Wavelet bidomain sample entropy analysis to predict spontaneous termination of atrial fibrillation

The ability to predict if an atrial fibrillation (AF) episode terminates spontaneously or not through non-invasive techniques is a challenging problem of great clinical interest. This fact could avoid useless therapeutic interventions and minimize the risks for the patient. The present work introduces a robust AF prediction methodology carried out by estimating, through sample entropy (SampEn), the atrial activity (AA) organization increase prior to AF termination from the surface electrocardiogram (ECG). This regularity variation appears as a consequence of the decrease in the number of reentries wandering throughout the atrial tissue. AA was obtained from surface ECG recordings by applying a QRST cancellation technique. Next, a robust and reliable classification process for terminating and non-terminating AF episodes was developed, making use of two different wavelet decomposition strategies. Finally, the AA organization both in time and wavelet domains (bidomain) was estimated via SampEn. The methodology was validated using a training set consisting of 20 AF recordings with known termination properties and a test set of 30 recordings. All the training signals and 93.33% of the test set were correctly classified into terminating and sustained AF, obtaining 93.75% sensitivity and 92.86% specificity. It can be concluded that spontaneous AF termination can be reliably and noninvasively predicted by applying wavelet bidomain sample entropy.     

样本熵分析与胎儿宫内缺氧程度敏感性关系的研究

目的:介绍样本熵分析方法在胎儿心率变异性研究中的应用,并探讨样本熵与胎儿缺氧程度的相关性。方法:对61例胎心电子监护数据进行样本熵分析;脐动脉血气分析;样本熵按pH和氧分压(PO2)值分成3组,第1组为正常组(pH≥7.20并PO2≥2.7kPa,n=36),第2组为怀疑缺氧组(pH≥7.20并PO2<2.7kPa,n=11),第3组为酸中毒组(pH<7.20,n=14)。对样本熵与血气指标作相关性分析。结果:怀疑缺氧组和酸中毒组的样本熵值明显低于正常组,差别有统计学意义(F=10.1,P<0.01;F=76.2,P<0.001)。而常规时域分析的指标各组间无显著性差异。相关分析显示样本熵值与血气分析各参数呈明显相关性,尤与pH、二氧化碳分压(PCO2)和碱过剩相关性最好(r=0.798,-0.598,0.641,P<0.01)。结论:样本熵值与血气分析各参数呈明显相关关系,提示样本熵可作为反映胎儿缺氧程度的较敏感的无创指标,为早期诊断胎儿窘迫提供一种新的定量方法。     

Multi-scale sample entropy of electroencephalography during sevoflurane anesthesia

The electroencephalogram (EEG) has been widely applied in the assessment of depth of anesthesia (DoA). Recent research has found that multi-scale EEG analysis describes brain dynamics better than traditional non-linear methods. In this study, we have adopted a modified sample entropy (MSpEn) method to analyze anesthetic EEG series as a measure of DoA. EEG data from a previous study consisting of 19 adult subjects undergoing sevoflurane anesthesia were used in the present investigation. In addition to the modified sample entropy method, the well-established EEG indices approximate entropy (ApEn), response entropy (RE), and state entropy (SE) were also computed for comparison. Pharmacokinetic/pharmacodynamic modeling and prediction probability (P _k ) were used to assess and compare the performance of the four methods for tracking anesthetic concentration. The influence of the number of scales on MSpEn was also investigated using a linear regression model. MSpEn correlated closely with anesthetic effect. The P _k (0.83 ± 0.05, mean ± SD) and the coefficient of determination R ² (0.87 ± 0.21) for the relationship between MSpEn and sevoflurane effect site concentration were highest for MSpEn (P _k : RE = 0.73 ± 0.08, SE = 0.72 ± 0.07, ApEn = 0.81 ± 0.04; R ²: RE = 0.75 ± 0.08, SE = 0.64 ± 0.09, ApEn = 0.81 ± 0.10). Scales 1, 3 and 5 tended to make the greatest contribution to MSpEn. For this data set, the MSpEn is superior to the ApEn, the RE and the SE for tracking drug concentration change during sevoflurane anesthesia. It is suggested that the MSpEn may be further studied for application in clinical monitoring of DoA.     

On the use of approximate entropy and sample entropy with centre of pressure time-series

Background

Approximate entropy (ApEn) and sample entropy (SampEn) have been previously used to quantify the regularity in centre of pressure (COP) time-series in different experimental groups and/or conditions. ApEn and SampEn are very sensitive to their input parameters: m (subseries length), r (tolerance) and N (data length). Yet, the effects of changing those parameters have been scarcely investigated in the analysis of COP time-series. This study aimed to investigate the effects of changing parameters m, r and N on ApEn and SampEn values in COP time-series, as well as the ability of these entropy measures to discriminate between groups.

Methods

A public dataset of COP time-series was used. ApEn and SampEn were calculated for m?=?{2, 3, 4, 5}, r?=?{0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5} and N?=?{600, 1200} (30 and 60?s, respectively). Subjects were stratified in young adults (age?<?60, n?=?85), and older adults (age?≥?60) with (n?=?18) and without (n?=?56) falls in the last year. The effects of changing parameters m, r and N on ApEn and SampEn were investigated with a three-way ANOVA. The ability of ApEn and SampEn to discriminate between groups was investigated with a mixed ANOVA (within-subject factors: m, r and N; between-subject factor: group). Specific combinations of m, r and N producing significant differences between groups were identified using the Tukey’s honest significant difference procedure.

Results

A significant three-way interaction between m, r and N confirmed the sensitivity of ApEn and SampEn to the input parameters. SampEn showed a higher consistency and ability to discriminate between groups than ApEn. Significant differences between groups were mostly observed in longer (N?=?1200) COP time-series in the anterior-posterior direction. Those differences were observed for specific combinations of m and r, highlighting the importance of an adequate selection of input parameters.

Conclusions

Future studies should favour SampEn over ApEn and longer time-series (≥ 60?s) over shorter ones (e.g. 30?s). The use of parameter combinations such as SampEn (m?=?{4, 5}, r?=?{0.25, 0.3, 0.35}) is recommended.

     

基于局部场电位样本熵分析的麻醉深度监测

背景：目前的麻醉深度监测多以大脑皮质脑电信号分析为主,然而,大脑皮质脑电信号不能反映皮质下组织的功能状况、不包含高频信息并且易受外界环境干扰,从而导致基于大脑皮质脑电信号分析的麻醉深度监测在稳定性、精确性等方面有固有缺陷。目的：分析局部场电位信号样本熵在麻醉深度监测中的效果,实现麻醉深度的实时监测。方法：以大鼠为模型动物进行实验,对整个麻醉过程中的大鼠初级视觉皮质局部场电位信号进行快速样本熵计算,并对样本熵曲线动态变化进行分析,判定麻醉状态;然后将样本熵分别与大鼠尾部受热刺激时的甩尾延迟时间、局部场电位信号的中心频率和边缘频率做统计分析,验证基于局部场电位快速样本熵分析的麻醉状态判定方法。结果与结论：局部场电位信号的样本熵可以快速、准确、稳定地反映大鼠的麻醉深度,用于麻醉深度实时监测。     

Complex analysis of intracranial hypertension using approximate entropy

OBJECTIVE: To determine whether decomplexification of intracranial pressure dynamics occurs during periods of severe intracranial hypertension (intracranial pressure >25 mm Hg for >5 mins in the absence of external noxious stimuli) in pediatric patients with intracranial hypertension. DESIGN: Retrospective analysis of clinical case series over a 30-month period from April 2000 through January 2003. SETTING: Multidisciplinary 16-bed pediatric intensive care unit. PATIENTS: Eleven episodes of intracranial hypertension from seven patients requiring ventriculostomy catheter for intracranial pressure monitoring and/or cerebral spinal fluid drainage. INTERVENTIONS: None. MEASUREMENTS AND MAIN RESULTS: We measured changes in the intracranial pressure complexity, estimated by the approximate entropy (ApEn), as patients progressed from a state of normal intracranial pressure (<25 mm Hg) to intracranial hypertension. We found the ApEn mean to be lower during the intracranial hypertension period than during the stable and recovering periods in all the 11 episodes (0.5158 +/- 0.0089, 0.3887 +/- 0.077, and 0.5096 +/- 0.0158, respectively, p < .01). Both the mean reduction in ApEn from the state of normal intracranial pressure (stable region) to intracranial hypertension (-0.1271) and the increase in ApEn from the ICH region to the recovering region (0.1209) were determined to be statistically significant (p < .01). CONCLUSIONS: Our results indicate that decreased complexity of intracranial pressure coincides with periods of intracranial hypertension in brain injury. This suggests that the complex regulatory mechanisms that govern intracranial pressure may be disrupted during acute periods of intracranial hypertension. This phenomenon of decomplexification of physiologic dynamics may have important clinical implications for intracranial pressure management.     

Retrospective analysis of landscape dynamics using normalized spectral entropy

Forest dynamics, such as deforestation, reforestation and afforestation, could be caused by the natural and human-induced disturbances. Traditional methods rarely quantify the history of such disturbances along a continuous temporal trajectory; yet, such disturbance history often determines system course and evolution. We adopted a retrospective perspective to study system history by implementing a newly proposed entropy index. The forest dynamics in the Amazon region, expressed by a time-series vegetation index, were taken as an example to demonstrate the application of such an entropy index. The results indicated that high entropy values were mainly distributed around the major cities with intensive land conversion rates, as well as the riverine areas with unsteady physiological and/or phenological fluctuations. Utilization of this index can measure forest dynamics in a retrospective way with accumulated information and therefore can provide a solid basis of information for current research and planning, such as for forest conservation and land-use plans.     

脑卒中偏瘫下肢表面肌电信号样本熵用于痉挛性肌张力量化评估的研究

目的：探讨表面肌电信号样本熵与脑卒中偏瘫下肢腓肠肌痉挛等级的相关性。方法：随机选取53例脑卒中恢复期患者为受试者,对偏瘫下肢腓肠肌进行改良Ashworth量表(modified Ashworth scale,MAS)评估,采用单通道无线蓝牙肌电传感器记录被动牵伸状态时腓肠肌表面肌电信号（surface electromyography,sEMG);引入样本熵计算方法提取sEMG的特征信息,分析其与痉挛等级的相关性,并对结果进行验证。结果：对采集的sEMG进行熵值分析,结果显示MAS评估为0级、Ⅰ级、Ⅰ+级、Ⅱ级、Ⅲ级的偏瘫下肢腓肠肌sEMG样本熵分别为：0.6947±0.169、0.7951±0.244、0.8249±0.145、0.8305±0.232、0.9489±0.371,对样本熵进行线性拟合,发现样本熵均值曲线随痉挛等级的升高呈上升趋势,且样本熵与MAS相关(r=0.745,P<0.05),进一步验证发现样本熵符合肌电信号特征与痉挛等级的映射关系。结论：sEMG样本熵可用于脑卒中偏瘫肢体痉挛性肌张力的量化评估,有望为病理性痉挛的精准康复提供有效的检测及评估手段。     

改进排列熵方法及其在心率变异复杂度分析中的应用

背景:心率变异信号蕴含着有关心血管系统调节的重要信息,很多非线性动力学方法和复杂性测度已被用于心率变异信号的分析.排列熵是近年提出的一种新的熵测度,具有概念简单,计算简洁等优点,在很多领域得到了广泛的应用.目的:针对心率变异信号特点,对排列熵方法进行等值状态处理的改进,在排列符号序列中以相同符号代表等值状态;通过临床数据实验,考察改进排列熵方法在心率变异性信号分析中的应用价值.方法:心率变异信号取自PhysioNet中MIT-BIH Fantasia 数据库和BIDMC Congestive Heart Failure(CHF)数据库,分为年轻健康人、老年健康人和充血性心力衰竭患者3组.应用排列熵和改进排列熵方法对3组数据分别进行分析,通过单因素方差分析和t检验对结果进行统计分析.结果与结论:排列熵的两种等值状态处理方法均无法对3组数据作出有效区分,尤其是年轻健康人和老年健康人两组数据;而改进排列熵方法可以对3组数据作出非常有效的区分,即使是在短时的心率变异性分析中(500个RR间期,6～7 min).提示改进排列熵方法可以有效提高生理、病理心率变异信号的区分度,比排列熵方法更有效的表征心率变异信号的复杂性.     

Shannon entropy applied to the analysis of event-related fMRI time series

Event-related functional magnetic resonance imaging (ER-fMRI) refers to the blood oxygen level-dependent (BOLD) signal in response to a short stimulus followed by a long period of rest. These paradigms have become more popular in the last few years due to some advantages over standard block techniques. Most of the analysis of the time series generated in such exams is based on a model of specific hemodynamic response function. In this paper we propose a new method for the analysis of ER-fMRI based in a specific aspect of information theory: the entropy of a signal using the Shannon formulation, which makes no assumption about the shape of the response. The results show the ability to discriminate between activated and resting cerebral regions for motor and visual stimuli. Moreover, the results of simulated data show a more stable pattern of the method, if compared to typical algorithms, when the signal to noise ratio decreases.     

Reduced force entropy in subacromial pain syndrome: A cross-sectional analysis

BackgroundGenerating a force at the hand requires moments about multiple joints by a theoretically infinite number of arm and shoulder muscle force combinations. This allows for learning and adaptation and can possibly be captured using the complexity (entropy) of an isometrically generated force curve. Patients with Subacromial Pain Syndrome have difficulty to explore alternative, pain-avoiding, motor strategies and we questioned whether loss of motor complexity may contribute to this. We assessed whether patients with Subacromial Pain Syndrome have reduced entropy of an isometrically generated abduction and adduction force curve.MethodsForty patients and thirty controls generated submaximal isometric ab- and adduction force at the wrist. The force curve was characterized by the magnitude of force variability [standard deviation and coefficient of variation], and the entropy (complexity) of force variability [approximate entropy].FindingsPatients showed reduced entropy both during the abduction (−0.16, confidence interval: [−0.33; −0.00], p: 0.048) and adduction task (−0.20, confidence interval: [−0.37; −0.03], p: 0.024) and reduced force variability during abduction (standard deviation: −0.006, confidence interval: [−0.011; −0.001], p: 0.013 and coefficient of variation: −0.51, confidence interval: [−0.93; −0. 10], p: 0.016).InterpretationsIsometric force curves of patients with Subacromial Pain Syndrome show reduced complexity compared to asymptomatic controls, which may indicate more narrow and stereotype use of motor options. In future studies, it should be investigated whether the finding of reduced force (motor) entropy indicates functional decline, contributing to decreased ability to acquire and optimize motor strategies in Subacromial Pain Syndrome.Level of evidenceLevel II prognostic study.     

Orientation entropy analysis of diffusion tensor in healthy and myelopathic spinal cord

The majority of nerve fibers in the spinal cord run longitudinally, playing an important role in connecting the brain to the peripheral nerves. There is a growing interest in applying diffusion tensor imaging (DTI) to the evaluation of spinal cord microarchitecture. The current study sought to compare the organization of longitudinal nerve fibers between healthy and myelopathic spinal cords using entropy-based analysis of principal eigenvector mapping. A total of 22 subjects were recruited, including 14 healthy subjects, seven cervical myelopathy (CM) patients with single-level compression, and one patient suffering from multi-level compression. Diffusion tensor magnetic resonance (MR) images of the cervical spinal cord were obtained using a pulsed gradient, spin-echo echo-planar imaging (SE-EPI) sequence with a 3T MR system. Regions of interest (ROIs) were drawn manually to cover the spinal cord, and Shannon entropy was calculated in principal eigenvector maps. The results revealed no significant differences in orientation entropy values along the whole length of cervical spinal cord in healthy subjects (C2-3: 0.73±0.05; C3-4: 0.71±0.07; C4-5: 0.72±0.048; C5-6: 0.71±0.07; C6-7: 0.72±0.07). In contrast, orientation entropy values in myelopathic cord were significantly higher at the compression site (0.91±0.03), and the adjacent levels (above: 0.85±0.03; below: 0.83±0.05). This study provides a novel approach to analyze the orientation information in diffusion MR images of healthy and diseased spinal cord. These results indicate that orientation entropy can be applied to determine the contribution of each compression level to the overall disorganization of principal nerve tracts of myelopathic spinal cord in cases with multi-level compression.     

Minimizing sample size when using exploratory factor analysis for measurement

Traditional protocol for the determination of an adequate sample size is power analysis. Such a protocol is not useful when the primary hypothesis focuses on psychometric measurement properties. Traditional psychometrics advises that there should be 10 respondents per item. Both hypothetical and real research examples illustrate the usefulness of subsample analysis in determining that a sample size of at least 50 and not more than 100 subjects is adequate to represent and evaluate the psychometric properties of measures of social constructs. The "10 respondents per item" advice builds a sample size disincentive into the research design; it also represents "sample size overkill." Sample-size overkill occurs when the research design specifies a number of cases needed, which is in excess of the number actually needed for a desired inference.