Associations between Neurocardiovascular Signal Entropy and Physical Frailty

In this cross-sectional study, the relationship between noninvasively measured neurocardiovascular signal entropy and physical frailty was explored in a sample of community-dwelling older adults from The Irish Longitudinal Study on Ageing (TILDA). The hypothesis under investigation was that dysfunction in the neurovascular and cardiovascular systems, as quantified by short-length signal complexity during a lying-to-stand test (active stand), could provide a marker for frailty. Frailty status (i.e., “non-frail”, “pre-frail”, and “frail”) was based on Fried’s criteria (i.e., exhaustion, unexplained weight loss, weakness, slowness, and low physical activity). Approximate entropy (ApEn) and sample entropy (SampEn) were calculated during resting (lying down), active standing, and recovery phases. There was continuously measured blood pressure/heart rate data from 2645 individuals (53.0% female) and frontal lobe tissue oxygenation data from 2225 participants (52.3% female); both samples had a mean (SD) age of 64.3 (7.7) years. Results revealed statistically significant associations between neurocardiovascular signal entropy and frailty status. Entropy differences between non-frail and pre-frail/frail were greater during resting state compared with standing and recovery phases. Compared with ApEn, SampEn seemed to have better discriminating power between non-frail and pre-frail/frail individuals. The quantification of entropy in short length neurocardiovascular signals could provide a clinically useful marker of the multiple physiological dysregulations that underlie physical frailty.     

基于模糊近似熵的抑郁症患者静息态功能磁共振成像信号复杂度分析

提出采用模糊近似熵的方法对功能磁共振成像(functional magnetic resonance imaging,fMRI)复杂度量化分析,并与样本熵进行比较.采用的22个成年抑郁症患者中,11位男性,年龄在18—65岁之间.我们期望测量的静息态fMRI信号复杂度与Goldberger/Lipsitz模型一致,越健康、越稳健其生理表现的复杂度越大,且复杂度随年龄的增大而降低.全脑平均模糊近似熵与年龄之间差异性显著(r=-0.512,p0.001).相比之下,样本熵与年龄之间差异性不显著(r=-0.102,p=0.482).模糊近似熵同样与年龄相关脑区(额叶、顶叶、边缘系统、颞叶、小脑顶叶)之间差异性显著(p0.05),样本熵与年龄相关脑区之间差异性不显著性.这些结果与Goldberger/Lipsitz模型一致,说明采用模糊近似熵分析fMRI数据复杂度是一个有效的新方法.     

Measuring time series regularity using nonlinear similarity-based sample entropy

Sampe Entropy (SampEn), a measure quantifying regularity and complexity, is believed to be an effective analyzing method of diverse settings that include both deterministic chaotic and stochastic processes, particularly operative in the analysis of physiological signals that involve relatively small amount of data. However, the similarity definition of vectors is based on Heaviside function, of which the boundary is discontinuous and hard, may cause some problems in the validity and accuracy of SampEn. Sigmoid function is a smoothed and continuous version of Heaviside function. To overcome the problems SampEn encountered, a modified SampEn (mSampEn) based on nonlinear Sigmoid function was proposed. The performance of mSampEn was tested on the independent identically distributed (i.i.d.) uniform random numbers, the MIX stochastic model, the Rossler map, and the Hennon map. The results showed that mSampEn was superior to SampEn in several aspects, including giving entropy definition in case of small parameters, better relative consistency, robust to noise, and more independence on record length when characterizing time series generated from either deterministic or stochastic system with different regularities.     

Using the modified sample entropy to detect determinism

A modified sample entropy (mSampEn), based on the nonlinear continuous and convex function, has been proposed and proven to be superior to the standard sample entropy (SampEn) in several aspects. In this Letter, we empirically investigate the ability of the mSampEn statistic combined with surrogate data method to detect determinism. The effects of the datasets length and noise on the proposed method to differentiate between deterministic and stochastic dynamics are tested on several benchmark time series. The noise performance of the mSampEn statistic is also compared with the singular value decomposition (SVD) and symplectic geometry spectrum (SGS) based methods. The results indicate that the mSampEn statistic is a robust index for detecting determinism in short and noisy time series.     

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.     

The Systematic Bias of Entropy Calculation in the Multi-Scale Entropy Algorithm

Entropy indicates irregularity or randomness of a dynamic system. Over the decades, entropy calculated at different scales of the system through subsampling or coarse graining has been used as a surrogate measure of system complexity. One popular multi-scale entropy analysis is the multi-scale sample entropy (MSE), which calculates entropy through the sample entropy (SampEn) formula at each time scale. SampEn is defined by the “logarithmic likelihood” that a small section (within a window of a length m) of the data “matches” with other sections will still “match” the others if the section window length increases by one. “Match” is defined by a threshold of r times standard deviation of the entire time series. A problem of current MSE algorithm is that SampEn calculations at different scales are based on the same matching threshold defined by the original time series but data standard deviation actually changes with the subsampling scales. Using a fixed threshold will automatically introduce systematic bias to the calculation results. The purpose of this paper is to mathematically present this systematic bias and to provide methods for correcting it. Our work will help the large MSE user community avoiding introducing the bias to their multi-scale SampEn calculation results.     

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.     

Empirical Mode Decomposition-Derived Entropy Features Are Beneficial to Distinguish Elderly People with a Falling History on a Force Plate Signal

Fall risk prediction is an important issue for the elderly. A center of pressure signal, derived from a force plate, is useful for the estimation of body calibration. However, it is still difficult to distinguish elderly people’s fall history by using a force plate signal. In this study, older adults with and without a history of falls were recruited to stand still for 60 s on a force plate. Forces in the x, y and z directions (Fx, Fy, and Fz) and center of pressure in the anteroposterior (COPx) and mediolateral directions (COPy) were derived. There were 49 subjects in the non-fall group, with an average age of 71.67 (standard derivation: 6.56). There were also 27 subjects in the fall group, with an average age of 70.66 (standard derivation: 6.38). Five signal series—forces in x, y, z (Fx, Fy, Fz), COPX, and COPy directions—were used. These five signals were further decomposed with empirical mode decomposition (EMD) with seven intrinsic mode functions. Time domain features (mean, standard derivation and coefficient of variations) and entropy features (approximate entropy and sample entropy) of the original signals and EMD-derived signals were extracted. Results showed that features extracted from the raw COP data did not differ significantly between the fall and non-fall groups. There were 10 features extracted using EMD, with significant differences observed among fall and non-fall groups. These included four features from COPx and two features from COPy, Fx and Fz.     

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.     

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.     

Sample Entropy as a Tool to Assess Lumbo-Pelvic Movements in a Clinical Test for Low-Back-Pain Patients

Low back pain (LBP) obviously reduces the quality of life but is also the world’s leading cause of years lived with disability. Alterations in motor response and changes in movement patterns are expected in LBP patients when compared to healthy people. Such changes in dynamics may be assessed by the nonlinear analysis of kinematical time series recorded from one patient’s motion. Since sample entropy (SampEn) has emerged as a relevant index measuring the complexity of a given time series, we propose the development of a clinical test based on SampEn of a time series recorded by a wearable inertial measurement unit for repeated bending and returns (b and r) of the trunk. Twenty-three healthy participants were asked to perform, in random order, 50 repetitions of this movement by touching a stool and another 50 repetitions by touching a box on the floor. The angular amplitude of the b and r movement and the sample entropy of the three components of the angular velocity and acceleration were computed. We showed that the repetitive b and r “touch the stool” test could indeed be the basis of a clinical test for the evaluation of low-back-pain patients, with an optimal duration of 70 s, acceptable in daily clinical practice.     

The Impact of the COVID-19 Pandemic on the Unpredictable Dynamics of the Cryptocurrency Market

The global economy is under great shock again in 2020 due to the COVID-19 pandemic; it has not been long since the global financial crisis in 2008. Therefore, we investigate the evolution of the complexity of the cryptocurrency market and analyze the characteristics from the past bull market in 2017 to the present the COVID-19 pandemic. To confirm the evolutionary complexity of the cryptocurrency market, three general complexity analyses based on nonlinear measures were used: approximate entropy (ApEn), sample entropy (SampEn), and Lempel-Ziv complexity (LZ). We analyzed the market complexity/unpredictability for 43 cryptocurrency prices that have been trading until recently. In addition, three non-parametric tests suitable for non-normal distribution comparison were used to cross-check quantitatively. Finally, using the sliding time window analysis, we observed the change in the complexity of the cryptocurrency market according to events such as the COVID-19 pandemic and vaccination. This study is the first to confirm the complexity/unpredictability of the cryptocurrency market from the bull market to the COVID-19 pandemic outbreak. We find that ApEn, SampEn, and LZ complexity metrics of all markets could not generalize the COVID-19 effect of the complexity due to different patterns. However, market unpredictability is increasing by the ongoing health crisis.     

基于符号相对熵的心电信号时间不可逆性分析

心电图(ECG)信号的时间不可逆性能够反映出心脏的生理功能和健康状态.从短时ECG信号中探测时间不可逆性特征具有重要的现实意义. 文章提出符号相对熵方法(先进行符号化处理,再分别计算它们的时间不可逆性),研究了从MIT-BIH标准数据库中提取的正常窦性心律(normal sinus rhythm,NSR)、心室纤颤(ventricular fibrillation,VF)、心脏猝死(sudden cardiac death,SCD)三种信号.结果表明,这三种信号的时间不可逆性有所不同:NSR信号的时间不可 关键词： 心电信号 相对熵 时间不可逆性     

基于虚拟开车环境的自闭症儿童脑电样本熵

自闭症谱系障碍是一种涉及感觉、情感、记忆、语言、智力、动作等认知功能和执行功能障碍的精神疾病. 本文从神经工效学角度出发, 用虚拟开车环境作为复杂多任务激励源将大脑系统与人体动作控制等有机地结合起来, 通过对脑电信号的滑动平均样本熵分析来探索自闭症儿童在虚拟开车环境中的脑活动特征. 研究发现不论是休息状态还是开车状态, 自闭症患者的滑动平均样本熵总体上低于健康者, 尤其在前额叶、颞叶、顶叶和枕叶功能区, 表明自闭症儿童的行为适应性较低. 不过, 自闭症患者的开车状态与健康受试者的休息状态比较接近, 表明虚拟开车环境或许有助于自闭症患者的干预治疗. 此外, 自闭症患者在颞叶区呈现显著性右半球优势性. 本研究为进一步深入开展自闭症疾病的机理研究及其诊断、评估和干预等研究提供一种新的研究思路.     

Characterizing continuously rotating detonation via nonlinear time series analysis

The sampled pressure signals in continuously rotating detonation combustors have the inherence of nonlinear dynamics. To dig out more information on combustion modes, the nonlinear time series analysis method is thus applied to the pressure-time series obtained at a hydrogen/air rotating detonation combustor by using the phase space reconstruction and wavelet entropy algorithm. The variation of wavelet entropy is approved to be associated with the periodicity variation of pressure signals. Different structures of attractor as well as wavelet entropy distribution in the phase diagram can distinguish the deflagration mode from the unstable and stable detonation modes under the conditions of different air flow rates. The limit-cycle oscillation is exhibited in the phase space diagram with a very low flow rate, here 25 g/s. The mean wavelet entropy of pressure-time series can be a quantitative index of different combustion modes occurring in the combustor. The present study is expected to enhance the understanding of the physical mechanism of continuously rotating detonation and contribute on the development of detonation propulsion technology.     

Entropy analysis of the dynamics of El Niño/Southern Oscillation during the Holocene

This study explores temporal changes in the dynamics of the Holocene ENSO proxy record of the Laguna Pallcacocha sedimentary data using two entropy quantifiers. In particular, we analyze the possible connections between changes in entropy and epochs of rapid climate change (RCC). Our results indicate that the dynamics of the ENSO proxy record during the RCC interval 9000-8000 BP displays very low entropy (high predictability) that is remarkably different from that of the other RCCs of the Holocene. Both entropy quantifiers point out to the existence of cycles with a period close to 2000 years during the mid-to-late Holocene. Within these cycles, we find a tendency for entropy to increase (predictability to decrease) during the two longer RCC periods (6000-5000 and 3500-2500 BP) which might be associated with the reported increased aridity of the low tropics.     

Thermoacoustic assessment of hematocrit changes in human forearms

Abnormal hematocrit(Hct) is associated with an increased risk of pre-hypertension and all-cause death in general population, and people with a high Hct value are susceptible to arterial cardiovascular disease and venous thromboembolism.In this study, we report for the first time on the ability of thermoacoustic imaging(TAI) for in vivo evaluating Hct changes in human forearms. In vitro blood samples with different Hct values from healthy volunteers(n = 3) were prepared after centrifugation. TAI was performed using these samples in comparison with the direct measurements of conductivity. In vivo TAI was conducted in the forearm of healthy volunteers(n = 7) where Hct changes were produced through a vascular occlusion stimulation over a period of time. The results of in vitro blood samples obtained from the 3 healthy subjects show that the thermoacoustic(TA) signals changes due to the variation of blood conductivity are closely related to the changes in Hct. In addition, the in vivo TA signals obtained from the 7 healthy subjects consistently increase in the artery/muscle and decrease in the vein during venous or arterial occlusion because of the changed Hct value in their forearms. These findings suggest that TAI has the potential to become a new tool for monitoring Hct changes for a variety of pre-clinical and clinical applications.     

Binaural unmasking in infants

Localization responses to a broadband noise signal presented against a broadband noise masker were obtained from 12-month-old infants and adults. Two loudspeakers, one to the left and one to the right of the listener, continuously presented identical broadband maskers. On a trial, a broadband signal was added to one of the loudspeakers. Subjects were required to identify the loudspeaker producing the signal. Noise signals were either coherent (from the same noise generator) or incoherent (from an independent noise generator). Both infants and adults found it easier to locate the incoherent signals even when the two types of signals were adjusted to produce equal increments in power. Since monaural performance, after this adjustment, should be equivalent for the two cases, superior performance for incoherent signals implies that binaural processing is involved. The same result was observed in control experiments in which coherent and incoherent signals were presented over earphones to adults. These results suggest that the mechanisms responsible for binaural unmasking are operative by 12 months of age.     

Self-Organization,Entropy Generation Rate,and Boundary Defects: A Control Volume Approach

Self-organization that leads to the discontinuous emergence of optimized new patterns is related to entropy generation and the export of entropy. Compared to the original pattern that the new, self-organized pattern replaces, the new features could involve an abrupt change in the pattern-volume. There is no clear principle of pathway selection for self-organization that is known for triggering a particular new self-organization pattern. The new pattern displays different types of boundary-defects necessary for stabilizing the new order. Boundary-defects can contain high entropy regions of concentrated chemical species. On the other hand, the reorganization (or refinement) of an established pattern is a more kinetically tractable process, where the entropy generation rate varies continuously with the imposed variables that enable and sustain the pattern features. The maximum entropy production rate (MEPR) principle is one possibility that may have predictive capability for self-organization. The scale of shapes that form or evolve during self-organization and reorganization are influenced by the export of specific defects from the control volume of study. The control volume (CV) approach must include the texture patterns to be located inside the CV for the MEPR analysis to be applicable. These hypotheses were examined for patterns that are well-characterized for solidification and wear processes. We tested the governing equations for bifurcations (the onset of new patterns) and for reorganization (the fine tuning of existing patterns) with published experimental data, across the range of solidification morphologies and nonequilibrium phases, for metallic glass and featureless crystalline solids. The self-assembling features of surface-texture patterns for friction and wear conditions were also modeled with the entropy generation (MEPR) principle, including defect production (wear debris). We found that surface texture and entropy generation in the control volume could be predictive for self-organization. The main results of this study provide support to the hypothesis that self-organized patterns are a consequence of the maximum entropy production rate per volume principle. Patterns at any scale optimize a certain outcome and have utility. We discuss some similarities between the self-organization behavior of both inanimate and living systems, with ideas regarding the optimizing features of self-organized pattern features that impact functionality, beauty, and consciousness.