Testing pattern synchronization in coupled systems through different entropy-based measures

Which Multivariate Multi-Scale Entropy Algorithm Is More Suitable for Analyzing the EEG Characteristics of Mild Cognitive Impairment?

So far, most articles using the multivariate multi-scale entropy algorithm mainly use algorithms to analyze the multivariable signal complexity without clearly describing what characteristics of signals these algorithms measure and what factors affect these algorithms. This paper analyzes six commonly used multivariate multi-scale entropy algorithms from a new perspective. It clarifies for the first time what characteristics of signals these algorithms measure and which factors affect them. It also studies which algorithm is more suitable for analyzing mild cognitive impairment (MCI) electroencephalograph (EEG) signals. The simulation results show that the multivariate multi-scale sample entropy (mvMSE), multivariate multi-scale fuzzy entropy (mvMFE), and refined composite multivariate multi-scale fuzzy entropy (RCmvMFE) algorithms can measure intra- and inter-channel correlation and multivariable signal complexity. In the joint analysis of coupling and complexity, they all decrease with the decrease in signal complexity and coupling strength, highlighting their advantages in processing related multi-channel signals, which is a discovery in the simulation. Among them, the RCmvMFE algorithm can better distinguish different complexity signals and correlations between channels. It also performs well in anti-noise and length analysis of multi-channel data simultaneously. Therefore, we use the RCmvMFE algorithm to analyze EEG signals from twenty subjects (eight control subjects and twelve MCI subjects). The results show that the MCI group had lower entropy than the control group on the short scale and the opposite on the long scale. Moreover, frontal entropy correlates significantly positively with the Montreal Cognitive Assessment score and Auditory Verbal Learning Test delayed recall score on the short scale.

Investigating the Stroke- and Aging-Related Changes in Global and Instantaneous Intermuscular Coupling Using Cross-Fuzzy Entropy

Intermuscular coupling is essential in the coordination of agonist and antagonist muscles. However, its dynamic characteristics are not fully understood, especially the alterations of intermuscular coupling induced by stroke and aging. This study aimed to investigate the aging- and stroke-related changes in the global and instantaneous intermuscular coupling between agonist and antagonist muscles. In the experiment, 8 patients after stroke, 18 healthy young subjects and 10 healthy middle-aged subjects were recruited and instructed to finish the elbow flexion and extension tasks. Cross-fuzzy entropy (C-FuzzyEn) and instantaneous C-FuzzyEn ( [Formula: see text]-FuzzyEn) based on a sliding window were used to analyze the global and instantaneous intermuscular coupling, respectively. Instantaneous FuzzyEn ( i -FuzzyEn) based on a sliding window was also applied to investigate the dynamic complexity of the EMG segment. Pearson correlation analysis revealed that i -FuzzyEn values were negatively correlated with [Formula: see text]-FuzzyEn values in most cases, which implied that there was a positive correlation between EMG complexity and intermuscular coupling. The C-FuzzyEn values between agonist and antagonist muscles increased significantly in both tasks of the patients after stroke than those of the healthy subjects (p < 0.05), which might be due to the decrease in intermuscular coupling induced by the damage of the corticospinal pathways after stroke. The combined application of C-FuzzyEn, [Formula: see text]-FuzzyEn and i -FuzzyEn provides a more comprehensive understanding of the global and instantaneous intermuscular coupling.

Discrimination of Patients with Varying Degrees of Coronary Artery Stenosis by ECG and PCG Signals Based on Entropy

Coronary heart disease (CHD) is the leading cause of cardiovascular death. This study aimed to propose an effective method for mining cardiac mechano-electric coupling information and to evaluate its ability to distinguish patients with varying degrees of coronary artery stenosis (VDCAS). Five minutes of electrocardiogram and phonocardiogram signals was collected synchronously from 191 VDCAS patients to construct heartbeat interval (RRI)-systolic time interval (STI), RRI-diastolic time interval (DTI), HR-corrected QT interval (QTcI)-STI, QTcI-DTI, Tpeak-Tend interval (TpeI)-STI, TpeI-DTI, Tpe/QT interval (Tpe/QTI)-STI, and Tpe/QTI-DTI series. Then, the cross sample entropy (XSampEn), cross fuzzy entropy (XFuzzyEn), joint distribution entropy (JDistEn), magnitude-squared coherence function, cross power spectral density, and mutual information were applied to evaluate the coupling of the series. Subsequently, support vector machine recursive feature elimination and XGBoost were utilized for feature selection and classification, respectively. Results showed that the joint analysis of XSampEn, XFuzzyEn, and JDistEn had the best ability to distinguish patients with VDCAS. The classification accuracy of severe CHD-mild-to-moderate CHD group, severe CHD-chest pain and normal coronary angiography (CPNCA) group, and mild-to-moderate CHD-CPNCA group were 0.8043, 0.7659, and 0.7500, respectively. The study indicates that the joint analysis of XSampEn, XFuzzyEn, and JDistEn can effectively capture the cardiac mechano-electric coupling information of patients with VDCAS, which can provide valuable information for clinicians to diagnose CHD.

Multiscale Transfer Spectral Entropy for Quantifying Corticomuscular Interaction

Corticomuscular coupling reflects nonlinear interactions and multi-layer neural information transmission between the motor cortex and effector muscle in the sensorimotor system. Transfer spectral entropy (TSE) method has been used to describe corticomuscular coupling within single scale. As an extension of TSE, multiscale transfer spectral entropy (MSTSE) is proposed in this paper to depict multi-layer of neural information transfer between two coupling signals. The reliability and effectiveness of MSTSE were verified on data generated by nonlinear numerical models and those of a force tracking task. Compared with TSE, MSTSE is more robust to the embedding dimension and performs optimally in the detection of the coupling properties. Further analysis of the physiological signals showed that the MSTSE provided more detailed band characteristics than the single scale TSE measurement. MSTSE indicates significant coupling scattered in alpha, beta and low gamma bands during the force tracking task. Besides, the coupling strength in the descending direction of the beta band was significantly higher than that in the ascending direction. This study constructs multi-scale coupling information to provide a new perspective for exploring corticomuscular interaction.

Short-Term Effect of Percutaneous Coronary Intervention on Heart Rate Variability in Patients with Coronary Artery Disease

Myocardial ischemia in patients with coronary artery disease (CAD) leads to imbalanced autonomic control that increases the risk of morbidity and mortality. To systematically examine how autonomic function responds to percutaneous coronary intervention (PCI) treatment, we analyzed data of 27 CAD patients who had admitted for PCI in this pilot study. For each patient, five-minute resting electrocardiogram (ECG) signals were collected before and after the PCI procedure. The time intervals between ECG collection and PCI were both within 24 h. To assess autonomic function, normal sinus RR intervals were extracted and were analyzed quantitatively using traditional linear time- and frequency-domain measures [i.e., standard deviation of the normal-normal intervals (SDNN), the root mean square of successive differences (RMSSD), powers of low frequency (LF) and high frequency (HF) components, LF/HF] and nonlinear entropy measures [i.e., sample entropy (SampEn), distribution entropy (DistEn), and conditional entropy (CE)], as well as graphical metrics derived from Poincaré plot [i.e., Porta’s index (PI), Guzik’s index (GI), slope index (SI) and area index (AI)]. Results showed that after PCI, AI and PI decreased significantly (p < 0.002 and 0.015, respectively) with effect sizes of 0.88 and 0.70 as measured by Cohen’s d static. These changes were independent of sex. The results suggest that graphical AI and PI metrics derived from Poincaré plot of short-term ECG may be potential for sensing the beneficial effect of PCI on cardiovascular autonomic control. Further studies with bigger sample sizes are warranted to verify these observations.

Transfer Information Assessment in Diagnosis of Vasovagal Syncope Using Transfer Entropy

The paper presents an application of Transfer Entropy (TE) to the analysis of information transfer between biosignals (heart rate expressed as R-R intervals (RRI), blood pressure (sBP, dBP) and stroke volume (SV)) measured during head up tilt testing (HUTT) in patients with suspected vasovagal syndrome. The study group comprised of 80 patients who were divided into two groups: the HUTT(+) group consisting of 57 patients who developed syncope during the passive phase of the test and HUTT(-) group consisting of 23 patients who had a negative result of the passive phase and experienced syncope after provocation with nitroglycerin. In both groups the information transfer depends on the phase of the tilt test. In supine position the highest transfer occurred between driver RRI and other components. In upright position it is the driver sBP that plays the crucial role. The pre-syncope phase features the highest information transfer from driver SV to blood pressure components. In each group the comparisons of TE between different phases of HUT test showed significant differences for RRI and SV as drivers.

Cardiorespiratory Coupling Analysis Based on Entropy and Cross-Entropy in Distinguishing Different Depression Stages

Aims

This study used entropy- and cross entropy-based methods to explore the cardiorespiratory coupling of depressive patients, and thus to assess the values of those entropy methods for identifying depression patients with different disease severities.

Methods

Electrocardiogram (ECG) and respiration signals from 69 depression patients were recorded simultaneously for 5 min. Patients were classified into three groups according to the Hamilton Depression Rating Scale (HDRS) scores: group Non-De (HDRS 0–7), Mid-De (HDRS 8–17), and Con-De (HDRS >17). Sample entropy (SEn), fuzzy measure entropy (FMEn) and high-frequency power (HF) were computed on the original RR interval time series and breath-to-breath interval time series. Cross sample entropy (CSEn) and cross fuzzy measure entropy (CFMEn) were computed on interval time series resampled at 2 Hz and 4 Hz, respectively. The difference among three patient groups and correlation between entropy values and HDRS scores were analyzed by statistical analysis. Surrogate data were also employed to confirm the validation of entropy measures in this study.

Results

A consistent increasing trend has been found among most entropy measures from Non-De, to Mid-De, and to Con-De groups, and a significant (p < 0.05) difference in FMEn of RR intervals exists between Non-De and Mid-De or Con-De groups. Significant differences have been also found in all cross entropies, between Non-De and Con-De groups and between Mid-De and Con-De groups. Furthermore, significant correlations also exist between HDRS scores and FMEn of RR intervals (R = 0.24, p < 0.05), CSEn at 4 Hz (R = 0.26, p < 0.05) or 2 Hz (R = 0.28, p < 0.05) resampling, and CFMEn at 4 Hz (R = 0.31, p < 0.01) or 2 Hz (R = 0.30, p < 0.05) resampling. A significant difference of cardiorespiratory coupling parameters between different depression stages and significant correlations between entropy measures and depression severity both indicate central autonomic dysregulation in depression patients and reflect varying degrees of vagal modulation reduction among different depression levels. Analysis based on surrogate data confirms that the non-linear properties of the physiological signals played a major role in depression recognition.

Conclusion

The current study demonstrates the potential of cardiorespiratory coupling in the auxiliary diagnosis of depression based on the entropy method.

Multidimensional and fuzzy sample entropy (SampEnMF) for quantifying H&E histological images of colorectal cancer

In this study, we propose to use a method based on the combination of sample entropy with multiscale and multidimensional approaches, along with a fuzzy function. The model was applied to quantify and classify H&E histological images of colorectal cancer. The multiscale approach was defined by analysing windows of different sizes and variations in tolerance for determining pattern similarity. The multidimensional strategy was performed by considering each pixel in the colour image as an n-dimensional vector, which was analysed from the Minkowski distance. The fuzzy strategy was a Gaussian function used to verify the pertinence of the distances between windows. The result was a method capable of computing similarities between pixels contained in windows of various sizes, as well as the information present in the colour channels. The power of quantification was tested in a public colorectal image dataset, which was composed of both benign and malignant classes. The results were given as inputs for classifiers of different categories and analysed by applying the k-fold cross-validation and holdout methods. The derived performances indicate that the proposed association was capable of distinguishing the benign and malignant groups, with values that surpassed those results obtained with important techniques available in the Literature. The best performance was an AUC value of 0.983, an important result, mainly when we consider the difficulties of clinical practice for the diagnosis of the colorectal cancer.

Optimization of relative parameters in transfer entropy estimation and application to corticomuscular coupling in humans

BACKGROUND

As a non-modeled information theoretical measure, the transfer entropy (TE) could be applied to quantitatively analyze the linear and nonlinear coupling characteristics between two observations. However, the parameters selection of TE (the parameters used in state space reconstruction and estimating Shannon entropy) has a serious influence on the accuracy of its results.

NEW METHOD

In this study, the hybrid particle swarm optimization (HPSO) was applied to improve the accuracy of TE by optimizing its parameters. In HPSO, the TE calculation and significant analysis were integrated into the fitness function, and the optimal parameters group within the parameter space could be automatically found through an iteration process.

RESULTS

The TE results computed under the parameters optimized by HPSO (HPSO-TE), was assessed with a numerical non-linear model, the neural mass model and the recorded electroencephalogram (EEG) and electromyogram (EMG) signals. Compared with TE, HPSO-TE could reduce the 'false positive' in non-linear model, and 'spurious coupling', i.e. two nonzero TEs for unidirectionally coupled systems, especially when coupling strength was weak. The robustness against noise and long time-delay was improved. Moreover, the experimental data analysis showed HPSO-TE revealed the dominant direction (EEG → EMG) in corticomuscular coupling, and had higher values than TE which showed the same dominant direction.

COMPARISON WITH EXISTING METHOD

The implication of HPSO improved the accuracy of TE in estimating the coupling strength and direction.

CONCLUSIONS

The efficiency of TE could be improved by HPSO for estimating coupling relationships, especially for weakly coupled, strong noisy and long time-delay series.

Area asymmetry of heart rate variability signal

BACKGROUND

Heart rate fluctuates beat-by-beat asymmetrically which is known as heart rate asymmetry (HRA). It is challenging to assess HRA robustly based on short-term heartbeat interval series.

METHOD

An area index (AI) was developed that combines the distance and phase angle information of points in the Poincaré plot. To test its performance, the AI was used to classify subjects with: (i) arrhythmia, and (ii) congestive heart failure, from the corresponding healthy controls. For comparison, the existing Porta's index (PI), Guzik's index (GI), and slope index (SI) were calculated. To test the effect of data length, we performed the analyses separately using long-term heartbeat interval series (derived from >3.6-h ECG) and short-term segments (with length of 500 intervals). A second short-term analysis was further carried out on series extracted from 5-min ECG.

RESULTS

For long-term data, SI showed acceptable performance for both tasks, i.e., for task i p < 0.001, Cohen's d = 0.93, AUC (area under the receiver-operating characteristic curve) = 0.86; for task ii p < 0.001, d = 0.88, AUC = 0.75. AI performed well for task ii (p < 0.001, d = 1.0, AUC = 0.78); for task i, though the difference was statistically significant (p < 0.001, AUC = 0.76), the effect size was small (d = 0.11). PI and GI failed in both tasks (p > 0.05, d < 0.4, AUC < 0.7 for all). However, for short-term segments, AI indicated better distinguishability for both tasks, i.e., for task i, p < 0.001, d = 0.71, AUC = 0.71; for task ii, p < 0.001, d = 0.93, AUC = 0.74. The rest three measures all failed with small effect sizes and AUC values (d < 0.5, AUC < 0.7 for all) although the difference in SI for task i was statistically significant (p < 0.001). Besides, AI displayed smaller variations across different short-term segments, indicating more robust performance. Results from the second short-term analysis were in keeping with those findings.

CONCLUSION

The proposed AI indicated better performance especially for short-term heartbeat interval data, suggesting potential in the ambulatory application of cardiovascular monitoring.

Short-term pulse rate variability is better characterized by functional near-infrared spectroscopy than by photoplethysmography

Pulse rate variability (PRV) can be extracted from functional near-infrared spectroscopy (fNIRS) (PRV(NIRS)) and photoplethysmography (PPG) (PRV(PPG)) signals. The present study compared the accuracy of simultaneously acquired PRV(NIRS) and PRV(PPG), and evaluated their different characterizations of the sympathetic (SNS) and parasympathetic (PSNS) autonomous nervous system activity. Ten healthy subjects were recorded during resting-state (RS) and respiratory challenges in two temperature conditions, i.e., room temperature (23°C) and cold temperature (4°C). PRV(NIRS) was recorded based on fNIRS measurement on the head, whereas PRV(PPG) was determined based on PPG measured at the finger. Accuracy between PRV(NIRS) and PRV(PPG), as assessed by cross-covariance and cross-sample entropy, demonstrated a high degree of correlation (r > 0.9), which was significantly reduced by respiration and cold temperature. Characterization of SNS and PSNS using frequency-domain, time-domain, and nonlinear methods showed that PRV(NIRS) provided significantly better information on increasing PSNS activity in response to respiration and cold temperature than PRV(PPG). The findings show that PRV(NIRS) may outperform PRV(PPG) under conditions in which respiration and temperature changes are present, and may, therefore, be advantageous in research and clinical settings, especially if characterization of the autonomous nervous system is desired.

Detection of Coupling in Short Physiological Series by a Joint Distribution Entropy Method

OBJECTIVE

In this study, we developed a joint distribution entropy (JDistEn) method to robustly estimate the coupling in short physiological series.

METHODS

The JDistEn method is derived from a joint distance matrix which is constructed from a combination of the distance matrix corresponding to each individual data channel using a geometric mean calculation. A coupled Rössler system and a coupled dual-kinetics neural mass model were used to examine how well JDistEn performed, specifically, its sensitivity for detecting weak coupling, its consistency in gauging coupling strength, and its reliability in processing input of decreased data length. Performance of JDistEn in estimating physiological coupling was further examined with bivariate electroencephalography data from rats and RR interval and diastolic time interval series from human beings. Cross-sample entropy (XSampEn), cross-conditional entropy (XCE), and Shannon entropy of diagonal lines in the joint recurrence plots (JENT) were applied for purposes of comparison.

RESULTS

Simulation results suggest that JDistEn showed markedly higher sensitivity than XSampEn, XCE, and JENT for dynamics in weak coupling, although as the simulation models were more intensively coupled, JDistEn performance was comparable to the three others. In addition, this improved sensitivity was much more pronounced for short datasets. Experimental results further confirmed that JDistEn outperformed XSampEn, XCE, and JENT for detecting weak coupling, especially for short physiological data.

CONCLUSION

This study suggested that our proposed JDistEn could be useful for continuous and even real-time coupling analysis for physiological signals in clinical practice.

Analysis of short-term heart rate and diastolic period variability using a refined fuzzy entropy method

BACKGROUND

Heart rate variability (HRV) has been widely used in the non-invasive evaluation of cardiovascular function. Recent studies have also attached great importance to the cardiac diastolic period variability (DPV) examination. Short-term variability measurement (e.g., 5 min) has drawn increasing attention in clinical practice, since it is able to provide almost immediate measurement results and enables the real-time monitoring of cardiovascular function. However, it is still a contemporary challenge to robustly estimate the HRV and DPV parameters based on short-term recordings.

METHODS

In this study, a refined fuzzy entropy (rFuzzyEn) was developed by substituting a piecewise fuzzy membership function for the Gaussian function in conventional fuzzy entropy (FuzzyEn) measure. Its stability and robustness against additive noise compared with sample entropy (SampEn) and FuzzyEn, were examined by two well-accepted simulation models-the [Formula: see text] noise and the Logistic attractor. The rFuzzyEn was further applied to evaluate clinical short-term (5 min) HRV and DPV of the patients with coronary artery stenosis and healthy volunteers.

RESULTS

Simulation results showed smaller fluctuations in the rFuzzyEn than in SampEn and FuzzyEn values when the data length was decreasing. Besides, rFuzzyEn could distinguish the simulation models with different amount of additive noise even when the percentage of additive noise reached 60%, but neither SampEn nor FuzzyEn showed comparable performance. Clinical HRV analysis did not indicate any significant differences between the patients with coronary artery disease and the healthy volunteers in all the three mentioned entropy measures (all p > 0.20). But clinical DPV analysis showed that the patient group had a significantly higher rFuzzyEn (p < 0.01) than the healthy group. However, no or less significant difference was observed between the two groups in either SampEn (p = 0.14) or FuzzyEn (p = 0.05).

CONCLUSIONS

Our proposed rFuzzyEn outperformed conventional SampEn and FuzzyEn in terms of both stability and robustness against additive noise, particularly when the data set was relatively short. Analysis of DPV using rFuzzyEn may provide more valuable information to assess the cardiovascular states than the other entropy measures and has a potential for clinical application.