Duration Restitution Kinetics Is Associated with Induction of Ventricular Tachycardia/Fibrillation in Humans , 2004, Journal of cardiovascular electrophysiology.

[68]  M. Koller,et al.  Dynamic restitution of action potential duration during electrical alternans and ventricular fibrillation. , 1998, American journal of physiology. Heart and circulatory physiology.

[69]  S Yasui,et al.  Significance of discordant ST alternans in ventricular fibrillation. , 1990, Circulation.

[70]  Wenjun Ying,et al.  An Ionically Based Mapping Model with Memory for Cardiac Restitution , 2007, Bulletin of mathematical biology.

[71]  M. Diaz,et al.  Sarcoplasmic Reticulum Calcium Content Fluctuation Is the Key to Cardiac Alternans , 2004, Circulation research.

[72]  L Glass,et al.  Alternans and period-doubling bifurcations in atrioventricular nodal conduction. , 1995, Journal of theoretical biology.

[73]  José Jalife,et al.  Action potential duration restitution portraits of mammalian ventricular myocytes: role of calcium current. , 2006, Biophysical journal.

[74]  J. Nolasco,et al.  A graphic method for the study of alternation in cardiac action potentials. , 1968, Journal of applied physiology.

[75]  N. B. Strydom,et al.  The influence of boot weight on the energy expenditure of men walking on a treadmill and climbing steps , 2004, Internationale Zeitschrift für angewandte Physiologie einschließlich Arbeitsphysiologie.

[76]  A. Garfinkel,et al.  Preventing ventricular fibrillation by flattening cardiac restitution. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[77]  M. Courtemanche,et al.  Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model. , 1998, The American journal of physiology.

[78]  A Garfinkel,et al.  Spatiotemporal heterogeneity in the induction of ventricular fibrillation by rapid pacing: importance of cardiac restitution properties. , 1999, Circulation research.

[79]  M. Oliver.  Benefits and Risks of Drugs in Secondary Prevention of Ischaemic Heart Diseasc—a Summary , 1986 .

[80]  J Jalife,et al.  Supernormal excitability as a mechanism of chaotic dynamics of activation in cardiac Purkinje fibers. , 1990, Circulation research.

[81]  J. Ruskin,et al.  Electrical alternans and vulnerability to ventricular arrhythmias. , 1994, The New England journal of medicine.

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

[83]  Daniel J Gauthier,et al.  Period-doubling bifurcation to alternans in paced cardiac tissue: crossover from smooth to border-collision characteristics. , 2007, Physical review letters.

[84]  G Duckett,et al.  Modeling the dynamics of cardiac action potentials. , 2000, Physical review letters.

[85]  A Garfinkel,et al.  Intracellular Ca(2+) dynamics and the stability of ventricular tachycardia. , 1999, Biophysical journal.

[86]  Wanda Krassowska,et al.  Spatial heterogeneity of the restitution portrait in rabbit epicardium. , 2007, American journal of physiology. Heart and circulatory physiology.

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

[88]  J. Restrepo,et al.  A rabbit ventricular action potential model replicating cardiac dynamics at rapid heart rates. , 2007, Biophysical journal.

[89]  D DiFrancesco,et al.  A model of cardiac electrical activity incorporating ionic pumps and concentration changes. , 1985, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

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

[91]  M. Diaz,et al.  Depressed Ryanodine Receptor Activity Increases Variability and Duration of the Systolic Ca2+ Transient in Rat Ventricular Myocytes , 2002, Circulation research.

[92]  B. Surawicz,et al.  Cycle length effect on restitution of action potential duration in dog cardiac fibers. , 1983, The American journal of physiology.

[93]  H. E. Hering,et al.  Experimentalle studien an säugethieren über das elektrocardiogramm , 1909 .

[94]  D. Rosenbaum,et al.  T-wave alternans for risk stratification and prevention of sudden cardiac death , 2003, Current cardiology reports.

[95]  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.

[96]  Daniel J Gauthier,et al.  Condition for alternans and stability of the 1:1 response pattern in a "memory" model of paced cardiac dynamics. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[97]  R. Aliev,et al.  A simple two-variable model of cardiac excitation , 1996 .

[98]  R. Gilmour,et al.  Memory models for the electrical properties of local cardiac systems. , 1997, Journal of theoretical biology.

[99]  C. Budd,et al.  Review of ”Piecewise-Smooth Dynamical Systems: Theory and Applications by M. di Bernardo, C. Budd, A. Champneys and P. 2008” , 2020 .