Entropy

Research

19 pages, 4031 KiB

Open AccessArticle

Theil Entropy as a Non-Lineal Analysis for Spectral Inequality of Physiological Oscillations

by Ramón Carrazana-Escalona, Miguel Enrique Sánchez-Hechavarría and Ariel Ávila

Entropy 2022, 24(3), 370; https://doi.org/10.3390/e24030370 - 4 Mar 2022

Cited by 3 | Viewed by 3010

Theil entropy is a statistical measure used in economics to quantify income inequalities. However, it can be applied to any data distribution including biological signals. In this work, we applied different spectral methods on heart rate variability signals and cellular calcium oscillations previously [...] Read more.

Theil entropy is a statistical measure used in economics to quantify income inequalities. However, it can be applied to any data distribution including biological signals. In this work, we applied different spectral methods on heart rate variability signals and cellular calcium oscillations previously to Theil entropy analysis. The behavior of Theil entropy and its decomposable property was investigated using exponents in the range of [−1, 2], on the spectrum of synthetic and physiological signals. Our results suggest that the best spectral decomposition method to analyze the spectral inequality of physiological oscillations is the Lomb–Scargle method, followed by Theil entropy analysis. Moreover, our results showed that the exponents that provide more information to describe the spectral inequality in the tested signals were zero, one, and two. It was also observed that the intra-band component is the one that contributes the most to total inequality for the studied oscillations. More in detail, we found that in the state of mental stress, the inequality determined by the Theil entropy analysis of heart rate increases with respect to the resting state. Likewise, the same analytical approach shows that cellular calcium oscillations present on developing interneurons display greater inequality distribution when inhibition of a neurotransmitter system is in place. In conclusion, we propose that Theil entropy is useful for analyzing spectral inequality and to explore its origin in physiological signals. Full article

(This article belongs to the Special Issue Entropy in Biomedical Engineering)

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13 pages, 1163 KiB

Open AccessArticle

Cross-Entropy Learning for Aortic Pathology Classification of Artificial Multi-Sensor Impedance Cardiography Signals

by Tobias Spindelböck, Sascha Ranftl and Wolfgang von der Linden

Entropy 2021, 23(12), 1661; https://doi.org/10.3390/e23121661 - 10 Dec 2021

Cited by 4 | Viewed by 2998

Abstract

An aortic dissection, a particular aortic pathology, occurs when blood pushes through a tear between the layers of the aorta and forms a so-called false lumen. Aortic dissection has a low incidence compared to other diseases, but a relatively high mortality that increases [...] Read more.

An aortic dissection, a particular aortic pathology, occurs when blood pushes through a tear between the layers of the aorta and forms a so-called false lumen. Aortic dissection has a low incidence compared to other diseases, but a relatively high mortality that increases with disease progression. An early identification and treatment increases patients’ chances of survival. State-of-the-art medical imaging techniques have several disadvantages; therefore, we propose the detection of aortic dissections through their signatures in impedance cardiography signals. These signatures arise due to pathological blood flow characteristics and a blood conductivity that strongly depends on the flow field, i.e., the proposed method is, in principle, applicable to any aortic pathology that changes the blood flow characteristics. For the signal classification, we trained a convolutional neural network (CNN) with artificial impedance cardiography data based on a simulation model for a healthy virtual patient and a virtual patient with an aortic dissection. The network architecture was tailored to a multi-sensor, multi-channel time-series classification with a categorical cross-entropy loss function as the training objective. The trained network typically yielded a specificity of

(93.9 \pm 0.1) %

and a sensitivity of

(97.5 \pm 0.1) %

. A study of the accuracy as a function of the size of an aortic dissection yielded better results for a small false lumen with larger noise, which emphasizes the question of the feasibility of detecting aortic dissections in an early state. Full article

(This article belongs to the Special Issue Entropy in Biomedical Engineering)

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13 pages, 26288 KiB

Open AccessArticle

Determination of Parameters for an Entropy-Based Atrial Fibrillation Detector

by Lina Zhao, Jianqing Li, Xiangkui Wan, Shoushui Wei and Chengyu Liu

Entropy 2021, 23(9), 1199; https://doi.org/10.3390/e23091199 - 11 Sep 2021

Cited by 3 | Viewed by 2422

Abstract

Entropy algorithm is an important nonlinear method for cardiovascular disease detection due to its power in analyzing short-term time series. In previous a study, we proposed a new entropy-based atrial fibrillation (AF) detector, i.e., Entropy_AF, which showed a high classification accuracy [...] Read more.

Entropy algorithm is an important nonlinear method for cardiovascular disease detection due to its power in analyzing short-term time series. In previous a study, we proposed a new entropy-based atrial fibrillation (AF) detector, i.e., Entropy_AF, which showed a high classification accuracy in identifying AF and non-AF rhythms. As a variation of entropy measures, Entropy_AF has two parameters that need to be initialized before the calculation: (1) tolerance threshold r and (2) similarity weight n. In this study, a comprehensive analysis for the two parameters determination was presented, aiming to achieve a high detection accuracy for AF events. Data were from the MIT-BIH AF database. RR interval recordings were segmented using a 30-beat time window. The parameters r and n were initialized from a relatively small value, then gradually increased, and finally the best parameter combination was determined using grid searching. AUC (area under curve) values from the receiver operator characteristic curve (ROC) were compared under different parameter combinations of parameters r and n, and the results demonstrated that the selection of these two parameters plays an important role in AF/non-AF classification. Small values of parameters r and n can lead to a better detection accuracy than other selections. The best AUC value for AF detection was 98.15%, and the corresponding parameter combinations for Entropy_AF were as follows: r = 0.01, n = 0.0625, 0.125, 0.25, or 0.5; r = 0.05 and n = 0.0625, 0.125, or 0.25; and r = 0.10 and n = 0.0625 or 0.125. Full article

(This article belongs to the Special Issue Entropy in Biomedical Engineering)

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13 pages, 1095 KiB

Open AccessArticle

A Two-Steps-Ahead Estimator for Bubble Entropy

by George Manis, Matteo Bodini, Massimo W. Rivolta and Roberto Sassi

Entropy 2021, 23(6), 761; https://doi.org/10.3390/e23060761 - 16 Jun 2021

Cited by 8 | Viewed by 2671

Abstract

Aims: Bubble entropy (

b E n

) is an entropy metric with a limited dependence on parameters.

b E n

does not directly quantify the conditional entropy of the series, but it assesses the change in entropy of the ordering of [...] Read more.

Aims: Bubble entropy (

b E n

) is an entropy metric with a limited dependence on parameters.

b E n

does not directly quantify the conditional entropy of the series, but it assesses the change in entropy of the ordering of portions of its samples of length m, when adding an extra element. The analytical formulation of

b E n

for autoregressive (AR) processes shows that, for this class of processes, the relation between the first autocorrelation coefficient and

b E n

changes for odd and even values of m. While this is not an issue, per se, it triggered ideas for further investigation. Methods: Using theoretical considerations on the expected values for AR processes, we examined a two-steps-ahead estimator of

b E n

, which considered the cost of ordering two additional samples. We first compared it with the original

b E n

estimator on a simulated series. Then, we tested it on real heart rate variability (HRV) data. Results: The experiments showed that both examined alternatives showed comparable discriminating power. However, for values of

10 < m < 20

, where the statistical significance of the method was increased and improved as m increased, the two-steps-ahead estimator presented slightly higher statistical significance and more regular behavior, even if the dependence on parameter m was still minimal. We also investigated a new normalization factor for

b E n

, which ensures that

b E n

= 1

when white Gaussian noise (WGN) is given as the input. Conclusions: The research improved our understanding of bubble entropy, in particular in the context of HRV analysis, and we investigated interesting details regarding the definition of the estimator. Full article

(This article belongs to the Special Issue Entropy in Biomedical Engineering)

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34 pages, 3057 KiB

Open AccessArticle

CEPS: An Open Access MATLAB Graphical User Interface (GUI) for the Analysis of Complexity and Entropy in Physiological Signals

by David Mayor, Deepak Panday, Hari Kala Kandel, Tony Steffert and Duncan Banks

Entropy 2021, 23(3), 321; https://doi.org/10.3390/e23030321 - 8 Mar 2021

Cited by 20 | Viewed by 8346

Abstract

Background: We developed CEPS as an open access MATLAB^® GUI (graphical user interface) for the analysis of Complexity and Entropy in Physiological Signals (CEPS), and demonstrate its use with an example data set that shows the effects of paced breathing (PB) on [...] Read more.

Background: We developed CEPS as an open access MATLAB^® GUI (graphical user interface) for the analysis of Complexity and Entropy in Physiological Signals (CEPS), and demonstrate its use with an example data set that shows the effects of paced breathing (PB) on variability of heart, pulse and respiration rates. CEPS is also sufficiently adaptable to be used for other time series physiological data such as EEG (electroencephalography), postural sway or temperature measurements. Methods: Data were collected from a convenience sample of nine healthy adults in a pilot for a larger study investigating the effects on vagal tone of breathing paced at various different rates, part of a development programme for a home training stress reduction system. Results: The current version of CEPS focuses on those complexity and entropy measures that appear most frequently in the literature, together with some recently introduced entropy measures which may have advantages over those that are more established. Ten methods of estimating data complexity are currently included, and some 28 entropy measures. The GUI also includes a section for data pre-processing and standard ancillary methods to enable parameter estimation of embedding dimension m and time delay τ (‘tau’) where required. The software is freely available under version 3 of the GNU Lesser General Public License (LGPLv3) for non-commercial users. CEPS can be downloaded from Bitbucket. In our illustration on PB, most complexity and entropy measures decreased significantly in response to breathing at 7 breaths per minute, differentiating more clearly than conventional linear, time- and frequency-domain measures between breathing states. In contrast, Higuchi fractal dimension increased during paced breathing. Conclusions: We have developed CEPS software as a physiological data visualiser able to integrate state of the art techniques. The interface is designed for clinical research and has a structure designed for integrating new tools. The aim is to strengthen collaboration between clinicians and the biomedical community, as demonstrated here by using CEPS to analyse various physiological responses to paced breathing. Full article

(This article belongs to the Special Issue Entropy in Biomedical Engineering)

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Graphical abstract

12 pages, 2849 KiB

Open AccessArticle

Multistage Segmentation of Prostate Cancer Tissues Using Sample Entropy Texture Analysis

by Tariq Ali, Khalid Masood, Muhammad Irfan, Umar Draz, Arfan Ali Nagra, Muhammad Asif, Bandar M. Alshehri, Adam Glowacz, Ryszard Tadeusiewicz, Mater H. Mahnashi and Sana Yasin

Entropy 2020, 22(12), 1370; https://doi.org/10.3390/e22121370 - 4 Dec 2020

Cited by 12 | Viewed by 2803

Abstract

In this study, a multistage segmentation technique is proposed that identifies cancerous cells in prostate tissue samples. The benign areas of the tissue are distinguished from the cancerous regions using the texture of glands. The texture is modeled based on wavelet packet features [...] Read more.

In this study, a multistage segmentation technique is proposed that identifies cancerous cells in prostate tissue samples. The benign areas of the tissue are distinguished from the cancerous regions using the texture of glands. The texture is modeled based on wavelet packet features along with sample entropy values. In a multistage segmentation process, the mean-shift algorithm is applied on the pre-processed images to perform a coarse segmentation of the tissue. Wavelet packets are employed in the second stage to obtain fine details of the structured shape of glands. Finally, the texture of the gland is modeled by the sample entropy values, which identifies epithelial regions from stroma patches. Although there are three stages of the proposed algorithm, the computation is fast as wavelet packet features and sample entropy values perform robust modeling for the required regions of interest. A comparative analysis with other state-of-the-art texture segmentation techniques is presented and dice ratios are computed for the comparison. It has been observed that our algorithm not only outperforms other techniques, but, by introducing sample entropy features, identification of cancerous regions of tissues is achieved with 90% classification accuracy, which shows the robustness of the proposed algorithm. Full article

(This article belongs to the Special Issue Entropy in Biomedical Engineering)

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26 pages, 3842 KiB

Open AccessArticle

On the Variability of Heart Rate Variability—Evidence from Prospective Study of Healthy Young College Students

by Xingran Cui, Leirong Tian, Zhengwen Li, Zikai Ren, Keyang Zha, Xinruo Wei and Chung-Kang Peng

Entropy 2020, 22(11), 1302; https://doi.org/10.3390/e22111302 - 15 Nov 2020

Cited by 18 | Viewed by 4373

Abstract

Heart rate variability (HRV) has been widely used as indices for autonomic regulation, including linear analyses, entropy and multi-scale entropy based nonlinear analyses, and however, it is strongly influenced by the conditions under which the signal is being recorded. To investigate the variability [...] Read more.

Heart rate variability (HRV) has been widely used as indices for autonomic regulation, including linear analyses, entropy and multi-scale entropy based nonlinear analyses, and however, it is strongly influenced by the conditions under which the signal is being recorded. To investigate the variability of healthy HRV under different settings, we recorded electrocardiograph (ECG) signals from 56 healthy young college students (20 h for each participant) at campus using wearable single-lead ECG device. Accurate R peak to R peak (RR) intervals were extracted by combing the advantages of five commonly used R-peak detection algorithms to eliminate data quality influence. Thorough and detailed linear and nonlinear HRV analyses were performed. Variability of HRV metrics were evaluated from five categories: (1) different states of daily activities; (2) different recording time period in the same day during free-running daily activities; (3) body postures of sitting and lying; (4) lying on the left, right and back; and (5) gender influence. For most of the analyzed HRV metrics, significant differences (p < 0.05) were found among different recording conditions within the five categories except lying on different positions. Results suggested that the standardization of ECG data collection and HRV analysis should be implemented in HRV related studies, especially for entropy and multi-scale entropy based analyses. Furthermore, this preliminary study provides reference values of HRV indices under various recording conditions of healthy young subjects that could be useful information for different applications (e.g., health monitoring and management). Full article

(This article belongs to the Special Issue Entropy in Biomedical Engineering)

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25 pages, 5870 KiB

Open AccessArticle

Improving Accuracy of Heart Failure Detection Using Data Refinement

by Jinle Xiong, Xueyu Liang, Lina Zhao, Benny Lo, Jianqing Li and Chengyu Liu

Entropy 2020, 22(5), 520; https://doi.org/10.3390/e22050520 - 2 May 2020

Cited by 5 | Viewed by 3381

Abstract

Due to the wide inter- and intra-individual variability, short-term heart rate variability (HRV) analysis (usually 5 min) might lead to inaccuracy in detecting heart failure. Therefore, RR interval segmentation, which can reflect the individual heart condition, has been a key research challenge for [...] Read more.

Due to the wide inter- and intra-individual variability, short-term heart rate variability (HRV) analysis (usually 5 min) might lead to inaccuracy in detecting heart failure. Therefore, RR interval segmentation, which can reflect the individual heart condition, has been a key research challenge for accurate detection of heart failure. Previous studies mainly focus on analyzing the entire 24-h ECG recordings from all individuals in the database which often led to poor detection rate. In this study, we propose a set of data refinement procedures, which can automatically extract heart failure segments and yield better detection of heart failure. The procedures roughly contain three steps: (1) select fast heart rate sequences, (2) apply dynamic time warping (DTW) measure to filter out dissimilar segments, and (3) pick out individuals with large numbers of segments preserved. A physical threshold-based Sample Entropy (SampEn) was applied to distinguish congestive heart failure (CHF) subjects from normal sinus rhythm (NSR) ones, and results using the traditional threshold were also discussed. Experiment on the PhysioNet/MIT RR Interval Databases showed that in SampEn analysis (embedding dimension m = 1, tolerance threshold r = 12 ms and time series length N = 300), the accuracy value after data refinement has increased to 90.46% from 75.07%. Meanwhile, for the proposed procedures, the area under receiver operating characteristic curve (AUC) value has reached 95.73%, which outperforms the original method (i.e., without applying the proposed data refinement procedures) with AUC of 76.83%. The results have shown that our proposed data refinement procedures can significantly improve the accuracy in heart failure detection. Full article

(This article belongs to the Special Issue Entropy in Biomedical Engineering)

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