Chronic obstructive pulmonary disease (COPD) is one of the most prevalent lung diseases worldwide. COPD patients show major dysfunction in cardiac autonomic modulation due to sustained hypoxaemia, which has been significantly related to higher risk of cardiovascular disease. Obstructive sleep apnoea syndrome (OSAS) is a frequent comorbidity in COPD patients. It has been found that patients suffering from both COPD and OSAS simultaneously, the so-called overlap syndrome, have notably higher morbidity and mortality. Heart rate variability (HRV) has demonstrated to be useful to assess changes in autonomic functioning in different clinical conditions. However, there is still little scientific evidence on the magnitude of changes in cardiovascular dynamics elicited by the combined effect of both respiratory diseases, particularly during sleep, when apnoeic events occur. In this regard, we hypothesised that a non-linear analysis is able to provide further insight into long-term dynamics of overnight cardiovascular modulation. Accordingly, this study is aimed at assessing the usefulness of sample entropy (SampEn) to distinguish changes in overnight pulse rate variability (PRV) recordings among three patient groups while sleeping: COPD, moderate-to-severe OSAS, and overlap syndrome. In order to achieve this goal, a population composed of 297 patients were studied: 22 with COPD alone, 213 showing moderate-to-severe OSAS, and 62 with COPD and moderate-to-severe OSAS simultaneously (COPD+OSAS). Cardiovascular dynamics were analysed using pulse rate (PR) recordings from unattended pulse oximetry carried out at patients’ home. Conventional time- and frequency- domain analyses were performed to characterise sympathetic and parasympathetic activation of the nervous system, while SampEn was applied to quantify long-term changes in irregularity. Our analyses revealed that overnight PRV recordings from COPD+OSAS patients were significantly more irregular (higher SampEn) than those from patients with COPD alone (0.267 [0.210–0.407] vs. 0.212 [0.151–0.267]; p < 0.05) due to recurrent apnoeic events during the night. Similarly, COPD + OSAS patients also showed significantly higher irregularity in PRV during the night than subjects with OSAS alone (0.267 [0.210–0.407] vs. 0.241 [0.189–0.325]; p = 0.05), which suggests that the cumulative effect of both diseases increases disorganization of pulse rate while sleeping. On the other hand, no statistical significant differences were found between COPD and COPD + OSAS patients when traditional frequency bands (LF and HF) were analysed. We conclude that SampEn is able to properly quantify changes in overnight cardiovascular dynamics of patients with overlap syndrome, which could be useful to assess cardiovascular impairment in COPD patients due to the presence of concomitant OSAS. Full article

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. Full article

To optimize long-term nocturnal non-invasive ventilation in patients with chronic obstructive pulmonary disease, surface diaphragm electromyography (EMGdi) might be helpful to detect patient-ventilator asynchrony. However, visual analysis is labor-intensive and EMGdi is heavily corrupted by electrocardiographic (ECG) activity. Therefore, we developed an automatic method to detect inspiratory onset from EMGdi envelope using fixed sample entropy (fSE) and a dynamic threshold based on kernel density estimation (KDE). Moreover, we combined fSE with adaptive filtering techniques to reduce ECG interference and improve onset detection. The performance of EMGdi envelopes extracted by applying fSE and fSE with adaptive filtering was compared to the root mean square (RMS)-based envelope provided by the EMG acquisition device. Automatic onset detection accuracy, using these three envelopes, was evaluated through the root mean square error (RMSE) between the automatic and mean visual onsets (made by two observers). The fSE-based method provided lower RMSE, which was reduced from 298 ms to 264 ms when combined with adaptive filtering, compared to 301 ms provided by the RMS-based method. The RMSE was negatively correlated with the proposed EMGdi quality indices. Following further validation, fSE with KDE, combined with adaptive filtering when dealing with low quality EMGdi, indicates promise for detecting the neural onset of respiratory drive. Full article

The effect of motivation and attention could play an important role in providing personalized learning services and improving learners toward smart education. These effects on brain activity could be quantified by EEG and open the path to analyze the efficiency of services during the learning process. Many studies reported the appearance of EEG alpha desynchronization during the attention period, resulting in better cognitive performance. Motivation was also found to be reflected in EEG. This study investigated the effect of intrinsic motivation on the alpha desynchronization pattern in terms of the complexity of time series data. The sample entropy method was used to quantify the complexity of event-related spectral perturbation (ERSP) of EEG data. We found that when participants can remember the stimulus, ERSP was significantly less complex than when they cannot. However, the effect of intrinsic motivation cannot be defined by using sample entropy directly. ERSP’s main effect showed that motivation affects the complexity of ERSP data; longer continuous alpha desynchronization patterns were found when participants were motivated. Therefore, we introduced an algorithm to identify the longest continuous alpha desynchronization pattern. The method allowed us to understand that intrinsic motivation has an effect on recognition at the frontal and left parietal area directly. Full article

Brain–computer interfaces (BCI) have traditionally worked using synchronous paradigms. In recent years, much effort has been put into reaching asynchronous management, providing users with the ability to decide when a command should be selected. However, to the best of our knowledge, entropy metrics have not yet been explored. The present study has a twofold purpose: (i) to characterize both control and non-control states by examining the regularity of electroencephalography (EEG) signals; and (ii) to assess the efficacy of a scaled version of the sample entropy algorithm to provide asynchronous control for BCI systems. Ten healthy subjects participated in the study, who were asked to spell words through a visual oddball-based paradigm, attending (i.e., control) and ignoring (i.e., non-control) the stimuli. An optimization stage was performed for determining a common combination of hyperparameters for all subjects. Afterwards, these values were used to discern between both states using a linear classifier. Results show that control signals are more complex and irregular than non-control ones, reaching an average accuracy of $94.40\%$ in classification. In conclusion, the present study demonstrates that the proposed framework is useful in monitoring the attention of a user, and granting the asynchrony of the BCI system. Full article

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. Full article

Natural magnetotelluric signals are extremely weak and susceptible to various types of noise pollution. To obtain more useful magnetotelluric data for further analysis and research, effective signal-noise identification and separation is critical. To this end, we propose a novel method of magnetotelluric signal-noise identification and separation based on ApEn-MSE and Stagewise orthogonal matching pursuit (StOMP). Parameters with good irregularity metrics are introduced: Approximate entropy (ApEn) and multiscale entropy (MSE), in combination with k-means clustering, can be used to accurately identify the data segments that are disturbed by noise. Stagewise orthogonal matching pursuit (StOMP) is used for noise suppression only in data segments identified as containing strong interference. Finally, we reconstructed the signal. The results show that the proposed method can better preserve the low-frequency slow-change information of the magnetotelluric signal compared with just using StOMP, thus avoiding the loss of useful information due to over-processing, while producing a smoother and more continuous apparent resistivity curve. Moreover, the results more accurately reflect the inherent electrical structure information of the measured site itself. Full article

Catheter ablation of critical electrical propagation sites is a promising tool for reducing the recurrence of atrial fibrillation (AF). The spatial identification of the arrhythmogenic mechanisms sustaining AF requires the evaluation of electrograms (EGMs) recorded over the atrial surface. This work aims to characterize functional reentries using measures of entropy to track and detect a reentry core. To this end, different AF episodes are simulated using a 2D model of atrial tissue. Modified Courtemanche human action potential and Fenton–Karma models are implemented. Action potential propagation is modeled by a fractional diffusion equation, and virtual unipolar EGM are calculated. Episodes with stable and meandering rotors, figure-of-eight reentry, and disorganized propagation with multiple reentries are generated. Shannon entropy ( $ShEn$ ), approximate entropy ( $ApEn$ ), and sample entropy ( $SampEn$ ) are computed from the virtual EGM, and entropy maps are built. Phase singularity maps are implemented as references. The results show that $ApEn$ and $SampEn$ maps are able to detect and track the reentry core of rotors and figure-of-eight reentry, while the $ShEn$ results are not satisfactory. Moreover, $ApEn$ and $SampEn$ consistently highlight a reentry core by high entropy values for all of the studied cases, while the ability of $ShEn$ to characterize the reentry core depends on the propagation dynamics. Such features make the $ApEn$ and $SampEn$ maps attractive tools for the study of AF reentries that persist for a period of time that is similar to the length of the observation window, and reentries could be interpreted as AF-sustaining mechanisms. Further research is needed to determine and fully understand the relation of these entropy measures with fibrillation mechanisms other than reentries. Full article

Fixed sample entropy (fSampEn) has been successfully applied to myographic signals for inspiratory muscle activity estimation, attenuating interference from cardiac activity. However, several values have been suggested for fSampEn parameters depending on the application, and there is no consensus standard for optimum values. This study aimed to perform a thorough evaluation of the performance of the most relevant fSampEn parameters in myographic respiratory signals, and to propose, for the first time, a set of optimal general fSampEn parameters for a proper estimation of inspiratory muscle activity. Different combinations of fSampEn parameters were used to calculate fSampEn in both non-invasive and the gold standard invasive myographic respiratory signals. All signals were recorded in a heterogeneous population of healthy subjects and chronic obstructive pulmonary disease patients during loaded breathing, thus allowing the performance of fSampEn to be evaluated for a variety of inspiratory muscle activation levels. The performance of fSampEn was assessed by means of the cross-covariance of fSampEn time-series and both mouth and transdiaphragmatic pressures generated by inspiratory muscles. A set of optimal general fSampEn parameters was proposed, allowing fSampEn of different subjects to be compared and contributing to improving the assessment of inspiratory muscle activity in health and disease. Full article

Analysis of eye movement has attracted a lot of attention recently in terms of exploring areas of people’s interest, cognitive ability, and skills. The basis for eye movement usage in these applications is the detection of its main components—namely, fixations and saccades, which facilitate understanding of the spatiotemporal processing of a visual scene. In the presented research, a novel approach for the detection of eye movement events is proposed, based on the concept of approximate entropy. By using the multiresolution time-domain scheme, a structure entitled the Multilevel Entropy Map was developed for this purpose. The dataset was collected during an experiment utilizing the “jumping point” paradigm. Eye positions were registered with a 1000 Hz sampling rate. For event detection, the knn classifier was applied. The best classification efficiency in recognizing the saccadic period ranged from 83% to 94%, depending on the sample size used. These promising outcomes suggest that the proposed solution may be used as a potential method for describing eye movement dynamics. Full article

Pressure ulcers are one of the most common complications of a spinal cord injury (SCI). Prolonged unrelieved pressure is thought to be the primary causative factor resulting in tissue ischemia and eventually pressure ulcers. Previous studies suggested that local cooling reduces skin ischemia of the compressed soft tissues based on smaller hyperemic responses. However, the effect of local cooling on nonlinear properties of skin blood flow (SBF) during hyperemia is unknown. In this study, 10 wheelchair users with SCI and 10 able-bodied (AB) controls underwent three experimental protocols, each of which included a 10-min period as baseline, a 20-min intervention period, and a 20-min period for recovering SBF. SBF was measured using a laser Doppler flowmetry. During the intervention period, a pressure of 60 mmHg was applied to the sacral skin, while three skin temperature settings were tested, including no temperature change, a decrease by 10 °C, and an increase by 10 °C, respectively. A multiscale entropy (MSE) method was employed to quantify the degree of regularity of blood flow oscillations (BFO) associated with the SBF control mechanisms during baseline and reactive hyperemia. The results showed that under pressure with cooling, skin BFO both in people with SCI and AB controls were more regular at multiple time scales during hyperemia compared to baseline, whereas under pressure with no temperature change and particularly pressure with heating, BFO were more irregular during hyperemia compared to baseline. Moreover, the results of surrogate tests indicated that changes in the degree of regularity of BFO from baseline to hyperemia were only partially attributed to changes in relative amplitudes of endothelial, neurogenic, and myogenic components of BFO. These findings support the use of MSE to assess the efficacy of local cooling on reactive hyperemia and assess the degree of skin ischemia in people with SCI. Full article

The modeling and forecasting of BBS (Bulletin Board System) posts time series is crucial for government agencies, corporations and website operators to monitor public opinion. Accurate prediction of the number of BBS posts will assist government agencies or corporations in making timely decisions and estimating the future number of BBS posts will help website operators to allocate resources to deal with the possible hot events pressure. By combining sample entropy (SampEn) and deep neural networks (DNN), an approach (SampEn-DNN) is proposed for BBS posts time series modeling and forecasting. The main idea of SampEn-DNN is to utilize SampEn to decide the input vectors of DNN with smallest complexity, and DNN to enhance the prediction performance of time series. Selecting Tianya Zatan new posts as the data source, the performances of SampEn-DNN were compared with auto-regressive integrated moving average (ARIMA), seasonal ARIMA, polynomial regression, neural networks, etc. approaches for prediction of the daily number of new posts. From the experimental results, it can be found that the proposed approach SampEn-DNN outperforms the state-of-the-art approaches for BBS posts time series modeling and forecasting. Full article

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. Full article

This paper analyses the performance of SampEn and one of its derivatives, Fuzzy Entropy (FuzzyEn), in the context of artifacted blood glucose time series classification. This is a difficult and practically unexplored framework, where the availability of more sensitive and reliable measures could be of great clinical impact. Although the advent of new blood glucose monitoring technologies may reduce the incidence of the problems stated above, incorrect device or sensor manipulation, patient adherence, sensor detachment, time constraints, adoption barriers or affordability can still result in relatively short and artifacted records, as the ones analyzed in this paper or in other similar works. This study is aimed at characterizing the changes induced by such artifacts, enabling the arrangement of countermeasures in advance when possible. Despite the presence of these disturbances, results demonstrate that SampEn and FuzzyEn are sufficiently robust to achieve a significant classification performance, using records obtained from patients with duodenal-jejunal exclusion. The classification results, in terms of area under the ROC of up to 0.9, with several tests yielding AUC values also greater than 0.8, and in terms of a leave-one-out average classification accuracy of 80%, confirm the potential of these measures in this context despite the presence of artifacts, with SampEn having slightly better performance than FuzzyEn. Full article

Sample entropy (SE) has relative consistency using biologically-derived, discrete data >500 data points. For certain populations, collecting this quantity is not feasible and continuous data has been used. The effect of using continuous versus discrete data on SE is unknown, nor are the relative effects of sampling rate and input parameters m (comparison vector length) and r (tolerance). Eleven subjects walked for 10-minutes and continuous joint angles (480 Hz) were calculated for each lower-extremity joint. Data were downsampled (240, 120, 60 Hz) and discrete range-of-motion was calculated. SE was quantified for angles and range-of-motion at all sampling rates and multiple combinations of parameters. A differential relationship between joints was observed between range-of-motion and joint angles. Range-of-motion SE showed no difference; whereas, joint angle SE significantly decreased from ankle to knee to hip. To confirm findings from biological data, continuous signals with manipulations to frequency, amplitude, and both were generated and underwent similar analysis to the biological data. In general, changes to m, r, and sampling rate had a greater effect on continuous compared to discrete data. Discrete data was robust to sampling rate and m. It is recommended that different data types not be compared and discrete data be used for SE. Full article

The present study aimed at testing the hypothesis that application of multiscale cross-approximate entropy (MCAE) analysis in the study of nonlinear coupling behavior of two synchronized time series of different natures [i.e., R-R interval (RRI) and crest time (CT, the time interval from foot to peakof a pulse wave)] could yield information on complexity related to diabetes-associated vascular changes. Signals of a single waveform parameter (i.e., CT) from photoplethysmography and RRI from electrocardiogram were simultaneously acquired within a period of one thousand cardiac cycles for the computation of different multiscale entropy indices from healthy young adults (n = 22) (Group 1), upper-middle aged non-diabetic subjects (n = 34) (Group 2) and diabetic patients (n = 34) (Group 3). The demographic (i.e., age), anthropometric (i.e., body height, body weight, waist circumference, body-mass index), hemodynamic (i.e., systolic and diastolic blood pressures), and serum biochemical (i.e., high- and low-density lipoprotein cholesterol, total cholesterol, and triglyceride) parameters were compared with different multiscale entropy indices including small- and large-scale multiscale entropy indices for CT and RRI [MEI_SS(CT), MEI_LS(CT), MEI_SS(RRI), MEI_LS(RRI), respectively] as well as small- and large-scale multiscale cross-approximate entropy indices [MCEI_SS, MCEI_LS, respectively]. The results demonstrated that both MEI_LS(RRI) and MCEI_LS significantly differentiated between Group 2 and Group 3 (all p < 0.017). Multivariate linear regression analysis showed significant associations of MEI_LS(RRI) and MCEI_LS(RRI,CT) with age and glycated hemoglobin level (all p < 0.017). The findings highlight the successful application of a novel multiscale cross-approximate entropy index in non-invasively identifying diabetes-associated subtle changes in vascular functional integrity, which is of clinical importance in preventive medicine. Full article