Abstract

We present a combined wavelet and analytic signal approach to study biological and physiological nonstationary time series. The method enables one to reduce the effects of nonstationarity and to identify dynamical features on different time scales. Such an approach can test for the existence of universal scaling properties in the underlying complex dynamics. We applied the technique to human cardiac dynamics and find a universal scaling form for the heartbeat variability in healthy subjects. A breakdown of this scaling is associated with pathological conditions.

Introduction

The central task of statistical physics is to study macroscopic phenomena that result from microscopic interactions among many individual components. This problem is akin to many investigations undertaken in biology. In particular, physiological systems under neuroautonomic regulation, such as heart rate regulation, are good candidates for such an approach, since: (i) the systems often include multiple components, thus leading to very large numbers of degrees of freedom, and (ii) the systems usually are driven by competing forces. Therefore, it seems reasonable to consider the possibility that dynamical systems under neural regulation may exhibit temporal structures which are similar, under certain conditions, to those found in physical systems. Indeed, concepts and techniques originating in statistical physics are showing promise as useful tools for quantitative analysis of complicated physiological systems. An unsolved problem in biology is the quantitative analysis of a nonstationary time series generated under free-running conditions [1-3].