Everyday episodic memory in amnestic mild cognitive impairment: a preliminary investigation

Background

In humans, rapid eye movements (REM) density during REM sleep plays a prominent role in psychiatric diseases. Especially in depression, an increased REM density is a vulnerability marker for depression. In clinical practice and research measurement of REM density is highly standardized. In basic animal research, almost no tools are available to obtain and systematically evaluate eye movement data, although, this would create increased comparability between human and animal sleep studies.

Methods

We obtained standardized electroencephalographic (EEG), electromyographic (EMG) and electrooculographic (EOG) signals from freely behaving mice. EOG electrodes were bilaterally and chronically implanted with placement of the electrodes directly between the musculus rectus superior and musculus rectus lateralis. After recovery, EEG, EMG and EOG signals were obtained for four days. Subsequent to the implantation process, we developed and validated an Eye Movement scoring in Mice Algorithm (EMMA) to detect REM as singularities of the EOG signal, based on wavelet methodology.

Results

The distribution of wakefulness, non-REM (NREM) sleep and rapid eye movement (REM) sleep was typical of nocturnal rodents with small amounts of wakefulness and large amounts of NREM sleep during the light period and reversed proportions during the dark period. REM sleep was distributed correspondingly. REM density was significantly higher during REM sleep than NREM sleep. REM bursts were detected more often at the end of the dark period than the beginning of the light period. During REM sleep REM density showed an ultradian course, and during NREM sleep REM density peaked at the beginning of the dark period. Concerning individual eye movements, REM duration was longer and amplitude was lower during REM sleep than NREM sleep. The majority of single REM and REM bursts were associated with micro-arousals during NREM sleep, but not during REM sleep.

Conclusions

Sleep-stage specific distributions of REM in mice correspond to human REM density during sleep. REM density, now also assessable in animal models through our approach, is increased in humans after acute stress, during PTSD and in depression. This relationship can now be exploited to match animal models more closely to clinical situations, especially in animal models of depression.     

模糊熵算法在混沌序列复杂度分析中的应用

为了准确分析混沌序列的复杂性, 采用模糊熵算法(FuzzyEn) 对典型离散混沌系统和连续混沌系统的复杂度进行分析. 与近似熵(ApEn)、 样本熵(SampEn) 和强度统计复杂度算法相比, FuzzyEn算法是一种更有效的混沌复杂度测度算法, 且对相空间维数(m)、 相似容限度(r) 和序列长度(N) 的敏感性、 依赖性更低, 鲁棒性和测度值的连续性更好. 对混沌系统的复杂性分析表明, 连续混沌系统的复杂度远小于离散混沌系统, 但是如果利用高复杂度的离散混沌伪随机序列或经典 m序列对连续混沌系统产生的伪随机序列进行扰动, 则能大大提高混沌序列的复杂性. 为混沌序列在密码学和混沌保密通信中的应用提供了理论依据.     

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.     

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.     

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.     

Cardiovascular Signal Entropy Predicts All-Cause Mortality: Evidence from The Irish Longitudinal Study on Ageing (TILDA)

In this study, the relationship between cardiovascular signal entropy and the risk of seven-year all-cause mortality was explored in a large sample of community-dwelling older adults from The Irish Longitudinal Study on Ageing (TILDA). The hypothesis under investigation was that physiological dysregulation might be quantifiable by the level of sample entropy (SampEn) in continuously noninvasively measured resting-state systolic (sBP) and diastolic (dBP) blood pressure (BP) data, and that this SampEn measure might be independently predictive of mortality. Participants’ date of death up to 2017 was identified from official death registration data and linked to their TILDA baseline survey and health assessment data (2010). BP was continuously monitored during supine rest at baseline, and SampEn values were calculated for one-minute and five-minute sections of this data. In total, 4543 participants were included (mean (SD) age: 61.9 (8.4) years; 54.1% female), of whom 214 died. Cox proportional hazards regression models were used to estimate the hazard ratios (HRs) with 95% confidence intervals (CIs) for the associations between BP SampEn and all-cause mortality. Results revealed that higher SampEn in BP signals was significantly predictive of mortality risk, with an increase of one standard deviation in sBP SampEn and dBP SampEn corresponding to HRs of 1.19 and 1.17, respectively, in models comprehensively controlled for potential confounders. The quantification of SampEn in short length BP signals could provide a novel and clinically useful predictor of mortality risk in older adults.     

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.     

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.     

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.     

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.     

On the Variability of Heart Rate Variability—Evidence from Prospective Study of Healthy Young College Students

Heart rate variability (HRV) has been widely used as indices for autonomic regulation, including linear analyses, entropy and multi-scale entropy based nonlinear analyses, and however, it is strongly influenced by the conditions under which the signal is being recorded. To investigate the variability of healthy HRV under different settings, we recorded electrocardiograph (ECG) signals from 56 healthy young college students (20 h for each participant) at campus using wearable single-lead ECG device. Accurate R peak to R peak (RR) intervals were extracted by combing the advantages of five commonly used R-peak detection algorithms to eliminate data quality influence. Thorough and detailed linear and nonlinear HRV analyses were performed. Variability of HRV metrics were evaluated from five categories: (1) different states of daily activities; (2) different recording time period in the same day during free-running daily activities; (3) body postures of sitting and lying; (4) lying on the left, right and back; and (5) gender influence. For most of the analyzed HRV metrics, significant differences (p < 0.05) were found among different recording conditions within the five categories except lying on different positions. Results suggested that the standardization of ECG data collection and HRV analysis should be implemented in HRV related studies, especially for entropy and multi-scale entropy based analyses. Furthermore, this preliminary study provides reference values of HRV indices under various recording conditions of healthy young subjects that could be useful information for different applications (e.g., health monitoring and management).     

基于有限穿越水平可视图的短时睡眠心率变异性研究

心率数据是最易于获取的人体生理数据之一,基于心率变异性的睡眠分析是近年来各种用于日常健康管理的可穿戴设备功能的一个重要发展方向,需要不断探索可以应用于标准睡眠分期时间窗(约30 s)的各类短时特征参数.利用近期报道的有限穿越水平可视图,并进一步提出一种加权有限穿越水平可视图,将不同睡眠状态下的短时心率变异序列映射为网络,进而提取平均集聚系数、特征路径长度、集聚系数熵、路径分布熵、加权集聚系数熵和加权路径分布熵等网络特征参数进行统计分析.结果表明,各网络参数值在醒觉、浅睡期、深睡期和快速眼动期的幅度水平具有显著差异,体现了所述方法在基于短时心率变异数据的睡眠分期中的有效性.同时,进一步研究了健康年轻人和中老年人在不同睡眠状态下的网络参数值,发现两者虽然存在整体的水平差异,但是在不同睡眠状态间的变化仍具有相同的趋势,反映出相对于正常的年龄老化,睡眠调制对心脏动力学系统具有更显著的影响,也说明所述方法可作为基于心率变异性的睡眠研究的一种新的辅助工具.     

Time-series analysis of sleep-wake stage of rat EEG using time-dependent pattern entropy

We performed electroencephalography (EEG) for six male Wistar rats to clarify temporal behaviors at different levels of consciousness. Levels were identified both by conventional sleep analysis methods and by our novel entropy method. In our method, time-dependent pattern entropy is introduced, by which EEG is reduced to binary symbolic dynamics and the pattern of symbols in a sliding temporal window is considered. A high correlation was obtained between level of consciousness as measured by the conventional method and mean entropy in our entropy method. Mean entropy was maximal while awake (stage W) and decreased as sleep deepened. These results suggest that time-dependent pattern entropy may offer a promising method for future sleep research.     

Regularity in Stock Market Indices within Turbulence Periods: The Sample Entropy Approach

The aim of this study is to assess and compare changes in regularity in the 36 European and the U.S. stock market indices within major turbulence periods. Two periods are investigated: the Global Financial Crisis in 2007–2009 and the COVID-19 pandemic outbreak in 2020–2021. The proposed research hypothesis states that entropy of an equity market index decreases during turbulence periods, which implies that regularity and predictability of a stock market index returns increase in such cases. To capture sequential regularity in daily time series of stock market indices, the Sample Entropy algorithm (SampEn) is used. Changes in the SampEn values before and during the particular turbulence period are estimated. The empirical findings are unambiguous and confirm no reason to reject the research hypothesis. Moreover, additional formal statistical analyses indicate that the SampEn results are similar both for developed and emerging European economies. Furthermore, the rolling-window procedure is utilized to assess the evolution of SampEn over time.     

The Value of Heart Rhythm Complexity in Identifying High-Risk Pulmonary Hypertension Patients

Pulmonary hypertension (PH) is a fatal disease—even with state-of-the-art medical treatment. Non-invasive clinical tools for risk stratification are still lacking. The aim of this study was to investigate the clinical utility of heart rhythm complexity in risk stratification for PH patients. We prospectively enrolled 54 PH patients, including 20 high-risk patients (group A; defined as WHO functional class IV or class III with severely compromised hemodynamics), and 34 low-risk patients (group B). Both linear and non-linear heart rate variability (HRV) variables, including detrended fluctuation analysis (DFA) and multiscale entropy (MSE), were analyzed. In linear and non-linear HRV analysis, low frequency and high frequency ratio, DFAα1, MSE slope 5, scale 5, and area 6–20 were significantly lower in group A. Among all HRV variables, MSE scale 5 (AUC: 0.758) had the best predictive power to discriminate the two groups. In multivariable analysis, MSE scale 5 (p = 0.010) was the only significantly predictor of severe PH in all HRV variables. In conclusion, the patients with severe PH had worse heart rhythm complexity. MSE parameters, especially scale 5, can help to identify high-risk PH patients.     

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.     

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.