Complexity quantification of dense array EEG using sample entropy analysis

n this paper, a time series complexity analysis of dense array electroencephalogram signals is carried out using the recently introduced Sample Entropy (SampEn) measure. This statistic quantifies the regularity in signals recorded from systems that can vary from the purely deterministic to purely stochastic realm. The present analysis is conducted with an objective of gaining insight into complexity variations related to changing brain dynamics for EEG recorded from the three cases of passive, eyes closed condition, a mental arithmetic task and the same mental task carried out after a physical exertion task. It is observed that the statistic is a robust quantifier of complexity suited for short physiological signals such as the EEG and it points to the specific brain regions that exhibit lowered complexity during the mental task state as compared to a passive, relaxed state. In the case of mental tasks carried out before and after the performance of a physical exercise, the statistic can detect the variations brought in by the intermediate fatigue inducing exercise period. This enhances its utility in detecting subtle changes in the brain state that can find wider scope for applications in EEG based brain studies.

Evaluation of physiologic complexity in time series using generalized sample entropy and surrogate data analysis

Complexity in time series is an intriguing feature of living dynamical systems, with potential use for identification of system state. Although various methods have been proposed for measuring physiologic complexity, uncorrelated time series are often assigned high values of complexity, errouneously classifying them as a complex physiological signals. Here, we propose and discuss a method for complex system analysis based on generalized statistical formalism and surrogate time series. Sample entropy (SampEn) was rewritten inspired in Tsallis generalized entropy, as function of q parameter (qSampEn). qSDiff curves were calculated, which consist of differences between original and surrogate series qSampEn. We evaluated qSDiff for 125 real heart rate variability (HRV) dynamics, divided into groups of 70 healthy, 44 congestive heart failure (CHF), and 11 atrial fibrillation (AF) subjects, and for simulated series of stochastic and chaotic process. The evaluations showed that, for nonperiodic signals, qSDiff curves have a maximum point (qSDiff(max)) for q not equal 1. Values of q where the maximum point occurs and where qSDiff is zero were also evaluated. Only qSDiff(max) values were capable of distinguish HRV groups (p-values 5.10 x 10(-3); 1.11 x 10(-7), and 5.50 x 10(-7) for healthy vs. CHF, healthy vs. AF, and CHF vs. AF, respectively), consistently with the concept of physiologic complexity, and suggests a potential use for chaotic system analysis. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4758815]

Classification of 5-S epileptic EEG recordings using distribution entropy and sample entropy

Epilepsy is an electrophysiological disorder of the brain, the hallmark of which is recurrent and unprovoked seizures. Electroencephalogram (EEG) measures electrical activity of the brain that is commonly applied as a non-invasive technique for seizure detection. Although a vast number of publications have been published on intelligent algorithms to classify interictal and ictal EEG, it remains an open question whether they can be detected using short-length EEG recordings. In this study, we proposed three protocols to select 5 s EEG segment for classifying interictal and ictal EEG from normal. We used the publicly-accessible Bonn database, which consists of normal, interical, and ictal EEG signals with a length of 4097 sampling points (23.6 s) per record. In this study, we selected three segments of 868 points (5 s) length from each recordings and evaluated results for each of them separately. The well-studied irregularity measure-sample entropy (SampEn)-and a more recently proposed complexity measure-distribution entropy (DistEn)-were used as classification features. A total of 20 combinations of input parameters m and τ for the calculation of SampEn and DistEn were selected for compatibility. Results showed that SampEn was undefined for half of the used combinations of input parameters and indicated a large intra-class variance. Moreover, DistEn performed robustly for short-length EEG data indicating relative independence from input parameters and small intra-class fluctuations. In addition, it showed acceptable performance for all three classification problems (interictal EEG from normal, ictal EEG from normal, and ictal EEG from interictal) compared to SampEn, which showed better results only for distinguishing normal EEG from interictal and ictal. Both SampEn and DistEn showed good reproducibility and consistency, as evidenced by the independence of results on analysing protocol.

A new entropy measure based on the Renyi entropy rate using Gaussian kernels

The concept of entropy rate is well defined in dynamical systems theory but is impossible to apply it directly to finite real world data sets. With this in mind, Pincus developed Approximate Entropy (ApEn), which uses ideas from Eckmann and Ruelle to create a regularity measure based on entropy rate that can be used to determine the influence of chaotic behaviour in a real world signal. However, this measure was found not to be robust and so an improved formulation known as the Sample Entropy (SampEn) was created by Richman and Moorman to address these issues. We have developed a new, related, regularity measure which is not based on the theory provided by Eckmann and Ruelle and proves a more well-behaved measure of complexity than the previous measures whilst still retaining a low computational cost.

Entropy feature extraction of EEG signals for automatic person identification

The use of human brain electroencephalography (EEG) signals for automatic person identi cation has been investigated for a decade. It has been found that the performance of an EEG-based person identication system highly depends on what feature to be extracted from multi-channel EEG signals. Linear methods such as Power Spectral Density and Autoregressive Model have been used to extract EEG features. However these methods assumed that EEG signals are stationary. In fact, EEG signals are complex, non-linear, non-stationary, and random in nature. In addition, other factors such as brain condition or human characteristics may have impacts on the performance, however these factors have not been investigated and evaluated in previous studies. It has been found in the literature that entropy is used to measure the randomness of non-linear time series data. Entropy is also used to measure the level of chaos of braincomputer interface systems. Therefore, this thesis proposes to study the role of entropy in non-linear analysis of EEG signals to discover new features for EEG-based person identi- cation. Five dierent entropy methods including Shannon Entropy, Approximate Entropy, Sample Entropy, Spectral Entropy, and Conditional Entropy have been proposed to extract entropy features that are used to evaluate the performance of EEG-based person identication systems and the impacts of epilepsy, alcohol, age and gender characteristics on these systems. Experiments were performed on the Australian EEG and Alcoholism datasets. Experimental results have shown that, in most cases, the proposed entropy features yield very fast person identication, yet with compatible accuracy because the feature dimension is low. In real life security operation, timely response is critical. The experimental results have also shown that epilepsy, alcohol, age and gender characteristics have impacts on the EEG-based person identication systems.

The multiscale entropy algorithm and its variants: a review

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Distribution Entropy (DistEn) : a complexity measure to detect arrhythmia from short length RR interval time series

Heart rate complexity analysis is a powerful non-invasive means to diagnose several cardiac ailments. Non-linear tools of complexity measurement are indispensable in order to bring out the complete non-linear behavior of Physiological signals. The most popularly used non-linear tools to measure signal complexity are the entropy measures like Approximate entropy (ApEn) and Sample entropy (SampEn). But, these methods become unreliable and inaccurate at times, in particular, for short length data. Recently, a novel method of complexity measurement called Distribution Entropy (DistEn) was introduced, which showed reliable performance to capture complexity of both short term synthetic and short term physiologic data. This study aims to i) examine the competence of DistEn in discriminating Arrhythmia from Normal sinus rhythm (NSR) subjects, using RR interval time series data; ii) explore the level of consistency of DistEn with data length N; and iii) compare the performance of DistEn with ApEn and SampEn. Sixty six RR interval time series data belonging to two groups of cardiac conditions namely `Arrhythmia' and `NSR' have been used for the analysis. The data length N was varied from 50 to 1000 beats with embedding dimension m = 2 for all entropy measurements. Maximum ROC area obtained using ApEn, SampEn and DistEn were 0.83, 0.86 and 0.94 for data length 1000, 1000 and 500 beats respectively. The results show that DistEn undoubtedly exhibits a consistently high performance as a classification feature in comparison with ApEn and SampEn. Therefore, DistEn shows a promising behavior as bio marker for detecting Arrhythmia from short length RR interval data.

Effect of data length and bin numbers on distribution entropy (DistEn) measurement in analyzing healthy aging

Complexity analysis of a given time series is executed using various measures of irregularity, the most commonly used being Approximate entropy (ApEn), Sample entropy (SampEn) and Fuzzy entropy (FuzzyEn). However, the dependence of these measures on the critical parameter of tolerance `r' leads to precarious results, owing to random selections of r. Attempts to eliminate the use of r in entropy calculations introduced a new measure of entropy namely distribution entropy (DistEn) based on the empirical probability distribution function (ePDF). DistEn completely avoids the use of a variance dependent parameter like r and replaces it by a parameter M, which corresponds to the number of bins used in the histogram to calculate it. When tested for synthetic data, M has been observed to produce a minimal effect on DistEn as compared to the effect of r on other entropy measures. Also, DistEn is said to be relatively stable with data length (N) variations, as far as synthetic data is concerned. However, these claims have not been analyzed for physiological data. Our study evaluates the effect of data length N and bin number M on the performance of DistEn using both synthetic and physiologic time series data. Synthetic logistic data of `Periodic' and `Chaotic' levels of complexity and 40 RR interval time series belonging to two groups of healthy aging population (young and elderly) have been used for the analysis. The stability and consistency of DistEn as a complexity measure as well as a classifier have been studied. Experiments prove that the parameters N and M are more influential in deciding the efficacy of DistEn performance in the case of physiologic data than synthetic data. Therefore, a generalized random selection of M for a given data length N may not always be an appropriate combination to yield good performance of DistEn for physiologic data.

Distribution entropy analysis of epileptic EEG signals

It is an open-ended challenge to accurately detect the epileptic seizures through electroencephalogram (EEG) signals. Recently published studies have made elaborate attempts to distinguish between the normal and epileptic EEG signals by advanced nonlinear entropy methods, such as the approximate entropy, sample entropy, fuzzy entropy, and permutation entropy, etc. Most recently, a novel distribution entropy (DistEn) has been reported to have superior performance compared with the conventional entropy methods for especially short length data. We thus aimed, in the present study, to show the potential of DistEn in the analysis of epileptic EEG signals. The publicly-accessible Bonn database which consisted of normal, interictal, and ictal EEG signals was used in this study. Three different measurement protocols were set for better understanding the performance of DistEn, which are: i) calculate the DistEn of a specific EEG signal using the full recording; ii) calculate the DistEn by averaging the results for all its possible non-overlapped 5 second segments; and iii) calculate it by averaging the DistEn values for all the possible non-overlapped segments of 1 second length, respectively. Results for all three protocols indicated a statistically significantly increased DistEn for the ictal class compared with both the normal and interictal classes. Besides, the results obtained under the third protocol, which only used very short segments (1 s) of EEG recordings showed a significantly (p <; 0.05) increased DistEn for the interictal class in compassion with the normal class, whereas both analyses using relatively long EEG signals failed in tracking this difference between them, which may be due to a nonstationarity effect on entropy algorithm. The capability of discriminating between the normal and interictal EEG signals is of great clinical relevance since it may provide helpful tools for the detection of a seizure onset. Therefore, our study suggests that the DistEn analysis of EEG signals is very promising for clinical and even portable EEG monitoring.

Competing together : assessing the dynamics of team-team and player-team synchrony in professional association football

This study investigated movement synchronization of players within and between teams during competitive association football performance. Cluster phase analysis was introduced as a method to assess synchronies between whole teams and between individual players with their team as a function of time, ball possession and field direction. Measures of dispersion (SD) and regularity (sample entropy – SampEn – and cross sample entropy – Cross-SampEn) were used to quantify the magnitude and structure of synchrony. Large synergistic relations within each professional team sport collective were observed, particularly in the longitudinal direction of the field (0.89 ± 0.12) compared to the lateral direction (0.73 ± 0.16, p < .01). The coupling between the group measures of the two teams also revealed that changes in the synchrony of each team were intimately related (Cross-SampEn values of 0.02 ± 0.01). Interestingly, ball possession did not influence team synchronization levels. In player–team synchronization, individuals tended to be coordinated under near in-phase modes with team behavior (mean ranges between −7 and 5° of relative phase). The magnitudes of variations were low, but more irregular in time, for the longitudinal (SD: 18 ± 3°; SampEn: 0.07 ± 0.01), compared to the lateral direction (SD: 28 ± 5°; SampEn: 0.06 ± 0.01, p < .05) on-field. Increases in regularity were also observed between the first (SampEn: 0.07 ± 0.01) and second half (SampEn: 0.06 ± 0.01, p < .05) of the observed competitive game. Findings suggest that the method of analysis introduced in the current study may offer a suitable tool for examining team’s synchronization behaviors and the mutual influence of each team’s cohesiveness in competing social collectives.

Poincaré plot indexes of heart rate variability: Relationships with other nonlinear variables

The Poincaré plot for heart rate variability analysis is a technique considered geometrical and non-linear, that can be used to assess the dynamics of heart rate variability by a representation of the values of each pair of R-R intervals into a simplified phase space that describes the system's evolution. The aim of the present study was to verify if there is some correlation between SD1, SD2 and SD1/SD2 ratio and heart rate variability nonlinear indexes either in disease or healthy conditions. 114 patients with arterial coronary disease and 65 healthy subjects underwent 30. minute heart rate registration, in supine position and the analyzed indexes were as follows: SD1, SD2, SD1/SD2, Sample Entropy, Lyapunov Exponent, Hurst Exponent, Correlation Dimension, Detrended Fluctuation Analysis, SDNN, RMSSD, LF, HF and LF/HF ratio. Correlation coefficients between SD1, SD2 and SD1/SD2 indexes and the other variables were tested by the Spearman rank correlation test and a regression analysis. We verified high correlation between SD1/SD2 index and HE and DFA (α1) in both groups, suggesting that this ratio can be used as a surrogate variable. © 2013 Elsevier B.V.

Regularity analysis of nocturnal oximetry recordings to assist in the diagnosis of sleep apnoea syndrome

The relationship between sleep apnoea–hypopnoea syndrome (SAHS) severity and the regularity of nocturnal oxygen saturation (SaO2) recordings was analysed. Three different methods were proposed to quantify regularity: approximate entropy (AEn), sample entropy (SEn) and kernel entropy (KEn). A total of 240 subjects suspected of suffering from SAHS took part in the study. They were randomly divided into a training set (96 subjects) and a test set (144 subjects) for the adjustment and assessment of the proposed methods, respectively. According to the measurements provided by AEn, SEn and KEn, higher irregularity of oximetry signals is associated with SAHS-positive patients. Receiver operating characteristic (ROC) and Pearson correlation analyses showed that KEn was the most reliable predictor of SAHS. It provided an area under the ROC curve of 0.91 in two-class classification of subjects as SAHS-negative or SAHS-positive. Moreover, KEn measurements from oximetry data exhibited a linear dependence on the apnoea–hypopnoea index, as shown by a correlation coefficient of 0.87. Therefore, these measurements could be used for the development of simplified diagnostic techniques in order to reduce the demand for polysomnographies. Furthermore, KEn represents a convincing alternative to AEn and SEn for the diagnostic analysis of noisy biomedical signals.

Associations between step duration variability and inertial measurement unit derived gait characteristics

Inertial measurement units (IMU) provide a convenient tool for gait stability assessment. However, it is unclear how various gait characteristics relate to each other and whether gait characteristics can be obtained from resultant acceleration. Therefore, step duration variability was measured in treadmill walking from 39 young ambulant volunteers (age 24.2 [± 2.5] y; height 1.79 [± 0.09] m; mass 71.6 [± 12.0] kg) using motion capture. Accelerations and gyrations were simultaneously recorded with an IMU. Harmonic ratio, maximum Lyapunov exponents, and multiscale sample entropy (MSE) were calculated. Step duration variability was positively associated with MSE with coarseness levels = 3-6 (r = -.33 to -.42, P ≤ .045). Harmonic ratio and MSE with all coarseness levels were negatively associated (r = -.45 to -.57, P ≤ .004). The MSE with coarseness level = 2 was negatively associated with short-term maximum Lyapunov exponents (r = -.32, P = .047). The agreement between resultant and vertical acceleration derived gait characteristics was excellent (ICC = 0.97-0.99). In conclusion, MSE with varying coarseness levels was associated with the other gait characteristics evaluated in the study. Resultant and vertical acceleration derived results had excellent agreement, which suggests that resultant acceleration is a viable alternative to considering the acceleration dimensions independently.

Understanding ageing effects using complexity analysis of foot-ground clearance during walking

Ageing influences gait patterns which in turn can affect the balance control of human locomotion. Entropy-based regularity and complexity measures have been highly effective in analysing a broad range of physiological signals. Minimum toe clearance (MTC) is an event during the swing phase of the gait cycle and is highly sensitive to the spatial balance control properties of the locomotor system. The aim of this research was to investigate the regularity and complexity of the MTC time series due to healthy ageing and locomotors' disorders. MTC data from 30 healthy young (HY), 27 healthy elderly (HE) and 10 falls risk (FR) elderly subjects with balance problems were analysed. Continuous MTC data were collected and using the first 500 data points, MTC mean, standard deviation (SD) and entropy-based complexity analysis were performed using sample entropy (SampEn) for different window lengths (m) and filtering levels (r). The MTC SampEn values were lower in the FR group compared to the HY and HE groups for all m and r. The HY group had a greater mean SampEn value than both HE and FR reflecting higher complexity in their MTC series. The mean SampEn values of HY and FR groups were found significantly different for m = 2, 4, 5 and r = (0.1-0.9) × SD, (0.3-0.9) × SD and (0.3-0.9) × SD, respectively. They were also significant difference between HE and FR groups for m = 4-5 and r = (0.3-0.7) × SD, but no significant differences were seen between HY and HE groups for any m and r. A significant correlation of SampEn with SD of MTC was revealed for the HY and HE groups only, suggesting that locomotor disorders could significantly change the regularity or the complexity of the MTC series while healthy ageing does not. These results can be usefully applied to the early diagnosis of common gait pathologies.