Cardiac Interbeat Interval Time Series Research Articles

A new complex belief entropy of [formula omitted] divergence with its application in cardiac interbeat interval time series analysis

With outstanding capability to express uncertain information, complex evidence theory can be widely applied in a multiplicity of fields of representation and fusion of information. However, in complex evidence theory, conflict measurement is still an open issue. To address this problem, we propose a new complex belief χ2 divergence measure (CBχ2), which has the ability to measure the discrepancy between the complex basic belief assignments (CBBAs). In addition, the proposed CBχ2 divergence measure satisfies the properties of nonnegativity, nondegeneracy and symmetry. Particularly, when the CBBA degenerates to classical basic belief assignments (BBA), the proposed divergence can also measure the conflict well. On this basis, a novel BEoCBχ2D is proposed to measure the complexity of cardiac interbeat interval time series in biological system. An application in cardiac interbeat interval time series analysis demonstrates that BEoCBχ2D has better accuracy.

Belief entropy-of-entropy and its application in the cardiac interbeat interval time series analysis

How to measure the complexity of physiological signals in biological system is an open problem. Various entropy algorithms have been presented, but most of them fail to account for the complexity of time series with high accuracy. In this paper, the concept of Belief Entropy-of-Entropy (BEoE) is introduced, it expands entropy of entropy (EoE) into belief structure, and computes quadratic belief entropy to characterize the complexity of biological systems based on multiple time scales. The influence of inherent complex fluctuation, length bound, correlation of time windows, etc. is considered in the BEoE analysis. Application and discussion demonstrate that BEoE has better accurateness and applicability than many existing entropy algorithms.

Entropy of Entropy: Measurement of Dynamical Complexity for Biological Systems

Healthy systems exhibit complex dynamics on the changing of information embedded in physiologic signals on multiple time scales that can be quantified by employing multiscale entropy (MSE) analysis. Here, we propose a measure of complexity, called entropy of entropy (EoE) analysis. The analysis combines the features of MSE and an alternate measure of information, called superinformation, useful for DNA sequences. In this work, we apply the hybrid analysis to the cardiac interbeat interval time series. We find that the EoE value is significantly higher for the healthy than the pathologic groups. Particularly, short time series of 70 heart beats is sufficient for EoE analysis with an accuracy of 81% and longer series of 500 beats results in an accuracy of 90%. In addition, the EoE versus Shannon entropy plot of heart rate time series exhibits an inverted U relationship with the maximal EoE value appearing in the middle of extreme order and disorder.

Heart Rate Fragmentation: A New Approach to the Analysis of Cardiac Interbeat Interval Dynamics.

Background: Short-term heart rate variability (HRV) is most commonly attributed to physiologic vagal tone modulation. However, with aging and cardiovascular disease, the emergence of high short-term HRV, consistent with the breakdown of the neuroautonomic-electrophysiologic control system, may confound traditional HRV analysis. An apparent dynamical signature of such anomalous short-term HRV is frequent changes in heart rate acceleration sign, defined here as heart rate fragmentation.Objective: The aims were to: (1) introduce a set of metrics designed to probe the degree of sinus rhythm fragmentation; (2) test the hypothesis that the degree of fragmentation of heartbeat time series increases with the participants' age in a group of healthy subjects; (3) test the hypothesis that the heartbeat time series from patients with advanced coronary artery disease (CAD) are more fragmented than those from healthy subjects; and (4) compare the performance of the new fragmentation metrics with standard time and frequency domain measures of short-term HRV.Methods: We analyzed annotated, open-access Holter recordings (University of Rochester Holter Warehouse) from healthy subjects and patients with CAD using these newly introduced metrics of heart rate fragmentation, as well as standard time and frequency domain indices of short-term HRV, detrended fluctuation analysis and sample entropy.Results: The degree of fragmentation of cardiac interbeat interval time series increased significantly as a function of age in the healthy population as well as in patients with CAD. Fragmentation was higher for the patients with CAD than the healthy subjects. Heart rate fragmentation metrics outperformed traditional short-term HRV indices, as well as two widely used nonlinear measures, sample entropy and detrended fluctuation analysis short-term exponent, in distinguishing healthy subjects and patients with CAD. The same level of discrimination was obtained from the analysis of normal-to-normal sinus (NN) and cardiac interbeat interval (RR) time series.Conclusion: The fragmentation framework and accompanying metrics introduced here constitute a new way of assessing short-term HRV under free-running conditions, one which appears to overcome salient limitations of traditional HRV analysis. Fragmentation of sinus rhythm cadence may provide new dynamical biomarkers for probing the integrity of the neuroautonomic-electrophysiologic network controlling the heartbeat in health and disease.

Classification of heart rate signals of healthy and pathological subjects using threshold based symbolic entropy.

The dynamical fluctuations of biological signals provide a unique window to construe the underlying mechanism of the biological systems in health and disease. Recent research evidences suggest that a wide class of diseases appear to degrade the biological complexity and adaptive capacity of the system. Heart rate signals are one of the most important biological signals that have widely been investigated during the last two and half decades. Recent studies suggested that heart rate signals fluctuate in a complex manner. Various entropy based complexity analysis measures have been developed for quantifying the valuable information that may be helpful for clinical monitoring and for early intervention. This study is focused on determining HRV dynamics to distinguish healthy subjects from patients with certain cardiac problems using symbolic time series analysis technique. For that purpose, we have employed recently developed threshold based symbolic entropy to cardiac inter-beat interval time series of healthy, congestive heart failure and atrial fibrillation subjects. Normalized Corrected Shannon Entropy (NCSE) was used to quantify the dynamics of heart rate signals by continuously varying threshold values. A rule based classifier was implemented for classification of different groups by selecting threshold values for the optimal separation. The findings indicated that there is reduction in the complexity of pathological subjects as compared to healthy ones at wide range of threshold values. The results also demonstrated that complexity decreased with disease severity.

Dynamical density delay maps: simple, new method for visualising the behaviour of complex systems

BackgroundPhysiologic signals, such as cardiac interbeat intervals, exhibit complex fluctuations. However, capturing important dynamical properties, including nonstationarities may not be feasible from conventional time series graphical representations.MethodsWe introduce a simple-to-implement visualisation method, termed dynamical density delay mapping (“D3-Map” technique) that provides an animated representation of a system’s dynamics. The method is based on a generalization of conventional two-dimensional (2D) Poincaré plots, which are scatter plots where each data point, x(n), in a time series is plotted against the adjacent one, x(n + 1). First, we divide the original time series, x(n) (n = 1,…, N), into a sequence of segments (windows). Next, for each segment, a three-dimensional (3D) Poincaré surface plot of x(n), x(n + 1), h[x(n),x(n + 1)] is generated, in which the third dimension, h, represents the relative frequency of occurrence of each (x(n),x(n + 1)) point. This 3D Poincaré surface is then chromatised by mapping the relative frequency h values onto a colour scheme. We also generate a colourised 2D contour plot from each time series segment using the same colourmap scheme as for the 3D Poincaré surface. Finally, the original time series graph, the colourised 3D Poincaré surface plot, and its projection as a colourised 2D contour map for each segment, are animated to create the full “D3-Map.”ResultsWe first exemplify the D3-Map method using the cardiac interbeat interval time series from a healthy subject during sleeping hours. The animations uncover complex dynamical changes, such as transitions between states, and the relative amount of time the system spends in each state. We also illustrate the utility of the method in detecting hidden temporal patterns in the heart rate dynamics of a patient with atrial fibrillation. The videos, as well as the source code, are made publicly available.ConclusionsAnimations based on density delay maps provide a new way of visualising dynamical properties of complex systems not apparent in time series graphs or standard Poincaré plot representations. Trainees in a variety of fields may find the animations useful as illustrations of fundamental but challenging concepts, such as nonstationarity and multistability. For investigators, the method may facilitate data exploration.

Hierarchical entropy analysis for biological signals

We develop a hierarchical entropy (HE) method to quantify the complexity of a time series based on hierarchical decomposition and entropy analysis. The proposed method is applied to the Gaussian white noise and the 1 / f noise. We prove that the difference frequency components of the Gaussian white noise with the same scale factor have the same value of entropies, and the values decline as the scale factor increases. We also apply the HE method to the 1 / f noise, and prove mathematically that a lower frequency component of a 1 / f noise is also a 1 / f noise and verify numerically that a higher frequency component of a 1 / f random vector is approximately equal to a Gaussian random vector. The theoretical results are confirmed by numerical results. Moreover, we show that the HE method is an efficient method to analyze heartbeat signals by applying it to the cardiac interbeat interval time series of healthy young and elderly subjects, congestive heart failure (CHF) subjects and atrial fibrillation (AF) subjects.

Early detection of infection with continuous heart rate variability analysis in neutropenic patients

Hypothesis: Infection leading to organ failure kills more critically ill patients than any other cause. Early diagnosis of infection leading to timely antibiotics and resuscitation saves both patient lives and costs of care; however current techniques to diagnose infection are imprecise, insensitive and frequently late manifestations of infection. To address this problem, our aim is to uncover hidden information contained within cardiac interbeat-interval time series using advanced mathematical analysis rooted in complex systems science. Previous work has demonstrated altered heart rate variability (HRV) in patients with infection (more regular, less complex cardiac variation); not only is HRV altered with infection, the degree of HRV alteration also correlates with its severity. Building upon these results, our principal objective is to perform continuous HRV monitoring in adult patients at high risk for infection, and evaluate the hypothesis that change in HRV precedes traditional markers of infection.

Multiscale Analysis of Heart Rate Dynamics: Entropy and Time Irreversibility Measures

Cardiovascular signals are largely analyzed using traditional time and frequency domain measures. However, such measures fail to account for important properties related to multiscale organization and non-equilibrium dynamics. The complementary role of conventional signal analysis methods and emerging multiscale techniques, is, therefore, an important frontier area of investigation. The key finding of this presentation is that two recently developed multiscale computational tools--multiscale entropy and multiscale time irreversibility--are able to extract information from cardiac interbeat interval time series not contained in traditional methods based on mean, variance or Fourier spectrum (two-point correlation) techniques. These new methods, with careful attention to their limitations, may be useful in diagnostics, risk stratification and detection of toxicity of cardiac drugs.

Statistical physics approach to categorize biologic signals: From heart rate dynamics to DNA sequences

We recently proposed a novel approach to categorize information carried by symbolic sequences based on their usage of repetitive patterns. A simple quantitative index to measure the dissimilarity between two symbolic sequences can be defined. This information dissimilarity index, defined by our formula, is closely related to the Shannon entropy and rank order of the repetitive patterns in the symbolic sequences. Here we discuss the underlying statistical physics assumptions of this dissimilarity index. We use human cardiac interbeat interval time series and DNA sequences as examples to illustrate the applicability of this generic approach to real-world problems.

Behavioral-independent features of complex heartbeat dynamics.

We test whether the complexity of the cardiac interbeat interval time series is simply a consequence of the wide range of scales characterizing human behavior, especially physical activity, by analyzing data taken from healthy adult subjects under three conditions with controls: (i) a "constant routine" protocol where physical activity and postural changes are kept to a minimum, (ii) sympathetic blockade, and (iii) parasympathetic blockade. We find that when fluctuations in physical activity and other behavioral modifiers are minimized, a remarkable level of complexity of heartbeat dynamics remains, while for neuroautonomic blockade the multifractal complexity decreases.

Anxiety and autonomic flexibility: a cardiovascular approach

Autonomic characteristics of panickers, blood phobics, and nonanxious controls were compared with a variety of cardiovascular measures, including spectral analysis of the cardiac inter-beat interval time series (derived from the electrocardiogram). Responses to laboratory stressors (shock avoidance and cold face stress) of 16 participants who reported recent occurrences of frequent severe panic attacks, 15 participants who reported strong somatic reactions and fainting to the sight of blood, and 15 controls, were recorded. Results suggested distinct autonomic patterns among the three groups. Across conditions, panickers displayed the highest heart rates (HR) coupled with the least HR variability, which indicates low levels of cardiac vagal tone. Blood phobics showed more vagally mediated HR variability than panickers, with a significant association between cardiac rate and mean arterial pressure. Controls generally showed the most HR variability and `spectral reserve' (a quality that indicates flexible responsivity). Results are discussed in the context of traditional models of anxiety and autonomic activity in contrast to contemporary notions of stability and change in biological systems.