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Entropy in the Application of Biomedical Signals

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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Entropy and Biology".

Deadline for manuscript submissions: closed (25 July 2022) | Viewed by 22940

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Special Issue Editor

Dr. Philippe Ravier

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Guest Editor

Polytech Orléans, Laboratoire PRISME, Université d'Orléans INSA CVL, 45100 Orléans, France
Interests: signal processing; nonstationary processing methods; feature selection methods; biomedical signals (EMG, ECG, PCG), vibration signals, electrical appliance signals, radioastronomy signals

Special Issue Information

Dear Colleagues,

For many years, entropy methods have been used as powerful tools for analyzing signals or time series resulting from complex dynamics in biomedical systems. The potential of these methods for characterizing complex dynamics has led researchers to investigate many variants of entropy definitions and estimations, each being designed for its qualities suitable for application purpose and being adapted to many application constraints. For example, the well-known approximate entropy was developed by data length constraints commonly encountered in biomedical time series, like heart rate variability or electroencephalography time series. Permutation entropy was developed for discriminating complex structures from white noise, which is the reference case because it is fully asymptotically characterized.

These two examples show that existing challenges need to be further addressed by new theoretical and/or experimental research developments, motivated by the following facts:

1) Data in the biomedical domain are often not stationary, and there is a need for improving entropy measure performance in this non-asymptotical context;

2) Entropy measures can be advantageously augmented by combining them with deterministic complexity measures for a better characterization of complex dynamics of the underlying processes encountered in the field of biomedical applications.

In this Special Issue, we would like to collect papers focusing on finite-length time series entropy, theoretically or experimentally characterized, with applications to nonstationary or short-length biomedical data series. Any kind of entropy measure will be considered: approximate entropy, sample entropy, permutation entropy, fuzzy entropy, distribution entropy, dispersion entropy, etc. Any additional measure or extension combined with the entropy concept will be considered: multiscale measures, cross-entropy measures, multivariate approaches, multidimensional data approaches, and mixing with other complexity measures that describe deterministic underlying mechanisms of biomedical systems (Kolmogorov-like complexity, fractal dimensions, Lyapunov exponents, etc.).

The main topics of this Special Issue include (but are not limited to) the following:

Characterization and improvement of statistical performance of entropy estimators;
Improvement in the entropy measures in finite- or short-length time series;
Combinations of entropy methods with deterministic complexity measures;
Applications of the entropy techniques on nonstationary or short-length biomedical data series.

Dr. Philippe Ravier
Guest Editor

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Keywords

finite-length time series
entropy for short time series data
combination of complexity measures
biomedical applications
statistical performance of entropy estimators
complex dynamics characterization

Published Papers (10 papers)

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Research

17 pages, 820 KiB

Open AccessFeature PaperArticle

On the Genuine Relevance of the Data-Driven Signal Decomposition-Based Multiscale Permutation Entropy

by Meryem Jabloun, Philippe Ravier and Olivier Buttelli

Entropy 2022, 24(10), 1343; https://doi.org/10.3390/e24101343 - 23 Sep 2022

Cited by 2 | Viewed by 1333

Abstract

Ordinal pattern-based approaches have great potential to capture intrinsic structures of dynamical systems, and therefore, they continue to be developed in various research fields. Among these, the permutation entropy (PE), defined as the Shannon entropy of ordinal probabilities, is an attractive time series complexity measure. Several multiscale variants (MPE) have been proposed in order to bring out hidden structures at different time scales. Multiscaling is achieved by combining linear or nonlinear preprocessing with PE calculation. However, the impact of such a preprocessing on the PE values is not fully characterized. In a previous study, we have theoretically decoupled the contribution of specific signal models to the PE values from that induced by the inner correlations of linear preprocessing filters. A variety of linear filters such as the autoregressive moving average (ARMA), Butterworth, and Chebyshev were tested. The current work is an extension to nonlinear preprocessing and especially to data-driven signal decomposition-based MPE. The empirical mode decomposition, variational mode decomposition, singular spectrum analysis-based decomposition and empirical wavelet transform are considered. We identify possible pitfalls in the interpretation of PE values induced by these nonlinear preprocessing, and hence, we contribute to improving the PE interpretation. The simulated dataset of representative processes such as white Gaussian noise, fractional Gaussian processes, ARMA models and synthetic sEMG signals as well as real-life sEMG signals are tested. Full article

(This article belongs to the Special Issue Entropy in the Application of Biomedical Signals)

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23 pages, 2327 KiB

Open AccessArticle

An Entropy-Based Architecture for Detection of Sepsis in Newborn Cry Diagnostic Systems

by Zahra Khalilzad, Yasmina Kheddache and Chakib Tadj

Entropy 2022, 24(9), 1194; https://doi.org/10.3390/e24091194 - 26 Aug 2022

Cited by 5 | Viewed by 1574

Abstract

The acoustic characteristics of cries are an exhibition of an infant’s health condition and these characteristics have been acknowledged as indicators for various pathologies. This study focused on the detection of infants suffering from sepsis by developing a simplified design using acoustic features and conventional classifiers. The features for the proposed framework were Mel-frequency Cepstral Coefficients (MFCC), Spectral Entropy Cepstral Coefficients (SENCC) and Spectral Centroid Cepstral Coefficients (SCCC), which were classified through K-nearest Neighborhood (KNN) and Support Vector Machine (SVM) classification methods. The performance of the different combinations of the feature sets was also evaluated based on several measures such as accuracy, F1-score and Matthews Correlation Coefficient (MCC). Bayesian Hyperparameter Optimization (BHPO) was employed to tailor the classifiers uniquely to fit each experiment. The proposed methodology was tested on two datasets of expiratory cries (EXP) and voiced inspiratory cries (INSV). The highest accuracy and F-score were 89.99% and 89.70%, respectively. This framework also implemented a novel feature selection method based on Fuzzy Entropy (FE) as a final experiment. By employing FE, the number of features was reduced by more than 40%, whereas the evaluation measures were not hindered for the EXP dataset and were even enhanced for the INSV dataset. Therefore, it was deduced through these experiments that an entropy-based framework is successful for identifying sepsis in neonates and has the advantage of achieving high performance with conventional machine learning (ML) approaches, which makes it a reliable means for the early diagnosis of sepsis in deprived areas of the world. Full article

(This article belongs to the Special Issue Entropy in the Application of Biomedical Signals)

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14 pages, 26431 KiB

Open AccessArticle

Sample Entropy as a Tool to Assess Lumbo-Pelvic Movements in a Clinical Test for Low-Back-Pain Patients

by Paul Thiry, Olivier Nocent, Fabien Buisseret, William Bertucci, André Thevenon and Emilie Simoneau-Buessinger

Entropy 2022, 24(4), 437; https://doi.org/10.3390/e24040437 - 22 Mar 2022

Cited by 4 | Viewed by 2671

Abstract

Low back pain (LBP) obviously reduces the quality of life but is also the world’s leading cause of years lived with disability. Alterations in motor response and changes in movement patterns are expected in LBP patients when compared to healthy people. Such changes in dynamics may be assessed by the nonlinear analysis of kinematical time series recorded from one patient’s motion. Since sample entropy (SampEn) has emerged as a relevant index measuring the complexity of a given time series, we propose the development of a clinical test based on SampEn of a time series recorded by a wearable inertial measurement unit for repeated bending and returns (b and r) of the trunk. Twenty-three healthy participants were asked to perform, in random order, 50 repetitions of this movement by touching a stool and another 50 repetitions by touching a box on the floor. The angular amplitude of the b and r movement and the sample entropy of the three components of the angular velocity and acceleration were computed. We showed that the repetitive b and r “touch the stool” test could indeed be the basis of a clinical test for the evaluation of low-back-pain patients, with an optimal duration of 70 s, acceptable in daily clinical practice. Full article

(This article belongs to the Special Issue Entropy in the Application of Biomedical Signals)

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13 pages, 9148 KiB

Open AccessArticle

Entropy Analysis of Neonatal Electrodermal Activity during the First Three Days after Birth

by Zuzana Visnovcova, Marek Kozar, Zuzana Kuderava, Mirko Zibolen, Nikola Ferencova and Ingrid Tonhajzerova

Entropy 2022, 24(3), 422; https://doi.org/10.3390/e24030422 - 17 Mar 2022

Viewed by 1962

Abstract

The entropy-based parameters determined from the electrodermal activity (EDA) biosignal evaluate the complexity within the activity of the sympathetic cholinergic system. We focused on the evaluation of the complex sympathetic cholinergic regulation by assessing EDA using conventional indices (skin conductance level (SCL), non-specific skin conductance responses, spectral EDA indices), and entropy-based parameters (approximate, sample, fuzzy, permutation, Shannon, and symbolic information entropies) in newborns during the first three days of postnatal life. The studied group consisted of 50 healthy newborns (21 boys, average gestational age: 39.0 ± 0.2 weeks). EDA was recorded continuously from the feet at rest for three periods (the first day—2 h after birth, the second day—24 h after birth, and the third day—72 h after birth). Our results revealed higher SCL, spectral EDA index in a very-low frequency band, approximate, sample, fuzzy, and permutation entropy during the first compared to second and third days, while Shannon and symbolic information entropies were lower during the first day compared to other periods. In conclusion, EDA parameters seem to be sensitive in the detection of the sympathetic regulation changes in early postnatal life and which can represent an important step towards a non-invasive early diagnosis of the pathological states linked to autonomic dysmaturation in newborns. Full article

(This article belongs to the Special Issue Entropy in the Application of Biomedical Signals)

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17 pages, 689 KiB

Open AccessArticle

The Refined Composite Downsampling Permutation Entropy Is a Relevant Tool in the Muscle Fatigue Study Using sEMG Signals

by Philippe Ravier, Antonio Dávalos, Meryem Jabloun and Olivier Buttelli

Entropy 2021, 23(12), 1655; https://doi.org/10.3390/e23121655 - 9 Dec 2021

Cited by 4 | Viewed by 2374

Abstract

Surface electromyography (sEMG) is a valuable technique that helps provide functional and structural information about the electric activity of muscles. As sEMG measures output of complex living systems characterized by multiscale and nonlinear behaviors, Multiscale Permutation Entropy (MPE) is a suitable tool for capturing useful information from the ordinal patterns of sEMG time series. In a previous work, a theoretical comparison in terms of bias and variance of two MPE variants—namely, the refined composite MPE (rcMPE) and the refined composite downsampling (rcDPE), was addressed. In the current paper, we assess the superiority of rcDPE over MPE and rcMPE, when applied to real sEMG signals. Moreover, we demonstrate the capacity of rcDPE in quantifying fatigue levels by using sEMG data recorded during a fatiguing exercise. The processing of four consecutive temporal segments, during biceps brachii exercise maintained at 70% of maximal voluntary contraction until exhaustion, shows that the 10th-scale of rcDPE was capable of better differentiation of the fatigue segments. This scale actually brings the raw sEMG data, initially sampled at 10 kHz, to the specific 0–500 Hz sEMG spectral band of interest, which finally reveals the inner complexity of the data. This study promotes good practices in the use of MPE complexity measures on real data. Full article

(This article belongs to the Special Issue Entropy in the Application of Biomedical Signals)

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14 pages, 2937 KiB

Open AccessArticle

Decreased Resting-State Functional Complexity in Elderly with Subjective Cognitive Decline

by Huangjing Ni, Zijie Song, Lei Liang, Qiaowen Xing, Jiaolong Qin and Xiaochuan Wu

Entropy 2021, 23(12), 1591; https://doi.org/10.3390/e23121591 - 27 Nov 2021

Cited by 4 | Viewed by 1807

Abstract

Individuals with subjective cognitive decline (SCD) are at high risk of developing preclinical or clinical state of Alzheimer’s disease (AD). Resting state functional magnetic resonance imaging, which can indirectly reflect neuron activities by measuring the blood-oxygen-level-dependent (BOLD) signals, is promising in the early detection of SCD. This study aimed to explore whether the nonlinear complexity of BOLD signals can describe the subtle differences between SCD and normal aging, and uncover the underlying neuropsychological implications of these differences. In particular, we introduce amplitude-aware permutation entropy (AAPE) as the novel measure of brain entropy to characterize the complexity in BOLD signals in each brain region of the Brainnetome atlas. Our results demonstrate that AAPE can reflect the subtle differences between both groups, and the SCD group presented significantly decreased complexities in subregions of the superior temporal gyrus, the inferior parietal lobule, the postcentral gyrus, and the insular gyrus. Moreover, the results further reveal that lower complexity in SCD may correspond to poorer cognitive performance or even subtle cognitive impairment. Our findings demonstrated the effectiveness and sensitiveness of the novel brain entropy measured by AAPE, which may serve as the potential neuroimaging marker for exploring the subtle changes in SCD. Full article

(This article belongs to the Special Issue Entropy in the Application of Biomedical Signals)

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21 pages, 3329 KiB

Open AccessArticle

Associations between Cardiovascular Signal Entropy and Cognitive Performance over Eight Years

by Silvin P. Knight, Louise Newman, Siobhan Scarlett, John D. O’Connor, James Davis, Celine De Looze, Rose Anne Kenny and Roman Romero-Ortuno

Entropy 2021, 23(10), 1337; https://doi.org/10.3390/e23101337 - 14 Oct 2021

Cited by 7 | Viewed by 2874

Abstract

In this study, the relationship between non-invasively measured cardiovascular signal entropy and global cognitive performance was explored in a sample of community-dwelling older adults from The Irish Longitudinal Study on Ageing (TILDA), both cross-sectionally at baseline (n = 4525; mean (SD) age: 61.9 (8.4) years; 54.1% female) and longitudinally. We hypothesised that signal disorder in the cardiovascular system, as quantified by short-length signal entropy during rest, could provide a marker for cognitive function. Global cognitive function was assessed via Mini Mental State Examination (MMSE) across five longitudinal waves (8 year period; n = 4316; mean (SD) age: 61.9 (8.4) years; 54.4% female) and the Montreal Cognitive Assessment (MOCA) across two longitudinal waves (4 year period; n = 3600; mean (SD) age: 61.7 (8.2) years; 54.1% female). Blood pressure (BP) was continuously monitored during supine rest at baseline, and sample entropy values were calculated for one-minute and five-minute sections of this data, both for time-series data interpolated at 5 Hz and beat-to-beat data. Results revealed significant associations between BP signal entropy and cognitive performance, both cross-sectionally and longitudinally. Results also suggested that as regards associations with cognitive performance, the entropy analysis approach used herein potentially outperformed more traditional cardiovascular measures such as resting heart rate and heart rate variability. The quantification of entropy in short-length BP signals could provide a clinically useful marker of the cardiovascular dysregulations that potentially underlie cognitive decline. Full article

(This article belongs to the Special Issue Entropy in the Application of Biomedical Signals)

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16 pages, 786 KiB

Open AccessArticle

Parameter Analysis of Multiscale Two-Dimensional Fuzzy and Dispersion Entropy Measures Using Machine Learning Classification

by Ryan Furlong, Mirvana Hilal, Vincent O’Brien and Anne Humeau-Heurtier

Entropy 2021, 23(10), 1303; https://doi.org/10.3390/e23101303 - 3 Oct 2021

Cited by 10 | Viewed by 2256

Abstract

Two-dimensional fuzzy entropy, dispersion entropy, and their multiscale extensions (

{MFuzzyEn}_{2 D}

and

{MDispEn}_{2 D}

, respectively) have shown promising results for image classifications. However, these results rely on the selection of key parameters that may largely influence the entropy values [...] Read more.

Two-dimensional fuzzy entropy, dispersion entropy, and their multiscale extensions (

{MFuzzyEn}_{2 D}

and

{MDispEn}_{2 D}

, respectively) have shown promising results for image classifications. However, these results rely on the selection of key parameters that may largely influence the entropy values obtained. Yet, the optimal choice for these parameters has not been studied thoroughly. We propose a study on the impact of these parameters in image classification. For this purpose, the entropy-based algorithms are applied to a variety of images from different datasets, each containing multiple image classes. Several parameter combinations are used to obtain the entropy values. These entropy values are then applied to a range of machine learning classifiers and the algorithm parameters are analyzed based on the classification results. By using specific parameters, we show that both

{MFuzzyEn}_{2 D}

and

{MDispEn}_{2 D}

approach state-of-the-art in terms of image classification for multiple image types. They lead to an average maximum accuracy of more than 95% for all the datasets tested. Moreover,

{MFuzzyEn}_{2 D}

results in a better classification performance than that extracted by

{MDispEn}_{2 D}

as a majority. Furthermore, the choice of classifier does not have a significant impact on the classification of the extracted features by both entropy algorithms. The results open new perspectives for these entropy-based measures in textural analysis. Full article

(This article belongs to the Special Issue Entropy in the Application of Biomedical Signals)

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11 pages, 2702 KiB

Open AccessArticle

Multi-Scale Permutation Entropy: A Potential Measure for the Impact of Sleep Medication on Brain Dynamics of Patients with Insomnia

by Yanping Guo, Yingying Chen, Qianru Yang, Fengzhen Hou, Xinyu Liu and Yan Ma

Entropy 2021, 23(9), 1101; https://doi.org/10.3390/e23091101 - 25 Aug 2021

Cited by 2 | Viewed by 2076

Abstract

Insomnia is a common sleep disorder that is closely associated with the occurrence and deterioration of cardiovascular disease, depression and other diseases. The evaluation of pharmacological treatments for insomnia brings significant clinical implications. In this study, a total of 20 patients with mild insomnia and 75 healthy subjects as controls (HC) were included to explore alterations of electroencephalogram (EEG) complexity associated with insomnia and its pharmacological treatment by using multi-scale permutation entropy (MPE). All participants were recorded for two nights of polysomnography (PSG). The patients with mild insomnia received a placebo on the first night (Placebo) and temazepam on the second night (Temazepam), while the HCs had no sleep-related medication intake for either night. EEG recordings from each night were extracted and analyzed using MPE. The results showed that MPE decreased significantly from pre-lights-off to the period during sleep transition and then to the period after sleep onset, and also during the deepening of sleep stage in the HC group. Furthermore, results from the insomnia subjects showed that MPE values were significantly lower for the Temazepam night compared to MPE values for the Placebo night. Moreover, MPE values for the Temazepam night showed no correlation with age or gender. Our results indicated that EEG complexity, measured by MPE, may be utilized as an alternative approach to measure the impact of sleep medication on brain dynamics. Full article

(This article belongs to the Special Issue Entropy in the Application of Biomedical Signals)

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18 pages, 1011 KiB

Open AccessArticle

Benchmarking Transfer Entropy Methods for the Study of Linear and Nonlinear Cardio-Respiratory Interactions

by Andrea Rozo, John Morales, Jonathan Moeyersons, Rohan Joshi, Enrico G. Caiani, Pascal Borzée, Bertien Buyse, Dries Testelmans, Sabine Van Huffel and Carolina Varon

Entropy 2021, 23(8), 939; https://doi.org/10.3390/e23080939 - 23 Jul 2021

Cited by 10 | Viewed by 2635

Abstract

Transfer entropy (

T E

) has been used to identify and quantify interactions between physiological systems. Different methods exist to estimate

T E

, but there is no consensus about which one performs best in specific applications. In this study, five methods [...] Read more.

Transfer entropy (

T E

) has been used to identify and quantify interactions between physiological systems. Different methods exist to estimate

T E

, but there is no consensus about which one performs best in specific applications. In this study, five methods (linear, k-nearest neighbors, fixed-binning with ranking, kernel density estimation and adaptive partitioning) were compared. The comparison was made on three simulation models (linear, nonlinear and linear + nonlinear dynamics). From the simulations, it was found that the best method to quantify the different interactions was adaptive partitioning. This method was then applied on data from a polysomnography study, specifically on the ECG and the respiratory signals (nasal airflow and respiratory effort around the thorax). The hypothesis that the linear and nonlinear components of cardio-respiratory interactions during light and deep sleep change with the sleep stage, was tested. Significant differences, after performing surrogate analysis, indicate an increased

T E

during deep sleep. However, these differences were found to be dependent on the type of respiratory signal and sampling frequency. These results highlight the importance of selecting the appropriate signals, estimation method and surrogate analysis for the study of linear and nonlinear cardio-respiratory interactions. Full article

(This article belongs to the Special Issue Entropy in the Application of Biomedical Signals)

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