近似熵、互近似熵的性质、快速算法及其在脑电与认知研究中的初步应用

本文从信号处理的角度介绍了近似嫡、互近似熵的概念、性质与应用,并给出了一种计算近似熵、互近似熵的实用快速算法．本文还通过实际算例说明了近似烟在表征信号的复杂性、互近似熵在表征信号的模式相似性方面的能力及其在脑电与认知研究中的初步应用。     

Nonlinear Analysis of Clinical Epileptic EEG by Approximate Entropy

By the means of computing approximate entropy (ApEn) of video-EEG from some clinical epileptic, ApEn of EEG with epileptiform discharges is found significantly different from that of EEG without epileptiforrn discharges, (p=0.002). Meanwhile, dynamic ApEn shows consistent change of EEG signal with discharges of epileptic waves inside. These results suggest that ApEn may be a useful tool for automatic recognition and detection of epileptic activity and for understanding epileptogenic mechanism.     

Approximate entropy-based epileptic EEG detection using artificial neural networks.

The electroencephalogram (EEG) signal plays an important role in the diagnosis of epilepsy. The EEG recordings of the ambulatory recording systems generate very lengthy data and the detection of the epileptic activity requires a time-consuming analysis of the entire length of the EEG data by an expert. The traditional methods of analysis being tedious, many automated diagnostic systems for epilepsy have emerged in recent years. This paper proposes a neural-network-based automated epileptic EEG detection system that uses approximate entropy (ApEn) as the input feature. ApEn is a statistical parameter that measures the predictability of the current amplitude values of a physiological signal based on its previous amplitude values. It is known that the value of the ApEn drops sharply during an epileptic seizure and this fact is used in the proposed system. Two different types of neural networks, namely, Elman and probabilistic neural networks, are considered in this paper. ApEn is used for the first time in the proposed system for the detection of epilepsy using neural networks. It is shown that the overall accuracy values as high as 100% can be achieved by using the proposed system.     

Interpretation of approximate entropy: analysis of intracranial pressure approximate entropy during acute intracranial hypertension

We studied changes in intracranial pressure (ICP) complexity, estimated by the approximate entropy (ApEn) of the ICP signal, as subjects progressed from a state of normal ICP (< 20-25 mmHg) to acutely elevated ICP (an ICP "spike" defined as ICP > 25 mmHg for < or = 5 min). We hypothesized that the measures of intracranial pressure (ICP) complexity and irregularity would decrease during acute elevations in ICP. To test this hypothesis we studied ICP spikes in pediatric subjects with severe traumatic brain injury (TBI). We conclude that decreased complexity of ICP coincides with episodes of intracranial hypertension (ICH) in TBI. This suggests that the complex regulatory mechanisms that govern intracranial pressure are disrupted during acute rises in ICP. Furthermore, we carried out a series of experiments where ApEn was used to analyze synthetic signals of different characteristics with the objective of gaining a better understanding of ApEn itself, especially its interpretation in biomedical signal analysis.     

EEG complexity as a measure of depth of anesthesia for patients

A new approach for quantifying the relationship between brain activity patterns and depth of anesthesia (DOA) is presented by analyzing the spatio-temporal patterns in the electroencephalogram (EEG) using Lempel-Ziv complexity analysis. Twenty-seven patients undergoing vascular surgery were studied under general anesthesia with sevoflurane, isoflurane, propofol, or desflurane. The EEG was recorded continuously during the procedure and patients' anesthesia states were assessed according to the responsiveness component of the observer's assessment of alertness/sedation (OAA/S) score. An OAA/S score of zero or one was considered asleep and two or greater was considered awake. Complexity of the EEG was quantitatively estimated by the measure C(n), whose performance in discriminating awake and asleep states was analyzed by statistics for different anesthetic techniques and different patient populations. Compared with other measures, such as approximate entropy, spectral entropy, and median frequency, C(n) not only demonstrates better performance (93% accuracy) across all of the patients, but also is an easier algorithm to implement for real-time use. The study shows that C(n) is a very useful and promising EEG-derived parameter for characterizing the (DOA) under clinical situations.     

Spectral and nonlinear analyses of MEG background activity in patients with Alzheimer's disease.

The aim of the present study is to analyze the magnetoencephalogram (MEG) background activity from patients with Alzheimer's disease (AD) and elderly control subjects. MEG recordings from 20 AD patients and 21 controls were analyzed by means of two spectral [median frequency (MF) and spectral entropy (SpecEn)] and two nonlinear parameters [approximate entropy (ApEn) and Lempel-Ziv complexity (LZC)]. In the AD diagnosis, the highest accuracy of 75.6% (80% sensitivity, 71.4% specificity) was obtained with the MF according to a linear discriminant analysis (LDA) with a leave-one-out cross-validation procedure. Moreover, we wanted to assess whether these spectral and nonlinear analyses could provide complementary information to improve the AD diagnosis. After a forward stepwise LDA with a leave-one-out cross-validation procedure, one spectral (MF) and one nonlinear parameter (ApEn) were automatically selected. In this model, an accuracy of 80.5% (80.0% sensitivity, 81.0% specificity) was achieved. We conclude that spectral and nonlinear analyses from spontaneous MEG activity could be complementary methods to help in AD detection.     

Spectral and Nonlinear Analyses of MEG Background Activity in Patients With Alzheimer's Disease

The aim of the present study is to analyze the magnetoencephalogram (MEG) background activity from patients with Alzheimer's disease (AD) and elderly control subjects. MEG recordings from 20 AD patients and 21 controls were analyzed by means of two spectral [median frequency (MF) and spectral entropy (SpecEn)] and two nonlinear parameters [approximate entropy (ApEn) and Lempel-Ziv complexity (LZC)]. In the AD diagnosis, the highest accuracy of 75.6% (80% sensitivity, 71.4% specificity) was obtained with the MF according to a linear discriminant analysis (LDA) with a leave-one-out cross-validation procedure. Moreover, we wanted to assess whether these spectral and nonlinear analyses could provide complementary information to improve the AD diagnosis. After a forward stepwise LDA with a leave-one-out cross-validation procedure, one spectral (MF) and one nonlinear parameter (ApEn) were automatically selected. In this model, an accuracy of 80.5% (80.0% sensitivity, 81.0% specificity) was achieved. We conclude that spectral and nonlinear analyses from spontaneous MEG activity could be complementary methods to help in AD detection.     

Monotonicity of approximate entropy during transition from awareness to unresponsiveness due to propofol anesthetic induction

The ability to monitor the physiological effects of sedative medication accurately is of interest in clinical practice. During the anesthetic agent driven transition to unresponsiveness, nonstationary changes such as signal amplitude variations appear in electroencephalography. In this paper, it is studied whether the application of the approximate entropy (ApEn) method to electroencephalographic (EEG) signal produces a monotonic response curve during the transition from awareness to unresponsiveness. Data from fourteen patients, undergoing propofol anesthetic induction were studied. To optimize the ApEn performance, different parameter choices were carefully evaluated. It was assumed with our protocol, that the level of anesthesia changes monotonically with the elapsed induction time. The monotonicity of the ApEn change was assessed with the prediction probability statistic (PK). The monotonicity of the ApEn time-series depends on the parameters employed in the algorithm and the varying signal amplitude. Depending on the parameter values, the median PK value ranged from 0.886 to 0.527. Thus, a good directionality and concordance was observed, but the nonstationarity of the signal affected the results. In conclusion, EEG-based ApEn measure shows a nonlinear response during propofol induction. With a judicious choice of parameters, a monotonic response is confirmed using PK statistic.     

基于熵特征的雷达辐射源信号识别

针对现有方法识别率低和没有考虑噪声影响的问题, 提出一种新的雷达辐射源信号识别方法. 将近似熵(ApEn)和范数熵(NoEn)构成特征向量, 用神经网络分类器实现自动分类识别. ApEn是定量描述信号复杂性和不规则性的有效测度, NoEn是定量表征信号能量分布的有效参数. 理论分析和实验结果表明, 熵特征类内聚集性强、类间分离度大, 在较大信噪比范围内均能获得非常满意的正确识别率, 证实了所提出方法的有效性.     

Epileptic seizures detection in EEG using DWT-based ApEn and artificial neural network

There are numerous neurological disorders such as dementia, headache, traumatic brain injuries, stroke, and epilepsy. Out of these epilepsy is the most prevalent neurological disorder in the human after stroke. Electroencephalogram (EEG) contains valuable information related to different physiological state of the brain. A scheme is presented for detecting epileptic seizures from EEG data recorded from normal subjects and epileptic patients. The scheme is based on discrete wavelet transform (DWT) analysis and approximate entropy (ApEn) of EEG signals. Seizure detection is performed in two stages. In the first stage, EEG signals are decomposed by DWT to calculate approximation and detail coefficients. In the second stage, ApEn values of the approximation and detail coefficients are calculated. Significant differences have been found between the ApEn values of the epileptic and the normal EEG allowing us to detect seizures with 100 % classification accuracy using artificial neural network. The analysis results depicted that during seizure activity, EEG had lower ApEn values compared to normal EEG. This gives that epileptic EEG is more predictable or less complex than the normal EEG. In this study, feed-forward back-propagation neural network has been used for classification and training algorithm for this network that updates the weight and bias values according to Levenberg–Marquardt optimization technique.     

ICA去除EEG中眼动伪差和工频干扰方法研究

眼动伪差和工频干扰是临床脑电图(EEG)中常见噪声,严重影响其有用信息提取.本文尝试采用独立分量分析(Independent Component Analysis,ICA)方法分离EEG中此类噪声.通过对早老性痴呆症(Alzheimer disease,AD)患者临床EEG信号(含眼动伪差和混入工频干扰,信噪比仅0dB)作ICA分析,比较了最大熵(Infomax)和扩展最大熵(Extended Infomax)ICA算法的分离效果,证实虽然最大熵算法可以分离出眼动慢波,但难以消除工频干扰,为此需采用扩展的最大熵算法;并知ICA方法在极低信噪比时也有较好的抗干扰性,且在处理非平稳信号时有好的鲁棒性;文中还结合近似熵(approximate entropy,ApEn)分析说明利用ICA去除干扰后有助于恢复和保持原始EEG信号的非线性特征.研究结果表明ICA方法在生物医学信号处理中具有潜在的重要应用价值,值得深入研究和推广.     

Characterizing the Complexity of Spontaneous Electrical Signals in Cultured Neuronal Networks Using Approximate Entropy

In this paper, neurons were cultured on a substrate above a multielectrode array, so the changes of electrophysiological activity patterns during development of the neuronal network or in response to environmental perturbations were monitored. But the complexity of these spontaneous activity patterns is not well understood. In order to solve the problem, a comprehensive method (approximate entropy (ApEn) in combination with a ldquosliding windowrdquo over the data) is introduced to quantify the complexity of four spontaneous activity patterns (sporadic spikes, tonic spikes, pseudobursts, and typical bursts) in cultured hippocampal neuronal networks. The results show that the dynamic curves of ApEn illustrate vivid differences between the four patterns and the values of ApEn fall into different ranges. Among these patterns, the complexity of tonic spikes is the highest while that of pseudobursts is the lowest. This suggests that the proposed method is a valid procedure for tracking the dynamic variation in neuronal signals and can distinguish the different firing patterns of neuronal networks in terms of their complexity.     

Automatic selection of the threshold value R for approximate entropy

Calculation of approximate entropy (ApEn) requires a priori determination of two unknown parameters, $m$ and $r$. While the recommended values of $r$, in the range of 0.1–0.2 times the standard deviation of the signal, have been shown to be applicable for a wide variety of signals, in certain cases, $r$ values within this prescribed range can lead to an incorrect assessment of the complexity of a given signal. To circumvent this limitation, we recently advocated finding the maximum ApEn value by assessing all values of $r$ from 0 to 1, and found that maximum ApEn does not always occur within the prescribed range of $r$ values. Our results indicate that finding the maximum ApEn leads to the correct interpretation of a signal's complexity. One major limitation, however, is that the calculation of all choices of $r$ values is often impractical due to the computational burden. Our new method, based on a heuristic stochastic model, overcomes this computational burden, and leads to the automatic selection of the maximum ApEn value for any given signal. Based on Monte Carlo simulations, we derive general equations that can be used to estimate the maximum ApEn with high accuracy for a given value of $m$. Application to both synthetic and experimental data confirmed the advantages claimed with the proposed approach.      

有源干扰感知的熵理论方法

面对日益复杂的电磁环境,用户对干扰感知技术提出了更高的要求。本文采用一种基于熵理论的干扰感知方法,对六种常见的有源干扰（三种压制式干扰和三种欺骗式干扰）进行特征提取,通过仿真结果分析其在不同熵特征下的差异,得出了熵理论可用于干扰感知技术的结论。其中,信息熵和指数熵能够区分噪声调幅干扰,范数熵能够较好地区分三种压制式干扰和速度欺骗干扰;但三种熵理论方法均难以区分距离欺骗干扰和速度欺骗干扰。同时,通过比较三种熵理论特征提取方法的仿真时间,分析了三种特征提取方法的计算复杂度,得出了范数熵计算复杂度最低的结论。最后,通过朴素贝叶斯分类器确定了三种熵理论方法的识别率。      

睡眠脑电时间序列的非线性样本熵研究

比较了样本熵与近似熵算法的区别,通过对构造的一个由随机信号和确定性信号组成的混合系统进行分析可以看出在公差阈值小于0.2时,样本熵比近似熵更适合于时间序列信号的复杂度分析.然后,对采集的整夜睡眠脑电信号,用样本熵作为睡眠脑电数据的特征值,分析了睡眠过程不同阶段的实验数据.结果表明,不同睡眠时期样本熵有差别,随睡眠深度的加深,样本熵值变小.因此,样本熵可以很好地区分不同睡眠时期并作为睡眠自动分期的一个重要的非线性特征参数.     

Variability, regularity, and complexity of time series generated by schizophrenic patients and control subjects

We analyzed time series generated by 20 schizophrenic patients and 20 sex- and age-matched control subjects using three nonlinear methods of time series analysis as test statistics: central tendency measure (CTM) from the scatter plots of first differences of data, approximate entropy (ApEn), and Lempel-Ziv (LZ) complexity. We divided our data into a training set (10 patients and 10 control subjects) and a test set (10 patients and 10 control subjects). The training set was used for algorithm development and optimum threshold selection. Each method was assessed prospectively using the test dataset. We obtained 80% sensitivity and 90% specificity with LZ complexity, 90% sensitivity, and 60% specificity with ApEn, and 70% sensitivity and 70% specificity with CTM. Our results indicate that there exist differences in the ability to generate random time series between schizophrenic subjects and controls, as estimated by the CTM, ApEn, and LZ. This finding agrees with most previous results showing that schizophrenic patients are characterized by less complex neurobehavioral and neuropsychologic measurements.     

A study of wavelet entropy measure definition and its application for fault feature pick-up and classification

Shannon entropy in time domain is a measure of signal or system uncertainty.When based on spectrum entropy,Shannon entropy can be taken as a measure of signal or system complexity. Therefore,wavelet analysis based on wavelet entropy measure can signify the complexity of non-steady signal or system in both time and frequency domain.In this paper,in order to meet the requirements of post-analysis on abundant wavelet transform result data and the need of information mergence,the basic definition of wavelet entropy measure is proposed,corresponding algorithms of several wavelet entropies,such as wavelet average entropy,wavelet time-frequency entropy,wavelet distance entropy, etc.are put forward,and the physical meanings of these entropies are analyzed as well.The application principle of wavelet entropy measure in ElectroEncephaloGraphy (EEG) signal analysis,mechanical fault diagnosis,fault detection and classification in power system are analyzed.Finally,take the transmission line fault detection in power system for example,simulations in two different systems,a 10kV automatic blocking and continuous power transmission line and a 500kV Extra High Voltage (EHV) transmission line,are carried out,and the two methods,wavelet entropy and wavelet modulus maxima,are compared,the results show feasibility and application prospect of the six wavelet entro- pies.     

Comparison of entropy-based regularity estimators: application to the fetal heart rate signal for the identification of fetal distress

This paper considers the multiscale entropy (MSE) approach for estimating the regularity of time series at different scales. Sample entropy (SampEn) and approximate entropy (ApEn) are evaluated in MSE analysis on simulated data to enhance the main features of both estimators. We applied the approximate entropy and the sample entropy estimators to fetal heart rate signals on both single and multiple scales for an early identification of fetal sufferance antepartum. Our results show that the ApEn index significantly distinguishes suffering from normal fetuses between the 30th and the 35th week of gestation. Furthermore, our data shows that the MSE entropy values are reliable indicators of the fetal distress associated with the presence of a pathological condition at birth.     

Influence of the vagus nerve on respiratory patterns during early maturation

Nonlinear dynamical analysis was performed on the phrenic neurogram before and after vagotomy in order to study the influence of the vagus nerve on the complexity of the phrenic neurogram in piglets in three age groups: 3-7 days (n = 7); 11-19 days (n = 6); and 29-34 days (n = 8). The phrenic neurogram, generated by the respiratory neural networks in the medulla, projects on the diaphragm muscles and initiate the respiratory movement. On the other hand, the vagus nerves carry the information from mechanoreceptors, located at the lower airway and lungs, to the medulla. The data was recorded during normal breathing (eupnea) before and after vagotomy while piglets were ventilated with 40% O2 in N2 and analyzed using the approximate entropy (ApEn) method. The mean values of the approximate entropy before and after vagotomy during the first 7 days of the postnatal age were 1.32 +/- 0.1 (standard deviation) and 1.34 +/- 0.07, respectively. These values before and after vagotomy during the 11-19 days age group were 1.15 +/- 0.09 and 1.12 +/- 0.05, respectively. For the 29-34 days age group, they were 1.14 +/- 0.05 before vagotomy and 1.19 +/- 0.08 after vagotomy. These differences in the ApEn (complexity) values of the phrenic neurogram before and after vagotomy are not statistically different at each age group. However, the mean mean approximate entropy (complexity) values between the 3-7 days age group and the other two groups were significantly different both before and after vagotomy (p < 0.05) using an analysis off variance test. These results suggest that the vagus nerve may not be mature during early maturation in piglets.     

Inter-individual differences in fMRI entropy measurements in old age

We investigated the association between individual differences in cognitive performance in old age and the approximate entropy (ApEn) measured from functional magnetic resonance imaging (fMRI) data acquired from 40 participants of the Aberdeen Birth Cohort 1936 (ABC1936), while undergoing a visual information processing task: inspection time (IT). Participants took a version of the Moray House Test (MHT) No. 12 at age 11, a valid measure of childhood intelligence. The same individuals completed a test of non-verbal reasoning (Raven's Standard Progressive Matrices [RPM]) aged about 68 years. The IT, MHT and RPM scores were used as indicators of cognitive performance. Our results show that higher regional signal entropy is associated with better cognitive performance. This finding was independent of ability in childhood but not independent of current cognitive ability. ApEn is used for the first time to identify a potential source of individual differences in cognitive ability using fMRI data.