Time series analysis of complex dynamics in physiology and medicine.

A variety of mathematical methods have been developed to characterize complex rhythms that are observed in physiological systems. These methods include classical techniques such as the mean, standard deviation, and power spectrum, as well as newer methods suggested by nonlinear dynamics including the dimension, Lyapunov number, and entropy. This paper reviews the various ways in which these measures have been applied to analyze physiological dynamics with emphasis on the potential advantages and pitfalls of the various approaches. We conclude that these methods may be useful to help characterize complex time series, but only rarely is it possible to use these methods to establish deterministic chaos in a given time series.

[1]  J Persson,et al.  Comments on "Modeling the stationarity and Gaussianity of spontaneous electroencephalographic activity". , 1977, IEEE transactions on bio-medical engineering.

[2]  D. O. Walter,et al.  On automatic methods of sleep staging by EEG spectra. , 1970, Electroencephalography and clinical neurophysiology.

[3]  H. Abarbanel,et al.  Lyapunov exponents from observed time series. , 1990, Physical review letters.

[4]  D. T. Kaplan,et al.  Aging and the complexity of cardiovascular dynamics. , 1991, Biophysical journal.

[5]  L. Glass,et al.  Chaos in multi-looped negative feedback systems. , 1990, Journal of theoretical biology.

[6]  D. T. Kaplan,et al.  Dynamics of heart rate. , 1991, Chaos.

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

[8]  K. Aihara,et al.  Forced Oscillations and Routes to Chaos in the Hodgkin-Huxley Axons and Squid Giant Axons , 1987 .

[9]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[10]  Hatsuo Hayashi,et al.  Chaos in Molluscan Neuron , 1987 .

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

[12]  G Fox,et al.  Muscle pressure and flow during expiration in infants. , 1984, The American review of respiratory disease.

[13]  Leon Glass,et al.  Coarse-grained embeddings of time series: random walks, Gaussian random processes, and deterministic chaos , 1993 .

[14]  B. Mandelbrot,et al.  RANDOM WALK MODELS FOR THE SPIKE ACTIVITY OF A SINGLE NEURON. , 1964, Biophysical journal.

[15]  Saul Krasner,et al.  The Ubiquity of chaos , 1990 .

[16]  J. Mortola,et al.  Respiration in newborns: development of the control of breathing. , 1982, The American review of respiratory disease.

[17]  A. Babloyantz,et al.  Some Remarks on Nonlinear Data Analysis of Physiological Time Series , 1989 .

[18]  R. Eykholt,et al.  Estimating the Lyapunov-exponent spectrum from short time series of low precision. , 1991, Physical review letters.

[19]  A. Gallant,et al.  Finding Chaos in Noisy Systems , 1992 .

[20]  M. Silverman,et al.  Basic mechanisms of pediatric respiratory disease , 1993 .

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

[22]  M W Kroll,et al.  Slope filtered pointwise correlation dimension algorithm and its evaluation with prefibrillation heart rate data. , 1992, Journal of electrocardiology.

[23]  G G Haddad,et al.  Heart rate control in normal and aborted-SIDS infants. , 1993, The American journal of physiology.

[24]  L. Glass,et al.  PATHOLOGICAL CONDITIONS RESULTING FROM INSTABILITIES IN PHYSIOLOGICAL CONTROL SYSTEMS * , 1979, Annals of the New York Academy of Sciences.

[25]  L Glass,et al.  Complex dynamics and bifurcations in neurology. , 1989, Journal of theoretical biology.

[26]  Ernst Fernando Lopes Da Silva Niedermeyer,et al.  Electroencephalography, basic principles, clinical applications, and related fields , 1982 .

[27]  J. A. Stewart,et al.  Nonlinear Time Series Analysis , 2015 .

[28]  James Theiler,et al.  Using surrogate data to detect nonlinearity in time series , 1991 .

[29]  L Glass,et al.  Complex oscillations in a human motor system. , 1989, Journal of motor behavior.

[30]  Richard I. Kitney,et al.  The Study of heart-rate variability , 1980 .

[31]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[32]  October I.  Physical Review Letters , 2022 .

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

[34]  J. Miller,et al.  Decreased heart rate variability and its association with increased mortality after acute myocardial infarction. , 1987, The American journal of cardiology.

[35]  W. Black,et al.  Sudden cardiac death: etiologies, pathogenesis, and management. , 1989, Disease-a-month : DM.

[36]  F. Yates,et al.  Dimensional analysis of nonlinear oscillations in brain, heart, and muscle , 1988 .

[37]  Raymond E. Ideker,et al.  Chaos in the Heart: Implications for Clinical Cardiology , 1990, Bio/Technology.

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

[39]  W. Pritchard,et al.  Dimensional analysis of no-task human EEG using the Grassberger-Procaccia method. , 1992, Psychophysiology.

[40]  D. T. Kaplan,et al.  Geometrical techniques for analyzing ECG dynamics. , 1992, Journal of electrocardiology.

[41]  Richard Langendorf,et al.  Interpretation of Complex Arrhythmias , 1979 .

[42]  G. Donaldson,et al.  The chaotic behaviour of resting human respiration. , 1992, Respiration physiology.

[43]  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.

[44]  D. T. Kaplan,et al.  Direct test for determinism in a time series. , 1992, Physical review letters.

[45]  L. Glass,et al.  Theory of heart : biomechanics, biophysics, and nonlinear dynamics of cardiac function , 1991 .

[46]  M. Casdagli.  Chaos and Deterministic Versus Stochastic Non‐Linear Modelling , 1992 .

[47]  George Sugihara,et al.  Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series , 1990, Nature.

[48]  W. Freeman,et al.  How brains make chaos in order to make sense of the world , 1987, Behavioral and Brain Sciences.

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

[50]  L. Olsen,et al.  Chaos in biological systems , 1985, Quarterly Reviews of Biophysics.