scholarly journals Entropy Measures as Descriptors to Identify Apneas in Rheoencephalographic Signals

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 605
Author(s):  
Carmen González ◽  
Erik Jensen ◽  
Pedro Gambús ◽  
Montserrat Vallverdú
Keyword(s):  
Healthy Subjects ◽  
A Priori ◽  
Conditional Entropy ◽  
Approximate Entropy ◽  
Sample Entropy ◽  
P Value ◽  
Embedding Dimension ◽  
P Values ◽  
Entropy Measures ◽  
Inexpensive Technique

Rheoencephalography (REG) is a simple and inexpensive technique that intends to monitor cerebral blood flow (CBF), but its ability to reflect CBF changes has not been extensively proved. Based on the hypothesis that alterations in CBF during apnea should be reflected in REG signals under the form of increased complexity, several entropy metrics were assessed for REG analysis during apnea and resting periods in 16 healthy subjects: approximate entropy (ApEn), sample entropy (SampEn), fuzzy entropy (FuzzyEn), corrected conditional entropy (CCE) and Shannon entropy (SE). To compute these entropy metrics, a set of parameters must be defined a priori, such as, for example, the embedding dimension m, and the tolerance threshold r. A thorough analysis of the effects of parameter selection in the entropy metrics was performed, looking for the values optimizing differences between apnea and baseline signals. All entropy metrics, except SE, provided higher values for apnea periods (p-values < 0.025). FuzzyEn outperformed all other metrics, providing the lowest p-value (p = 0.0001), allowing to conclude that REG signals during apnea have higher complexity than in resting periods. Those findings suggest that REG signals reflect CBF changes provoked by apneas, even though further studies are needed to confirm this hypothesis.

scholarly journals Analyzing EEG of Quasi-Brain-Death Based on Dynamic Sample Entropy Measures

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Li Ni ◽  
Jianting Cao ◽  
Rubin Wang
Keyword(s):  
Brain Death ◽  
Real Time ◽  
Time Window ◽  
Approximate Entropy ◽  
Sample Entropy ◽  
Well Performance ◽  
Entropy Measures ◽  
Brain Death Determination ◽  
Death Determination ◽  
The Brain

To give a more definite criterion using electroencephalograph (EEG) approach on brain death determination is vital for both reducing the risks and preventing medical misdiagnosis. This paper presents several novel adaptive computable entropy methods based on approximate entropy (ApEn) and sample entropy (SampEn) to monitor the varying symptoms of patients and to determine the brain death. The proposed method is a dynamic extension of the standard ApEn and SampEn by introducing a shifted time window. The main advantages of the developed dynamic approximate entropy (DApEn) and dynamic sample entropy (DSampEn) are for real-time computation and practical use. Results from the analysis of 35 patients (63 recordings) show that the proposed methods can illustrate effectiveness and well performance in evaluating the brain consciousness states.

scholarly journals A review of entropy measures for uncertainty quantification of stochastic processes

2019 ◽  
Vol 11 (6) ◽  
pp. 168781401985735 ◽  
Author(s):  
Alireza Namdari ◽  
Zhaojun (Steven) Li
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Uncertainty Quantification ◽  
Lithium Ion ◽  
Second Law Of Thermodynamics ◽  
Approximate Entropy ◽  
Sample Entropy ◽  
Permutation Entropy ◽  
Battery Capacity ◽  
Entropy Measures

Entropy is originally introduced to explain the inclination of intensity of heat, pressure, and density to gradually disappear over time. Based on the concept of entropy, the Second Law of Thermodynamics, which states that the entropy of an isolated system is likely to increase until it attains its equilibrium state, is developed. More recently, the implication of entropy has been extended beyond the field of thermodynamics, and entropy has been applied in many subjects with probabilistic nature. The concept of entropy is applicable and useful in characterizing the behavior of stochastic processes since it represents the uncertainty, ambiguity, and disorder of the processes without being restricted to the forms of the theoretical probability distributions. In order to measure and quantify the entropy, the existing probability of every event in the stochastic process must be determined. Different entropy measures have been studied and presented including Shannon entropy, Renyi entropy, Tsallis entropy, Sample entropy, Permutation entropy, Approximate entropy, and Transfer entropy. This review surveys the general formulations of the uncertainty quantification based on entropy as well as their various applications. The results of the existing studies show that entropy measures are powerful predictors for stochastic processes with uncertainties. In addition, we examine the stochastic process of lithium-ion battery capacity data and attempt to determine the relation between the changes in battery capacity over different cycles and two entropy measures: Sample entropy and Approximate entropy.

scholarly journals Frontal Alpha Complexity of Different Severity Depression Patients

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Lulu Zhao ◽  
Licai Yang ◽  
Baimin Li ◽  
Zhonghua Su ◽  
Chengyu Liu
Keyword(s):  
Neuronal Activity ◽  
Healthy Subjects ◽  
Sample Entropy ◽  
Rank Test ◽  
Mild Depression ◽  
Healthy Group ◽  
Significant Difference ◽  
Entropy Measures ◽  
The Difference ◽  
State Group

Depression is a leading cause of disability worldwide, and objective biomarkers are required for future computer-aided diagnosis. This study aims to assess the variation of frontal alpha complexity among different severity depression patients and healthy subjects, therefore to explore the depressed neuronal activity and to suggest valid biomarkers. 69 depression patients (divided into three groups according to the disease severity) and 14 healthy subjects were employed to collect 3-channel resting Electroencephalogram signals. Sample entropy and Lempel–Ziv complexity methods were employed to evaluate the Electroencephalogram complexity among different severity depression groups and healthy group. Kruskal–Wallis rank test and group t-test were performed to test the difference significance among four groups and between each two groups separately. All indexes values show that depression patients have significantly increased complexity compared to healthy subjects, and furthermore, the complexity keeps increasing as the depression deepens. Sample entropy measures exhibit superiority in distinguishing mild depression from healthy group with significant difference even between nondepressive state group and healthy group. The results confirm the altered neuronal activity influenced by depression severity and suggest sample entropy and Lempel–Ziv complexity as promising biomarkers in future depression evaluation and diagnosis.

scholarly journals An Evaluation of Entropy Measures for Microphone Identification

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1235
Author(s):  
Gianmarco Baldini ◽  
Irene Amerini
Keyword(s):  
A Priori ◽  
Approximate Entropy ◽  
Identification Accuracy ◽  
Permutation Entropy ◽  
Features Selection ◽  
Statistical Features ◽  
Audio Signals ◽  
Trade Off ◽  
Entropy Measures ◽  
Physical Features

Research findings have shown that microphones can be uniquely identified by audio recordings since physical features of the microphone components leave repeatable and distinguishable traces on the audio stream. This property can be exploited in security applications to perform the identification of a mobile phone through the built-in microphone. The problem is to determine an accurate but also efficient representation of the physical characteristics, which is not known a priori. Usually there is a trade-off between the identification accuracy and the time requested to perform the classification. Various approaches have been used in literature to deal with it, ranging from the application of handcrafted statistical features to the recent application of deep learning techniques. This paper evaluates the application of different entropy measures (Shannon Entropy, Permutation Entropy, Dispersion Entropy, Approximate Entropy, Sample Entropy, and Fuzzy Entropy) and their suitability for microphone classification. The analysis is validated against an experimental dataset of built-in microphones of 34 mobile phones, stimulated by three different audio signals. The findings show that selected entropy measures can provide a very high identification accuracy in comparison to other statistical features and that they can be robust against the presence of noise. This paper performs an extensive analysis based on filter features selection methods to identify the most discriminating entropy measures and the related hyper-parameters (e.g., embedding dimension). Results on the trade-off between accuracy and classification time are also presented.

scholarly journals Variational Embedding Multiscale Sample Entropy: A Tool for Complexity Analysis of Multichannel Systems

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 26
Author(s):  
Hongjian Xiao ◽  
Danilo P. Mandic
Keyword(s):  
Real World ◽  
Complexity Analysis ◽  
Structural Complexity ◽  
Conditional Entropy ◽  
Sample Entropy ◽  
Embedding Dimension ◽  
World Systems ◽  
Entropy Methods ◽  
Data Channel ◽  
Noise Resilience

Entropy-based methods have received considerable attention in the quantification of structural complexity of real-world systems. Among numerous empirical entropy algorithms, conditional entropy-based methods such as sample entropy, which are associated with amplitude distance calculation, are quite intuitive to interpret but require excessive data lengths for meaningful evaluation at large scales. To address this issue, we propose the variational embedding multiscale sample entropy (veMSE) method and conclusively demonstrate its ability to operate robustly, even with several times shorter data than the existing conditional entropy-based methods. The analysis reveals that veMSE also exhibits other desirable properties, such as the robustness to the variation in embedding dimension and noise resilience. For rigor, unlike the existing multivariate methods, the proposed veMSE assigns a different embedding dimension to every data channel, which makes its operation independent of channel permutation. The veMSE is tested on both stimulated and real world signals, and its performance is evaluated against the existing multivariate multiscale sample entropy methods. The proposed veMSE is also shown to exhibit computational advantages over the existing amplitude distance-based entropy methods.

Suggested modification of presentation of stroke trial results

2018 ◽  
Vol 13 (7) ◽  
pp. 669-672 ◽  
Author(s):  
Mayank Goyal ◽  
Aravind Ganesh ◽  
Scott Brown ◽  
Bijoy K Menon ◽  
Michael D Hill
Keyword(s):  
Statistical Tests ◽  
Statistical Significance ◽  
A Priori ◽  
Control Group ◽  
P Value ◽  
Modified Rankin Scale ◽  
P Values ◽  
Scale Scores ◽  
Proposed Modification ◽  
Suggested Modification

The modified Rankin Scale (mRS) at 90 days after stroke onset has become the preferred outcome measure in acute stroke trials, including recent trials of interventional therapies. Reporting the range of modified Rankin Scale scores as a paired horizontal stacked bar graph (colloquially known as “Grotta bars”) has become the conventional method of visualizing modified Rankin Scale results. Grotta bars readily illustrate the levels of the ordinal modified Rankin Scale in which benefit may have occurred. However, complementing the available graphical information by including additional features to convey statistical significance may be advantageous. We propose a modification of the horizontal stacked bar graph with illustrative examples. In this suggested modification, the line joining the segments of the bar graph (e.g. modified Rankin Scale 1–2 in treatment arm to modified Rankin Scale 1–2 in control arm) is given a color and thickness based on the p-value of the result at that level (in this example, the p-value of modified Rankin Scale 0–1 vs. 2–6)—a thick green line for p-values <0.01, thin green for p-values of 0.01 to <0.05, gray for 0.05 to <0.10, thin red for 0.10 to <0.90, and thick red for p-values ≥0.90 or outcome favoring the control group. Illustrative examples from four recent trials (ESCAPE, SWIFT-PRIME, IST-3, ASTER) are shown to demonstrate the range of significant and non-significant effects that can be captured using this proposed method. By formalizing a display of outcomes which includes statistical tests of all possible dichotomizations of the Rankin scale, this approach also encourages pre-specification of such hypotheses. Prespecifying tests of all six dichotomizations of the Rankin scale provides all possible statistical information in an a priori fashion. Since the result of our proposed approach is six distinct dichotomized tests in addition to a primary test, e.g. of the ordinal Rankin shift, it may be prudent to account for multiplicity in testing by using dichotomized p-values only after adjustment, such as by the Bonferroni or Hochberg-Holm methods. Whether p-values are nominal or adjusted may be left to the discretion of the presenter as long as the presence or absence is clearly stated in the statistical methods. Our proposed modification results in a visually intuitive summary of both the size of the effect—represented by the matched bars and their connecting segments—as well as its statistical relevance.

scholarly journals Entropy Measures in Analysis of Head up Tilt Test Outcome for Diagnosing Vasovagal Syncope

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 976 ◽  
Author(s):  
Katarzyna Buszko ◽  
Agnieszka Piątkowska ◽  
Edward Koźluk ◽  
Tomasz Fabiszak ◽  
Grzegorz Opolski
Keyword(s):  
Supine Position ◽  
Vasovagal Syncope ◽  
Conditional Entropy ◽  
Sample Entropy ◽  
Permutation Entropy ◽  
Tilt Test ◽  
Entropy Measures ◽  
Head Up Tilt ◽  
Head Up Tilt Test ◽  
Passive Phase

The paper presents possible applications of entropy measures in analysis of biosignals recorded during head up tilt testing (HUTT) in patients with suspected vasovagal syndrome. The study group comprised 80 patients who developed syncope during HUTT (57 in the passive phase of the test (HUTT(+) group) and 23 who had negative result of passive phase and developed syncope after provocation with nitroglycerine (HUTT(−) group)). The paper focuses on assessment of monitored signals’ complexity (heart rate expressed as R-R intervals (RRI), blood pressure (sBP, dBP) and stroke volume (SV)) using various types of entropy measures (Sample Entropy (SE), Fuzzy Entropy (FE), Shannon Entropy (Sh), Conditional Entropy (CE), Permutation Entropy (PE)). Assessment of the complexity of signals in supine position indicated presence of significant differences between HUTT(+) versus HUTT(−) patients only for Conditional Entropy (CE(RRI)). Values of CE(RRI) higher than 0.7 indicate likelihood of a positive result of HUTT already at the passive phase. During tilting, in the pre-syncope phase, significant differences were found for: (SE(sBP), SE(dBP), FE(RRI), FE(sBP), FE(dBP), FE(SV), Sh(sBP), Sh(SV), CE(sBP), CE(dBP)). HUTT(+) patients demonstrated significant changes in signals’ complexity more frequently than HUTT(−) patients. When comparing entropy measurements done in the supine position with those during tilting, SV assessed in HUTT(+) patients was the only parameter for which all tested measures of entropy (SE(SV), FE(SV), Sh(SV), CE(SV), PE(SV)) showed significant differences.

scholarly journals Low Computational Cost for Sample Entropy

Entropy ◽  
2018 ◽  
Vol 20 (1) ◽  
pp. 61 ◽  
Author(s):  
George Manis ◽  
Md Aktaruzzaman ◽  
Roberto Sassi
Keyword(s):  
Time Series ◽  
Dimensional Space ◽  
A Priori ◽  
Computational Cost ◽  
Approximate Entropy ◽  
Sample Entropy ◽  
Series Length ◽  
Approximation Techniques ◽  
Computationally Intensive ◽  
Definition Of

Sample Entropy is the most popular definition of entropy and is widely used as a measure of the regularity/complexity of a time series. On the other hand, it is a computationally expensive method which may require a large amount of time when used in long series or with a large number of signals. The computationally intensive part is the similarity check between points in m dimensional space. In this paper, we propose new algorithms or extend already proposed ones, aiming to compute Sample Entropy quickly. All algorithms return exactly the same value for Sample Entropy, and no approximation techniques are used. We compare and evaluate them using cardiac inter-beat (RR) time series. We investigate three algorithms. The first one is an extension of the k d -trees algorithm, customized for Sample Entropy. The second one is an extension of an algorithm initially proposed for Approximate Entropy, again customized for Sample Entropy, but also improved to present even faster results. The last one is a completely new algorithm, presenting the fastest execution times for specific values of m, r, time series length, and signal characteristics. These algorithms are compared with the straightforward implementation, directly resulting from the definition of Sample Entropy, in order to give a clear image of the speedups achieved. All algorithms assume the classical approach to the metric, in which the maximum norm is used. The key idea of the two last suggested algorithms is to avoid unnecessary comparisons by detecting them early. We use the term unnecessary to refer to those comparisons for which we know a priori that they will fail at the similarity check. The number of avoided comparisons is proved to be very large, resulting in an analogous large reduction of execution time, making them the fastest algorithms available today for the computation of Sample Entropy.

scholarly journals HRV analysis: undependability of approximate entropy at locating optimum complexity in malnourished children

2021 ◽  
pp. 1-6
Author(s):  
David M. Garner ◽  
Gláucia S. Barreto ◽  
Vitor E. Valenti ◽  
Franciele M. Vanderlei ◽  
Andrey A. Porto ◽  
...  
Keyword(s):  
Statistical Significance ◽  
Accurate Determination ◽  
Approximate Entropy ◽  
Effect Sizes ◽  
Potential Hazard ◽  
Autonomic Modulation ◽  
Embedding Dimension ◽  
Malnourished Children ◽  
Hrv Analysis

Abstract Introduction: Approximate Entropy is an extensively enforced metric to evaluate chaotic responses and irregularities of RR intervals sourced from an eletrocardiogram. However, to estimate their responses, it has one major problem – the accurate determination of tolerances and embedding dimensions. So, we aimed to overt this potential hazard by calculating numerous alternatives to detect their optimality in malnourished children. Materials and methods: We evaluated 70 subjects split equally: malnourished children and controls. To estimate autonomic modulation, the heart rate was measured lacking any physical, sensory or pharmacologic stimuli. In the time series attained, Approximate Entropy was computed for tolerance (0.1→0.5 in intervals of 0.1) and embedding dimension (1→5 in intervals of 1) and the statistical significances between the groups by their Cohen’s ds and Hedges’s gs were totalled. Results: The uppermost value of statistical significance accomplished for the effect sizes for any of the combinations was −0.2897 (Cohen’s ds) and −0.2865 (Hedges’s gs). This was achieved with embedding dimension = 5 and tolerance = 0.3. Conclusions: Approximate Entropy was able to identify a reduction in chaotic response via malnourished children. The best values of embedding dimension and tolerance of the Approximate Entropy to identify malnourished children were, respectively, embedding dimension = 5 and embedding tolerance = 0.3. Nevertheless, Approximate Entropy is still an unreliable mathematical marker to regulate this.

Over-expression of IL-6 coding gene in the peripheral blood of migraine with aura patients

2021 ◽  
pp. 1-5
Author(s):  
Mahdi Ramezani ◽  
Alireza Komaki ◽  
Mohammad Mahdi Eftekharian ◽  
Mehrdokht Mazdeh ◽  
Soudeh Ghafouri-Fard
Keyword(s):  
Migraine With Aura ◽  
Peripheral Blood ◽  
Healthy Subjects ◽  
Migraine Without Aura ◽  
P Value ◽  
Healthy Controls ◽  
Over Expression ◽  
Significant Difference ◽  
Male Patients ◽  
Years Lived With Disability

Migraine is a common disorder which is placed among the top ten reasons of years lived with disability. Cytokines are among the molecules that contribute in the pathophysiology of migraine. In the current study, we evaluated expression levels of IL-6 coding gene in the peripheral blood of 120 migraine patients (54 migraine without aura and 66 migraine with aura patients) and 40 healthy subjects. No significant difference was detected in expression of IL-6 between total migraine patients and healthy controls (Posterior beta = 0.253, P value = 0.199). The interaction effect between gender and group was significant (Posterior beta =-1.274, P value = 0.011), therefore, we conducted subgroup analysis within gender group. Such analysis revealed that while expression of this gene is not different between male patients and male controls (Posterior beta =-0.371, P value > 0.999), it was significantly over-expressed in female patients compared with female controls (Posterior beta = 0.86, P= 0.002). Expression of IL-6 was significantly higher in patients with aura compared with controls (Posterior beta = 0.63, adjusted P value = 0.019). However, expression of this cytokine coding gene was not different between patients without aura and healthy subjects (Posterior beta = 0.193, adjusted P value = 0.281). Therefore, IL-6 might be involved in the pathophysiology of migraine among females and migraine with aura among both sexes.

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