Practical problems of determining the dimensions of heart rate data

The practical problems are explored of determining the dimension of the phase space set generated from real, experimental and simulated data of the times between consecutive hearbeats in normal and diseased rabbits. It is determined how different measures of dimension have depended on the procedures used to construct the phase space set and on such properties of the data as the amount of data, noise, long-term trends and stationarity. Reproducible estimates of the dimensions of different physiological states are found to require considerable amounts of data recorded under stationary conditions.

[1]  Theiler,et al.  Spurious dimension from correlation algorithms applied to limited time-series data. , 1986, Physical review. A, General physics.

[2]  P. Grassberger,et al.  NONLINEAR TIME SEQUENCE ANALYSIS , 1991 .

[3]  L. Liebovitch,et al.  A fast algorithm to determine fractal dimensions by box counting , 1989 .

[4]  Neil Gershenfeld,et al.  An Experimentalist’s Introduction to the Observation of Dynamical Systems , 1988 .

[5]  James P. Crutchfield,et al.  Geometry from a Time Series , 1980 .

[6]  D. Hoyer,et al.  Nonlinear analysis of heart rate and respiratory dynamics , 1997, IEEE Engineering in Medicine and Biology Magazine.

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

[8]  Bruce J. West,et al.  Some observations on the questions: is ventricular fibrillation chaos? , 1996 .

[9]  J E Skinner,et al.  Correlation dimension of heartbeat intervals is reduced in conscious pigs by myocardial ischemia. , 1991, Circulation research.

[10]  U Zwiener,et al.  Deterministic--chaotic and periodic properties of heart rate and arterial pressure fluctuations and their mediation in piglets. , 1996, Cardiovascular research.

[11]  Gabriel B. Mindlin,et al.  An efficient algorithm for fast O(N*ln(N)) box counting , 1990 .

[12]  H. Abarbanel,et al.  Prediction in chaotic nonlinear systems: Methods for time series with broadband Fourier spectra. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[13]  U Zwiener,et al.  Relations between parameters of spectral power densities and deterministic chaos of heart-rate variability. , 1996, Journal of the autonomic nervous system.

[14]  H. Schellnhuber,et al.  Efficient box-counting determination of generalized fractal dimensions. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[15]  Arnold J. Mandell,et al.  Dynamical complexity and pathological order in the cardiac monitoring problem , 1987 .

[16]  L. Glass,et al.  Global bifurcations of a periodically forced biological oscillator , 1984 .

[17]  D. Ruelle,et al.  Recurrence Plots of Dynamical Systems , 1987 .

[18]  J. Yorke,et al.  Dimension of chaotic attractors , 1982 .

[19]  Schreiber,et al.  Noise reduction in chaotic time-series data: A survey of common methods. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  Mike E. Davies,et al.  Noise reduction by gradient descent , 1993 .

[21]  Schwartz,et al.  Singular-value decomposition and the Grassberger-Procaccia algorithm. , 1988, Physical review. A, General physics.

[22]  Mingzhou Ding,et al.  Estimating correlation dimension from a chaotic time series: when does plateau onset occur? , 1993 .

[23]  S M Pincus,et al.  Approximate entropy as a measure of system complexity. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[24]  P E Rapp,et al.  A guide to dynamical analysis , 1994, Integrative physiological and behavioral science : the official journal of the Pavlovian Society.

[25]  D. Ruelle,et al.  Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems , 1992 .

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

[27]  Leonard A. Smith.  Intrinsic limits on dimension calculations , 1988 .