Is fibrillation chaos?

Ventricular fibrillation is examined to determine whether it is an instance of deterministic chaos. Surface ECGs from dogs in fibrillation were used to generate a state space representation of fibrillation. Our analysis failed to identify a low-dimensional attractor that could be associated with fibrillation. The results suggest that fibrillation is similar to a nonchaotic random signal. We note, however, that such random-looking but nonchaotic behavior can also be generated by a nonlinear deterministic system.

[1]  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 .

[2]  The Mechanism and Nature of Ventricular Fibrillation , 1941 .

[3]  W. Rheinboldt,et al.  A COMPUTER MODEL OF ATRIAL FIBRILLATION. , 1964, American heart journal.

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

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

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

[7]  R. M. Heethaar,et al.  Signal analysis of ventricular fibrillation , 1979 .

[8]  D Durrer,et al.  Computer Simulation of Arrhythmias in a Network of Coupled Excitable Elements , 1980, Circulation research.

[9]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

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

[11]  R. Ideker,et al.  The Transition to Ventricular Fibrillation Induced by Reperfusion After Acute Ischemia in the Dog: A Period of Organized Epicardial Activation , 1981, Circulation.

[12]  C. Sparrow.  The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors , 1982 .

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

[14]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[15]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

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

[17]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[18]  Peter W. Milonni,et al.  Dimensions and entropies in chaotic systems: Quantification of complex behavior , 1986 .

[19]  A. Babloyantz,et al.  Low-dimensional chaos in an instance of epilepsy. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[20]  G. P. King,et al.  Extracting qualitative dynamics from experimental data , 1986 .

[21]  GOTTFRIED MAYER‐KRESS AND,et al.  Dimensionality of the Human Electroencephalogram , 1987, Annals of the New York Academy of Sciences.

[22]  R J Cohen,et al.  Electrical alternans and cardiac electrical instability. , 1988, Circulation.

[23]  James P. Keener,et al.  A mathematical model for the vulnerable phase in myocardium , 1988 .

[24]  John J. Tyson,et al.  When Time Breaks Down: The Three‐Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias , 1988 .

[25]  D. T. Kaplan,et al.  Nonlinear dynamics in cardiac conduction. , 1988, Mathematical biosciences.

[26]  Crutchfield,et al.  Are attractors relevant to turbulence? , 1988, Physical review letters.

[27]  Joseph P. Zbilut,et al.  Dimensional analysis of heart rate variability in heart transplant recipients , 1988 .

[28]  J. Havstad,et al.  Attractor dimension of nonstationary dynamical systems from small data sets. , 1989, Physical review. A, General physics.

[29]  A. Provenzale,et al.  Finite correlation dimension for stochastic systems with power-law spectra , 1989 .