Dorota Wejer

Entropic Measures of Complexity of Short-Term Dynamics of Nocturnal Heartbeats in an Aging Population

Two entropy-based approaches are investigated to study patterns describing differences in time intervals between consecutive heartbeats. The first method explores matrices arising from networks of transitions constructed following events represented by a time series. The second method considers distributions of ordinal patterns of length three, whereby patterns with repeated values are counted as different patterns. Both methods provide estimators of dynamical aspects of short-term heartbeat signals obtained from nocturnal Holter electrocardiogram (ECG) recordings of healthy people of different ages and genders. The deceleration capacity, arising from the adjacency matrix of the network, and the entropy rate, resulting from the transition matrix of the network, are also calculated, and both significantly decay with aging. As people age, the permutation entropy grows, due to the increase in patterns with repeated values. All of these estimators describe in a consistent way changes in the beat-to-beat heart period dynamics caused by aging. An overall slowing down of heart period changes is observed, and an increase of permutation entropy results from the progressive increase of patterns with repeated values. This result points to the sympathetic drive becoming dominant in cardiac regulation of nocturnal heart rate with age.

Chronographic Imprint of Age-Induced Alterations in Heart Rate Dynamical Organization

Beat-to-beat changes in the heart period are transformed into a network of increments between subsequent RR-intervals, which enables graphical descriptions of short-term heart period variability. Three types of such descriptions are considered: (1) network graphs arising from a set of vertices and directed edges, (2) contour plots of adjacency matrices A, representing the networks and transition matrices T, resulting from A, and (3) vector plots of gradients of the matrices A and T. Two indices are considered which summarize properties of A and T: the approximate deceleration capacity and the entropy rate. The method, applied to time series of nocturnal RR-intervals recorded from healthy subjects of different ages, reveals important aspect of changes in the autonomic activity caused by biological aging. Independent of the subject’s age, following accelerations, a pendulum-like dynamics appears. With decelerations, this dynamics develops in line with the subject’s age. This aging transition can be graphically visualized by vectors connecting the maxima of the transition probabilities of T, which, metaphorically, resemble a chronometer or the hands of a clock.

Entropy Measures in the Assessment of Heart Rate Variability in Patients with Cardiodepressive Vasovagal Syncope

Sample entropy (SampEn) was reported to be useful in the assessment of the complexity of heart rate dynamics. Permutation entropy (PermEn) is a new measure based on the concept of order and was previously shown to be accurate for short, non-stationary datasets. The aim of the present study is to assess if SampEn and PermEn obtained from baseline recordings might differentiate patients with various outcomes of the head-up tilt test (HUTT). Time-domain heart rate variability (HRV) indices and several nonlinear parameters were calculated using 500 RR interval-long ECG recordings done before tilting in patients with a history suggesting vasovagal syncope. Groups of patients with so-called cardiodepressive vasovagal syncope (VVS_2) during HUTT and patients who did not faint during the test were compared. Two types of HUT tests were analyzed: with spontaneous (SB) or controlled breathing (CB). In our study, SampEn was higher in VVS_2 patients during SB, and PermEn was higher in VVS_2 patients during CB. Irrespective of the type of breathing during the test, SampEn and PermEn were similar in patients with the same type of reaction during HUTT. The use of several entropy-based parameters seems to be useful in HRV assessment in patients with vasovagal fainting.

Complexity of cardiovascular rhythms during head-up tilt test by entropy of patterns

OBJECTIVE The head-up tilt (HUT) test, which provokes transient dynamical alterations in the regulation of cardiovascular system, provides insights into complex organization of this system. Based on signals with heart period intervals (RR-intervals) and/or systolic blood pressure (SBP), differences in the cardiovascular regulation between vasovagal patients (VVS) and the healthy people group (CG) are investigated. APPROACH Short-term relations among signal data represented symbolically by three-beat patterns allow to qualify and quantify the complexity of the cardiovascular regulation by Shannon entropy. Four types of patterns: permutation, ordinal, deterministic and dynamical, are used, and different resolutions of signal values in the the symbolization are applied in order to verify how entropy of patterns depends on a way in which values of signals are preprocessed. MAIN RESULTS At rest, in the physiologically important signal resolution ranges, independently of the type of patterns used in estimates, the complexity of SBP signals in VVS is different from the complexity found in CG. Entropy of VVS is higher than CG what could be interpreted as substantial presence of noisy ingredients in SBP of VVS. After tilting this relation switches. Entropy of CG occurs significantly higher than VVS for SBP signals. In the case of RR-intervals and large resolutions, the complexity after the tilt becomes reduced when compared to the complexity of RR-intervals at rest for both groups. However, in the case of VVS patients this reduction is significantly stronger than in CG. SIGNIFICANCE Our observations about opposite switches in entropy between CG and VVS might support a hypothesis that baroreflex in VVS affects stronger the heart rate because of the inefficient regulation (possibly impaired local vascular tone alternations) of the blood pressure.

Generalised heart rate statistics reveal neurally mediated homeostasis transients

Distributions of accelerations and decelerations, obtained from increments of heart rate recorded during a head-up tilt table (HUTT) test provide short-term characterization of the complex cardiovascular response to a rapid controlled dysregulation of homeostasis. A generalised statistic is proposed for evaluating the neural reflexes responsible for restoring the homeostatic dynamics. An evaluation of the effects on heart rate of the neural regulation involved in achieving homeostasis indicates a distinction between vasovagal patients and healthy subjects who are not susceptible to spontaneous fainting. A healthy cardiovascular response to the HUTT test is identified in the sympathetic tone appropriately punctuated by vagal activity.

Causal relationships in the variability of cardiovascular system evoked by orthostatic stress by transfer entropy.

The coupling between cardiac and vascular systems in healthy volunteers, elicited by the head-up tilt test is estimated by means of transfer entropy with non-uniform embedding. The method applied to beat-to-beat recordings with heart periods and systolic blood pressure, supports the commonly accepted model, that baroreflex is the key factor in maintaining homeostatic blood distribution after tilting. However the method applied to changes of heart periods and changes of blood pressure, display switches in the driving system, from vascular in the early tilt, to cardiac just after the early tilt and back to vascular in the late tilt.

Dynamical Pattern Representation of Cardiovascular Couplings Evoked by Head-up Tilt Test

Shannon entropy (ShE) is a recognised tool for the quantization of the temporal organization of time series. Transfer entropy (TE) provides insight into the dependence between coupled systems. Here, signals are analysed that were produced by the cardiovascular system when a healthy human underwent a provocation test using the head-up tilt (HUT) protocol. The information provided by ShE and TE is evaluated from two aspects: that of the algorithmic stability and that of the recognised physiology of the cardiovascular response to the HUT test. To address both of these aspects, two types of symbolization of three-element subsequent values of a signal are considered: one, well established in heart rate research, referring to the variability in a signal, and a novel one, revealing primarily the dynamical trends. The interpretation of ShE shows a strong dependence on the method that was used in signal pre-processing. In particular, results obtained from normalized signals turn out to be less conclusive than results obtained from non-normalized signals. Systematic investigations based on surrogate data tests are employed to discriminate between genuine properties—in particular inter-system coupling—and random, incidental fluctuations. These properties appear to determine the occurrence of a high percentage of zero values of TE, which strongly limits the reliability of the couplings measured. Nevertheless, supported by statistical corroboration, we identify distinct timings when: (i) evoking cardiac impact on the vascular system, and (ii) evoking vascular impact on the cardiac system, within both the principal sub-systems of the baroreflex loop.

Network approach to increments of RR-intervals for visualization of dynamics of cardiac regulation

The transition network for RR-increments is presented in a directed and weighted graph, with vertices representing RR-increments and edges corresponding to the order in a sequence of increments. The adjacency matrix and the transition matrix of this network provide a graphical tool which could be useful in the assessment of cardiac regulation. As an example, the method is applied in detecting differences between diurnal activity and nocturnal rest.

Temporal changes in complexity of cardiovascular regulation during head-up tilt test by entropic measures of fluctuations of heart period intervals and systolic blood pressure

Dynamical aspects of cardiovascular regulation in the head-up tilt test are revealed through the properties of the approximate entropy and sample entropy of increments between subsequent heart period intervals and increments between subsequent systolic blood pressure values. Marked differences are observed in the dynamical response to the tilt test of healthy subjects prone to spontaneous fainting and those who are less susceptible to fainting.