Equal heartbeat intervals and their effects on the nonlinearity of permutation-based time irreversibility in heart rate

Abstract

The association of equal heartbeat intervals with cardiac conditions and the effect of the equality on permutationbased time irreversibility are investigated in this paper. We measure the distributions of equal heartbeat intervals under three conditions, namely congestive heart failure (CHF), healthy young and elderly, whose time irreversibility of heartbeats is detected by measuring the probabilistic difference between permutations instead of raw vectors. We demonstrate that heartbeats contain high rates of equal states, particularly the CHF with around 20% equalities, and the distributions of equal values discriminate the heartbeats at very short data length. The CHF have more equal values than the healthy young (p<1.47 * 10 −15 ) and elderly (p<2.48 * 10 −11 ), and the healthy young have less equalities than the elderly (p<3.16 * 10 −4 ). Time irreversibility considering equal values is promising to extract nonlinear behaviors of heartbeats, confirming the decreased nonlinear complexity of the diseased and aging heart rates, while that involving no equality leads to erroneous nonlinearity detection. In our contribution, we highlight the pathological or physiological information contained by the distribution of equal heartbeat intervals that might contribute to develop relevant biomarkers in the area of heart analysis, and demonstrate the effectiveness of equality-based time irreversibility in the nonlinearity detection of heartbeats.Electrocardiography (ECG) is a common process of recording the cardiac electrical activities to obtain the heart structure and/or function. Derived from the ECG, different cardiac intervals, like the PR interval (from the beginning of P wave to QRS complex), QRS interval, ST interval (between the end of QRS complex and the start of T wave), etc, carry a lot of important information, among which the RR interval between successive R waves, generally used to represent heart rate, has more clinical and scientific applications and arguably manifests with nonlinear properties [1,2,3]. As a consequence, besides the time and frequency domains techniques, nonlinear dynamics is adopted to detect subtle nonlinear changes in heart rate to provide indices of cardiac autonomic regulation, such as Poincare plot [4], fractal measures [5,6], symbolic dynamics [7,8,9,10], entropy methods [11,12,13], and so on [14,15].

A novel parameter for nonequilibrium analysis in reconstructed state spaces

“…As for the cardiac dynamics in heartbeats, the healthy young heartbeats should have the greatest degree of complexity, whereas the elderly and particularly the CHF heartbeats should have less-complex dynamics because of the reduced adaptive capabilities of cardiac regulation. The wisdom of complexity loss theory has been widely proved using entropy measures [19], irreversibility [4,5,25,35], and fractality [36,37], and is now further confirmed by KPD.…”

“…Additionally, the heart rates of 20 healthy young adults (mean age 25.8±4.3 years, ranging from 21 to 34) and 20 healthy elderly adults (mean age 74.5±4.4 years, ranging from 68 to 85), both with equal numbers of women and men, were recorded in a resting state with a sinus rhythm while watching the movie 'Fantasia.' Similar groups of heartbeats have been widely used to analyze the cardiac dynamics with regard to cardiac regulation [4,5,19,25,35]. Exemplary heartbeat intervals of the CHF, healthy elderly, and healthy young subjects are depicted in Fig.…”

Econophysics of cryptocurrency crashes: an overview

“…They also demonstrated how the proposed approach can help elucidate the complex irreversibility dynamics of financial time series, representing 30 major European stocks and 12 world indices [313] and gait analysis on late stages of neurodegenerative dementias [317]. This technique was also used to analyze the irreversibility of time series in ecology (the time series of lynx abundance), epidemiology (dengue prevalence), economy (the S&P price-index series), neuroscience (electroencephalographic data from an epileptic patient) [318,319], and heart rate [320].…”

Variations of Time Irreversibility of Heart Rate Variability Under Normobaric Hypoxic Exposure

“…Time irreversibility is one of the basic features of nonlinear systems. It describes the process of how the physical state and statistical characteristics of a system depend on the direction of time ( Yao et al, 2019 ). If a sequence has the same joint probability distribution with its reversal sequence, it is said to be time invertible.…”