Mechanisms of ventricular arrhythmias: a dynamical systems-based perspective.

Defining the cellular electrophysiological mechanisms for ventricular tachyarrhythmias is difficult, given the wide array of potential mechanisms, ranging from abnormal automaticity to various types of reentry and kk activity. The degree of difficulty is increased further by the fact that any particular mechanism may be influenced by the evolving ionic and anatomic environments associated with many forms of heart disease. Consequently, static measures of a single electrophysiological characteristic are unlikely to be useful in establishing mechanisms. Rather, the dynamics of the electrophysiological triggers and substrates that predispose to arrhythmia development need to be considered. Moreover, the dynamics need to be considered in the context of a system, one that displays certain predictable behaviors, but also one that may contain seemingly stochastic elements. It also is essential to recognize that even the predictable behaviors of this complex nonlinear system are subject to small changes in the state of the system at any given time. Here we briefly review some of the short-, medium-, and long-term alterations of the electrophysiological substrate that accompany myocardial disease and their potential impact on the initiation and maintenance of ventricular arrhythmias. We also provide examples of cases in which small changes in the electrophysiological substrate can result in rather large differences in arrhythmia outcome. These results suggest that an interrogation of cardiac electrical dynamics is required to provide a meaningful assessment of the immediate risk for arrhythmia development and for evaluating the effects of putative antiarrhythmic interventions.

[1]  A Mugelli,et al.  Ionic basis of action potential prolongation of hypertrophied cardiac myocytes isolated from hypertensive rats of different ages. , 1994, Cardiovascular research.

[2]  Jiqiu Chen,et al.  PRESERVATION OF MECHANICAL AND ENERGETIC FUNCTION AFTER ADENOVIRAL GENE TRANSFER IN NORMAL RAT HEARTS , 2007, Clinical and experimental pharmacology & physiology.

[3]  G. Beatch,et al.  Kinetics of rate‐dependent shortening of action potential duration in guinea‐pig ventricle; effects of IK1 and IKr blockade , 1999, British journal of pharmacology.

[4]  R. Hullin,et al.  Increased availability and open probability of single L-type calcium channels from failing compared with nonfailing human ventricle. , 1998, Circulation.

[5]  Elizabeth M Cherry,et al.  A tale of two dogs: analyzing two models of canine ventricular electrophysiology. , 2007, American journal of physiology. Heart and circulatory physiology.

[6]  Wouter-Jan Rappel,et al.  Filament instability and rotational tissue anisotropy: A numerical study using detailed cardiac models. , 2001, Chaos.

[7]  Mark T. Nelson,et al.  Targeted disruption of Kir2.1 and Kir2.2 genes reveals the essential role of the inwardly rectifying K(+) current in K(+)-mediated vasodilation. , 2000, Circulation research.

[8]  ARM Gelzer,et al.  Dynamically-induced spatial dispersion of repolarization and the development of VF in an animal model of sudden death , 2009, 2009 36th Annual Computers in Cardiology Conference (CinC).

[9]  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.

[10]  A Varró,et al.  Intracellular calcium and electrical restitution in mammalian cardiac cells. , 1998, Acta physiologica Scandinavica.

[11]  H. Engel,et al.  Chemical turbulence and standing waves in a surface reaction model: The influence of global coupling and wave instabilities. , 1994, Chaos.

[12]  C. Henriquez,et al.  Simulation and prediction of functional block in the presence of structural and ionic heterogeneity. , 2001, American journal of physiology. Heart and circulatory physiology.

[13]  Philippe Comtois,et al.  Multistability of reentrant rhythms in an ionic model of a two-dimensional annulus of cardiac tissue. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  L A Moyé,et al.  The cardiac arrhythmia suppression trial. Casting suppression in a different light. , 1995, Circulation.

[15]  Dongling Zhao,et al.  Nuclear Factor &kgr;B Downregulates the Transient Outward Potassium Current Ito,f Through Control of KChIP2 Expression , 2011, Circulation research.

[16]  Héctor H. Valdivia,et al.  Abnormal Ca 2 Release , but Normal Ryanodine Receptors , in Canine and Human Heart Failure , 2002 .

[17]  Bertram Pitt,et al.  Effect of d-sotalol on mortality in patients with left ventricular dysfunction after recent and remote myocardial infarction , 1996, The Lancet.

[18]  R. Gilmour,et al.  Reduction of the transient outward potassium current in canine x‐linked muscular dystrophy , 1994, Circulation.

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

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

[21]  Tong Zhang,et al.  Transgenic CaMKII&dgr;C Overexpression Uniquely Alters Cardiac Myocyte Ca2+ Handling: Reduced SR Ca2+ Load and Activated SR Ca2+ Release , 2003, Circulation research.

[22]  V. Krinsky Self-Organization Autowaves and Structures Far from Equilibrium , 1984 .

[23]  Alan Murray,et al.  Medical physics: Explaining the T-wave shape in the ECG , 2000, Nature.

[24]  A. Garfinkel,et al.  Vulnerable window for conduction block in a one-dimensional cable of cardiac cells, 1: single extrasystoles. , 2006, Biophysical journal.

[25]  A Garfinkel,et al.  Scroll wave dynamics in a three-dimensional cardiac tissue model: roles of restitution, thickness, and fiber rotation. , 2000, Biophysical journal.

[26]  E. Erdmann,et al.  Alterations of K+ currents in isolated human ventricular myocytes from patients with terminal heart failure. , 1993, Circulation research.

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

[28]  Steven H. Strogatz,et al.  Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering , 1994 .

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

[30]  D. T. Kaplan,et al.  Repolarization Inhomogeneities in Ventricular Myocardium Change Dynamically With Abrupt Cycle Length Shortening , 1991, Circulation.

[31]  B. R. Jewell,et al.  Analysis of the effects of changes in rate and rhythm upon electrical activity in the heart. , 1980, Progress in biophysics and molecular biology.

[32]  Vadim V Fedorov,et al.  Termination of sustained atrial flutter and fibrillation using low-voltage multiple-shock therapy. , 2011, Heart rhythm.

[33]  Richard T. Lee,et al.  Cardiomyocyte hypertrophy and degradation of connexin43 through spatially restricted autocrine/paracrine heparin-binding EGF. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[34]  C. Valdivia,et al.  Increased late sodium current in myocytes from a canine heart failure model and from failing human heart. , 2005, Journal of molecular and cellular cardiology.

[35]  Ruediger Becker,et al.  There is no transmural heterogeneity in an index of action potential duration in the canine left ventricle. , 2009, Heart rhythm.

[36]  Kenneth R. Laurita,et al.  Transmural Heterogeneity of Calcium Handling in Canine , 2003, Circulation research.

[37]  D. Rosenbaum,et al.  Transmural Electrophysiological Heterogeneities Underlying Arrhythmogenesis in Heart Failure , 2003, Circulation research.

[38]  Elizabeth M Cherry,et al.  Properties of two human atrial cell models in tissue: restitution, memory, propagation, and reentry. , 2008, Journal of theoretical biology.

[39]  Roger Dzwonczyk,et al.  Electrotonic remodeling following myocardial infarction in dogs susceptible and resistant to sudden cardiac death. , 2008, Journal of applied physiology.

[40]  Itsuo Kodama,et al.  Potassium Channel Subunit Remodeling in Rabbits Exposed to Long-Term Bradycardia or Tachycardia: Discrete Arrhythmogenic Consequences Related to Differential Delayed-Rectifier Changes , 2006, Circulation.

[41]  G. Hasenfuss,et al.  Calcium handling proteins in the failing human heart , 2004, Basic Research in Cardiology.

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

[43]  S. Luther,et al.  Termination of Atrial Fibrillation Using Pulsed Low-Energy Far-Field Stimulation , 2009, Circulation.

[44]  M R Franz,et al.  Electrical and mechanical restitution of the human heart at different rates of stimulation. , 1983, Circulation research.

[45]  W. Baxter,et al.  Spiral waves of excitation underlie reentrant activity in isolated cardiac muscle. , 1993, Circulation research.

[46]  Ruben Coronel,et al.  Activation Delay After Premature Stimulation in Chronically Diseased Human Myocardium Relates to the Architecture of Interstitial Fibrosis , 2001, Circulation.

[47]  A. Panfilov,et al.  Wave propagation in an excitable medium with a negatively sloped restitution curve. , 2002, Chaos.

[48]  D. Mozaffarian,et al.  Executive summary: heart disease and stroke statistics--2010 update: a report from the American Heart Association. , 2010, Circulation.

[49]  Alvin Shrier,et al.  Spiral wave generation in heterogeneous excitable media. , 2002, Physical review letters.

[50]  J. Rogers Wave front fragmentation due to ventricular geometry in a model of the rabbit heart. , 2002, Chaos.

[51]  Ruben Coronel,et al.  Repolarization Gradients in the Canine Left Ventricle Before and After Induction of Short-Term Cardiac Memory , 2005, Circulation.

[52]  T Liu,et al.  Ventricular hypertrophy amplifies transmural repolarization dispersion and induces early afterdepolarization. , 2001, American journal of physiology. Heart and circulatory physiology.

[53]  Robert F Gilmour,et al.  Control of electrical alternans in canine cardiac purkinje fibers. , 2006, Physical review letters.

[54]  B. O’Rourke,et al.  Enhanced Ca(2+)-activated Na(+)-Ca(2+) exchange activity in canine pacing-induced heart failure. , 2000, Circulation research.

[55]  M. Link,et al.  Marked Variability in Susceptibility to Ventricular Fibrillation in an Experimental Commotio Cordis Model , 2010, Circulation.

[56]  Arun V. Holden,et al.  Tension of organizing filaments of scroll waves , 1994, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[57]  Kenneth B. Margulies,et al.  L-Type Ca2+Channel α1cSubunit Isoform Switching in Failing Human Ventricular Myocardium , 2000 .

[58]  Arthur C. Guyton,et al.  Handbook of Physiology—The Cardiovascular System , 1985 .

[59]  J W Buchanan,et al.  The Effects of Antiarrhythmic Drugs, Stimulation Frequency, and Potassium‐Induced Resting Membrane: Potential Changes on Conduction Velocity and dV/dtmax in Guinea Pig Myocardium , 1985, Circulation research.

[60]  Robert F. Gilmour,et al.  Altered Dynamics of Action Potential Restitution and Alternans in Humans With Structural Heart Disease , 2005, Circulation.

[61]  D. Kass,et al.  Cellular basis of ventricular arrhythmias and abnormal automaticity in heart failure. , 1999, American Journal of Physiology.

[62]  Nitish V. Thakor,et al.  Dynamic differences between ventricular fibrillation types induced in human patients by different types of stimulation , 1997, Computers in Cardiology 1997.

[63]  David D Spragg,et al.  Mechanisms Underlying Conduction Slowing and Arrhythmogenesis in Nonischemic Dilated Cardiomyopathy , 2004, Circulation research.

[64]  Gary M Brittenham,et al.  Optical mapping reveals conduction slowing and impulse block in iron-overload cardiomyopathy. , 2003, The Journal of laboratory and clinical medicine.

[65]  Richard H Clayton,et al.  Regional differences in APD restitution can initiate wavebreak and re-entry in cardiac tissue: A computational study , 2005, Biomedical engineering online.

[66]  I Kodama,et al.  Pacing-induced heart failure causes a reduction of delayed rectifier potassium currents along with decreases in calcium and transient outward currents in rabbit ventricle. , 2000, Cardiovascular research.

[67]  N S Peters,et al.  Disturbed connexin43 gap junction distribution correlates with the location of reentrant circuits in the epicardial border zone of healing canine infarcts that cause ventricular tachycardia. , 1997, Circulation.

[68]  J M de Bakker,et al.  Triggered activity and automaticity in ventricular trabeculae of failing human and rabbit hearts. , 1994, Cardiovascular research.

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

[70]  Takeshi Aiba,et al.  Electrical remodeling in the failing heart , 2010, Current opinion in cardiology.

[71]  Donald M. Bers,et al.  Upregulated Na/Ca exchange is involved in both contractile dysfunction and arrhythmogenesis in heart failure , 2002, Basic Research in Cardiology.

[72]  A. Garfinkel,et al.  Vulnerable window for conduction block in a one-dimensional cable of cardiac cells, 2: multiple extrasystoles. , 2006, Biophysical journal.

[73]  H L Greene,et al.  Mortality and morbidity in patients receiving encainide, flecainide, or placebo. The Cardiac Arrhythmia Suppression Trial. , 1991, The New England journal of medicine.

[74]  H. N. Sabbah,et al.  Repolarization abnormalities in cardiomyocytes of dogs with chronic heart failure: role of sustained inward current , 1999, Cellular and Molecular Life Sciences CMLS.

[75]  M J Lab,et al.  Cycle length dependence of the electrophysiological effects of increased load on the myocardium. , 1996, Circulation.

[76]  Gan-XinYan,et al.  Characteristics and Distribution of M Cells in Arterially Perfused Canine Left Ventricular Wedge Preparations , 1998 .

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

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

[79]  R. Winslow,et al.  Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure, II: model studies. , 1999, Circulation research.

[80]  L. Gettes,et al.  Effect of Rate on Changes in Conduction Velocity and Extracellular Potassium Concentration During Acute Ischemia in the In Situ Pig Heart , 1993, Journal of cardiovascular electrophysiology.

[81]  Hongwei Jin,et al.  Arrhythmia Mechanisms in the Failing Heart , 2008, Pacing and clinical electrophysiology : PACE.

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

[83]  Sawa Kostin,et al.  Connexin 43 expression and distribution in compensated and decompensated cardiac hypertrophy in patients with aortic stenosis. , 2004, Cardiovascular research.

[84]  A. Garfinkel,et al.  Alternans and Arrhythmias: From Cell to Heart , 2011, Circulation research.

[85]  Leon Glass,et al.  Cardiac arrhythmia , 2008, Scholarpedia.

[86]  Abhijit Patwardhan,et al.  Restitution of Action Potential Duration During Sequential Changes in Diastolic Intervals Shows Multimodal Behavior , 2004, Circulation research.

[87]  S. Pogwizd,et al.  Nonreentrant mechanisms underlying spontaneous ventricular arrhythmias in a model of nonischemic heart failure in rabbits. , 1995, Circulation.

[88]  Y. Takagishi,et al.  Gap junction remodeling in hypertrophied left ventricles of aortic-banded rats: prevention by angiotensin II type 1 receptor blockade. , 2001, Journal of molecular and cellular cardiology.

[89]  P R Ershler,et al.  Myocardial electrical propagation in patients with idiopathic dilated cardiomyopathy. , 1993, The Journal of clinical investigation.

[90]  Shien-Fong Lin,et al.  Two Types of Ventricular Fibrillation in Isolated Rabbit Hearts: Importance of Excitability and Action Potential Duration Restitution , 2002, Circulation.

[91]  Hani N Sabbah,et al.  Modulation of late sodium current by Ca2+, calmodulin, and CaMKII in normal and failing dog cardiomyocytes: similarities and differences. , 2008, American journal of physiology. Heart and circulatory physiology.

[92]  C. Lau,et al.  Transmural action potential and ionic current remodeling in ventricles of failing canine hearts. , 2002, American journal of physiology. Heart and circulatory physiology.

[93]  Gang Hu,et al.  Hysteresis and bistability in periodically paced cardiac tissue. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[94]  D. Kass,et al.  Dynamic changes in conduction velocity and gap junction properties during development of pacing-induced heart failure. , 2007, American journal of physiology. Heart and circulatory physiology.

[95]  D H Singer,et al.  Sodium current in isolated human ventricular myocytes. , 1993, The American journal of physiology.

[96]  Flavio H. Fenton,et al.  Fiber-Rotation-Induced Vortex Turbulence in Thick Myocardium , 1998 .

[97]  S. Houser,et al.  Contribution of reverse-mode sodium-calcium exchange to contractions in failing human left ventricular myocytes. , 1998, Cardiovascular research.

[98]  David C. Warltier,et al.  Characterization of a Novel PKA Phosphorylation Site, Serine-2030, Reveals No PKA Hyperphosphorylation of the Cardiac Ryanodine Receptor in Canine Heart Failure , 2005, Circulation research.

[99]  S Simonsen,et al.  Monophasic action potentials in patients with coronary artery disease: reproducibility and electrical restitution and conduction at different stimulation rates. , 1987, Cardiovascular research.

[100]  Brian D. Sleeman,et al.  WAVE FRONT PROPAGATION AND ITS FAILURE IN COUPLED SYSTEMS OF DISCRETE BISTABLE CELLS MODELLED BY FITZHUGH-NAGUMO DYNAMICS , 1995 .

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

[102]  R. Price,et al.  Increased Association of ZO-1 With Connexin43 During Remodeling of Cardiac Gap Junctions , 2002, Circulation research.

[103]  Steven Poelzing,et al.  Altered connexin43 expression produces arrhythmia substrate in heart failure. , 2004, American journal of physiology. Heart and circulatory physiology.

[104]  Dmitry Terentyev,et al.  Redox Modification of Ryanodine Receptors Contributes to Sarcoplasmic Reticulum Ca2+ Leak in Chronic Heart Failure , 2008, Circulation research.

[105]  D. Noble,et al.  Cellular basis for the T wave of the electrocardiogram , 1976, Nature.

[106]  Li Li,et al.  Arrhythmogenesis and Contractile Dysfunction in Heart Failure: Roles of Sodium-Calcium Exchange, Inward Rectifier Potassium Current, and Residual &bgr;-Adrenergic Responsiveness , 2001, Circulation research.

[107]  Steven R Houser,et al.  L-Type Ca2+ Channel Density and Regulation Are Altered in Failing Human Ventricular Myocytes and Recover After Support With Mechanical Assist Devices , 2002, Circulation research.

[108]  V. Fast,et al.  [Drift of vortex in the myocardium]. , 1990, Biofizika.

[109]  M. Hirsch,et al.  Differential Equations, Dynamical Systems, and an Introduction to Chaos , 2003 .

[110]  Olivier Bernus,et al.  Alternating conduction in the ischaemic border zone as precursor of reentrant arrhythmias: a simulation study. , 2005, 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.

[111]  R. Haworth,et al.  Abnormal Ca2+ Release, but Normal Ryanodine Receptors, in Canine and Human Heart Failure , 2002, Circulation research.

[112]  A J Levi,et al.  The electrophysiological characteristics of hypertrophied ventricular myocytes from the spontaneously hypertensive rat , 1993, Journal of hypertension.

[113]  A. Pertsov,et al.  Ventricular ¯brillation: Evolution of the Multiple-wavelet Hypothesis , 2001 .

[114]  A. L. Wit Afterdepolarizations and triggered activity: distinction from automaticity as an arrhythmogenic mechanism. , 1992 .

[115]  Igor R Efimov,et al.  Multiple monophasic shocks improve electrotherapy of ventricular tachycardia in a rabbit model of chronic infarction. , 2009, Heart rhythm.

[116]  Igor R Efimov,et al.  Mechanisms of Fibrillation: Neurogenic or Myogenic? Reentrant or Focal? Multiple or Single?: Still Puzzling After 160 Years of Inquiry , 2010, Journal of cardiovascular electrophysiology.

[117]  D. Kass,et al.  Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure, I: experimental studies. , 1999, Circulation research.

[118]  Brian O'Rourke,et al.  Enhanced Ca2+-Activated Na+-Ca2+ Exchange Activity in Canine Pacing-Induced Heart Failure , 2000 .

[119]  V. S. Chakravarthy,et al.  Bistable dynamics of cardiac cell models coupled by dynamic gap junctions linked to Cardiac Memory , 2010, Biological Cybernetics.

[120]  Jie Zhang,et al.  Gap junction remodeling and cardiac arrhythmogenesis in a murine model of oculodentodigital dysplasia , 2007, Proceedings of the National Academy of Sciences.

[121]  Michael Kohlhaas,et al.  Increased Sarcoplasmic Reticulum Calcium Leak but Unaltered Contractility by Acute CaMKII Overexpression in Isolated Rabbit Cardiac Myocytes , 2006, Circulation research.

[122]  D. Burkhoff,et al.  Evolution and resolution of long-term cardiac memory. , 1998, Circulation.

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

[124]  Silvia G Priori,et al.  The fifteen years of discoveries that shaped molecular electrophysiology: time for appraisal. , 2010, Circulation research.

[125]  Edward J Ciaccio,et al.  Heterogeneous gap junction remodeling in reentrant circuits in the epicardial border zone of the healing canine infarct. , 2006, Cardiovascular research.

[126]  Mark von Zastrow,et al.  Microtubule Plus-End-Tracking Proteins Target Gap Junctions Directly from the Cell Interior to Adherens Junctions , 2007, Cell.

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

[128]  Stanley Nattel,et al.  Transmural expression of transient outward potassium current subunits in normal and failing canine and human hearts , 2004, The Journal of physiology.

[129]  H. Calkins,et al.  Beat-to-beat QT interval variability: novel evidence for repolarization lability in ischemic and nonischemic dilated cardiomyopathy. , 1997, Circulation.

[130]  J P Keener On the formation of circulating patterns of excitation in anisotropic excitable media , 1988, Journal of mathematical biology.

[131]  K. Endresen,et al.  Electrical Restitution and Conduction Intervals of Ventricular Premature Beats in Man: Influence of Heart Rate , 1989, Pacing and clinical electrophysiology : PACE.

[132]  A Garfinkel,et al.  Model of intracellular calcium cycling in ventricular myocytes. , 2003, Biophysical journal.

[133]  Robert F Gilmour,et al.  Contribution of IKr to Rate-Dependent Action Potential Dynamics in Canine Endocardium , 2004, Circulation research.

[134]  B. Albat,et al.  Calcium Currents in Diseased Human Cardiac Cells , 1995, Journal of cardiovascular pharmacology.

[135]  G. Rozanski,et al.  Electrophysiology of rabbit ventricular myocytes following sustained rapid ventricular pacing. , 1997, Journal of molecular and cellular cardiology.

[136]  A. T. Winfree,et al.  Evolving perspectives during 12 years of electrical turbulence. , 1998, Chaos.

[137]  Donald M. Bers,et al.  Requirement for Ca 2+/calmodulin-dependent kinase II in the transition from pressure overload-induced cardiac hypertrophy to heart failure in mice (Journal of Clinical Investigation (2009) 119, 5, (1230-1240) doi: 10.1172/JCI38022) , 2012 .

[138]  Niels F Otani,et al.  Theory of action potential wave block at-a-distance in the heart. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[139]  Alan Garfinkel,et al.  Electrical Restitution and Cardiac Fibrillation , 2002, Journal of cardiovascular electrophysiology.

[140]  M. Janse,et al.  Electrophysiological changes in heart failure and their relationship to arrhythmogenesis. , 2004, Cardiovascular research.

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

[142]  W Grossman,et al.  Expression of dihydropyridine receptor (Ca2+ channel) and calsequestrin genes in the myocardium of patients with end-stage heart failure. , 1992, The Journal of clinical investigation.

[143]  J. Keener,et al.  The effects of discrete gap junction coupling on propagation in myocardium. , 1991, Journal of theoretical biology.

[144]  S. Nattel,et al.  Arrhythmogenic ion-channel remodeling in the heart: heart failure, myocardial infarction, and atrial fibrillation. , 2007, Physiological reviews.

[145]  F. T. Arecchi,et al.  SUPEREXCITABILITY INDUCED SPIRAL BREAKUP IN EXCITABLE SYSTEMS , 1996 .

[146]  D. Chialvo,et al.  Low dimensional chaos in cardiac tissue , 1990, Nature.

[147]  N. Alpert,et al.  Alterations in sarcoplasmic reticulum gene expression in human heart failure. A possible mechanism for alterations in systolic and diastolic properties of the failing myocardium. , 1993, Circulation research.

[148]  Robert F. Gilmour,et al.  Dynamic mechanism for conduction block in heart tissue , 2003 .

[149]  J M de Bakker,et al.  Reentry as a cause of ventricular tachycardia in patients with chronic ischemic heart disease: electrophysiologic and anatomic correlation. , 1988, Circulation.

[150]  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.

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

[152]  古塚 大介,et al.  ペンチレンテトラゾール誘発痙攣によるマウス脳Ca^ /calmodulin dependent protein kinase II活性の変化 , 1996 .

[153]  J. Pu,et al.  Alterations of Na+ currents in myocytes from epicardial border zone of the infarcted heart. A possible ionic mechanism for reduced excitability and postrepolarization refractoriness. , 1997, Circulation research.

[154]  Elizabeth M Cherry,et al.  Termination of equine atrial fibrillation by quinidine: an optical mapping study. , 2008, Journal of veterinary cardiology : the official journal of the European Society of Veterinary Cardiology.

[155]  Stanley Nattel,et al.  Mechanisms Underlying Rate-Dependent Remodeling of Transient Outward Potassium Current in Canine Ventricular Myocytes , 2008, Circulation research.

[156]  C E THOMAS,et al.  The muscular architecture of the ventricles of hog and dog hearts. , 1957, The American journal of anatomy.

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

[158]  Charles Antzelevitch,et al.  Role of spatial dispersion of repolarization in inherited and acquired sudden cardiac death syndromes. , 2007, American journal of physiology. Heart and circulatory physiology.

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

[160]  R. Gray,et al.  Spatial and temporal organization during cardiac fibrillation , 1998, Nature.

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

[162]  David A. Kass,et al.  Abstract 1511: Gap Junction Internalization and Autophagic Degradation in the Failing Heart , 2008 .

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

[164]  Donald M. Bers,et al.  β-Adrenergic Enhancement of Sarcoplasmic Reticulum Calcium Leak in Cardiac Myocytes Is Mediated by Calcium/Calmodulin-Dependent Protein Kinase , 2007 .

[165]  A. Lopatin,et al.  Dominant-negative suppression of I(K1) in the mouse heart leads to altered cardiac excitability. , 2003, Journal of molecular and cellular cardiology.

[166]  Stanley Nattel,et al.  Wave block formation in homogeneous excitable media following premature excitations: dependence on restitution relations. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[167]  Raymond E. Ideker,et al.  Activation Patterns of Purkinje Fibers During Long-Duration Ventricular Fibrillation in an Isolated Canine Heart Model , 2007, Circulation.

[168]  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.

[169]  D. Kass,et al.  Ionic mechanism of action potential prolongation in ventricular myocytes from dogs with pacing-induced heart failure. , 1996, Circulation research.

[170]  Mark E Anderson,et al.  Multiple downstream proarrhythmic targets for calmodulin kinase II: moving beyond an ion channel-centric focus. , 2007, Cardiovascular research.

[171]  E. Marbán,et al.  Gene Therapy to Inhibit the Calcium Channel &bgr; Subunit: Physiological Consequences and Pathophysiological Effects in Models of Cardiac Hypertrophy , 2007, Circulation research.

[172]  L. J. Leon,et al.  Spatiotemporal evolution of ventricular fibrillation , 1998, Nature.

[173]  Jochen Rose,et al.  Molecular correlates of altered expression of potassium currents in failing rabbit myocardium. , 2005, American journal of physiology. Heart and circulatory physiology.

[174]  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.

[175]  I. Efimov,et al.  The role of dynamic instability and wavelength in arrhythmia maintenance as revealed by panoramic imaging with blebbistatin vs. 2,3-butanedione monoxime. , 2012, American journal of physiology. Heart and circulatory physiology.

[176]  D. Burkhoff,et al.  PKA Phosphorylation Dissociates FKBP12.6 from the Calcium Release Channel (Ryanodine Receptor) Defective Regulation in Failing Hearts , 2000, Cell.

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

[178]  S. Pogwizd,et al.  Mechanisms underlying spontaneous and induced ventricular arrhythmias in patients with idiopathic dilated cardiomyopathy. , 1996, Circulation.

[179]  Tong Zhang,et al.  Requirement for Ca2+/calmodulin-dependent kinase II in the transition from pressure overload-induced cardiac hypertrophy to heart failure in mice. , 2009, The Journal of clinical investigation.

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

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

[182]  Guy Vassort,et al.  Protein Kinase A Phosphorylation of the Cardiac Calcium Release Channel (Ryanodine Receptor) in Normal and Failing Hearts , 2003, The Journal of Biological Chemistry.

[183]  W. Baxter,et al.  Stationary and drifting spiral waves of excitation in isolated cardiac muscle , 1992, Nature.

[184]  Donald M Bers,et al.  Beta-adrenergic enhancement of sarcoplasmic reticulum calcium leak in cardiac myocytes is mediated by calcium/calmodulin-dependent protein kinase. , 2007, Circulation research.

[185]  L. Glass Synchronization and rhythmic processes in physiology , 2001, Nature.

[186]  G. Salama,et al.  Adaptation of Cardiac Action Potential Durations to Stimulation History with Random Diastolic Intervals , 2004, Journal of cardiovascular electrophysiology.

[187]  M. Bootman,et al.  Increased InsP3Rs in the junctional sarcoplasmic reticulum augment Ca2+ transients and arrhythmias associated with cardiac hypertrophy , 2009, Proceedings of the National Academy of Sciences.

[188]  R. Gilmour,et al.  Decreased Density of Ito in Left Ventricular Myocytes from German Shepherd Dogs with Inherited Arrhythmias , 1997, Journal of cardiovascular electrophysiology.

[189]  E Erdmann,et al.  Characteristics of transient outward current in human ventricular myocytes from patients with terminal heart failure. , 1993, Circulation research.

[190]  P. Poole‐Wilson,et al.  Reduced content of connexin43 gap junctions in ventricular myocardium from hypertrophied and ischemic human hearts. , 1993, Circulation.

[191]  D. Noble,et al.  Multistability property in cardiac ionic models of mammalian and human ventricular cells. , 2010, Progress in biophysics and molecular biology.

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

[193]  F. Fenton,et al.  Visualization of spiral and scroll waves in simulated and experimental cardiac tissue , 2008 .

[194]  Harold M. Hastings,et al.  Memory in an Excitable Medium: A Mechanism for Spiral Wave Breakup in the Low-Excitability Limit , 1999 .

[195]  Harold M. Hastings,et al.  Transition from ventricular tachycardia to ventricular fibrillation as function of tissue characteristics computer model , 2000, Proceedings of the 22nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society (Cat. No.00CH37143).

[196]  G. Steinbeck,et al.  Molecular basis of transient outward potassium current downregulation in human heart failure: a decrease in Kv4.3 mRNA correlates with a reduction in current density. , 1998, Circulation.

[197]  James Coromilas,et al.  Stabilization of cardiac ryanodine receptor prevents intracellular calcium leak and arrhythmias , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[198]  M. Janse,et al.  Electrophysiological mechanisms of ventricular arrhythmias resulting from myocardial ischemia and infarction. , 1989, Physiological reviews.

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

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

[201]  P. Wolf,et al.  Mechanism of Ventricular Vulnerability to Single Premature Stimuli in Open‐Chest Dogs , 1988, Circulation research.

[202]  E Erdmann,et al.  Characteristics of calcium-current in isolated human ventricular myocytes from patients with terminal heart failure. , 1991, Journal of molecular and cellular cardiology.

[203]  Wen Dun,et al.  Remodeled cardiac calcium channels. , 2006, Journal of molecular and cellular cardiology.

[204]  Robert F Gilmour,et al.  Suppression of electrical alternans by overexpression of HERG in canine ventricular myocytes. , 2004, American journal of physiology. Heart and circulatory physiology.

[205]  Antonis A Armoundas,et al.  Role of Sodium-Calcium Exchanger in Modulating the Action Potential of Ventricular Myocytes From Normal and Failing Hearts , 2003, Circulation research.

[206]  S. Pogwizd,et al.  Focal Mechanisms Underlying Ventricular Tachycardia During Prolonged Ischemic Cardiomyopathy , 1994, Circulation.

[207]  Nicholas S. Peters,et al.  Remodeling of Gap Junctional Channel Function in Epicardial Border Zone of Healing Canine Infarcts , 2003, Circulation research.

[208]  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.

[209]  I. Efimov,et al.  Transmural Dispersion of Repolarization in Failing and Nonfailing Human Ventricle , 2010, Circulation research.

[210]  R. Gilmour,et al.  Dynamic restitution of action potential duration during electrical alternans and ventricular fibrillation. , 1998, The American journal of physiology.

[211]  A. Kleber,et al.  Electrical uncoupling and increase of extracellular resistance after induction of ischemia in isolated, arterially perfused rabbit papillary muscle. , 1987, Circulation research.

[212]  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.

[213]  R. Myerburg,et al.  The ionic mechanism of reperfusion-induced early afterdepolarizations in feline left ventricular hypertrophy. , 1993, The Journal of clinical investigation.

[214]  Robert F Gilmour,et al.  Ionic mechanism of electrical alternans. , 2002, American journal of physiology. Heart and circulatory physiology.

[215]  Niels F. Otani,et al.  Dynamic Mechanism for Initiation of Ventricular Fibrillation In Vivo , 2008, Circulation.

[216]  D. Bers,et al.  Ca2+/Calmodulin–Dependent Protein Kinase Modulates Cardiac Ryanodine Receptor Phosphorylation and Sarcoplasmic Reticulum Ca2+ Leak in Heart Failure , 2005, Circulation research.

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

[218]  Joseph A. Hill,et al.  Electrical remodeling in cardiac hypertrophy. , 2003, Trends in cardiovascular medicine.

[219]  F. Leclercq,et al.  Ca2+ currents in compensated hypertrophy and heart failure. , 1998, Cardiovascular research.

[220]  D. Noble,et al.  A model for human ventricular tissue. , 2004, American journal of physiology. Heart and circulatory physiology.

[221]  Aoxiang Xu,et al.  Alternans and higher-order rhythms in an ionic model of a sheet of ischemic ventricular muscle. , 2000, Chaos.

[222]  J Jalife,et al.  Ventricular fibrillation: mechanisms of initiation and maintenance. , 2000, Annual review of physiology.

[223]  G. Gintant,et al.  Heterogeneity within the ventricular wall. Electrophysiology and pharmacology of epicardial, endocardial, and M cells. , 1991, Circulation research.

[224]  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.

[225]  R. Gilmour,et al.  Reduction of the transient outward potassium current in a canine model of Chagas' disease. , 1995, The American journal of physiology.

[226]  R. Clayton,et al.  Whole heart action potential duration restitution properties in cardiac patients: a combined clinical and modelling study , 2006, Experimental physiology.

[227]  Stefan Herzig,et al.  Cardiac L-type Calcium Channel β-Subunits Expressed in Human Heart Have Differential Effects on Single Channel Characteristics* , 2003, Journal of Biological Chemistry.

[228]  James P. Keener,et al.  Propagation and its failure in coupled systems of discrete excitable cells , 1987 .

[229]  A V Panfilov,et al.  Generation of Reentry in Anisotropic Myocardium , 1993, Journal of cardiovascular electrophysiology.

[230]  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.

[231]  P. Ursell,et al.  Structural and Electrophysiological Changes in the Epicardial Border Zone of Canine Myocardial Infarcts during Infarct Healing , 1985, Circulation research.

[232]  Wanda Krassowska,et al.  Bistability and Correlation with Arrhythmogenesis in a Model of the Right Atrium , 2005, Annals of Biomedical Engineering.

[233]  W Peters,et al.  Cellular Mechanisms of Differential Action Potential Duration Restitution in Canine Ventricular Muscle Cells During Single Versus Double Premature Stimuli , 1992, Circulation.

[234]  Antonis A Armoundas,et al.  Molecular mechanisms underlying K+ current downregulation in canine tachycardia-induced heart failure. , 2005, American journal of physiology. Heart and circulatory physiology.

[235]  Woo Jin Park,et al.  Restoration of mechanical and energetic function in failing aortic-banded rat hearts by gene transfer of calcium cycling proteins. , 2007, Journal of molecular and cellular cardiology.

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

[237]  S. Houser,et al.  Adrenergic Regulation of Cardiac Contractility Does Not Involve Phosphorylation of the Cardiac Ryanodine Receptor at Serine 2808 , 2008, Circulation research.