Nonlinear Methods Most Applied to Heart-Rate Time Series: A Review

Abstract

The heart-rate dynamics are one of the most analyzed physiological interactions. Many mathematical methods were proposed to evaluate heart-rate variability. These methods have been successfully applied in research to expand knowledge concerning the cardiovascular dynamics in healthy as well as in pathological conditions. Notwithstanding, they are still far from clinical practice. In this paper, we aim to review the nonlinear methods most used to assess heart-rate dynamics. We focused on methods based on concepts of chaos, fractality, and complexity: Poincaré plot, recurrence plot analysis, fractal dimension (and the correlation dimension), detrended fluctuation analysis, Hurst exponent, Lyapunov exponent entropies (Shannon, conditional, approximate, sample entropy, and multiscale entropy), and symbolic dynamics. We present the description of the methods along with their most notable applications.

Time irreversibility and complexity of heart rate variability

“…For long-term HRV records of MIT-BIH database for Normal Sinus Rhythm (NSR), Congestive Heart Failure (CHF) and Atrial Fibrillation (AF), we have compared values of z-score, which statistically defines the limit of irreversibility of time series, and values of HRV complexity indicators: entropy EnRE [18] and correlation dimension D2 [19]. We have analyzed the behavior of said nonlinear HRV parameters in each specific case and noted the following:  heart rate variability is time irreversible nonlinear dynamic process, with the exception of AF episodes;  nonlinear indicators of HRV complexityentropy EnRE and correlation dimension D2 -have been analyzed, and there is a conclusive difference between Normal Sinus Rhythm and analyzed pathological states;…”

“…In this article, complexity of HRV will be described by two parameters: entropy EnRE [18] and correlation dimension D2 [19]. There are a lot of definitions for complexity, but 'one of the most consensual is that complexity is a property of every system that quantifies the amount of structured information' [20].…”

“…Новий статистичний тест для оцінки ймовірності незворотності часового ряду був розроблений і протестований на сукупності відомих прикладів оборотних і необоротних часових рядів. Для коротких записів ВСР, обраних з 24-годинних записів бази даних ВСР MIT-BIH для NSR, CHF і AF груп, був виконаний їх аналіз на незворотність (z-score) і показників комплексності ВСР: ентропії EnRE [18] і кореляційної розмірності D2 [19]. Було відзначено наступне:…”

Anticipation of ventricular tachyarrhythmias by a novel mathematical method: Further insights towards an early warning system in implantable cardioverter defibrillators

“…Since visibility graphs is a qualitative methodology, the values of a time series derived from these graphs would vary in an interval, whose length would be different for each point in the time series. The framework of complex networks for analyzing heart rate variability data towards the detection of early warnings and the design of clinical tools for disease management has been considered before as other nonlinear methods [19]. Visibility graphs have been applied to the analysis of congestive heart failure [20].…”

Age-Related Changes in Standing Balance in Preschoolers Using Traditional and Nonlinear Methods

“…These results indicate that conventional methods may ignore some critical information about standing balance. In contrast, many nonlinear methods are based on concepts of chaos, fractals, and complexity ( Ma et al, 2018 ; Henriques et al, 2020 ), which have been used to evaluate the COP signals to understand the dynamics of standing balance in different groups ( Doyle et al, 2005 ; Seigle et al, 2009 ; Ramdani et al, 2013 ; Rigoldi et al, 2014 ; Zhou et al, 2017 ; Lobo Da Costa et al, 2019 ). Postural sway variability can be quantified using multiscale entropy (MSE) and fractal dimension (FD).…”