Multiscale Entropy Analysis: Application to Cardio-Respiratory Coupling

Cardiovascular systems essentially have multiscale control mechanisms. Multiscale entropy (MSE) analysis permits the dynamic characterization of the cardiovascular time series for both short-term and long-term processes, and thus can be more illuminating. The traditional MSE analysis for heart rate variability (HRV) is performed on the original RR interval time series (named as MSE_RR). In this study, we proposed an MSE analysis for the differential RR interval time series signal, named as MSE_dRR. The motivation of using the differential RR interval time series signal is that this signal has a direct link with the inherent non-linear property of electrical rhythm of the heart. The effectiveness of the MSE_RR and MSE_dRR were tested and compared on the long-term MIT-Boston’s Beth Israel Hospital (MIT-BIH) 54 normal sinus rhythm (NSR) and 29 congestive heart failure (CHF) RR interval recordings, aiming to explore which one is better for distinguishing the CHF patients from the NSR subjects. Four RR interval length for analysis were used ( N = 500 , N = 1000 , N = 2000 and N = 5000 ). The results showed that MSE_RR did not report significant differences between the NSR and CHF groups at several scales for each RR segment length type (Scales 7, 8 and 10 for N = 500 , Scales 3 and 10 for N = 1000 , Scales 2 and 3 for both N = 2000 and N = 5000 ). However, the new MSE_dRR gave significant separation for the two groups for all RR segment length types except N = 500 at Scales 9 and 10. The area under curve (AUC) values from the receiver operating characteristic (ROC) curve were used to further quantify the performances. The mean AUC of the new MSE_dRR from Scales 1–10 are 79.5%, 83.1%, 83.5% and 83.1% for N = 500 , N = 1000 , N = 2000 and N = 5000 , respectively, whereas the mean AUC of MSE_RR are only 68.6%, 69.8%, 69.6% and 67.1%, respectively. The five-fold cross validation support vector machine (SVM) classifier reports the classification Accuracy ( A c c ) of MSE_RR as 73.5%, 75.9% and 74.6% for N = 1000 , N = 2000 and N = 5000 , respectively, while for the new MSE_dRR analysis accuracy was 85.5%, 85.6% and 85.6%. Different biosignal editing methods (direct deletion and interpolation) did not change the analytical results. In summary, this study demonstrated that compared with MSE_RR, MSE_dRR reports better statistical stability and better discrimination ability for the NSR and CHF groups.

Quantifying the complexity of physiologic time series has been of considerable interest. Several entropy-based measures have been proposed, although there is no straightforward correspondence between entropy and complexity. These traditional algorithms may generate misleading results because an increase in system entropy is not always associated with an increase in its complexity, and because the algorithms are based on single time scales. Recently, we introduced a new method, multiscale entropy (MSE) analysis, to calculate entropy over a wide range of scales. In this study, we sought to determine whether loss of complexity due to aging could be distinguished from that due to major cardiac pathology. We analyzed RR time series from young subjects (n = 26), elderly subjects (n = 46) and subjects with congestive heart failure (n = 43). The mean MSE measures of each of the three groups revealed characteristic curves, suggesting that they capture fundamental changes in the heart rate dynamics due to age and disease. We used Fisher's linear discriminant to evaluate the use of MSE features for classification. In discriminant tests on the training data, we found that MSE features could separate elderly, young and heart failure subjects with 92% accuracy and that older healthy subjects (mean age = 65.9) could be separated from subjects with heart failure (mean age = 55.5) with 94% accuracy. Also, we discriminated data from heart failure subjects and elderly healthy subjects with a positive predictivity of 76% and a specificity of 83% using only the MSE features. Larger databases will be needed to confirm if automatic classification results can match separation results. We conclude that MSE features capture differences in complexity due to aging and heart failure. These differences have implications for modeling neuroautonomic perturbations in health and disease.

Objective. This study explored the feasibility of detecting hidden muscle activity in surface electromyogram (EMG) baseline. Approach. Power spectral density (PSD) analysis and multi-scale entropy (MSE) analysis were used. Both analyses were applied to computer simulations of surface EMG baseline with the presence (representing activity data) or absence (representing reference data) of hidden muscle activity, as well as surface electrode array EMG baseline recordings of healthy control and amyotrophic lateral sclerosis (ALS) subjects. Main results. Although the simulated reference data and the activity data yielded no distinguishable difference in the time domain, they demonstrated a significant difference in the frequency and signal complexity domains with the PSD and MSE analyses. For a comparison using pooled data, such a difference was also observed when the PSD and MSE analyses were applied to surface electrode array EMG baseline recordings of healthy control and ALS subjects, which demonstrated no distinguishable difference in the time domain. Compared with the PSD analysis, the MSE analysis appeared to be more sensitive for detecting the difference in surface EMG baselines between the two groups. Significance. The findings implied the presence of a hidden muscle activity in surface EMG baseline recordings from the ALS subjects. To promote the presented analysis as a useful diagnostic or investigatory tool, future studies are necessary to assess the pathophysiological nature or origins of the hidden muscle activity, as well as the baseline difference at the individual subject level.

Complexity of spontaneous BOLD activity in default mode network is correlated with cognitive function in normal male elderly: a multiscale entropy analysis

The present study explored multi-scale entropy (MSE) analysis to investigate the entropy of resting state fMRI signals across multiple time scales. MSE analysis was developed to distinguish random noise from complex signals since the entropy of the former decreases with longer time scales while the latter signal maintains its entropy due to a "self-resemblance" across time scales. A long resting state BOLD fMRI (rs-fMRI) scan with 1000 data points was performed on five healthy young volunteers to investigate the spatial and temporal characteristics of entropy across multiple time scales. A shorter rs-fMRI scan with 240 data points was performed on a cohort of subjects consisting of healthy young (age 23 ± 2 years, n = 8) and aged volunteers (age 66 ± 3 years, n = 8) to investigate the effect of healthy aging on the entropy of rs-fMRI. The results showed that MSE of gray matter, rather than white matter, resembles closely that of f (-1) noise over multiple time scales. By filtering out high frequency random fluctuations, MSE analysis is able to reveal enhanced contrast in entropy between gray and white matter, as well as between age groups at longer time scales. Our data support the use of MSE analysis as a validation metric for quantifying the complexity of rs-fMRI signals.

COVID-19 is known to be a cause of microvascular disease due, for example, to the cytokine storm inflammatory response and the result of blood coagulation. This study reports an investigation on Heart Rate Variability (HRV) extracted from photoplethysmography (PPG) signals measured from healthy subjects and COVID-19 affected patients. We aimed to determine a statistical difference between HRV parameters among subjects' groups. Specifically, statistical analysis through Mann-Whitney U Test (MWUT) was applied to compare 42 dif-ferent parameters extracted from PPG signals of 143 subjects: 50 healthy subjects (i.e. group 0) and 93 affected from COVID-19 patients stratified through increasing COVID severity index (i.e. groups 1 and 2). Results showed significant statistical differences between groups in several HRV parameters. In particular, Multiscale Entropy (MSE) analysis provided the master key in patient stratification assessment. In fact, MSE11, MSE12, MSE15, MSE16, MSE17, MSE18, MSE19 and MSE20 keep statistical significant difference during all the comparisons between healthy subjects and patients from all the pathological groups. Our preliminary results suggest that it could be possible to distinguish between healthy and COVID-19 affected subjects based on cardiovascular dynamics. This study opens to future evaluations in using machine learning models for automatic decision-makers to distinguish between healthy and COVID-19 subjects, as well as within COVID-19 severity levels. Clinical Relevance - This establishes the possibility to distin-guish healthy subjects from COVID-19 affected patients basing on HRV parameters monitored non invasively by PPG.

Many patients with severe obstructive sleep apnea (OSA) do not complain of excessive daytime sleepiness (EDS), possibly due to increased sympathetic nervous activity (SNA) and accompanying heightened alertness. We hypothesized that in patients with OSA, those without subjective EDS (Epworth Sleepiness Scale, ESS score < 11) would have higher very low frequency (VLF) heart rate variability (HRV) during sleep, reflecting greater sympathetic heart rate modulation than patients with an ESS score ≥ 11. Patients with severe OSA (AHI ≥ 30: 26 with and 65 without heart failure) were divided into those with and without EDS. Heart rate (HR) signals were acquired in stage 2 sleep during periods of recurrent apneas and hypopneas and submitted to coarse graining spectral analysis, which extracts harmonic, neurally mediated contributions to HRV from total spectral power. Because the apnea-hyperpnea cycle entrains muscle SNA at VLF (0 to 0.04 Hz), VLF power was our principal between-group comparison. Subjects without EDS had higher harmonic VLF power (944 ± 839 vs 447 ± 461 msec(2), p = 0.003) than those with EDS, irrespective of the presence or absence of heart failure (1218 ± 944 vs 426 ± 299 msec(2), p = 0.043, and 1029 ± 873 vs 503 ± 533 msec(2), p = 0.003, respectively). ESS scores correlated inversely with VLF power in all (r = -0.294, p = 0.005) and in heart failure subjects (r = -0.468, p = 0.016). Patients with severe OSA but without EDS have higher VLF-HRV than those with EDS. This finding suggests that patients with severe OSA but without EDS have greater sympathetic modulation of HRV than those with EDS that may reflect elevated adrenergically mediated alertness. Taranto Montemurro L; Floras JS; Picton P; Kasai T; Alshaer H; Gabriel JM; Bradley TD. Relationship of heart rate variability to sleepiness in patients with obstructive sleep apnea with and without heart failure.

Multi-scale entropy analysis and Hurst exponent

Chronic heart failure (CHF) is one of the most significant medical, economic and social problems of the 21st century and remains the main cause of morbidity and mortality worldwide.The purpose. To study the indicators of Holter ECG monitoring, the dynamics of ischemic changes, heart rate, indicators of heart rhythm variability and blood pressure in patients with heart failure and atrial fibrillation.Material and methods. 150 patients aged 45-65 were examined. All patients were divided into groups: Group I – patients with HF with sinus rhythm or atrial fibrillation (AF) (permanent or persistent form), (n=75). Group II – patients without HF with AF, (n=75). Group III – control group: 36 practically healthy people. All patients underwent a clinical examination, ECG, echocardiography (ECHOKG), Holter ECG monitoring (HM ECG) and daily BP monitoring (DMAT).Research results. The analysis of the ECG of the examined patients indicates the presence of heart rhythm disorders, which is an important risk factor and progression of CHF. The results of XM ECG indicate the presence of ventricular arrhythmias of various gradations along with AF. There was a probable difference in the direction of an increase in the number of ventricular extrasystoles (VAS), both single and, most importantly, extrasystoles of high gradations, in patients with CHF and AF compared with healthy subjects. In addition, the number of SHEs in patients with CHF and AF was likely lower than in patients with CHF with sinus rhythm. Indicators of maximum heart rate, ST segment depression and QT interval dispersion in patients with CHF and AF were significantly higher (p&lt;0.05) than similar parameters in patients without CHF with AF.Conclusions: Ventricular heart rhythm disturbances were detected in the examined patients, which is a predictor of an unfavorable prognosis in patients with chronic heart failure. There was a probable difference in the direction of increased levels of maximum heart rate, maximum depression, ST segment elevation, dispersion of the QT interval, QTc, an increase in the total duration of episodes of myocardial ischemia, in patients with chronic heart failure and atrial fibrillation in comparison with healthy subjects.

HEART SOUNDS CHARACTERISTICS FROM A 3D ACCELEROMETER IN HEART FAILURE PATIENTS

Nonlinear properties of cardiac rhythm and respiratory signal under paced breathing in young and middle-aged healthy subjects

Until recently, preclinical and clinical work on diabetes has focused on the understanding of blood glucose elevation and its detrimental metabolic sequelae. The advent of continuous glucose monitoring (CGM) technology now allows real time monitoring of blood glucose levels as a time series, and thus the exploration of glucose dynamics at short time scales. Previous work has shown decreases in the complexity of glucose dynamics, as measured by multiscale entropy (MSE) analysis, in diabetes in humans, mice, and rats. Analyses for non-human primates (NHP) have not been reported, nor is it known if anti-diabetes compounds affect complexity of glucose dynamics. We instrumented four healthy and six diabetic rhesus monkeys with CGM probes in the carotid artery and collected glucose values at a frequency of one data point per second for the duration of the sensors’ life span. Sensors lasted between 45 and 78 days. Five of the diabetic rhesus monkeys were also administered the anti-diabetic drug liraglutide daily beginning at day 39 of the CGM monitoring period. Glucose levels fluctuated during the day in both healthy and diabetic rhesus monkeys, peaking between 12 noon – 6 pm. MSE analysis showed reduced complexity of glucose dynamics in diabetic monkeys compared to healthy animals. Although liraglutide decreased glucose levels, it did not restore complexity in diabetic monkeys consistently. Complexity varied by time of day, more strongly for healthy animals than for diabetic animals. And by dividing the monitoring period into 3-day or 1-week subperiods, we were able to estimate within-animal variability of MSE curves. Our data reveal that decreased complexity of glucose dynamics is a conserved feature of diabetes from rodents to NHPs to man.

This paper presents a novel framework for the complexity analysis of rainfall, runoff, and runoff coefficient (RC) time series using multiscale entropy (MSE). The MSE analysis of RC time series was used to investigate changes in the complexity of rainfall-runoff processes due to human activities. Firstly, a coarse graining process was applied to a time series. The sample entropy was then computed for each coarse-grained time series, and plotted as a function of the scale factor. The proposed method was tested in a case study of daily rainfall and runoff data for the upstream Wu–Tu watershed. Results show that the entropy measures of rainfall time series are higher than those of runoff time series at all scale factors. The entropy measures of the RC time series are between the entropy measures of the rainfall and runoff time series at various scale factors. Results also show that the entropy values of rainfall, runoff, and RC time series increase as scale factors increase. The changes in the complexity of RC time series indicate the changes of rainfall-runoff relations due to human activities and provide a reference for the selection of rainfall-runoff models that are capable of dealing with great complexity and take into account of obvious self-similarity can be suggested to the modeling of rainfall-runoff processes. Moreover, the robustness of the MSE results were tested to confirm that MSE analysis is consistent and the same results when removing 25% data, making this approach suitable for the complexity analysis of rainfall, runoff, and RC time series.

Because of the complexity and randomness of the gas-solid two-phase flow, it is still hard to fully understand the dynamic behavior of the flow. The electrostatic signal contains rich information of the particulate flow. Multiscale entropy (MSE) analysis of electrostatic fluctuation signal was conducted in this paper. The electrostatic signals were obtained from the horizontal pipeline in dilute pneumatic conveying system. The influence of sequence length on MSE of electrostatic signal was analyzed at first. Then the influence of solids concentration and superficial air velocity on MSE was shown, which reflects that it is helpful for understanding of the dynamics of two phase flow.

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 (&gt;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, rL = rG = r) are for FuzzyMEn (in addition to setting nL = 3 and nG = 2) were recommended to yield the fine classification results for the NSR and CHF groups.