Low dimensional chaos in cardiac tissue

CHAOS is a term uvd to characterize aperiodic activity arising in a dynamical system, or in a set of equations describing the system's temporal evolution as a result of a deterministic mechanism that has sensitive dependence on initial conditions1. Chaos, in that sense, has been proposed to make an important contribution to normal and abnormal cardiac rhythms2–6. To date, however, descriptions of chaos in heart tissue have been limited primarily to periodically forced cardiac pacemakers2,6. Because many cardiac rhythm disturbances, particularly those initiated or perpetuated by re-entrant excitation, originate from within non-pacemaker cardiac tissues7–9, demonstrations of chaos in non-pacemaker tissue might provide a deterministic explanation for a wide variety of complex dysrhythmias. Here we report experimental evidence for chaotic patterns of activation and action potential characteristics in externally driven, non-spontaneously active Purkinje fibres and ventricular muscle. The results indicate that there is an apparent link between the mechanism of low dimensional chaos and the occurrence of reflected responses which could lead to more spatially disorganized phenomena. A detailed mechanism for the low dimensional chaos observed experimentally is pursued using a difference equation model. Critical features of the model include a non-monotonic relationship between recovery time during rhythmic stimulation and the state of membrane properties, and a steeply sloped recovery of membrane properties over certain ranges of recovery times. Besides explaining our results, the analytical model may pertain to irregular dynamics in other excitable systems, particularly the intact dysrhythmic heart.

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

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

[3]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[4]  M. Feigenbaum.  Quantitative universality for a class of nonlinear transformations , 1978 .

[5]  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.

[6]  T. Colatsky,et al.  Effects of External Calcium, Calcium Channel‐Blocking Agents, and Stimulation Frequency on Cycle Length‐Dependent Changes in Canine Cardiac Action Potential Duration , 1980, Circulation research.

[7]  C Antzelevitch,et al.  Characteristics of Reflection as a Mechanism of Reentrant Arrhythmias and Its Relationship to Parasystole , 1980, Circulation.

[8]  P. Linsay.  Period Doubling and Chaotic Behavior in a Driven Anharmonic Oscillator , 1981 .

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

[10]  L. Glass,et al.  Phase locking, period-doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells. , 1981, Science.

[11]  A. Wolf,et al.  One-Dimensional Dynamics in a Multicomponent Chemical Reaction , 1982 .

[12]  N. El-Sherif,et al.  Ventricular Activation Patterns of Spontaneous and Induced Ventricular Rhythms in Canine One‐Day‐Old Myocardial Infarction: Evidence for Focal and Reentrant Mechanisms , 1982, Circulation research.

[13]  Pierre Bergé,et al.  Order within chaos : towards a deterministic approach to turbulence , 1984 .

[14]  D. Adam,et al.  Period multupling-evidence for nonlinear behaviour of the canine heart , 1984, Nature.

[15]  R. Cohen,et al.  Simple finite-element model accounts for wide range of cardiac dysrhythmias. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Robert Shaw,et al.  The Dripping Faucet As A Model Chaotic System , 1984 .

[17]  J E Saffitz,et al.  Intramural Reentry as a Mechanism of Ventricular Tachycardia during Evolving Canine Myocardial Infarction , 1985, Circulation research.

[18]  B. Surawicz,et al.  Effect of antiarrhythmic drugs on the premature action potential duration in canine cardiac Purkinje fibers. , 1985, The Journal of pharmacology and experimental therapeutics.

[19]  Alvin Shrier,et al.  11. Chaotic cardiac rhythms , 1986 .

[20]  E. Haber,et al.  The heart and cardiovascular system , 1986 .

[21]  R. Gilmour,et al.  Overdrive suppression of conduction at the canine Purkinje-muscle junction. , 1987, Circulation.

[22]  D. Chialvo,et al.  Non-linear dynamics of cardiac excitation and impulse propagation , 1987, Nature.

[23]  Alvin Shrier,et al.  Nonlinear dynamics, chaos and complex cardiac arrhythmias , 1987, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[24]  K. Aihara,et al.  Chaos and phase locking in normal squid axons , 1987 .

[25]  E. Dowell,et al.  Chaotic Vibrations: An Introduction for Applied Scientists and Engineers , 1988 .

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

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

[28]  Michael C. Mackey,et al.  From Clocks to Chaos , 1988 .