Application of a Modified Entropy Computational Method in Assessing the Complexity of Pulse Wave Velocity Signals in Healthy and Diabetic Subjects

Benefits of Zero-Phase or Linear Phase Filters to Design Multiscale Entropy: Theory and Application

In various applications, multiscale entropy (MSE) is often used as a feature to characterize the complexity of the signals in order to classify them. It consists of estimating the sample entropies (SEs) of the signal under study and its coarse-grained (CG) versions, where the CG process amounts to (1) filtering the signal with an average filter whose order is the scale and (2) decimating the filter output by a factor equal to the scale. In this paper, we propose to derive a new variant of the MSE. Its novelty stands in the way to get the sequences at different scales by avoiding distortions during the decimation step. To this end, a linear-phase or null-phase low-pass filter whose cutoff frequency is well suited to the scale is used. Interpretations on how the MSE behaves and illustrations with a sum of sinusoids, as well as white and pink noises, are given. Then, an application to detect attentional tunneling is presented. It shows the benefit of the new approach in terms of p value when one aims at differentiating the set of MSEs obtained in the attentional tunneling state from the set of MSEs obtained in the nominal state. It should be noted that CG versions can be replaced not only for the MSE but also for other variants.

EMD-based analysis of complexity with dissociated EEG amplitude and frequency information: a data-driven robust tool -for Autism diagnosis- compared to multi-scale entropy approach

OBJECTIVE

Autism spectrum disorder (ASD) is usually characterised by altered social skills, repetitive behaviours, and difficulties in verbal/nonverbal communication. It has been reported that electroencephalograms (EEGs) in ASD are characterised by atypical complexity. The most commonly applied method in studies of ASD EEG complexity is multiscale entropy (MSE), where the sample entropy is evaluated across several scales. However, the accuracy of MSE-based classifications between ASD and neurotypical EEG activities is poor owing to several shortcomings in scale extraction and length, the overlap between amplitude and frequency information, and sensitivity to frequency. The present study proposes a novel, nonlinear, non-stationary, adaptive, data-driven, and accurate method for the classification of ASD and neurotypical groups based on EEG complexity and entropy without the shortcomings of MSE.

APPROACH

The proposed method is as follows: (a) each ASD and neurotypical EEG (122 subjects × 64 channels) is decomposed using empirical mode decomposition (EMD) to obtain the intrinsic components (intrinsic mode functions). (b) The extracted components are normalised through the direct quadrature procedure. (c) The Hilbert transforms of the components are computed. (d) The analytic counterparts of components (and normalised components) are found. (e) The instantaneous frequency function of each analytic normalised component is calculated. (f) The instantaneous amplitude function of each analytic component is calculated. (g) The Shannon entropy values of the instantaneous frequency and amplitude vectors are computed. (h) The entropy values are classified using a neural network (NN). (i) The achieved accuracy is compared to that obtained with MSE-based classification. (j) The consistency of the results of entropy 3D mapping with clinical data is assessed.

MAIN RESULTS

The results demonstrate that the proposed method outperforms MSE (accuracy: 66.4%), with an accuracy of 93.5%. Moreover, the entropy 3D mapping results are more consistent with the available clinical data regarding brain topography in ASD.

SIGNIFICANCE

This study presents a more robust alternative to MSE, which can be used for accurate classification of ASD/neurotypical as well as for the examination of EEG entropy across brain zones in ASD.

Multiscale Entropy Analysis of Short Signals: The Robustness of Fuzzy Entropy-Based Variants Compared to Full-Length Long Signals

Multiscale entropy (MSE) analysis is a fundamental approach to access the complexity of a time series by estimating its information creation over a range of temporal scales. However, MSE may not be accurate or valid for short time series. This is why previous studies applied different kinds of algorithm derivations to short-term time series. However, no study has systematically analyzed and compared their reliabilities. This study compares the MSE algorithm variations adapted to short time series on both human and rat heart rate variability (HRV) time series using long-term MSE as reference. The most used variations of MSE are studied: composite MSE (CMSE), refined composite MSE (RCMSE), modified MSE (MMSE), and their fuzzy versions. We also analyze the errors in MSE estimations for a range of incorporated fuzzy exponents. The results show that fuzzy MSE versions-as a function of time series length-present minimal errors compared to the non-fuzzy algorithms. The traditional multiscale entropy algorithm with fuzzy counting (MFE) has similar accuracy to alternative algorithms with better computing performance. For the best accuracy, the findings suggest different fuzzy exponents according to the time series length.

Entropy Profiling: A Reduced-Parametric Measure of Kolmogorov-Sinai Entropy from Short-Term HRV Signal

Entropy profiling is a recently introduced approach that reduces parametric dependence in traditional Kolmogorov-Sinai (KS) entropy measurement algorithms. The choice of the threshold parameter r of vector distances in traditional entropy computations is crucial in deciding the accuracy of signal irregularity information retrieved by these methods. In addition to making parametric choices completely data-driven, entropy profiling generates a complete profile of entropy information as against a single entropy estimate (seen in traditional algorithms). The benefits of using "profiling" instead of "estimation" are: (a) precursory methods such as approximate and sample entropy that have had the limitation of handling short-term signals (less than 1000 samples) are now made capable of the same; (b) the entropy measure can capture complexity information from short and long-term signals without multi-scaling; and (c) this new approach facilitates enhanced information retrieval from short-term HRV signals. The novel concept of entropy profiling has greatly equipped traditional algorithms to overcome existing limitations and broaden applicability in the field of short-term signal analysis. In this work, we present a review of KS-entropy methods and their limitations in the context of short-term heart rate variability analysis and elucidate the benefits of using entropy profiling as an alternative for the same.

Multiscale entropy profiling to estimate complexity of heart rate dynamics

In the analysis of signal regularity from a physiological system such as the human heart, Approximate entropy (H_{A}) and Sample entropy (H_{S}) have been the most popular statistical tools used so far. While studying heart rate dynamics, it nevertheless becomes more important to extract information about complexities associated with the heart, rather than the regularity of signal patterns produced by it. A complex physiological system does not necessarily produce irregular signals and vice versa. In order to equip a regularity statistic to see through the respective system's level of complexity, the idea of multiscaling was introduced in H_{S} estimation. Multiscaling ideally requires an input signal to be (a) long and (b) stationary. However, the longer the data is the less stationary it is. The requirement multiscaling places on its data length largely limits its accuracy. We propose a novel method of entropy profiling that makes multiscaling require very short signal segments, granting better prospects of signal stationarity and estimation accuracy. With entropy profiling, an efficient multiscale H_{S} based analysis requires only 500-beat signals of atrial fibrillated data, as opposed to the earlier case that required at least 20 000 beats.

Influence of Chronic Obstructive Pulmonary Disease and Moderate-To-Severe Sleep Apnoea in Overnight Cardiac Autonomic Modulation: Time, Frequency and Non-Linear Analyses

Chronic obstructive pulmonary disease (COPD) is one of the most prevalent lung diseases worldwide. COPD patients show major dysfunction in cardiac autonomic modulation due to sustained hypoxaemia, which has been significantly related to higher risk of cardiovascular disease. Obstructive sleep apnoea syndrome (OSAS) is a frequent comorbidity in COPD patients. It has been found that patients suffering from both COPD and OSAS simultaneously, the so-called overlap syndrome, have notably higher morbidity and mortality. Heart rate variability (HRV) has demonstrated to be useful to assess changes in autonomic functioning in different clinical conditions. However, there is still little scientific evidence on the magnitude of changes in cardiovascular dynamics elicited by the combined effect of both respiratory diseases, particularly during sleep, when apnoeic events occur. In this regard, we hypothesised that a non-linear analysis is able to provide further insight into long-term dynamics of overnight cardiovascular modulation. Accordingly, this study is aimed at assessing the usefulness of sample entropy (SampEn) to distinguish changes in overnight pulse rate variability (PRV) recordings among three patient groups while sleeping: COPD, moderate-to-severe OSAS, and overlap syndrome. In order to achieve this goal, a population composed of 297 patients were studied: 22 with COPD alone, 213 showing moderate-to-severe OSAS, and 62 with COPD and moderate-to-severe OSAS simultaneously (COPD+OSAS). Cardiovascular dynamics were analysed using pulse rate (PR) recordings from unattended pulse oximetry carried out at patients’ home. Conventional time- and frequency- domain analyses were performed to characterise sympathetic and parasympathetic activation of the nervous system, while SampEn was applied to quantify long-term changes in irregularity. Our analyses revealed that overnight PRV recordings from COPD+OSAS patients were significantly more irregular (higher SampEn) than those from patients with COPD alone (0.267 [0.210–0.407] vs. 0.212 [0.151–0.267]; p < 0.05) due to recurrent apnoeic events during the night. Similarly, COPD + OSAS patients also showed significantly higher irregularity in PRV during the night than subjects with OSAS alone (0.267 [0.210–0.407] vs. 0.241 [0.189–0.325]; p = 0.05), which suggests that the cumulative effect of both diseases increases disorganization of pulse rate while sleeping. On the other hand, no statistical significant differences were found between COPD and COPD + OSAS patients when traditional frequency bands (LF and HF) were analysed. We conclude that SampEn is able to properly quantify changes in overnight cardiovascular dynamics of patients with overlap syndrome, which could be useful to assess cardiovascular impairment in COPD patients due to the presence of concomitant OSAS.

Multiscale Entropy Analysis of Page Views: A Case Study of Wikipedia

In this study, the Wikipedia page views for four selected topics, namely, education, the economy/finance, medicine, and nature/environment from 2016–2018 are collected and the sample entropies of the three years’ page views are estimated and investigated using a short-time series multiscale entropy (sMSE) algorithm for a comprehensible understanding of the complexity of human website searching activities. The sample entropies of the selected topics are found to exhibit different temporal variations. In the past three years, the temporal characteristics of the sample entropies are vividly revealed, and the sample entropies of the selected topics follow the same tendencies and can be quantitatively ranked. By taking the 95% confidence interval into account, the temporal variations of sample entropies are further validated by statistical analysis (non-parametric), including the Wilcoxon signed-rank test and the Mann-Whitney U-test. The results suggest that the sample entropies estimated by the sMSE algorithm are feasible for analyzing the temporal variations of complexity for certain topics, whereas the regular variations of estimated sample entropies of different selected topics can’t simply be accepted as is. Potential explanations and paths in forthcoming studies are also described and discussed.

Assessing multiscale complexity of short heart rate variability series through a model-based linear approach

We propose a multiscale complexity (MSC) method assessing irregularity in assigned frequency bands and being appropriate for analyzing the short time series. It is grounded on the identification of the coefficients of an autoregressive model, on the computation of the mean position of the poles generating the components of the power spectral density in an assigned frequency band, and on the assessment of its distance from the unit circle in the complex plane. The MSC method was tested on simulations and applied to the short heart period (HP) variability series recorded during graded head-up tilt in 17 subjects (age from 21 to 54 years, median = 28 years, 7 females) and during paced breathing protocols in 19 subjects (age from 27 to 35 years, median = 31 years, 11 females) to assess the contribution of time scales typical of the cardiac autonomic control, namely in low frequency (LF, from 0.04 to 0.15 Hz) and high frequency (HF, from 0.15 to 0.5 Hz) bands to the complexity of the cardiac regulation. The proposed MSC technique was compared to a traditional model-free multiscale method grounded on information theory, i.e., multiscale entropy (MSE). The approach suggests that the reduction of HP variability complexity observed during graded head-up tilt is due to a regularization of the HP fluctuations in LF band via a possible intervention of sympathetic control and the decrement of HP variability complexity observed during slow breathing is the result of the regularization of the HP variations in both LF and HF bands, thus implying the action of physiological mechanisms working at time scales even different from that of respiration. MSE did not distinguish experimental conditions at time scales larger than 1. Over a short time series MSC allows a more insightful association between cardiac control complexity and physiological mechanisms modulating cardiac rhythm compared to a more traditional tool such as MSE.

Aging effect on microcirculation: A multiscale entropy approach on laser speckle contrast images

PURPOSE

It has long been known that age plays a crucial role in the deterioration of microvessels. The assessment of such deteriorations can be achieved by monitoring microvascular blood flow. Laser speckle contrast imaging (LSCI) is a powerful optical imaging tool that provides two-dimensional information on microvascular blood flow. The technique has recently been commercialized, and hence, few works discuss the postacquisition processing of laser speckle contrast images recorded in vivo. By applying entropy-based complexity measures to LSCI time series, we present herein the first attempt to study the effect of aging on microcirculation by measuring the complexity of microvascular signals over multiple time scales.

METHODS

Forearm skin microvascular blood flow was studied with LSCI in 18 healthy subjects. The subjects were subdivided into two age groups: younger (20-30 years old, n = 9) and older (50-68 years old, n = 9). To estimate age-dependent changes in microvascular blood flow, we applied three entropy-based complexity algorithms to LSCI time series.

RESULTS

The application of entropy-based complexity algorithms to LSCI time series can differentiate younger from older groups: the data fluctuations in the younger group have a significantly higher complexity than those obtained from the older group.

CONCLUSIONS

The effect of aging on microcirculation can be estimated by using entropy-based complexity algorithms to LSCI time series.

Serial heart rhythm complexity changes in patients with anterior wall ST segment elevation myocardial infarction

Heart rhythm complexity analysis has been shown to have good prognostic power in patients with cardiovascular disease. The aim of this study was to analyze serial changes in heart rhythm complexity from the acute to chronic phase of acute myocardial infarction (MI). We prospectively enrolled 27 patients with anterior wall ST segment elevation myocardial infarction (STEMI) and 42 control subjects. In detrended fluctuation analysis (DFA), the patients had significantly lower DFAα2 in the acute stage (within 72 hours) and lower DFAα1 at 3 months and 12 months after MI. In multiscale entropy (MSE) analysis, the patients had a lower slope 5 in the acute stage, which then gradually increased during the follow-up period. The areas under the MSE curves for scale 1 to 5 (area 1–5) and 6 to 20 (area 6–20) were lower throughout the chronic stage. Area 6–20 had the greatest discriminatory power to differentiate the post-MI patients (at 1 year) from the controls. In both the net reclassification improvement and integrated discrimination improvement models, MSE parameters significantly improved the discriminatory power of the linear parameters to differentiate the post-MI patients from the controls. In conclusion, the patients with STEMI had serial changes in cardiac complexity.