Robust Estimation of the Scaling Exponent in Detrended Fluctuation Analysis of Beat Rate Variability

Abstract

Detrended fluctuation analysis is a popular method for studying fractal scaling properties in time series. The method has been successfully employed in studying heart rate variability and discovering distinct scaling properties in different pathological conditions. Traditionally the analysis has been performed by extracting two scaling exponents from linear fits, for short-and long-range correlations respectively. The extent of these ranges is subjective and the linear two-range model potentially disregards additional information present in the data. Here we present a method based on the Kalman smoother for obtaining a whole spectrum of scaling exponents as a function of the scale. Additionally, we present an optimization scheme to obtain data-adaptive segmentation of the fluctuation function into approximately linear regimes. The methods are parameter-free and resistant to statistical noise in the fluctutation function. We employ the methods in the analysis of the heart rate variability of patients with different heart conditions. The methods enhance the classification of these conditions, revealing more complex structure in the scaling exponents beyond the two-range model.

Non-Linear Heart Rate Variability Measures in Sleep Stage Analysis with Photoplethysmography

“…However, in practice many phenomena deviate from exact power law scaling, which is often observed only over limited ranges of scales. This could be taken into account by computing a whole spectrum of scaling exponents α(s) as a function of the scale [4][5][6]. The scaling may also exhibit temporal variations due to changes in external conditions, or the process itself may be comprised of distinct intrinsic modes.…”

Online Tool for Dynamical Heart Rate Variability Analysis

“…Hence, our tool focuses on the dynamical implementation of DFA (DDFA). The conventional division into arbitrary short-(α 1 , 4-16 beats) and long-scale (α 2 , 16-64 beats) scaling exponents [4] does not often fully reflect the fractal scaling properties of the RR intervals [7]. Therefore, we compute individual scaling exponents for each scale to obtain a landscape of scaling exponents α(t, s) as the function of both time and scale.…”

Dynamical Heart Beat Correlations during Running

“…However, experimental time series rarely exhibit exact scaling over several scales. Many previous studies have focused on finding a robust determination of the scaling regimes [37,38], or on extracting a spectra of scaling exponents α(s) [39][40][41][42][43]. These methods are based on the notion that the spectra may be defined as the local slope of the logarithmic fluctuation function,…”