Evaluation of renormalised entropy for risk stratification using heart rate variability data

Association between Mean Heart Rate and Recurrence Quantification Analysis of Heart Rate Variability in End-Stage Renal Disease

Linear heart rate variability (HRV) indices are dependent on the mean heart rate, which has been demonstrated in different models (from sinoatrial cells to humans). The association between nonlinear HRV indices, including those provided by recurrence plot quantitative analysis (RQA), and the mean heart rate (or the mean cardiac period, also called meanNN) has been scarcely studied. For this purpose, we analyzed RQA indices of five minute-long HRV time series obtained in the supine position and during active standing from 30 healthy subjects and 29 end-stage renal disease (ESRD) patients (before and after hemodialysis). In the supine position, ESRD patients showed shorter meanNN (i.e., faster heart rate) and decreased variability compared to healthy subjects. The healthy subjects responded to active standing by shortening the meanNN and decreasing HRV indices to reach similar values of ESRD patients. Bivariate correlations between all RQA indices and meanNN were significant in healthy subjects and ESRD after hemodialysis and for most RQA indices in ESRD patients before hemodialysis. Multiple linear regression analyses showed that RQA indices were also dependent on the position and the ESRD condition. Then, future studies should consider the association among RQA indices, meanNN, and these other factors for a correct interpretation of HRV.

The complexity-entropy causality plane based on multiscale power spectrum entropy of financial time series

The complexity of financial time series is an important issue for nonlinear dynamic systems. We propose multiscale power spectral entropy. Based on this method, this paper uses the complex entropy causal plane ( C p s e ) to evaluate the complexity of the stock market. Multiscale power spectral entropy takes full advantage of the interrelationships between data in state space and estimates system complexity from different temporal resolutions. Then, we use a complex causal entropy plane to track changes in stock signals. The simulation data are used to test the performance of this method. Finally, we compare the C p s e method with the traditional power spectral entropy method. The results show that the C p s e method is more sensitive to changes in the stock market and can fully extract the intrinsic dynamics of the stock sequence.

Heart rate differences between symptomatic and asymptomatic Brugada syndrome patients at night

OBJECTIVE

Ventricular arrhythmias in Brugada syndrome (BS) mainly occur at rest, especially during nighttime, suggesting that parasympathetic activity at night may play an important role in the arrhythmogenesis of the disease. This study examined and compared the autonomic function of symptomatic and asymptomatic BS patients overnight.

APPROACH

We analyzed various heart rate variability (HRV) and heart rate complexity (HRC) markers in a clinical series including 87 BS patients, where 23 were symptomatic.

MAIN RESULTS

Statistically significant differences were found in markers MIRR, SDNN, SDANN, [Formula: see text] and SampEn, suggesting that symptomatic patients may be related to lower heart rate variability and complexity values, as well as to greater circadian fluctuations overnight.

SIGNIFICANCE

The results provide further evidence for the role of autonomic imbalance in the pathophysiology of BS, highlighting the relevance of nighttime analysis to the unmasking of significant ANS changes. Based on these outcomes, the role of HRV and HRC assessment at night could be a step forward towards the understanding of BS and the risk for the occurrence of symptoms in these patients, with a potential future impact on therapeutic strategies.

Entropy measures, entropy estimators, and their performance in quantifying complex dynamics: Effects of artifacts, nonstationarity, and long-range correlations

Entropy measures are widely applied to quantify the complexity of dynamical systems in diverse fields. However, the practical application of entropy methods is challenging, due to the variety of entropy measures and estimators and the complexity of real-world time series, including nonstationarities and long-range correlations (LRC). We conduct a systematic study on the performance, bias, and limitations of three basic measures (entropy, conditional entropy, information storage) and three traditionally used estimators (linear, kernel, nearest neighbor). We investigate the dependence of entropy measures on estimator- and process-specific parameters, and we show the effects of three types of nonstationarities due to artifacts (trends, spikes, local variance change) in simulations of stochastic autoregressive processes. We also analyze the impact of LRC on the theoretical and estimated values of entropy measures. Finally, we apply entropy methods on heart rate variability data from subjects in different physiological states and clinical conditions. We find that entropy measures can only differentiate changes of specific types in cardiac dynamics and that appropriate preprocessing is vital for correct estimation and interpretation. Demonstrating the limitations of entropy methods and shedding light on how to mitigate bias and provide correct interpretations of results, this work can serve as a comprehensive reference for the application of entropy methods and the evaluation of existing studies.

Entropy-based complexity measures for gait data of patients with Parkinson's disease

Shannon, Kullback-Leibler, and Klimontovich's renormalized entropies are applied as three different complexity measures on gait data of patients with Parkinson's disease (PD) and healthy control group. We show that the renormalized entropy of variability of total reaction force of gait is a very efficient tool to compare patients with respect to disease severity. Moreover, it is a good risk predictor such that the sensitivity, i.e., the percentage of patients with PD who are correctly identified as having PD, increases from 25% to 67% while the Hoehn-Yahr stage increases from 2.5 to 3.0 (this stage goes from 0 to 5 as the disease severity increases). The renormalized entropy method for stride time variability of gait is found to correctly identify patients with a sensitivity of 80%, while the Shannon entropy and the Kullback-Leibler relative entropy can do this with a sensitivity of only 26.7% and 13.3%, respectively.

Complexity of the autonomic heart rate control in coronary artery occlusion in patients with and without prior myocardial infarction

Autonomic nervous system (ANS) is governed by complex interactions arising from feedback loops of nonlinear systems that operate over a wide range of temporal and spatial scales, enabling the organism to adapt to stress, metabolic changes and diseases. This study is aimed to assess multifractal and nonlinear characteristics of the ANS during ischemic events provoked by a prolonged percutaneous coronary intervention (PCI) procedure. Eighty-seven patients from the STAFF III database were used. Patients were classified into 2 groups: (1) with prior myocardial infarction (MI) and (2) without MI (noMI). R-R signals during three 3-min stages of the procedures were analyzed using multifractal and surrogate data techniques. Multifractal indices increased significantly from the pre-inflation stage to the post-deflation stage. These variations were more marked for the noMI group. Multifractal changes significantly correlated with both the decreased parasympathetic and the increased sympathetic modulations accounted by classical linear indices. Multifractal measures resulted to be a more powerful indicator than linear HRV indices in quantifying the ischemia-induced changes. Right coronary artery (RCA) occlusions provoke greater multifractal reactions throughout the PCI procedure. Our findings suggest reduced complex multifractal and nonlinear reactions of ANS activity in patients with prior MI in comparison to the noMI group, possibly due to degradation in the complexity of control mechanism of heart rate generation.

Discrimination power of long-term heart rate variability measures for chronic heart failure detection

The aim of this study was to investigate the discrimination power of standard long-term heart rate variability (HRV) measures for the diagnosis of chronic heart failure (CHF). The authors performed a retrospective analysis on four public Holter databases, analyzing the data of 72 normal subjects and 44 patients suffering from CHF. To assess the discrimination power of HRV measures, an exhaustive search of all possible combinations of HRV measures was adopted and classifiers based on Classification and Regression Tree (CART) method was developed, which is a non-parametric statistical technique. It was found that the best combination of features is: Total spectral power of all NN intervals up to 0.4 Hz (TOTPWR), square root of the mean of the sum of the squares of differences between adjacent NN intervals (RMSSD) and standard deviation of the averages of NN intervals in all 5-min segments of a 24-h recording (SDANN). The classifiers based on this combination achieved a specificity rate and a sensitivity rate of 100.00 and 89.74%, respectively. The results are comparable with other similar studies, but the method used is particularly valuable because it provides an easy to understand description of classification procedures, in terms of intelligible "if … then …" rules. Finally, the rules obtained by CART are consistent with previous clinical studies.

Cardiac magnetic field map topology quantified by Kullback-Leibler entropy identifies patients with hypertrophic cardiomyopathy

Hypertrophic cardiomyopathy (HCM) is a common primary inherited cardiac muscle disorder, defined clinically by the presence of unexplained left ventricular hypertrophy. The detection of affected patients remains challenging. Genetic testing is limited because only in 50%-60% of all HCM diagnoses an underlying mutation can be found. Furthermore, the disease has a varied clinical course and outcome, with many patients having little or no discernible cardiovascular symptoms, whereas others develop profound exercise limitation and recurrent arrhythmias or sudden cardiac death. Therefore prospective screening of HCM family members is strongly recommended. According to the current guidelines this includes serial echocardiographic and electrocardiographic examinations. In this study we investigated the capability of cardiac magnetic field mapping (CMFM) to detect patients suffering from HCM. We introduce for the first time a combined diagnostic approach based on map topology quantification using Kullback-Leibler (KL) entropy and regional magnetic field strength parameters. The cardiac magnetic field was recorded over the anterior chest wall using a multichannel-LT-SQUID system. CMFM was calculated based on a regular 36 point grid. We analyzed CMFM in patients with confirmed diagnosis of HCM (HCM, n=33, 43.8+/-13 years, 13 women, 20 men), a control group of healthy subjects (NORMAL, n=57, 39.6+/-8.9 years; 22 women and 35 men), and patients with confirmed cardiac hypertrophy due to arterial hypertension (HYP, n=42, 49.7+/-7.9 years, 15 women and 27 men). A subgroup analysis was performed between HCM patients suffering from the obstructive (HOCM, n=19) and nonobstructive (HNCM, n=14) form of the disease. KL entropy based map topology quantification alone identified HCM patients with a sensitivity of 78.8% and specificity of 86.9% (overall classification rate 84.8%). The combination of the KL parameters with a regional field strength parameter improved the overall classification rate to 87.9% (sensitivity: 84.8%, specificity: 88.9%, area under ROC curve: 0.94). KL measures applied to discriminate between HOCM and HNCM patients showed a correct classification of 78.8%. The combination of one KL and one regional parameter again improved the overall classification rate to 97%. A preliminary prospective analysis in two HCM families showed the feasibility of this diagnostic approach with a correct diagnosis of all 22 screened family members (1 HOCM, 4 HNCM, 17 normal). In conclusion, Cardiac Magnetic Field Mapping including KL entropy based topology quantifications is a suitable tool for HCM screening.

Analysis of cardiovascular oscillations: a new approach to the early prediction of pre-eclampsia

Pre-eclampsia (PE) is a serious disorder with high morbidity and mortality occurring during pregnancy; 3%-5% of all pregnant women are affected. Early prediction is still insufficient in clinical practice. Although most pre-eclamptic patients show pathological uterine perfusion in the second trimester, this parameter has a positive predictive accuracy of only 30%, which makes it unsuitable for early, reliable prediction. The study is based on the hypothesis that alterations in cardiovascular regulatory behavior can be used to predict PE. Ninety-six pregnant women in whom Doppler investigation detected perfusion disorders of the uterine arteries were included in the study. Twenty-four of these pregnant women developed PE after the 30th week of gestation. During pregnancy, additional several noninvasive continuous blood pressure recordings were made over 30 min under resting conditions by means of a finger cuff. The time series extracted of systolic as well as diastolic beat-to-beat pressures and the heart rate were studied by variability and coupling analysis to find predictive factors preceding genesis of the disease. In the period between the 18th and 26th weeks of pregnancy, three special variability and baroreflex parameters were able to predict PE several weeks before clinical manifestation. Discriminant function analysis of these parameters was able to predict PE with a sensitivity and specificity of 87.5% and a positive predictive value of 70%. The combined clinical assessment of uterine perfusion and cardiovascular variability demonstrates the best current prediction several weeks before clinical manifestation of PE.

Autonomic cardiac control in animal models of cardiovascular diseases. I. Methods of variability analysis

Analysis of heart rate variability (HRV) and blood pressure variability (BPV) and baroreceptor sensitivity (BRS) has become a proven tool in clinical cardiovascular diagnostics and risk stratification. In the present work, traditional and new methodological approaches for analysis of HRV, BPV, and BRS data are summarized. HRV, BPV, and BRS parameters were obtained from animal studies designed to study pathogenetic mechanisms of distinct cardiovascular diseases. Different non-linear approaches for HRV and BPV analysis are presented here, in particular measures of complexity based on symbolic dynamics. The dual sequence method (DSM) was employed for BRS analysis. In comparison to the classical measure of BRS using the average slope [ms/mm Hg], DSM offers additional information about the time-variant coupling between BPV and HRV. Since cardiovascular regulation shares common features among different species, data on HRV and BPV, as well as BRS, in animal models might be useful for understanding the pathogenetic mechanisms of cardiovascular diseases in humans and in the development of new diagnostic approaches.

Large-scale dimension densities for heart rate variability analysis

In this work, we reanalyze the heart rate variability (HRV) data from the 2002 Computers in Cardiology (CiC) Challenge using the concept of large-scale dimension densities and additionally apply this technique to data of healthy persons and of patients with cardiac diseases. The large-scale dimension density (LASDID) is estimated from the time series using a normalized Grassberger-Procaccia algorithm, which leads to a suitable correction of systematic errors produced by boundary effects in the rather large scales of a system. This way, it is possible to analyze rather short, nonstationary, and unfiltered data, such as HRV. Moreover, this method allows us to analyze short parts of the data and to look for differences between day and night. The circadian changes in the dimension density enable us to distinguish almost completely between real data and computer-generated data from the CiC 2002 challenge using only one parameter. In the second part we analyzed the data of 15 patients with atrial fibrillation (AF), 15 patients with congestive heart failure (CHF), 15 elderly healthy subjects (EH), as well as 18 young and healthy persons (YH). With our method we are able to separate completely the AF (rho (mu/ls) = 0.97 +/- 0.02) group from the others and, especially during daytime, the CHF patients show significant differences from the young and elderly healthy volunteers (CHF, 0.65 +/- 0.13; EH, 0.54 +/- 0.05; YH, 0.57 +/- 0.05; p < 0.05 for both comparisons). Moreover, for the CHF patients we find no circadian changes in rho (mu/ls) (day, 0.65 +/- 0.13; night, 0.66 +/- 0.12; n.s.) in contrast to healthy controls (day, 0.54 +/- 0.05; night, 0.61 +/- 0.05; p=0.002). Correlation analysis showed no statistical significant relation between standard HRV and circadian LASDID, demonstrating a possibly independent application of our method for clinical risk stratification.

Nonlinear additive autoregressive model-based analysis of short-term heart rate variability

In this contribution we test the hypothesis that nonlinear additive autoregressive model-based data analysis improves the diagnostic ability based on short-term heart rate variability. For this purpose, a nonlinear regression approach, namely, the maximal correlation method is applied to the data of 37 patients with dilated cardiomyopathy as well as of 37 age- and sex-matched healthy subjects. We find that this approach is a powerful tool in discriminating both groups and promising for further model-based analyses.

Gait variability: methods, modeling and meaning

The study of gait variability, the stride-to-stride fluctuations in walking, offers a complementary way of quantifying locomotion and its changes with aging and disease as well as a means of monitoring the effects of therapeutic interventions and rehabilitation. Previous work has suggested that measures of gait variability may be more closely related to falls, a serious consequence of many gait disorders, than are measures based on the mean values of other walking parameters. The Current JNER series presents nine reports on the results of recent investigations into gait variability. One novel method for collecting unconstrained, ambulatory data is reviewed, and a primer on analysis methods is presented along with a heuristic approach to summarizing variability measures. In addition, the first studies of gait variability in animal models of neurodegenerative disease are described, as is a mathematical model of human walking that characterizes certain complex (multifractal) features of the motor control's pattern generator. Another investigation demonstrates that, whereas both healthy older controls and patients with a higher-level gait disorder walk more slowly in reduced lighting, only the latter's stride variability increases. Studies of the effects of dual tasks suggest that the regulation of the stride-to-stride fluctuations in stride width and stride time may be influenced by attention loading and may require cognitive input. Finally, a report of gait variability in over 500 subjects, probably the largest study of this kind, suggests how step width variability may relate to fall risk. Together, these studies provide new insights into the factors that regulate the stride-to-stride fluctuations in walking and pave the way for expanded research into the control of gait and the practical application of measures of gait variability in the clinical setting.

Correlation dimension analysis of heart rate variability in patients with dilated cardiomyopathy

A correlation dimension analysis of heart rate variability (HRV) was applied to a group of 55 patients with dilated cardiomyopathy (DCM) and 55 healthy subjects as controls. The 24-h RR time series for each subject was divided into segments of 10,000 beats to determine the correlation dimension (CD) per segment. A study of the influence of the time delay (lag) in the calculation of CD was performed. Good discrimination between both groups (p<0.005) was obtained with lag values of 5 or greater. CD values of DCM patients (8.4+/-1.9) were significantly lower than CD values for controls (9.5+/-1.9). An analysis of CD values of HRV showed that for healthy people, CD night values (10.6+/-1.8) were significant greater than CD day values (9.2+/-1.9), revealing a circadian rhythm. In DCM patients, this circadian rhythm was lost and there were no differences between CD values in day (8.8+/-2.4) and night (8.9+/-2.1).

Magnetic field exposure and arrythmic risk: evaluation in railway drivers

Recent studies suggest that professional exposure to Extremely Low Frequency-Electro Magnetic Field (ELF-EMF) can increase the risk of sudden cardiac death. Aim of our work was to find predictive parameters of arrhythmic risk in a population of 28 railways drivers exposed to ELF-EMF. Our findings were that the exposure did not reduce HRV and did not increase the risk of arrhythmias.

A quantitative comparison of different methods to detect cardiorespiratory coordination during night-time sleep

Background

The univariate approaches used to analyze heart rate variability have recently been extended by several bivariate approaches with respect to cardiorespiratory coordination. Some approaches are explicitly based on mathematical models which investigate the synchronization between weakly coupled complex systems. Others use an heuristic approach, i.e. characteristic features of both time series, to develop appropriate bivariate methods.

Objective

In this study six different methods used to analyze cardiorespiratory coordination have been quantitatively compared with respect to their performance (no. of sequences with cardiorespiratory coordination, no. of heart beats coordinated with respiration). Five of these approaches have been suggested in the recent literature whereas one method originates from older studies.

Results

The methods were applied to the simultaneous recordings of an electrocardiogram and a respiratory trace of 20 healthy subjects during night-time sleep from 0:00 to 6:00. The best temporal resolution and the highest number of coordinated heart beats were obtained with the analysis of 'Phase Recurrences'. Apart from the oldest method, all methods showed similar qualitative results although the quantities varied between the different approaches. In contrast, the oldest method detected considerably fewer coordinated heart beats since it only used part of the maximum amount of information available in each recording.

Conclusions

The method of 'Phase Recurrences' should be the method of choice for the detection of cardiorespiratory coordination since it offers the best temporal resolution and the highest number of coordinated sequences and heart beats. Excluding the oldest method, the results of the heuristic approaches may also be interpreted in terms of the mathematical models.

Recurrence-plot-based measures of complexity and their application to heart-rate-variability data

The knowledge of transitions between regular, laminar or chaotic behaviors is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods that, however, require rather long time observations. To overcome these difficulties, we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart-rate-variability data. For the logistic map these measures enable us not only to detect transitions between chaotic and periodic states, but also to identify laminar states, i.e., chaos-chaos transitions. The traditional recurrence quantification analysis fails to detect the latter transitions. Applying our measures to the heart-rate-variability data, we are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event. Our findings could be of importance for the therapy of malignant cardiac arrhythmias.