Entropy Analysis of Short-Term Heartbeat Interval Time Series during Regular Walking

Complexity reduction of oxygen saturation variability signals in COVID-19 patients: Implications for cardiorespiratory control

BACKGROUND

Coronavirus disease 2019 (COVID-19) is a respiratory illness that leads to severe acute respiratory syndrome and various cardiorespiratory complications, contributing to morbidity and mortality. Entropy analysis has demonstrated its ability to monitor physiological states and system dynamics during health and disease. The main objective of the study is to extract information about cardiorespiratory control by conducting a complexity analysis of OSV signals using scale-based entropy measures following a two-month timeframe after recovery.

METHODS

This prospective study collected data from subjects meeting specific criteria, using a Beurer PO-80 pulse oximeter to measure oxygen saturation (SpO2) and pulse rate. Excluding individuals with a history of pulmonary/cardiovascular issues, the study analyzed 88 recordings from 44 subjects (26 men, 18 women, mean age 45.34 ± 14.40) during COVID-19 and two months post-recovery. Data preprocessing and scale-based entropy analysis were applied to assess OSV signals.

RESULTS

The study found a significant difference in mean OSV during illness (95.08 ± 0.15) compared to post-recovery (95.59 ± 1.03), indicating reduced cardiorespiratory dynamism during COVID-19. Multiscale entropy analyses (MSE, MPE, MFE) confirmed lower entropy values during illness across all time scales, particularly at higher scales. Notably, the maximum distinction between illness and recovery phases was seen at specific time scales and similarity criteria for each entropy measure, showing statistically significant differences.

CONCLUSIONS

The study demonstrates that the loss of complexity in OSV signals, quantified using scale-based entropy measures, has the potential to detect malfunctioning of cardiorespiratory control in COVID-19 patients. This finding suggests that OSV signals could serve as a valuable indicator for assessing the cardiorespiratory status of COVID-19 patients and monitoring their recovery progress.

Scale based entropy measures and deep learning methods for analyzing the dynamical characteristics of cardiorespiratory control system in COVID-19 subjects during and after recovery

COVID-19, known as Coronavirus Disease 2019 primarily targets the respiratory system and can impact the cardiovascular system, leading to a range of cardiorespiratory complications. The current forefront in analyzing the dynamical characteristics of physiological systems and aiding clinical decision-making involves the integration of entropy-based complexity techniques with artificial intelligence. Entropy-based measures offer promising prospects for identifying disturbances in cardiorespiratory control system (CRCS) among COVID-19 patients by assessing the oxygen saturation variability (OSV) signals. In this investigation, we employ scale-based entropy (SBE) methods, including multiscale entropy (MSE), multiscale permutation entropy (MPE), and multiscale fuzzy entropy (MFE), to characterize the dynamical characteristics of OSV signals. These measurements serve as features for the application of traditional machine learning (ML) and deep learning (DL) approaches in the context of classifying OSV signals from COVID-19 patients during their illness and subsequent recovery. We use the Beurer PO-80 pulse oximeter which non-invasively acquired OSV and pulse rate data from COVID-19 infected patients during the active infection phase and after a two-month recovery period. The dataset comprises of 88 recordings collected from 44 subjects(26 men and 18 women), both during their COVID-19 illness and two months post-recovery. Prior to analysis, data preprocessing is performed to remove artifacts and outliers. The application of SBE measures to OSV signals unveils a reduction in signal complexity during the course of COVID-19. Leveraging these SBE measures as feature sets, we employ two DL techniques, namely the radial basis function network (RBFN) and RBFN with dynamic delay algorithm (RBFNDDA), for the classification of OSV data collected during and after COVID-19 recovery. To evaluate the classification performance, we employ standard metrics such as sensitivity, specificity, false positive rate (FPR), and the area under the receiver operator characteristic curve (AUC). Among the three scale-based entropy measures, MFE outperformed MSE and MPE by achieving the highest classification performance using RBFN with 13 best features having sensitivity (0.84), FPR (0.30), specificity (0.70) and AUC (0.77). The outcomes of our study demonstrate that SBE measures combined with DL methods offer a valuable approach for categorizing OSV signals obtained during and after COVID-19, ultimately aiding in the detection of CRCS dysfunction.

Prediction models for lymph node metastasis in cervical cancer based on preoperative heart rate variability

Background

The occurrence of lymph node metastasis (LNM) is one of the critical factors in determining the staging, treatment and prognosis of cervical cancer (CC). Heart rate variability (HRV) is associated with LNM in patients with CC. The purpose of this study was to validate the feasibility of machine learning (ML) models constructed with preoperative HRV as a feature of CC patients in predicting CC LNM.

Methods

A total of 292 patients with pathologically confirmed CC admitted to the Department of Gynecological Oncology of the First Affiliated Hospital of Bengbu Medical University from November 2020 to September 2023 were included in the study. The patient' preoperative 5-min electrocardiogram data were collected, and HRV time-domain, frequency-domain and non-linear analyses were subsequently performed, and six ML models were constructed based on 32 parameters. Model performance was assessed using the area under the receiver operating characteristic curve (AUC), accuracy, sensitivity, and specificity.

Results

Among the 6 ML models, the random forest (RF) model showed the best predictive performance, as specified by the following metrics on the test set: AUC (0.852), accuracy (0.744), sensitivity (0.783), and specificity (0.785).

Conclusion

The RF model built with preoperative HRV parameters showed superior performance in CC LNM prediction, but multicenter studies with larger datasets are needed to validate our findings, and the physiopathological mechanisms between HRV and CC LNM need to be further explored.

Hybrid-FHR: a multi-modal AI approach for automated fetal acidosis diagnosis

BACKGROUND

In clinical medicine, fetal heart rate (FHR) monitoring using cardiotocography (CTG) is one of the most commonly used methods for assessing fetal acidosis. However, as the visual interpretation of CTG depends on the subjective judgment of the clinician, this has led to high inter-observer and intra-observer variability, making it necessary to introduce automated diagnostic techniques.

METHODS

In this study, we propose a computer-aided diagnostic algorithm (Hybrid-FHR) for fetal acidosis to assist physicians in making objective decisions and taking timely interventions. Hybrid-FHR uses multi-modal features, including one-dimensional FHR signals and three types of expert features designed based on prior knowledge (morphological time domain, frequency domain, and nonlinear). To extract the spatiotemporal feature representation of one-dimensional FHR signals, we designed a multi-scale squeeze and excitation temporal convolutional network (SE-TCN) backbone model based on dilated causal convolution, which can effectively capture the long-term dependence of FHR signals by expanding the receptive field of each layer's convolution kernel while maintaining a relatively small parameter size. In addition, we proposed a cross-modal feature fusion (CMFF) method that uses multi-head attention mechanisms to explore the relationships between different modalities, obtaining more informative feature representations and improving diagnostic accuracy.

RESULTS

Our ablation experiments show that the Hybrid-FHR outperforms traditional previous methods, with average accuracy, specificity, sensitivity, precision, and F1 score of 96.8, 97.5, 96, 97.5, and 96.7%, respectively.

CONCLUSIONS

Our algorithm enables automated CTG analysis, assisting healthcare professionals in the early identification of fetal acidosis and the prompt implementation of interventions.

Psychophysiological stress response after a 6-week Mindful Self-Compassion training in psychiatric rehabilitation inpatients: a randomized post-test only study

Objectives

Mindfulness-based interventions (including self-compassion interventions) are effective in improving stress management at psychological and physical levels. Mindful Self-Compassion (MSC) is a newly developed program particularly aimed at increasing self-compassion. The main objective of this study was to determine whether the psychophysiological stress response during a social-evaluative speaking task differs in inpatients participating in the MSC or the Progressive Muscle Relaxation (PMR) program at the end of their 6-week psychiatric rehabilitation stay (i.e., post-test only design).

Method

Data from 50 inpatients (25 MSC, 25 PMR, 35 female) aged 19 to 76 years (M = 47.22, SD = 12.44) were analyzed in terms of psychophysiological stress response. For this purpose, heart rate variability, heart rate, and blood pressure were assessed together with several psychometric variables: positive and negative affect (PANAS), subjective stress perception (Visual Analog Scale), self-compassion (Self-Compassion Scale), cognitive reappraisal and suppression (Emotion Regulation Questionnaire), psychological distress (Brief Symptom Inventory-18), and appraisal and rumination (selected items).

Results

After correction for alpha inflation no differences in the psychophysiological stress response and psychometric parameters between the MSC and PMR group were found.

Discussion

In general, our results indicate that MSC is not superior to PMR training. However, more research with clinical randomized controlled trials investigating larger samples are needed to further affirm these initial findings.

Visibility Graph Analysis of Heartbeat Time Series: Comparison of Young vs. Old, Healthy vs. Diseased, Rest vs. Exercise, and Sedentary vs. Active

Using the visibility graph algorithm (VGA), a complex network can be associated with a time series, such that the properties of the time series can be obtained by studying those of the network. Any value of the time series becomes a node of the network, and the number of other nodes that it is connected to can be quantified. The degree of connectivity of a node is positively correlated with its magnitude. The slope of the regression line is denoted by k-M, and, in this work, this parameter was calculated for the cardiac interbeat time series of different contrasting groups, namely: young vs. elderly; healthy subjects vs. patients with congestive heart failure (CHF); young subjects and adults at rest vs. exercising young subjects and adults; and, finally, sedentary young subjects and adults vs. active young subjects and adults. In addition, other network parameters, including the average degree and the average path length, of these time series networks were also analyzed. Significant differences were observed in the k-M parameter, average degree, and average path length for all analyzed groups. This methodology based on the analysis of the three mentioned parameters of complex networks has the advantage that such parameters are very easy to calculate, and it is useful to classify heartbeat time series of subjects with CHF vs. healthy subjects, and also for young vs. elderly subjects and sedentary vs. active subjects.

Irregular Autonomic Modulation Predicts Risky Drinking and Altered Ventromedial Prefrontal Cortex Response to Stress in Alcohol Use Disorder

AIMS

Autonomic dysfunction has been associated with risky drinking and alcohol use disorder (AUD). Although autonomic nervous system (ANS) activity has been attributed to the ventromedial prefrontal cortex (VmPFC)-limbic-striatal regions, the specific role of ANS disruption in AUD and its association with these regions remain unclear. Using functional magnetic resonance imaging (fMRI) and concurrent electrocardiogram (ECG), the current study examined neural correlates of ANS activity in AUD and its role in AUD pathology.

METHODS

Demographically matched 20 AUD patients and 20 social drinkers (SD) completed an fMRI task involving repeated exposure to stress, alcohol-cue and neutral-relaxing images in a block design. Based on the known VmPFC-limbic-striatal functions involved in emotions, reward and the ANS, we performed a regions of interest (ROI) analysis to examine the associations between ANS activity and neural responses in the VmPFC, amygdala, and ventral striatum.

RESULTS

Across conditions, AUD patients showed significantly higher levels of overall heart rate (HR) and approximate entropy (ApEn) compared to SD (Ps < 0.05). In all participants, increased HR was associated with greater drinking volume (P < 0.05). In addition, higher ApEn levels were associated with greater drinking volume (P < 0.05) and decreased right VmPFC response to stress (P < 0.05).

DISCUSSION

Our findings demonstrate ANS disruption in AUD indexed by high overall HR and ApEn. The association between ApEn and rVmPFC response suggests that ApEn may play a role in modulating drinking via interactions with neural regions of emotion regulation. These findings provide insight into patterns of ANS disruption and their relevance to AUD pathology.

Entropy Analysis of Heart Rate Variability in Different Sleep Stages

How the complexity or irregularity of heart rate variability (HRV) changes across different sleep stages and the importance of these features in sleep staging are not fully understood. This study aimed to investigate the complexity or irregularity of the RR interval time series in different sleep stages and explore their values in sleep staging. We performed approximate entropy (ApEn), sample entropy (SampEn), fuzzy entropy (FuzzyEn), distribution entropy (DistEn), conditional entropy (CE), and permutation entropy (PermEn) analyses on RR interval time series extracted from epochs that were constructed based on two methods: (1) 270-s epoch length and (2) 300-s epoch length. To test whether adding the entropy measures can improve the accuracy of sleep staging using linear HRV indices, XGBoost was used to examine the abilities to differentiate among: (i) 5 classes [Wake (W), non-rapid-eye-movement (NREM), which can be divide into 3 sub-stages: stage N1, stage N2, and stage N3, and rapid-eye-movement (REM)]; (ii) 4 classes [W, light sleep (combined N1 and N2), deep sleep (N3), and REM]; and (iii) 3 classes: (W, NREM, and REM). SampEn, FuzzyEn, and CE significantly increased from W to N3 and decreased in REM. DistEn increased from W to N1, decreased in N2, and further decreased in N3; it increased in REM. The average accuracy of the three tasks using linear and entropy features were 42.1%, 59.1%, and 60.8%, respectively, based on 270-s epoch length; all were significantly lower than the performance based on 300-s epoch length (i.e., 54.3%, 63.1%, and 67.5%, respectively). Adding entropy measures to the XGBoost model of linear parameters did not significantly improve the classification performance. However, entropy measures, especially PermEn, DistEn, and FuzzyEn, demonstrated greater importance than most of the linear parameters in the XGBoost model.300-s270-s.

Acute Effects of Various Movement Noise in Differential Learning of Rope Skipping on Brain and Heart Recovery Analyzed by Means of Multiscale Fuzzy Measure Entropy

In search of more detailed explanations for body-mind interactions in physical activity, neural and physiological effects, especially regarding more strenuous sports activities, increasingly attract interest. Little is known about the underlying manifold (neuro-)physiological impacts induced by different motor learning approaches. The various influences on brain or cardiac function are usually studied separately and modeled linearly. Limitations of these models have recently led to a rapidly growing application of nonlinear models. This study aimed to investigate the acute effects of various sequences of rope skipping on irregularity of the electrocardiography (ECG) and electroencephalography (EEG) signals as well as their interaction and whether these depend on different levels of active movement noise, within the framework of differential learning theory. Thirty-two males were randomly and equally distributed to one of four rope skipping conditions with similar cardiovascular but varying coordinative demand. ECG and EEG were measured simultaneously at rest before and immediately after rope skipping for 25 mins. Signal irregularity of ECG and EEG was calculated via the multiscale fuzzy measure entropy (MSFME). Statistically significant ECG and EEG brain area specific changes in MSFME were found with different pace of occurrence depending on the level of active movement noise of the particular rope skipping condition. Interaction analysis of ECG and EEG MSFME specifically revealed an involvement of the frontal, central, and parietal lobe in the interplay with the heart. In addition, the number of interaction effects indicated an inverted U-shaped trend presenting the interaction level of ECG and EEG MSFME dependent on the level of active movement noise. In summary, conducting rope skipping with varying degrees of movement variation appears to affect the irregularity of cardiac and brain signals and their interaction during the recovery phase differently. These findings provide enough incentives to foster further constructive nonlinear research in exercise-recovery relationship and to reconsider the philosophy of classical endurance training.

Time Series Segmentation Based on Stationarity Analysis to Improve New Samples Prediction

A wide range of applications based on sequential data, named time series, have become increasingly popular in recent years, mainly those based on the Internet of Things (IoT). Several different machine learning algorithms exploit the patterns extracted from sequential data to support multiple tasks. However, this data can suffer from unreliable readings that can lead to low accuracy models due to the low-quality training sets available. Detecting the change point between high representative segments is an important ally to find and thread biased subsequences. By constructing a framework based on the Augmented Dickey-Fuller (ADF) test for data stationarity, two proposals to automatically segment subsequences in a time series were developed. The former proposal, called Change Detector segmentation, relies on change detection methods of data stream mining. The latter, called ADF-based segmentation, is constructed on a new change detector derived from the ADF test only. Experiments over real-file IoT databases and benchmarks showed the improvement provided by our proposals for prediction tasks with traditional Autoregressive integrated moving average (ARIMA) and Deep Learning (Long short-term memory and Temporal Convolutional Networks) methods. Results obtained by the Long short-term memory predictive model reduced the relative prediction error from 1 to 0.67, compared to time series without segmentation.

Can Heart Rate Variability (HRV) Be Used as a Biomarker of Thermal Comfort for Mine Workers?

This study aimed to determine whether heart rate variability (HRV) can express the thermal comfort of mine workers. Eight subjects ran on a treadmill (5.5 km/h) to simulate heavy labor in three kinds of mining environments (22 °C/90%, 26 °C/90%, 30 °C/90%), respectively. Based on the measured electrocardiogram (ECG) data, the HRV of the subjects was calculated. The results showed that the HRV indices changed obviously under different temperature environments. In the neutral and hot environment, except for the LF, TP and LF/HF, there were significant differences in each index. However, there was no significant difference between the cold and neutral environments. The R-R intervals, the very low-frequency power (VLF), pNN20 and SampEN had strong negative correlation with the thermal sensation of people from sitting to work (ρ < −0.700). These indices may be used as thermal comfort predictive biomarkers of mine workers.

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

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.

Bivariate Entropy Analysis of Electrocardiographic RR-QT Time Series

QT interval variability (QTV) and heart rate variability (HRV) are both accepted biomarkers for cardiovascular events. QTV characterizes the variations in ventricular depolarization and repolarization. It is a predominant element of HRV. However, QTV is also believed to accept direct inputs from upstream control system. How QTV varies along with HRV is yet to be elucidated. We studied the dynamic relationship of QTV and HRV during different physiological conditions from resting, to cycling, and to recovering. We applied several entropy-based measures to examine their bivariate relationships, including cross sample entropy (XSampEn), cross fuzzy entropy (XFuzzyEn), cross conditional entropy (XCE), and joint distribution entropy (JDistEn). Results showed no statistically significant differences in XSampEn, XFuzzyEn, and XCE across different physiological states. Interestingly, JDistEn demonstrated significant decreases during cycling as compared with that during the resting state. Besides, JDistEn also showed a progressively recovering trend from cycling to the first 3 min during recovering, and further to the second 3 min during recovering. It appeared to be fully recovered to its level in the resting state during the second 3 min during the recovering phase. The results suggest that there is certain nonlinear temporal relationship between QTV and HRV, and that the JDistEn could help unravel this nuanced property.

Complexity-Based Decoding of the Coupling Among Heart Rate Variability (HRV) and Walking Path

Walking is an everyday activity in our daily life. Because walking affects heart rate variability, in this research, for the first time, we analyzed the coupling among the alterations of the complexity of walking paths and heart rate. We benefited from the fractal theory and sample entropy to evaluate the influence of the complexity of paths on the complexity of heart rate variability (HRV) during walking. We calculated the fractal exponent and sample entropy of the R-R time series for nine participants who walked on four paths with various complexities. The findings showed a strong coupling among the alterations of fractal dimension (an indicator of complexity) of HRV and the walking paths. Besides, the result of the analysis of sample entropy also verified the obtained results from the fractal analysis. In further studies, we can analyze the coupling among the alterations of the complexities of other physiological signals and walking paths.

Modified Distribution Entropy as a Complexity Measure of Heart Rate Variability (HRV) Signal

The complexity of a heart rate variability (HRV) signal is considered an important nonlinear feature to detect cardiac abnormalities. This work aims at explaining the physiological meaning of a recently developed complexity measurement method, namely, distribution entropy (DistEn), in the context of HRV signal analysis. We thereby propose modified distribution entropy (mDistEn) to remove the physiological discrepancy involved in the computation of DistEn. The proposed method generates a distance matrix that is devoid of over-exerted multi-lag signal changes. Restricted element selection in the distance matrix makes "mDistEn" a computationally inexpensive and physiologically more relevant complexity measure in comparison to DistEn.

Entropy Analysis of RR-Time Series From Stress Tests

The RR-interval time series or tachograms obtained from electrocardiograms have been widely studied since they reflect the cardiac variability, and this is an indicative of the health status of a person. The tachogram can be seen as a highly non-linear and complex time series, and therefore, should be analyzed with non-linear techniques. In this work, several entropy measures, Sample Entropy (SampEn), Approximate Entropy (ApEn), and Fuzzy Entropy (FuzzyEn) are used as a measure of heart rate variability (HRV). Tachograms belonging to thirty-nine subjects were obtained from a cardiac stress test consisting of a rest period followed by a period of moderate physical activity. Subjects are grouped according to their physical activity using the IPAQ sedentary and active questionnaire, we work with youth and middle-aged adults. The entropy measures for each group show that for the sedentary subjects the values are high at rest and decrease appreciably with moderate physical activity, This happens for both young and middle-aged adults. These results are highly reproducible. In the case of the subjects that exercise regularly, an increase in entropy is observed or they tend to retain the entropy value that they had at rest. It seems that there is a possible correlation between the physical condition of a person with the increase or decrease in entropy during moderate physical activity with respect to the entropy at rest. It was also observed that entropy during longer physical activity tests tends to decrease as fatigue accumulates, but this decrease is small compared to the change that occurs when going from rest to physical activity.

Are Strategies Favoring Pattern Matching a Viable Way to Improve Complexity Estimation Based on Sample Entropy?

It has been suggested that a viable strategy to improve complexity estimation based on the assessment of pattern similarity is to increase the pattern matching rate without enlarging the series length. We tested this hypothesis over short simulations of nonlinear deterministic and linear stochastic dynamics affected by various noise amounts. Several transformations featuring a different ability to increase the pattern matching rate were tested and compared to the usual strategy adopted in sample entropy (SampEn) computation. The approaches were applied to evaluate the complexity of short-term cardiac and vascular controls from the beat-to-beat variability of heart period (HP) and systolic arterial pressure (SAP) in 12 Parkinson disease patients and 12 age- and gender-matched healthy subjects at supine resting and during head-up tilt. Over simulations, the strategies estimated a larger complexity over nonlinear deterministic signals and a greater regularity over linear stochastic series or deterministic dynamics importantly contaminated by noise. Over short HP and SAP series the techniques did not produce any practical advantage, with an unvaried ability to discriminate groups and experimental conditions compared to the traditional SampEn. Procedures designed to artificially increase the number of matches are of no methodological and practical value when applied to assess complexity indexes.

Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its Applications

Permutation Entropy (PE) is a time series complexity measure commonly used in a variety of contexts, with medicine being the prime example. In its general form, it requires three input parameters for its calculation: time series length N, embedded dimension m, and embedded delay τ. Inappropriate choices of these parameters may potentially lead to incorrect interpretations. However, there are no specific guidelines for an optimal selection of N, m, or τ, only general recommendations such as N>>m!, τ=1, or m=3,…,7. This paper deals specifically with the study of the practical implications of N>>m!, since long time series are often not available, or non-stationary, and other preliminary results suggest that low N values do not necessarily invalidate PE usefulness. Our study analyses the PE variation as a function of the series length N and embedded dimension m in the context of a diverse experimental set, both synthetic (random, spikes, or logistic model time series) and real–world (climatology, seismic, financial, or biomedical time series), and the classification performance achieved with varying N and m. The results seem to indicate that shorter lengths than those suggested by N>>m! are sufficient for a stable PE calculation, and even very short time series can be robustly classified based on PE measurements before the stability point is reached. This may be due to the fact that there are forbidden patterns in chaotic time series, not all the patterns are equally informative, and differences among classes are already apparent at very short lengths.

EZ Entropy: a software application for the entropy analysis of physiological time-series

Background

Entropy analysis has been attracting increasing attentions in the recent two or three decades. It assesses complexity, or irregularity, of time-series which is extraordinarily relevant to physiology and diseases as demonstrated by tremendous studies. However, the complexity can hardly be appreciated by traditional methods including time-, frequency-domain analysis, and time-frequency analysis that are the common built-in options in commercialized measurement and statistical software. To facilitate the entropy analysis of physiological time-series, a new software application, namely EZ Entropy, was developed and introduced in this article.

Results

EZ Entropy was developed in MATLAB^® environment. It was programmed in an object-oriented style and was constructed with a graphical user interface. EZ Entropy is easy to operate through its compact graphical interface, thus allowing researchers without knowledge of programming like clinicians and physiologists to perform such kind of analysis. Besides, it offers various settings to meet different analysis needs including (1) processing single data recording, (2) batch processing multiple data files, (3) sliding window calculations, (4) recall, (5) displaying intermediate data and final results, (6) adjusting input parameters, and (7) exporting calculation results after the run or in real-time during the analysis. The analysis results could be exported, either manually or automatically, to comma-separated ASCII files, thus being compatible to and easily imported into the common statistical analysis software. Code-wise, EZ Entropy is object-oriented, thus being quite easy to maintain and extend.

Conclusions

EZ Entropy is a user-friendly software application to perform the entropy analysis of time-series, as well as to simplify and to speed up this useful analysis.

Electronic supplementary material

The online version of this article (10.1186/s12938-019-0650-5) contains supplementary material, which is available to authorized users.

Entropy Analysis for the Evaluation of Respiratory Changes Due to Asbestos Exposure and Associated Smoking

Breathing is a complex rhythmic motor act, which is created by integrating different inputs to the respiratory centres. Analysing nonlinear fluctuations in breathing may provide clinically relevant information in patients with complex illnesses, such as asbestosis. We evaluated the effect of exposition to asbestos on the complexity of the respiratory system by investigating the respiratory impedance sample entropy (SampEnZrs) and recurrence period density entropy (RPDEnZrs). Similar analyses were performed by evaluating the airflow pattern sample entropy (SampEnV') and recurrence period density entropy (RPDEnV'). Groups of 34 controls and 34 asbestos-exposed patients were evaluated in the respiratory impedance entropy analysis, while groups of 34 controls and 30 asbestos-exposed patients were investigated in the analysis of airflow entropy. Asbestos exposition introduced a significant reduction of RPDEnV' in non-smoker patients (p < 0.0004), which suggests that the airflow pattern becomes less complex in these patients. Smoker patients also presented a reduction in RPDEnV' (p < 0.05). These finding are consistent with the reduction in respiratory system adaptability to daily life activities observed in these patients. It was observed a significant reduction in SampEnV' in smoker patients in comparison with non-smokers (p < 0.02). Diagnostic accuracy evaluations in the whole group of patients (including non-smokers and smokers) indicated that RPDEnV' might be useful in the diagnosis of respiratory abnormalities in asbestos-exposed patients, showing an accuracy of 72.0%. In specific groups of non-smokers, RPDEnV' also presented adequate accuracy (79.0%), while in smoker patients, SampEnV' and RPDEnV' presented adequate accuracy (70.7% and 70.2%, respectively). Taken together, these results suggest that entropy analysis may provide an early and sensitive functional indicator of interstitial asbestosis.

Entropy Measures in Analysis of Head up Tilt Test Outcome for Diagnosing Vasovagal Syncope

The paper presents possible applications of entropy measures in analysis of biosignals recorded during head up tilt testing (HUTT) in patients with suspected vasovagal syndrome. The study group comprised 80 patients who developed syncope during HUTT (57 in the passive phase of the test (HUTT(+) group) and 23 who had negative result of passive phase and developed syncope after provocation with nitroglycerine (HUTT(−) group)). The paper focuses on assessment of monitored signals’ complexity (heart rate expressed as R-R intervals (RRI), blood pressure (sBP, dBP) and stroke volume (SV)) using various types of entropy measures (Sample Entropy (SE), Fuzzy Entropy (FE), Shannon Entropy (Sh), Conditional Entropy (CE), Permutation Entropy (PE)). Assessment of the complexity of signals in supine position indicated presence of significant differences between HUTT(+) versus HUTT(−) patients only for Conditional Entropy (CE(RRI)). Values of CE(RRI) higher than 0.7 indicate likelihood of a positive result of HUTT already at the passive phase. During tilting, in the pre-syncope phase, significant differences were found for: (SE(sBP), SE(dBP), FE(RRI), FE(sBP), FE(dBP), FE(SV), Sh(sBP), Sh(SV), CE(sBP), CE(dBP)). HUTT(+) patients demonstrated significant changes in signals’ complexity more frequently than HUTT(−) patients. When comparing entropy measurements done in the supine position with those during tilting, SV assessed in HUTT(+) patients was the only parameter for which all tested measures of entropy (SE(SV), FE(SV), Sh(SV), CE(SV), PE(SV)) showed significant differences.

Multiscale Distribution Entropy Analysis of Short-Term Heart Rate Variability

Electrocardiogram (ECG) signal has been commonly used to analyze the complexity of heart rate variability (HRV). For this, various entropy methods have been considerably of interest. The multiscale entropy (MSE) method, which makes use of the sample entropy (SampEn) calculation of coarse-grained time series, has attracted attention for analysis of HRV. However, the SampEn computation may fail to be defined when the length of a time series is not enough long. Recently, distribution entropy (DistEn) with improved stability for a short-term time series has been proposed. Here, we propose a novel multiscale DistEn (MDE) for analysis of the complexity of short-term HRV by utilizing a moving-averaging multiscale process and the DistEn computation of each moving-averaged time series. Thus, it provides an improved stability of entropy evaluation for short-term HRV extracted from ECG. To verify the performance of MDE, we employ the analysis of synthetic signals and confirm the superiority of MDE over MSE. Then, we evaluate the complexity of short-term HRV extracted from ECG signals of congestive heart failure (CHF) patients and healthy subjects. The experimental results exhibit that MDE is capable of quantifying the decreased complexity of HRV with aging and CHF disease with short-term HRV time series.

Assessment of tobacco smoke effects on neonatal cardiorespiratory control using a semi-automated processing approach

A semi-automated processing approach was developed to assess the effects of early postnatal environmental tobacco smoke (ETS) on the cardiorespiratory control of newborn lambs. The system consists of several steps beginning with artifact rejection, followed by the selection of stationary segments, and ending with feature extraction. This approach was used in six lambs exposed to 20 cigarettes/day for the first 15 days of life, while another six control lambs were exposed to room air. On postnatal day 16, electrocardiograph and respiratory signals were obtained from a 6-h polysomnographic recording. The effects of postnatal ETS exposure on heart rate variability, respiratory rate variability, and cardiorespiratory interrelations were explored. The unique results suggest that early postnatal ETS exposure increases respiratory rate variability and decreases the coupling between cardiac and respiratory systems. Potentially harmful consequences in early life include unstable breathing and decreased adaptability of cardiorespiratory function, particularly during early life challenges, such as prematurity or viral infection. Graphical abstract ᅟ.

Does the Temporal Asymmetry of Short-Term Heart Rate Variability Change during Regular Walking? A Pilot Study of Healthy Young Subjects

The acceleration and deceleration patterns in heartbeat fluctuations distribute asymmetrically, which is known as heart rate asymmetry (HRA). It is hypothesized that HRA reflects the balancing regulation of the sympathetic and parasympathetic nervous systems. This study was designed to examine whether altered autonomic balance during exercise can lead to HRA changes. Sixteen healthy college students were enrolled, and each student undertook two 5-min ECG measurements: one in a resting seated position and another while walking on a treadmill at a regular speed of 5 km/h. The two measurements were conducted in a randomized order, and a 30-min rest was required between them. RR interval time series were extracted from the 5-min ECG data, and HRA (short-term) was estimated using four established metrics, that is, Porta's index (PI), Guzik's index (GI), slope index (SI), and area index (AI), from both raw RR interval time series and the time series after wavelet detrending that removes the low-frequency component of <~0.03 Hz. Our pilot data showed a reduced PI but unchanged GI, SI, and AI during walking compared to resting seated position based on the raw data. Based on the wavelet-detrended data, reduced PI, SI, and AI were observed while GI still showed no significant changes. The reduced PI during walking based on both raw and detrended data which suggests less short-term HRA may underline the belief that vagal tone is withdrawn during low-intensity exercise. GI may not be sensitive to short-term HRA. The reduced SI and AI based on detrended data suggest that they may capture both short- and long-term HRA features and that the expected change in short-term HRA is amplified after removing the trend that is supposed to link to long-term component. Further studies with more subjects and longer measurements are warranted to validate our observations and to examine these additional hypotheses.

Heartbeats Do Not Make Good Pseudo-Random Number Generators: An Analysis of the Randomness of Inter-Pulse Intervals

The proliferation of wearable and implantable medical devices has given rise to an interest in developing security schemes suitable for these systems and the environment in which they operate. One area that has received much attention lately is the use of (human) biological signals as the basis for biometric authentication, identification and the generation of cryptographic keys. The heart signal (e.g., as recorded in an electrocardiogram) has been used by several researchers in the last few years. Specifically, the so-called Inter-Pulse Intervals (IPIs), which is the time between two consecutive heartbeats, have been repeatedly pointed out as a potentially good source of entropy and are at the core of various recent authentication protocols. In this work, we report the results of a large-scale statistical study to determine whether such an assumption is (or not) upheld. For this, we have analyzed 19 public datasets of heart signals from the Physionet repository, spanning electrocardiograms from 1353 subjects sampled at different frequencies and with lengths that vary between a few minutes and several hours. We believe this is the largest dataset on this topic analyzed in the literature. We have then applied a standard battery of randomness tests to the extracted IPIs. Under the algorithms described in this paper and after analyzing these 19 public ECG datasets, our results raise doubts about the use of IPI values as a good source of randomness for cryptographic purposes. This has repercussions both in the security of some of the protocols proposed up to now and also in the design of future IPI-based schemes.