Multiscale probability density function analysis: non-Gaussian and scale-Invariant fluctuations of healthy human heart rate

For a detailed characterization of intermittency and non-Gaussianity of human heart rate, we introduce an analysis method to investigate the deformation process of the probability density function (PDF) of detrended increments when going from fine to coarse scales. To characterize the scale dependence of the multiscale PDF, we use two methods: 1) calculation of Kullback-Leibler relative entropy; 2) parameter estimation based on Castaing's equation (B. Castaing et al., 1990). We compare scale-dependence of the increment PDFs between actual heart rate fluctuations and artificially generated Gaussian and non-Gaussian noise, including a widely used autoregressive model and a recently proposed multifractal model based on a random cascade process. Our analysis highlights an essential difference between heart rate fluctuations and those generated by other models. The outstanding feature of human heart rate is the robust scale-invariance of the non-Gaussian PDF, which is preserved not only in a quiescent condition, but also in a dynamic state during waking hours, in which the mean level of heart rate is dramatically changing. Our results strongly suggest the need for revising existing models of heart rate variability to incorporate the scale-invariance in the PDF.

I. Introduction

In the past decade, methods used mainly in statistical physics, including chaotic dynamics, have demonstrated that human heart rate variability (HRV) belongs to a special class of complex signals, showing long-range temporal autocorrelations [1] [2] [3], multifractal scaling properties [4], [5], and non-Gaussian probability density function (PDF) in its increments [1], [6]. While various models have been proposed [6] [7] [8] [9] to gain deeper insight into the nature of the complex fluctuations in heart rate, none of them has so far provided complete characteristics of actual HRV. One of the reasons for this might be that the exact mechanism behind heart rate complexity is still not completely understood. However, as it reflects the dynamics of the autonomic nervous system's control of heart rate [1], [5] and, thus, provides potential predictors for the mortality of cardiac patients [10]–[12] and indications for the therapy for malignant cardiac arrhythmias [13], elucidating this mechanism is considered important.