Bivariate Entropy Analysis of Electrocardiographic RR–QT Time Series

QT interval variability (QTV) and heart rate variability (HRV) are both accepted biomarkers for cardiovascular events. QTV characterizes the variations in ventricular depolarization and repolarization. It is a predominant element of HRV. However, QTV is also believed to accept direct inputs from upstream control system. How QTV varies along with HRV is yet to be elucidated. We studied the dynamic relationship of QTV and HRV during different physiological conditions from resting, to cycling, and to recovering. We applied several entropy-based measures to examine their bivariate relationships, including cross sample entropy (XSampEn), cross fuzzy entropy (XFuzzyEn), cross conditional entropy (XCE), and joint distribution entropy (JDistEn). Results showed no statistically significant differences in XSampEn, XFuzzyEn, and XCE across different physiological states. Interestingly, JDistEn demonstrated significant decreases during cycling as compared with that during the resting state. Besides, JDistEn also showed a progressively recovering trend from cycling to the first 3 min during recovering, and further to the second 3 min during recovering. It appeared to be fully recovered to its level in the resting state during the second 3 min during the recovering phase. The results suggest that there is certain nonlinear temporal relationship between QTV and HRV, and that the JDistEn could help unravel this nuanced property.     

心率变异性分析在新生儿疼痛检测中的应用

为了研究疼痛暴露对新生儿自主神经系统的影响,并建立基于心率变异性(heart rate variability,HRV)指标的新生儿疼痛检测模型,采用时域、频域和非线性方法对40名新生儿疼痛暴露前后的心电数据进行短时HRV分析,Wilcoxon符号秩检验用于统计分析,支持向量机(support vector machine,SVM)用于建立检测模型.结果表明,RR间期均值a RR、低频段功率LF、高频段功率HF等3个线性指标和近似熵Ap En、样本熵Samp En、递归率REC等9个非线性指标在疼痛前后具有统计学差异;基于a RR、相邻两个RR间期对差值大于50 ms的百分比p NN50,Ap En,关联维D2和REC等5个指标和SVM的疼痛检测模型检测正确率达到83.75%.HRV的相关指标可反映新生儿自主神经系统对疼痛暴露的应答,基于HRV指标和SVM的模型可用于新生儿疼痛检测.     

Influence of Ectopic Beats on Heart Rate Variability Analysis

The analysis of heart rate variability (HRV) plays a dominant role in the study of physiological signal variability. HRV reflects the information of the adjustment of sympathetic and parasympathetic nerves on the cardiovascular system and, thus, is widely used to evaluate the functional status of the cardiovascular system. Ectopic beats may affect the analysis of HRV. However, the quantitative relationship between the burden of ectopic beats and HRV indices, including entropy measures, has not yet been investigated in depth. In this work, we analyzed the effects of different numbers of ectopic beats on several widely accepted HRV parameters in time-domain (SDNN), frequency-domain (LF/HF), as well as non-linear features (SampEn and Pt-SampEn (physical threshold-based SampEn)). The results showed that all four indices were influenced by ectopic beats, and the degree of influence was roughly increased with the increase of the number of ectopic beats. Ectopic beats had the greatest impact on the frequency domain index LF/HF, whereas the Pt-SampEn was minimally accepted by ectopic beats. These results also indicated that, compared with the other three indices, Pt-SampEn had better robustness for ectopic beats.     

Quantitative analysis of heart rate variability

In the modern industrialized countries every year several hundred thousands of people die due to sudden cardiac death. The individual risk for this sudden cardiac death cannot be defined precisely by common available, noninvasive diagnostic tools like Holter monitoring, highly amplified ECG and traditional linear analysis of heart rate variability (HRV). Therefore, we apply some rather unconventional methods of nonlinear dynamics to analyze the HRV. Especially, some complexity measures that are based on symbolic dynamics as well as a new measure, the renormalized entropy, detect some abnormalities in the HRV of several patients who have been classified in the low risk group by traditional methods. A combination of these complexity measures with the parameters in the frequency domain seems to be a promising way to get a more precise definition of the individual risk. These findings have to be validated by a representative number of patients. (c) 1995 American Institute of Physics.     

基于Poincaré差值散点图的心率变异性分析方法研究

在心率变异性的非线性分析中, Poincaré散点图分析是一种重要手段.本文基于Poincaré差值散点图(modified Poincaré plot)提出了两个参数——区域分布熵和区域分布系数, 用于定量描述所考察区域内散点的分布趋势, 并提出对散点在4个象限中的分布进行分别计算.通过对MIT-BIH数据库中健康年轻人、健康老年人和充血性心力衰竭患者样本数据的分析, 发现两参数值均呈现显著的组间差异;同时, 不同象限的分析结果显示了四个象限具有不同的区分敏感性, 而其中尤以第一象限的区分度为最高, 反映出充血性心力衰竭患者相对健康人迷走神经调控功能的改变最为显著, 与以往的生理学研究结论相符.经验证, 该方法可用于短时数据, 更易于扩展至临床应用.     

Novel Application of Multiscale Cross-Approximate Entropy for Assessing Early Changes in the Complexity between Systolic Blood Pressure and ECG R-R Intervals in Diabetic Rats

Cardiac autonomic neuropathy (CAN) is a common complication of diabetes mellitus, and can be assessed using heart rate variability (HRV) and the correlations between systolic blood pressure (SBP) and ECG R-R intervals (RRIs), namely baroreflex sensitivity (BRS). In this study, we propose a novel parameter for the nonlinear association between SBP and RRIs based on multiscale cross-approximate entropy (MS-CXApEn). Sixteen male adult Wistar Kyoto rats were equally divided into two groups: streptozotocin-induced diabetes and age-matched controls. RRIs and SBP were acquired in control rats and the diabetic rats at the onset of hyperglycemia and insulin-treated euglycemia to determine HRV by the ratio of low-frequency to high-frequency power (LF/HF) and Poincaré plot as SSR (SD1/SD2), BRS, and MS-CXApEn. SSR and BRS were not significantly different among the three groups. The LF/HF was significantly higher in the hyperglycemic diabetics than those in the controls and euglycemic diabetic rats. MS-CXApEn was higher in the diabetic hyperglycemic rats than the control rats from scales 2 to 10, and approached the values of controls in diabetic euglycemic rats at scales 9 and 10. Conclusions: We propose MS-CXApEn as a novel parameter to quantify the dynamic nonlinear interactions between SBP and RRIs that reveals more apparent changes in early diabetic rats. Furthermore, changes in this parameter were related to correction of hyperglycemia and could be useful for detecting and assessing CAN in early diabetes.     

Entropy Analysis of Heart Rate Variability in Different Sleep Stages

How the complexity or irregularity of heart rate variability (HRV) changes across different sleep stages and the importance of these features in sleep staging are not fully understood. This study aimed to investigate the complexity or irregularity of the RR interval time series in different sleep stages and explore their values in sleep staging. We performed approximate entropy (ApEn), sample entropy (SampEn), fuzzy entropy (FuzzyEn), distribution entropy (DistEn), conditional entropy (CE), and permutation entropy (PermEn) analyses on RR interval time series extracted from epochs that were constructed based on two methods: (1) 270-s epoch length and (2) 300-s epoch length. To test whether adding the entropy measures can improve the accuracy of sleep staging using linear HRV indices, XGBoost was used to examine the abilities to differentiate among: (i) 5 classes [Wake (W), non-rapid-eye-movement (NREM), which can be divide into 3 sub-stages: stage N1, stage N2, and stage N3, and rapid-eye-movement (REM)]; (ii) 4 classes [W, light sleep (combined N1 and N2), deep sleep (N3), and REM]; and (iii) 3 classes: (W, NREM, and REM). SampEn, FuzzyEn, and CE significantly increased from W to N3 and decreased in REM. DistEn increased from W to N1, decreased in N2, and further decreased in N3; it increased in REM. The average accuracy of the three tasks using linear and entropy features were 42.1%, 59.1%, and 60.8%, respectively, based on 270-s epoch length; all were significantly lower than the performance based on 300-s epoch length (i.e., 54.3%, 63.1%, and 67.5%, respectively). Adding entropy measures to the XGBoost model of linear parameters did not significantly improve the classification performance. However, entropy measures, especially PermEn, DistEn, and FuzzyEn, demonstrated greater importance than most of the linear parameters in the XGBoost model.300-s270-s.     

Nonlinear Measures to Evaluate Upright Postural Stability: A Systematic Review

Conventional biomechanical analyses of human movement have been generally derived from linear mathematics. While these methods can be useful in many situations, they fail to describe the behavior of the human body systems that are predominately nonlinear. For this reason, nonlinear analyses have become more prevalent in recent literature. These analytical techniques are typically investigated using concepts related to variability, stability, complexity, and adaptability. This review aims to investigate the application of nonlinear metrics to assess postural stability. A systematic review was conducted of papers published from 2009 to 2019. Databases searched were PubMed, Google Scholar, Science-Direct and EBSCO. The main inclusion consisted of: Sample entropy, fractal dimension, Lyapunov exponent used as nonlinear measures, and assessment of the variability of the center of pressure during standing using force plate. Following screening, 43 articles out of the initial 1100 were reviewed including 33 articles on sample entropy, 10 articles on fractal dimension, and 4 papers on the Lyapunov exponent. This systematic study shows the reductions in postural regularity related to aging and the disease or injures in the adaptive capabilities of the movement system and how the predictability changes with different task constraints.     

多尺度多变量模糊熵分析

多尺度多变量样本熵评价同步多通道数据的多变量复杂度, 是非线性动态相互关系的一种反映, 但其统计稳定性差, 且不适用于非线性非平稳信号. 研究利用模糊隶属度函数代替模式相似判断的硬阈值准则, 并分析模糊隶属度函数形式的影响; 研究利用多变量经验模态分解算法进行多尺度化, 并对比其处理效果. 仿真试验表明, 模糊隶属度函数的引入可以有效提高算法的统计稳定性, 所构造的物理模糊隶属度函数的性能最为显著; 基于多变量经验模态分解算法的多尺度化过程可更有效地捕获信号的不同尺度成分, 从而更敏感地区分具有不同复杂度的信号. 对临床试验数据的分析支持以上结论, 且结果提示随着年龄增加或心脏疾病的发生, 心率变异性和心脏舒张间期变异性的多变量复杂度以不同的方式降低: 年龄增加会使低尺度熵值降低, 表示近程相关性的丢失; 而心脏疾病会同时影响各个尺度的熵值, 即同时丢失了近程和长时相关性. 该结论可用于指导心血管疾病的无创预警研究. 关键词： 多变量复杂度 多尺度多变量模糊熵 物理模糊隶属度函数 多变量经验模态分解     

Approximate Entropy of Brain Network in the Study of Hemispheric Differences

Human brain, a dynamic complex system, can be studied with different approaches, including linear and nonlinear ones. One of the nonlinear approaches widely used in electroencephalographic (EEG) analyses is the entropy, the measurement of disorder in a system. The present study investigates brain networks applying approximate entropy (ApEn) measure for assessing the hemispheric EEG differences; reproducibility and stability of ApEn data across separate recording sessions were evaluated. Twenty healthy adult volunteers were submitted to eyes-closed resting EEG recordings, for 80 recordings. Significant differences in the occipital region, with higher values of entropy in the left hemisphere than in the right one, show that the hemispheres become active with different intensities according to the performed function. Besides, the present methodology proved to be reproducible and stable, when carried out on relatively brief EEG epochs but also at a 1-week distance in a group of 36 subjects. Nonlinear approaches represent an interesting probe to study the dynamics of brain networks. ApEn technique might provide more insight into the pathophysiological processes underlying age-related brain disconnection as well as for monitoring the impact of pharmacological and rehabilitation treatments.     

Similarity Changes Analysis for Heart Rate Fluctuation Regularity as a New Screening Method for Congestive Heart Failure

Congestive heart failure (CHF) is a chronic cardiovascular condition associated with dysfunction of the autonomic nervous system (ANS). Heart rate variability (HRV) has been widely used to assess ANS. This paper proposes a new HRV analysis method, which uses information-based similarity (IBS) transformation and fuzzy approximate entropy (fApEn) algorithm to obtain the fApEn_IBS index, which is used to observe the complexity of autonomic fluctuations in CHF within 24 h. We used 98 ECG records (54 health records and 44 CHF records) from the PhysioNet database. The fApEn_IBS index was statistically significant between the control and CHF groups (p < 0.001). Compared with the classical indices low-to-high frequency power ratio (LF/HF) and IBS, the fApEn_IBS index further utilizes the changes in the rhythm of heart rate (HR) fluctuations between RR intervals to fully extract relevant information between adjacent time intervals and significantly improves the performance of CHF screening. The CHF classification accuracy of fApEn_IBS was 84.69%, higher than LF/HF (77.55%) and IBS (83.67%). Moreover, the combination of IBS, fApEn_IBS, and LF/HF reached the highest CHF screening accuracy (98.98%) with the random forest (RF) classifier, indicating that the IBS and LF/HF had good complementarity. Therefore, fApEn_IBS effusively reflects the complexity of autonomic nerves in CHF and is a valuable CHF assessment tool.     

Short-Term Effect of Percutaneous Coronary Intervention on Heart Rate Variability in Patients with Coronary Artery Disease

Myocardial ischemia in patients with coronary artery disease (CAD) leads to imbalanced autonomic control that increases the risk of morbidity and mortality. To systematically examine how autonomic function responds to percutaneous coronary intervention (PCI) treatment, we analyzed data of 27 CAD patients who had admitted for PCI in this pilot study. For each patient, five-minute resting electrocardiogram (ECG) signals were collected before and after the PCI procedure. The time intervals between ECG collection and PCI were both within 24 h. To assess autonomic function, normal sinus RR intervals were extracted and were analyzed quantitatively using traditional linear time- and frequency-domain measures [i.e., standard deviation of the normal-normal intervals (SDNN), the root mean square of successive differences (RMSSD), powers of low frequency (LF) and high frequency (HF) components, LF/HF] and nonlinear entropy measures [i.e., sample entropy (SampEn), distribution entropy (DistEn), and conditional entropy (CE)], as well as graphical metrics derived from Poincaré plot [i.e., Porta’s index (PI), Guzik’s index (GI), slope index (SI) and area index (AI)]. Results showed that after PCI, AI and PI decreased significantly (p < 0.002 and 0.015, respectively) with effect sizes of 0.88 and 0.70 as measured by Cohen’s d static. These changes were independent of sex. The results suggest that graphical AI and PI metrics derived from Poincaré plot of short-term ECG may be potential for sensing the beneficial effect of PCI on cardiovascular autonomic control. Further studies with bigger sample sizes are warranted to verify these observations.     

Dynamical complexity changes during two forms of meditation

Detection of dynamical complexity changes in natural and man-made systems has deep scientific and practical meaning. We use the base-scale entropy method to analyze dynamical complexity changes for heart rate variability (HRV) series during specific traditional forms of Chinese Chi and Kundalini Yoga meditation techniques in healthy young adults. The results show that dynamical complexity decreases in meditation states for two forms of meditation. Meanwhile, we detected changes in probability distribution of m-words during meditation and explained this changes using probability distribution of sine function. The base-scale entropy method may be used on a wider range of physiologic signals.     

小波变换的信号分形分析及其在心电信号处理中的应用研究

介绍了一种基于小波变换的分形分析方法,并将它成功地应用于心房纤颤的检测中.该方法提取了一个特征值r,结果表明在心房纤颤开始时,特征值是上升的,心房纤颤结束后,特征值又慢慢恢复到原来的数值,由此可以成功地检测出心房纤颤的开始和结束.此外,由于特征值同时反映了heartratevariability(HRV)信号的复杂程度,所以同时它也表明:心房纤颤开始后,HRV信号的复杂度是下降的 关键词： HRV 小波变换 分形     

Effects of Tau and Sampling Frequency on the Regularity Analysis of ECG and EEG Signals Using ApEn and SampEn Entropy Estimators

Electrocardiography (ECG) and electroencephalography (EEG) signals provide clinical information relevant to determine a patient’s health status. The nonlinear analysis of ECG and EEG signals allows for discovering characteristics that could not be found with traditional methods based on amplitude and frequency. Approximate entropy (ApEn) and sampling entropy (SampEn) are nonlinear data analysis algorithms that measure the data’s regularity, and these are used to classify different electrophysiological signals as normal or pathological. Entropy calculation requires setting the parameters r (tolerance threshold), m (immersion dimension), and τ (time delay), with the last one being related to how the time series is downsampled. In this study, we showed the dependence of ApEn and SampEn on different values of τ, for ECG and EEG signals with different sampling frequencies (F_s), extracted from a digital repository. We considered four values of F_s (128, 256, 384, and 512 Hz for the ECG signals, and 160, 320, 480, and 640 Hz for the EEG signals) and five values of τ (from 1 to 5). We performed parametric and nonparametric statistical tests to confirm that the groups of normal and pathological ECG and EEG signals were significantly different (p < 0.05) for each F and τ value. The separation between the entropy values of regular and irregular signals was variable, demonstrating the dependence of ApEn and SampEn with F_s and τ. For ECG signals, the separation between the conditions was more robust when using SampEn, the lowest value of F_s, and τ larger than 1. For EEG signals, the separation between the conditions was more robust when using SampEn with large values of F_s and τ larger than 1. Therefore, adjusting τ may be convenient for signals that were acquired with different F_s to ensure a reliable clinical classification. Furthermore, it is useful to set τ to values larger than 1 to reduce the computational cost.     

Composite Multivariate Multi-Scale Permutation Entropy and Laplacian Score Based Fault Diagnosis of Rolling Bearing

As a powerful tool for measuring complexity and randomness, multivariate multi-scale permutation entropy (MMPE) has been widely applied to the feature representation and extraction of multi-channel signals. However, MMPE still has some intrinsic shortcomings that exist in the coarse-grained procedure, and it lacks the precise estimation of entropy value. To address these issues, in this paper a novel non-linear dynamic method named composite multivariate multi-scale permutation entropy (CMMPE) is proposed, for optimizing insufficient coarse-grained process in MMPE, and thus to avoid the loss of information. The simulated signals are used to verify the validity of CMMPE by comparing it with the often-used MMPE method. An intelligent fault diagnosis method is then put forward on the basis of CMMPE, Laplacian score (LS), and bat optimization algorithm-based support vector machine (BA-SVM). Finally, the proposed fault diagnosis method is utilized to analyze the test data of rolling bearings and is then compared with the MMPE, multivariate multi-scale multiscale entropy (MMFE), and multi-scale permutation entropy (MPE) based fault diagnosis methods. The results indicate that the proposed fault diagnosis method of rolling bearing can achieve effective identification of fault categories and is superior to comparative methods.     

心率变异性的异方差特征研究

心率变异性数据具有非平稳和瞬时波动的特点,本文提出了采用自回归条件异方差(ARCH)分析方法分析这种波动.分析方法采用自回归移动平均模型消除序列的趋势和相关性,采用F检验法判断残差序列中是否存在ARCH效应,同时给出接受ARCH效应的概率.对充血性心衰竭病人和正常人的心率波动序列进行分析,两类人群ARCH特征接受概率及其变化率的统计值有较大差异,表明该方法可以区分不同的群体,为心电信息学研究提供了一种新的方法.     

Long-range correlations in heart rate variability during computer-mouse work under time pressure

The aim of this study was to investigate the influences of time pressure on long-range correlations in heart rate variability (HRV), the effects of relaxation on the cardiovascular regulation system and the advantages of detrended fluctuation analysis (DFA) over the conventional power spectral analysis in discriminating states of the cardiovascular systems under different levels of time pressure. Volunteer subjects (n=10, male/female=5/5) participated in a computer-mouse task consisting of five sessions, i.e. baseline session (BSS) which was free of time pressure, followed by sessions with 80% (SS80), 100% (SS100), 90% (SS90) and 150% (SS150) of the baseline time. Electrocardiogram (ECG) and task performance were recorded throughout the experiments. Two rest sessions before and after the computer-mouse work, i.e. RS1 and RS2, were also recorded as comparison. HRV series were subsequently analyzed by both conventional power spectral analysis and detrended fluctuation analysis (DFA). The long-term scaling exponent α₂ by DFA was significantly lower in SS80 than that in other sessions. It was also found that short-term release of time pressure had positive influences on the cardiovascular system, i.e. the α₂ in RS2 was significantly higher than that in SS80, SS100 and SS90. No significant differences were found between any two sessions by conventional power spectral analysis. Our results showed that DFA performed better in discriminating the states of cardiovascular autonomic modulation under time pressure than the conventional power spectral analysis.     

颠倒睡眠状态调制心率变异性信号的功率谱和基本尺度熵分析

心率变异性(HRV)信号能够提供心脏活动状态的重要信息.通过建立颠倒睡眠模型,联合功率谱和基本尺度熵方法分析颠倒睡眠状态下24 h的HRV信号,研究颠倒睡眠对自主神经相互作用以及HRV信号混沌强度的调制.结果表明,颠倒睡眠导致自主神经在昼夜间的活动节律发生颠倒,基本尺度熵在昼夜的变化趋势也随之发生逆转,因此HRV信号的混沌强度与自主神经的相互作用密切相关,进一步研究两者之间的关系发现:HRV信号的混沌强度与交感神经的调制强度正相关,与迷走神经的调制强度负相关.