Time reversal, symbolic series and irreversibility of human heartbeat

Cammarota, Camillo; Rogora, Enrico

doi:10.1016/j.chaos.2006.03.126

Cited by 67 publications

(35 citation statements)

References 17 publications

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“…For these processes, one can then meaningfully estimate properties about the underlying stationary distribution of the process (if this exists) through its estimation for finite series. In particular, one can quantify the amount of time irreversibility in stationary processes via a number of strategies and algorithms proposed in the literature, including simple statistical differences between forward and backward trajectories [2][3][4][5][6] or more sophisticated methods such as compression [7]. In every case, note that time series need to be symbolized before an irreversibility measure can be computed.…”

Section: Introductionmentioning

confidence: 99%

Time reversibility from visibility graphs of nonstationary processes

Lacasa

Flanagan

2015

Phys. Rev. E

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Visibility algorithms are a family of methods to map time series into networks, with the aim of describing the structure of time series and their underlying dynamical properties in graph-theoretical terms. Here we explore some properties of both natural and horizontal visibility graphs associated to several nonstationary processes, and we pay particular attention to their capacity to assess time irreversibility. Nonstationary signals are (infinitely) irreversible by definition (independently of whether the process is Markovian or producing entropy at a positive rate), and thus the link between entropy production and time series irreversibility has only been explored in nonequilibrium stationary states. Here we show that the visibility formalism naturally induces a new working definition of time irreversibility, which allows us to quantify several degrees of irreversibility for stationary and nonstationary series, yielding finite values that can be used to efficiently assess the presence of memory and off-equilibrium dynamics in nonstationary processes without the need to differentiate or detrend them. We provide rigorous results complemented by extensive numerical simulations on several classes of stochastic processes.

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Section: Introductionmentioning

confidence: 99%

Time reversibility from visibility graphs of nonstationary processes

Lacasa

Flanagan

2015

Phys. Rev. E

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“…Differences in heart rate dynamics before the onset of ventricular tachycardia [23] or during different stages of general anaesthesia [24] can be detected by this approach. A modification of this transformation using three symbols has been used to analyse irreversibility of interbeat interval data [25].…”

Section: Introductionmentioning

confidence: 99%

Strategies of symbolization in cardiovascular time series to test individual gestational development in the fetus

Cysarz

Edelhäuser

Leeuwen

2015

Phil. Trans. R. Soc. A.

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The analysis of symbolic dynamics applied to physiological time series retrieves dynamical properties of the underlying regulation which are robust against the symbolic transformation. In this study, three different transformations to produce a symbolic series were applied to fetal RR interval series to test whether they reflect individual changes of fetal heart rate variability in the course of pregnancy. Each transformation was applied to 215 heartbeat datasets obtained from 11 fetuses during the second and the third trimester of pregnancy (at least 10 datasets per fetus, median 17). In the symbolic series, the occurrence of symbolic sequences of length 3 was categorized according to the amount of variations in the sequence: no variation of the symbols, one variation, two variations. Linear regression with respect to gestational age showed that the individual course during pregnancy performed best using a binary transformation reflecting whether the RR interval differences are below or above a threshold. The median goodness of fit of the individual regression lines was 0.73 and also the variability among the individual slopes was low. Other transformations to symbolic dynamics performed worse but were still able to reflect the individual progress of fetal cardiovascular regulation.

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“…L. Lacasa et al [22] estimate the degree of irreversibility using the Kullback-CLeibler divergence between the in and out degree distributions based on horizontal visibility graph. And some symbolic methods, like the 'false flipped symbols' proposed by C. Daw [23], a data compression method introduced by M. Kennel [24], the ternary coding symbolic approach provided by C. Cammarota [25] and so forth [26,27], are proposed and show promising nonlinearity detection. J. Martinez et al [28] detect time reversibility by measuring the Jensen-Shannon divergence of time forward as well as its time-reversed counterpart by means of permutation, and M. Zanin et al [29] adopt the KL divergence to compare the probability distributions of symmetric order patterns.…”

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confidence: 99%

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

Yao

Wang

2019

Physics Letters A

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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].

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Time reversal, symbolic series and irreversibility of human heartbeat

Cited by 67 publications

References 17 publications

Time reversibility from visibility graphs of nonstationary processes

Time reversibility from visibility graphs of nonstationary processes

Strategies of symbolization in cardiovascular time series to test individual gestational development in the fetus

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

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