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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: closed (31 January 2016) | Viewed by 86677

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Prof. Dr. Raúl Alcaraz

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Research Group in Electronic, Biomedical and Telecommunication Engineering, Universidad de Castilla-La Mancha, Campus Universitario s/n, 16071 Cuenca, Spain
Interests: entropy; complexity; information theory; information geometry; nonlinear dynamics; computational mathematics and statistics in medicine; biomedical time series analysis; cardiac signal processing
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Dear Colleagues,

Beyond its original home in communication engineering, Information Theory (IT) has recently found a multitude of applications in an emerging area, bioengineering. Scientifically, it is very natural to consider some physiological systems as communication channels, and so analyze their information content. For instance, this has been particularly successful for neural systems. However, IT has also been applied to systems that are not designed to function as communication devices. In this case, the concepts involved only require well-defined probability distributions. Within this context, in the last years, metrics based on a wide variety of entropy, divergence, and distance definitions have been used to reveal clinically useful information from physiological recordings, such as electrocardiograms (ECG), electroencephalograms (EEG), electromyograms (EMG), or intracranial pressure (ICP) signals, among others. Similarly, the application of these concepts to medical images obtained from computed tomography (CT), medical resonance imaging (MRI) or positron emission tomography (PET) has also allowed to develop fast, reliable and accurate algorithms for their segmentation and registration. Moreover, it is worth noting that the information provided in this way is mainly related to underlying mechanisms, which cannot be quantified directly by clinicians in an exploratory examination, thus, providing a significant knowledge increase of diseases that still represent a clinical challenge.

The main goal of this Special Issue is to disseminate new and original research based on the use of IT concepts in clinical contexts to assist in the proper diagnosis and therapeutical decision-making of complex diseases. Nonetheless, manuscripts summarizing the most recent state-of-the-art of this topic will also be welcome.

Prof. Dr. Raúl Alcaraz Martínez
Guest Editor

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Keywords

Entropy or information content: Shannon entropy, Sample entropy, Rényi entropy, etc.
Joint entropy, conditional entropy and relative entropy.
Mutual information and Kullback-Leibler divergence.
Symbolic dynamics and coding.
Optimal coding.
Physiological signal processing (ECG, EEG, EMG ICP, etc.).
Medical image processing (CT, MRI, PET, SPECT, etc.).

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Information Theory Applied to Physiological Signals in Entropy (19 articles)

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Research

1752 KiB

Open AccessArticle

Acoustic Detection of Coronary Occlusions before and after Stent Placement Using an Electronic Stethoscope

by Andrei Dragomir, Allison Post, Yasemin M. Akay, Hani Jneid, David Paniagua, Ali Denktas, Biykem Bozkurt and Metin Akay

Entropy 2016, 18(8), 281; https://doi.org/10.3390/e18080281 - 29 Jul 2016

Cited by 9 | Viewed by 8192

Abstract

More than 370,000 Americans die every year from coronary artery disease (CAD). Early detection and treatment are crucial to reducing this number. Current diagnostic and disease-monitoring methods are invasive, costly, and time-consuming. Using an electronic stethoscope and spectral and nonlinear dynamics analysis of the recorded heart sound, we investigated the acoustic signature of CAD in subjects with only a single coronary occlusion before and after stent placement, as well as subjects with clinically normal coronary arteries. The CAD signature was evaluated by estimating power ratios of the total power above 150 Hz over the total power below 150 Hz of the FFT of the acoustic signal. Additionally, approximate entropy values were estimated to assess the differences induced by the stent placement procedure to the acoustic signature of the signals in the time domain. The groups were identified with this method with 82% sensitivity and 64% specificity (using the power ratio method) and 82% sensitivity and 55% specificity (using the approximate entropy). Power ratios and approximate entropy values after stent placement are not statistically different from those estimated from subjects with no coronary occlusions. Our approach demonstrates that the effect of stent placement on coronary occlusions can be monitored using an electronic stethoscope. Full article

(This article belongs to the Special Issue Recent Advances in Information Theory Application to Physiological Signals)

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3753 KiB

Open AccessArticle

Application of Entropy-Based Metrics to Identify Emotional Distress from Electroencephalographic Recordings

by Beatriz García-Martínez, Arturo Martínez-Rodrigo, Roberto Zangróniz Cantabrana, Jose Manuel Pastor García and Raúl Alcaraz

Entropy 2016, 18(6), 221; https://doi.org/10.3390/e18060221 - 3 Jun 2016

Cited by 60 | Viewed by 8233

Abstract

Recognition of emotions is still an unresolved challenge, which could be helpful to improve current human-machine interfaces. Recently, nonlinear analysis of some physiological signals has shown to play a more relevant role in this context than their traditional linear exploration. Thus, the present work introduces for the first time the application of three recent entropy-based metrics: sample entropy (SE), quadratic SE (QSE) and distribution entropy (DE) to discern between emotional states of calm and negative stress (also called distress). In the last few years, distress has received growing attention because it is a common negative factor in the modern lifestyle of people from developed countries and, moreover, it may lead to serious mental and physical health problems. Precisely, 279 segments of 32-channel electroencephalographic (EEG) recordings from 32 subjects elicited to be calm or negatively stressed have been analyzed. Results provide that QSE is the first single metric presented to date with the ability to identify negative stress. Indeed, this metric has reported a discriminant ability of around 70%, which is only slightly lower than the one obtained by some previous works. Nonetheless, discriminant models from dozens or even hundreds of features have been previously obtained by using advanced classifiers to yield diagnostic accuracies about 80%. Moreover, in agreement with previous neuroanatomy findings, QSE has also revealed notable differences for all the brain regions in the neural activation triggered by the two considered emotions. Consequently, given these results, as well as easy interpretation of QSE, this work opens a new standpoint in the detection of emotional distress, which may gain new insights about the brain’s behavior under this negative emotion. Full article

(This article belongs to the Special Issue Recent Advances in Information Theory Application to Physiological Signals)

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1631 KiB

Open AccessArticle

Specific Differential Entropy Rate Estimation for Continuous-Valued Time Series

by David Darmon

Entropy 2016, 18(5), 190; https://doi.org/10.3390/e18050190 - 19 May 2016

Cited by 19 | Viewed by 6547

Abstract

We introduce a method for quantifying the inherent unpredictability of a continuous-valued time series via an extension of the differential Shannon entropy rate. Our extension, the specific entropy rate, quantifies the amount of predictive uncertainty associated with a specific state, rather than averaged over all states. We provide a data-driven approach for estimating the specific entropy rate of an observed time series. Finally, we consider three case studies of estimating the specific entropy rate from synthetic and physiological data relevant to the analysis of heart rate variability. Full article

(This article belongs to the Special Issue Recent Advances in Information Theory Application to Physiological Signals)

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1171 KiB

Open AccessArticle

Fatiguing Effects on the Multi-Scale Entropy of Surface Electromyography in Children with Cerebral Palsy

by Tong Hong, Xu Zhang, Hongjun Ma, Yan Chen and Xiang Chen

Entropy 2016, 18(5), 177; https://doi.org/10.3390/e18050177 - 10 May 2016

Cited by 15 | Viewed by 4959

Abstract

The objective of this study was to investigate the effects of muscle fatigue on the multi-scale entropy of surface electromyography (EMG) in children with cerebral palsy (CP) and typical development (TD). Sixteen CP children and eighteen TD children participated in experiments where they performed upper limb cyclic lifting tasks following a muscle fatiguing process, while the surface EMG signals were recorded from their upper trapezius muscles. Multi-scale entropy (MSE) analyses of the surface EMG were applied by calculating sample entropy (SampEn) on individual intrinsic mode functions (IMFs) adaptively generated by empirical mode decomposition (EMD) of the original signal. The declining degree of the resultant MSE curve was found to reflect muscle fatigue level for all subjects, with its slope (purposely calculated over the first four scales) increasing significantly as the fatigue level increased. Further, such a slope increase was less significant for CP children as compared with TD children. Our findings confirmed that the decrease of muscle fiber conduction velocity (MFCV) and the increase of motor unit synchronization may be two possible factors induced by muscle fatigue, and further indicated that there appear to be some neuromuscular changes (such as MFCV decrease, motor unit synchronization increase, motor unit firing rates reduction, selective loss of larger motor units) that occur as a result of cerebral palsy. These changes may account for experimentally observed difference in fatiguing effects between subject groups. Our study provides an investigative tool to assess muscle fatigue as well as to help reveal complex neuropathological changes underlying the motor impairments of CP children. Full article

(This article belongs to the Special Issue Recent Advances in Information Theory Application to Physiological Signals)

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2236 KiB

Open AccessArticle

Measuring Electromechanical Coupling in Patients with Coronary Artery Disease and Healthy Subjects

by Lizhen Ji, Peng Li, Chengyu Liu, Xinpei Wang, Jing Yang and Changchun Liu

Entropy 2016, 18(4), 153; https://doi.org/10.3390/e18040153 - 21 Apr 2016

Cited by 7 | Viewed by 5536

Abstract

Coronary artery disease (CAD) is the most common cause of death globally. To detect CAD noninvasively at an early stage before clinical symptoms occur is still nowadays challenging. Analysis of the variation of heartbeat interval (RRI) opens a new avenue for evaluating the functional change of cardiovascular system which is accepted to occur at the subclinical stage of CAD. In addition, systolic time interval (STI) and diastolic time interval (DTI) also show potential. There may be coupling in these electromechanical time series due to their physiological connection. However, to the best of our knowledge no publication has systematically investigated how can the coupling be measured and how it changes in CAD patients. In this study, we enrolled 39 CAD patients and 36 healthy subjects and for each subject the electrocardiogram (ECG) and photoplethysmography (PPG) signals were recorded simultaneously for 5 min. The RRI series, STI series, and DTI series were constructed, respectively. We used linear cross correlation (CC), coherence function (CF), as well as nonlinear mutual information (MI), cross conditional entropy (XCE), cross sample entropy (XSampEn), and cross fuzzy entropy (XFuzzyEn) to analyse the bivariate RRI-DTI coupling, RRI-STI coupling, and STI-DTI coupling, respectively. Our results suggest that the linear CC and CF generally have no significant difference between the two groups for all three types of bivariate coupling. The MI only shows weak change in RRI-DTI coupling. By comparison, the three entropy-based coupling measurements show significantly decreased coupling in CAD patients except XSampEn for RRI-DTI coupling (less significant) and XCE for STI-DTI and RRI-STI coupling (not significant). Additionally, the XFuzzyEn performs best as it was still significant if we further applied the Bonferroni correction in our statistical analysis. Our study indicates that the intrinsic electromechanical coupling is most probably nonlinear and can better be measured by nonlinear entropy-based measurements especially the XFuzzyEn. Besides, CAD patients are accompanied by a loss of electromechanical coupling. Our results suggest that cardiac electromechanical coupling may potentially serve as a noninvasive diagnostic tool for CAD. Full article

(This article belongs to the Special Issue Recent Advances in Information Theory Application to Physiological Signals)

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1073 KiB

Open AccessArticle

Complexity Analysis of Surface EMG for Overcoming ECG Interference toward Proportional Myoelectric Control

by Xu Zhang, Xiaoting Ren, Xiaoping Gao, Xiang Chen and Ping Zhou

Entropy 2016, 18(4), 106; https://doi.org/10.3390/e18040106 - 30 Mar 2016

Cited by 20 | Viewed by 9399

Abstract

Electromyographic (EMG) signals from muscles in the body torso are often contaminated by electrocardiography (ECG) interferences, which consequently compromise EMG intensity estimation. The ECG interference has become a barrier to proportional control of myoelectric prosthesis using a neural machine interface called targeted muscle reinnervation (TMR), which involves transferring the residual amputated nerves to nonfunctional muscles (typically pectoralis muscles for high level amputations). This study investigates a novel approach toward implementation of proportional myoelectric control by applying sample entropy (SampEn) analysis of surface EMG signals for robust intensity estimation in the presence of significant ECG interference. Surface EMG data from able-bodied and TMR amputee subjects with different degrees of ECG interference were used for performance evaluation. The results showed that the SampEn analysis had high correlation with surface EMG amplitude measurement but low sensitivity to different degrees of ECG interference. Taking this advantage, SampEn analysis of surface EMG signal can be used to facilitate implementation of proportional myoelectric control against ECG interference. This is particularly important for TMR prosthesis users. Full article

(This article belongs to the Special Issue Recent Advances in Information Theory Application to Physiological Signals)

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611 KiB

Open AccessArticle

Assessment of Nociceptive Responsiveness Levels during Sedation-Analgesia by Entropy Analysis of EEG

by José F. Valencia, Umberto S. P. Melia, Montserrat Vallverdú, Xavier Borrat, Mathieu Jospin, Erik W. Jensen, Alberto Porta, Pedro L. Gambús and Pere Caminal

Entropy 2016, 18(3), 103; https://doi.org/10.3390/e18030103 - 18 Mar 2016

Cited by 10 | Viewed by 6240

Abstract

The level of sedation in patients undergoing medical procedures is decided to assure unconsciousness and prevent pain. The monitors of depth of anesthesia, based on the analysis of the electroencephalogram (EEG), have been progressively introduced into the daily practice to provide additional information about the state of the patient. However, the quantification of analgesia still remains an open problem. The purpose of this work was to analyze the capability of prediction of nociceptive responses based on refined multiscale entropy (RMSE) and auto mutual information function (AMIF) applied to EEG signals recorded in 378 patients scheduled to undergo ultrasonographic endoscopy under sedation-analgesia. Two observed categorical responses after the application of painful stimulation were analyzed: the evaluation of the Ramsay Sedation Scale (RSS) after nail bed compression and the presence of gag reflex (GAG) during endoscopy tube insertion. In addition, bispectrum (BIS), heart rate (HR), predicted concentrations of propofol (CeProp) and remifentanil (CeRemi) were annotated with a resolution of 1 s. Results showed that functions based on RMSE, AMIF, HR and CeRemi permitted predicting different stimulation responses during sedation better than BIS. Full article

(This article belongs to the Special Issue Recent Advances in Information Theory Application to Physiological Signals)

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1192 KiB

Open AccessArticle

Local Band Spectral Entropy Based on Wavelet Packet Applied to Surface EMG Signals Analysis

by Xiaoling Chen, Ping Xie, Huan Liu, Yan Song and Yihao Du

Entropy 2016, 18(2), 41; https://doi.org/10.3390/e18020041 - 26 Jan 2016

Cited by 7 | Viewed by 6259

Abstract

An efficient analytical method for electromyogram (EMG) signals is of great significance to research the inherent mechanism of a motor-control system. In this paper, we proposed an improved approach named wavelet-packet-based local band spectral entropy (WP-LBSE) by introducing the concept of frequency band local-energy (ELF) into the wavelet packet entropy, in order to characterize the time-varying complexity of the EMG signals in the local frequency band. The EMG data were recorded from the biceps brachii (BB) muscle and triceps brachii (TB) muscle at 40°, 100° and 180° of elbow flexion by 10 healthy participants. Significant differences existed among any pair of the three patterns (p < 0.05). The WP-LBSE values of the EMG signals in BB muscle and TB muscle demonstrated a decreased tendency from 40° to 180° of elbow flexion, while the distributions of spectral energy were decreased to a stable state as time periods progressed under the same pattern. The result of this present work is helpful to describe the time-varying complexity characteristics of the EMG signals under different joint angles, and is meaningful to research the dynamic variation of the activated motor units and muscle fibers in the motor-control system. Full article

(This article belongs to the Special Issue Recent Advances in Information Theory Application to Physiological Signals)

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482 KiB

Open AccessArticle

The Entropy of Laughter: Discriminative Power of Laughter’s Entropy in the Diagnosis of Depression

by Jorge Navarro, Raquel Del Moral, Pedro Cuesta-Alvaro, Rafael Lahoz-Beltra and Pedro C. Marijuán

Entropy 2016, 18(1), 36; https://doi.org/10.3390/e18010036 - 21 Jan 2016

Cited by 4 | Viewed by 9386

Abstract

Laughter is increasingly present in biomedical literature, both in analytical neurological aspects and in applied therapeutic fields. The present paper, bridging between the analytical and the applied, explores the potential of a relevant variable of laughter’s acoustic signature—entropy—in the detection of a widespread mental disorder, depression, as well as in gauging the severity of its diagnostic. In laughter, the Shannon–Wiener entropy of the distribution of sound frequencies, which is one of the key features distinguishing its acoustic signal from the utterances of spoken language, has not been a specific focus of research yet, although the studies of human language and of animal communication have pointed out that entropy is a very important factor regarding the vocal/acoustic expression of emotions. As the experimental survey of laughter in depression herein undertaken shows, it was possible to discriminate between patients and controls with an 82.1% accuracy just by using laughter’s entropy and by applying the decision tree procedure. These experimental results, discussed in the light of the current research on laughter, point to the relevance of entropy in the spontaneous bona fide extroversion of mental states toward other individuals, as the signal of laughter seems to imply. This is in line with recent theoretical approaches that rely on the optimization of a neuro-informational free energy (and associated entropy) as the main “stuff” of brain processing. Full article

(This article belongs to the Special Issue Recent Advances in Information Theory Application to Physiological Signals)

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512 KiB

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Measures of Morphological Complexity of Gray Matter on Magnetic Resonance Imaging for Control Age Grouping

by Tuan D. Pham, Taishi Abe, Ryuichi Oka and Yung-Fu Chen

Entropy 2015, 17(12), 8130-8151; https://doi.org/10.3390/e17127868 - 9 Dec 2015

Cited by 10 | Viewed by 5646

Abstract

Current brain-age prediction methods using magnetic resonance imaging (MRI) attempt to estimate the physiological brain age via some kind of machine learning of chronological brain age data to perform the classification task. Such a predictive approach imposes greater risk of either over-estimate or under-estimate, mainly due to limited training data. A new conceptual framework for more reliable MRI-based brain-age prediction is by systematic brain-age grouping via the implementation of the phylogenetic tree reconstruction and measures of information complexity. Experimental results carried out on a public MRI database suggest the feasibility of the proposed concept. Full article

(This article belongs to the Special Issue Recent Advances in Information Theory Application to Physiological Signals)

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883 KiB

Open AccessArticle

Analysis of Neural Oscillations on Drosophila’s Subesophageal Ganglion Based on Approximate Entropy

by Tian Mei, Jingda Qiao, Yi Zhou, Huaiyu Gu, Ziyi Chen, Xianghua Tian and Kuiying Gu

Entropy 2015, 17(10), 6854-6871; https://doi.org/10.3390/e17106854 - 10 Oct 2015

Cited by 2 | Viewed by 6060

Abstract

The suboesophageal ganglion (SOG), which connects to both central and peripheral nerves, is the primary taste-processing center in the Drosophila’s brain. The neural oscillation in this center may be of great research value yet it is rarely reported. This work aims to determine the amount of unique information contained within oscillations of the SOG and describe the variability of these patterns. The approximate entropy (ApEn) values of the spontaneous membrane potential (sMP) of SOG neurons were calculated in this paper. The arithmetic mean (MA), standard deviation (SDA) and the coefficient of variation (CVA) of ApEn were proposed as the three statistical indicators to describe the irregularity and complexity of oscillations. The hierarchical clustering method was used to classify them. As a result, the oscillations in SOG were divided into five categories, including: (1) Continuous spike pattern; (2) Mixed oscillation pattern; (3) Spikelet pattern; (4) Busting pattern and (5) Sparse spike pattern. Steady oscillation state has a low level of irregularity, and vice versa. The dopamine stimulation can distinctly cut down the complexity of the mixed oscillation pattern. The current study provides a quantitative method and some critera on mining the information carried in neural oscillations. Full article

(This article belongs to the Special Issue Recent Advances in Information Theory Application to Physiological Signals)

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326 KiB

Open AccessArticle

Determination of Sample Entropy and Fuzzy Measure Entropy Parameters for Distinguishing Congestive Heart Failure from Normal Sinus Rhythm Subjects

by Lina Zhao, Shoushui Wei, Chengqiu Zhang, Yatao Zhang, Xinge Jiang, Feng Liu and Chengyu Liu

Entropy 2015, 17(9), 6270-6288; https://doi.org/10.3390/e17096270 - 10 Sep 2015

Cited by 75 | Viewed by 8809

Abstract

Entropy provides a valuable tool for quantifying the regularity of physiological time series and provides important insights for understanding the underlying mechanisms of the cardiovascular system. Before any entropy calculation, certain common parameters need to be initialized: embedding dimension m, tolerance threshold r and time series length N. However, no specific guideline exists on how to determine the appropriate parameter values for distinguishing congestive heart failure (CHF) from normal sinus rhythm (NSR) subjects in clinical application. In the present study, a thorough analysis on the selection of appropriate values of m, r and N for sample entropy (SampEn) and recently proposed fuzzy measure entropy (FuzzyMEn) is presented for distinguishing two group subjects. 44 long-term NRS and 29 long-term CHF RR interval recordings from http://www.physionet.org were used as the non-pathological and pathological data respectively. Extreme (>2 s) and abnormal heartbeat RR intervals were firstly removed from each RR recording and then the recording was segmented with a non-overlapping segment length N of 300 and 1000, respectively. SampEn and FuzzyMEn were performed for each RR segment under different parameter combinations: m of 1, 2, 3 and 4, and r of 0.10, 0.15, 0.20 and 0.25 respectively. The statistical significance between NSR and CHF groups under each combination of m, r and N was observed. The results demonstrated that the selection of m, r and N plays a critical role in determining the SampEn and FuzzyMEn outputs. Compared with SampEn, FuzzyMEn shows a better regularity when selecting the parameters m and r. In addition, FuzzyMEn shows a better relative consistency for distinguishing the two groups, that is, the results of FuzzyMEn in the NSR group were consistently lower than those in the CHF group while SampEn were not. The selections of m of 2 and 3 and r of 0.10 and 0.15 for SampEn and the selections of m of 1 and 2 whenever r (herein, r_L = r_G = r) are for FuzzyMEn (in addition to setting n_L = 3 and n_G = 2) were recommended to yield the fine classification results for the NSR and CHF groups. Full article

(This article belongs to the Special Issue Recent Advances in Information Theory Application to Physiological Signals)

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