Multiscale multifractal analysis of heart rate variability recordings with a large number of occurrences of arrhythmia

Abstract

Human heart rate variability, in the form of time series of intervals between heart beats, shows complex, fractal properties. Recently, it was demonstrated many times that the fractal properties vary from point to point along the series, leading to multifractality. In this paper, we concentrate not only on the fact that the human heart rate has multifractal properties but also that these properties depend on the time scale in which the multifractality is measured. This time scale is related to the frequency band of the signal. We find that human heart rate variability appears to be far more complex than hitherto reported in the studies using a fixed time scale. We introduce a method called multiscale multifractal analysis (MMA), which allows us to extend the description of heart rate variability to include the dependence on the magnitude of the variability and time scale (or frequency band). MMA is relatively immune to additive noise and nonstationarity, including the nonstationarity due to inclusions into the time series of events of a different dynamics (e.g., arrhythmic events in sinus rhythm). The MMA method may provide new ways of measuring the nonlinearity of a signal, and it may help to develop new methods of medical diagnostics.

Multifractal‐Multiscale Analysis of Cardiovascular Signals: A DFA‐Based Characterization of Blood Pressure and Heart‐Rate Complexity by Gender

“…For these reasons, the more recent research in the field of heart-rate variability is aimed at proposing methods that take into account both the scale dependency of self-similarity and its multifractal nature [12,13]. Following this line of research, the aim of the present study is to describe the multifractal and multiscale characteristics of cardiovascular signals in healthy subjects under controlled conditions.…”

Assessment of Heart Rate Variability during an Endurance Mountain Trail Race by Multi-Scale Entropy Analysis

“…Primarily because of the non-linear interplay of different physiological control loops in generating the heart rate, linear methods are not adequate to fully describe such a complex system. Several non-linear HRV methods such as fractal scaling analysis, higher order spectra analysis, multi-scale entropy analysis, power law analysis, complexity analysis, symbolic dynamics analysis and heart rate turbulence analysis have been studied for various diseases [7][8][9][10][11][12][13][14][15]. It must be taken into account that while the collection of heart rate (HR) was initially only possible with expensive laboratory-based electrocardiograph recorders, the recent availability of specifically designed portable recorders has substantially boosted the use of HRV monitoring [16,17].…”

Fractal scaling analysis of groundwater dynamics in confined aquifers

“…Multiscale multifractal analysis (MMA) is a generalization of multifractal detrended fluctuation analysis (MF-DFA), which is developed from DFA (Gierałtowski et al, 2012). In contrast to MF-DFA, which requires the presumption of scaling ranges, MMA is capable of concurrently characterizing different fractal properties (monofractality or multifractality) of time series over a wide range (both small and large) of temporal scales.…”

“…Multiscale multifractal analysis (MMA) was proposed on the basis of MF-DFA, which normally analyzes time series with crossovers only on a predefined large or small scale to obtain the generalized Hurst surface, which simultaneously provides local fractal properties at various scale ranges (Gierałtowski et al, 2012;Wang et al, 2014). To the best of our knowledge, MMA has not yet been applied to analyze time series in hydrology or subsurface hydrology.…”