Deviations from uniform power law scaling in nonstationary time series.

A classic problem in physics is the analysis of highly nonstationary time series that typically exhibit long-range correlations. Here we test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat-to-beat fluctuations in the human heart rate. We develop techniques based on the Fano factor and Allan factor functions, as well as on detrended fluctuation analysis, for quantifying deviations from uniform power-law scaling in nonstationary time series. By analyzing extremely long data sets of up to N = 10(5) beats for 11 healthy subjects, we find that the fluctuations in the heart rate scale approximately uniformly over several temporal orders of magnitude. By contrast, we find that in data sets of comparable length for 14 subjects with heart disease, the fluctuations grow erratically, indicating a loss of scaling stability.

[1]  G. Vojta.  Fractals and Disordered Systems , 1997 .

[2]  W. Willinger,et al.  ESTIMATORS FOR LONG-RANGE DEPENDENCE: AN EMPIRICAL STUDY , 1995 .

[3]  A. Aldroubi,et al.  Wavelets in Medicine and Biology , 1997 .

[4]  J. Strackee,et al.  Comparing Spectra of a Series of Point Events Particularly for Heart Rate Variability Data , 1984, IEEE Transactions on Biomedical Engineering.

[5]  Robert G. Turcott,et al.  Long-duration correlation in the sequence of action potentials in an insect visual interneuron , 1995 .

[6]  D. W. Allan,et al.  A statistical model of flicker noise , 1966 .

[7]  H. Stanley,et al.  Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. , 1995, Chaos.

[8]  Shlomo Havlin,et al.  Scaling behaviour of heartbeat intervals obtained by wavelet-based time-series analysis , 1996, Nature.

[9]  Jeffrey M. Hausdorff,et al.  Long-range anticorrelations and non-Gaussian behavior of the heartbeat. , 1993, Physical review letters.

[10]  A. Goldberger.  Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside , 1996, The Lancet.

[11]  W. Cannon.  ORGANIZATION FOR PHYSIOLOGICAL HOMEOSTASIS , 1929 .

[12]  U. Fano.  Ionization Yield of Radiations. II. The Fluctuations of the Number of Ions , 1947 .

[13]  Steven B. Lowen,et al.  ESTIMATION AND SIMULATION OF FRACTAL STOCHASTIC POINT PROCESSES , 1995 .

[14]  Robert G. Turcott,et al.  Long-duration correlation and attractor topology of the heartbeat rate differ for healthy patients and those with heart failure , 1993, Optics & Photonics.

[15]  R. Mantegna,et al.  Long-range correlation properties of coding and noncoding DNA sequences: GenBank analysis. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.