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Long-Range Dependence in Heartbeat Dynamics

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Processes with Long-Range Correlations

Part of the book series: Lecture Notes in Physics ((LNP,volume 621))

Abstract

Physiologic signals are generated b complex self-regulating systems that process inputs with a broad range of characteristics [1,2,3]. Man physiological time series are extremely inhomogeneous and nonstationary, fluctuating in an irregular and complex manner. An important question is whether the “heterogeneous” structure of physiologic time series arises trivially from external and intrinsic perturbations which push the system away from a homeostatic set point. An alternative hypothesis is that the fluctuations are, at least in part, due to the underlying dynamics of the system. The key problem is how to decompose subtle fluctuations (due to intrinsic physiologic control)from other nonstationary trends associated with external stimuli. Till recently, the analysis of the fractal properties of such fluctuations has been restricted to second moment linear characteristics such as the power spectrum and the two-point autocorrelation function. These analyses reveal that the fractal behavior of healthy, free-running physiological systems is often characterized by 1/f-like scaling of the power spectra over a wide range of time scales [4,5,6 7,8]. A signal which exhibits such power-law long-range dependence and is homogeneous (i.e. different parts of the signal have different statistical properties) is called a monofractal signal. Man physiologic time series, however, are inhomogeneous with different parts of the signal characterized by different statistical properties. In addition, there is evidence that physiologic dynamics exhibits nonlinear properties [9,10,11 12,13,14,15]. Such features are often associated with multifractal behavior, i.e., presence of long-range power-law dependence in the higher moments which is a nonlinear function of the scaling of the second moment [16]. Up to now, robust demonstration of multifractalit for nonstationary time series has been hampered by problems related to a drastic bias in the estimate of the singularity spectrum due to diverging negative moments. Moreover, the classical approaches based on the box-counting technique and structure function formalism fail when a fractal function is composed of a multifractal singular part embedded in regular polynomial behavior [17]. By means of a wavelet-based multifractal formalism, we show that health human heartbeat dynamics exhibits even higher complexity (than previously expected from the finding of monofractal 1/f scaling) which is characterized by a broad multifractal spectrum [18].

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Authors and Affiliations

  1. Harvard Medical School, Beth Israel Deaconess Medical Center, Boston, USA

    Plamen Ch. Ivanov

  2. Center for Polymer Studies and Department of Physics, Boston University, Boston, USA

    Plamen Ch. Ivanov

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  1. Dept. of Mathematics, Indian Institute of Science, 560 012, Bangalore, India

    Govindan Rangarajan

  2. Center for Complex Systems and Brain Sciences, Florida Atlantic University, 33431, Boca Raton, FL, USA

    Mingzhou Ding

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Ivanov, P.C. (2003). Long-Range Dependence in Heartbeat Dynamics. In: Rangarajan, G., Ding, M. (eds) Processes with Long-Range Correlations. Lecture Notes in Physics, vol 621. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44832-2_19

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