Assessing the complexity of short-term heartbeat interval series by distribution entropy

Effects of Sensory Input Interactions on Components of Nonlinear Dynamics of Postural Sway in Aging

Postural control involves complex nonlinear dynamics influenced by the interaction and adaptation of different sensory inputs. However, it is not how these inputs interact with one another due to the complex complications associated with aging, particularly concerning the nonlinear dynamics of postural sway. This study aimed to examine how different sensory inputs, surface conditions, and aging factors to influence postural control mechanisms between young and older by investigating the nonlinear dynamics of postural control using the stabilogram diffusion analysis (SDA) and entropy methods. SDA parameters were much greater on foam surfaces than on firm surfaces for both groups in eyes-open and eyes-closed conditions (p ≤ 0.05). For older subjects, there were significant differences in entropy values between firm and foam surfaces (p ≤ 0.05) but no significant difference between eyes conditions (p > 0.05). For both SDA and entropy parameters, surface and age interaction potentially revealed significant differences between young and older subjects (p ≤ 0.05) than eyes and age interaction. The present study provided insight into uncovering the complex relationships between sensory inputs, surface conditions, age, and their potential interaction effects on postural control mechanisms that could mitigate falls and alleviate the fear of falling, particularly in older populations.

NLDyn - An open source MATLAB toolbox for the univariate and multivariate nonlinear dynamical analysis of physiological data

BACKGROUND AND OBJECTIVE

We present NLDyn, an open-source MATLAB toolbox tailored for in-depth analysis of nonlinear dynamics in biomedical signals. Our objective is to offer a user-friendly yet comprehensive platform for researchers to explore the intricacies of time series data.

METHODS

NLDyn integrates approximately 80 distinct methods, encompassing both univariate and multivariate nonlinear dynamics, setting it apart from existing solutions. This toolbox combines state-of-the-art nonlinear dynamical techniques with advanced multivariate entropy methods, providing users with powerful analytical capabilities. NLDyn enables analyses with or without a sliding window, and users can easily access and customize default parameters.

RESULTS

NLDyn generates results that are both exportable and visually informative, facilitating seamless integration into research and presentations. Its ongoing development ensures it remains at the forefront of nonlinear dynamics analysis.

CONCLUSIONS

NLDyn is a valuable resource for researchers in the biomedical field, offering an intuitive interface and a wide array of nonlinear analysis tools. Its integration of advanced techniques empowers users to gain deeper insights from their data. As we continually refine and expand NLDyn's capabilities, we envision it becoming an indispensable tool for the exploration of complex dynamics in biomedical signals.

Evaluation of skin sympathetic nervous activity for classification of intracerebral hemorrhage and outcome prediction

Classification and outcome prediction of intracerebral hemorrhage (ICH) is critical for improving the survival rate of patients. Early or delayed neurological deterioration is common in ICH patients, which may lead to changes in the autonomic nervous system (ANS). Therefore, we proposed a new framework for ICH classification and outcome prediction based on skin sympathetic nervous activity (SKNA) signals. A customized measurement device presented in our previous papers was used to collect data. 117 subjects (50 healthy control subjects and 67 ICH patients) were recruited for this study to obtain their 5-min electrocardiogram (ECG) and SKNA signals. We extracted the signal's time-domain, frequency-domain, and nonlinear features and analyzed their differences between healthy control subjects and ICH patients. Subsequently, we established the ICH classification and outcome evaluation model based on the eXtreme Gradient Boosting (XGBoost). In addition, heart rate variability (HRV) as an ANS assessment method was also included as a comparison method in this study. The results showed significant differences in most features of the SKNA signal between healthy control subjects and ICH patients. The ICH patients with good outcomes have a higher change rate and complexity of SKNA signal than those with bad outcomes. In addition, the accuracy of the model for ICH classification and outcome prediction based on the SKNA signal was more than 91% and 83%, respectively. The ICH classification and outcome prediction based on the SKNA signal proved to be a feasible method in this study. Furthermore, the features of change rate and complexity, such as entropy measures, can be used to characterize the difference in SKNA signals of different groups. The method can potentially provide a new tool for rapid classification and outcome prediction of ICH patients. Index Terms-intracerebral hemorrhage (ICH), skin sympathetic nervous activity (SKNA), classification, outcome prediction, cardiovascular and cerebrovascular diseases.

Ensemble Improved Permutation Entropy: A New Approach for Time Series Analysis

Entropy quantification approaches have gained considerable attention in engineering applications. However, certain limitations persist, including the strong dependence on parameter selection, limited discriminating power, and low robustness to noise. To alleviate these issues, this paper introduces two novel algorithms for time series analysis: the ensemble improved permutation entropy (EIPE) and multiscale EIPE (MEIPE). Our approaches employ a new symbolization process that considers both permutation relations and amplitude information. Additionally, the ensemble technique is utilized to reduce the dependence on parameter selection. We performed a comprehensive evaluation of the proposed methods using various synthetic and experimental signals. The results illustrate that EIPE is capable of distinguishing white, pink, and brown noise with a smaller number of samples compared to traditional entropy algorithms. Furthermore, EIPE displays the potential to discriminate between regular and non-regular dynamics. Notably, when compared to permutation entropy, weighted permutation entropy, and dispersion entropy, EIPE exhibits superior robustness against noise. In practical applications, such as RR interval data classification, bearing fault diagnosis, marine vessel identification, and electroencephalographic (EEG) signal classification, the proposed methods demonstrate better discriminating power compared to conventional entropy measures. These promising findings validate the effectiveness and potential of the algorithms proposed in this paper.

Characterization of autonomic states by complex sympathetic and parasympathetic dynamics

Assessment of heartbeat dynamics provides a promising framework for non-invasive monitoring of cardiovascular and autonomic states. Nevertheless, the non-specificity of such measurements among clinical populations and healthy conditions associated with different autonomic states severely limits their applicability and exploitation in naturalistic conditions. This limitation arises especially when pathological or postural change-related sympathetic hyperactivity is compared to autonomic changes across age and experimental conditions. In this frame, we investigate the intrinsic irregularity and complexity of cardiac sympathetic and vagal activity series in different populations, which are associated with different cardiac autonomic dynamics. Sample entropy, fuzzy entropy, and distribution entropy are calculated on the recently proposed sympathetic and parasympathetic activity indices (SAI and PAI) series, which are derived from publicly available heartbeat series of congestive heart failure patients, elderly and young subjects watching a movie in the supine position, and healthy subjects undergoing slow postural changes. Results show statistically significant differences between pathological/old subjects and young subjects in the resting state and during slow tilt, with interesting trends in SAI- and PAI-related entropy values. Moreover, while CHF patients and healthy subjects in upright position show the higher cardiac sympathetic activity, elderly and young subjects in resting state showed higher vagal activity. We conclude that quantification of intrinsic cardiac complexity from sympathetic and vagal dynamics may provide new physiology insights and improve on the non-specificity of heartbeat-derived biomarkers.

Complexity and Entropy in Physiological Signals (CEPS): Resonance Breathing Rate Assessed Using Measures of Fractal Dimension, Heart Rate Asymmetry and Permutation Entropy

BACKGROUND

As technology becomes more sophisticated, more accessible methods of interpretating Big Data become essential. We have continued to develop Complexity and Entropy in Physiological Signals (CEPS) as an open access MATLAB® GUI (graphical user interface) providing multiple methods for the modification and analysis of physiological data.

METHODS

To demonstrate the functionality of the software, data were collected from 44 healthy adults for a study investigating the effects on vagal tone of breathing paced at five different rates, as well as self-paced and un-paced. Five-minute 15-s recordings were used. Results were also compared with those from shorter segments of the data. Electrocardiogram (ECG), electrodermal activity (EDA) and Respiration (RSP) data were recorded. Particular attention was paid to COVID risk mitigation, and to parameter tuning for the CEPS measures. For comparison, data were processed using Kubios HRV, RR-APET and DynamicalSystems.jl software. We also compared findings for ECG RR interval (RRi) data resampled at 4 Hz (4R) or 10 Hz (10R), and non-resampled (noR). In total, we used around 190-220 measures from CEPS at various scales, depending on the analysis undertaken, with our investigation focused on three families of measures: 22 fractal dimension (FD) measures, 40 heart rate asymmetries or measures derived from Poincaré plots (HRA), and 8 measures based on permutation entropy (PE).

RESULTS

FDs for the RRi data differentiated strongly between breathing rates, whether data were resampled or not, increasing between 5 and 7 breaths per minute (BrPM). Largest effect sizes for RRi (4R and noR) differentiation between breathing rates were found for the PE-based measures. Measures that both differentiated well between breathing rates and were consistent across different RRi data lengths (1-5 min) included five PE-based (noR) and three FDs (4R). Of the top 12 measures with short-data values consistently within ± 5% of their values for the 5-min data, five were FDs, one was PE-based, and none were HRAs. Effect sizes were usually greater for CEPS measures than for those implemented in DynamicalSystems.jl.

CONCLUSION

The updated CEPS software enables visualisation and analysis of multichannel physiological data using a variety of established and recently introduced complexity entropy measures. Although equal resampling is theoretically important for FD estimation, it appears that FD measures may also be usefully applied to non-resampled data.

Sample, Fuzzy and Distribution Entropies of Heart Rate Variability: What Do They Tell Us on Cardiovascular Complexity?

Distribution Entropy (DistEn) has been introduced as an alternative to Sample Entropy (SampEn) to assess the heart rate variability (HRV) on much shorter series without the arbitrary definition of distance thresholds. However, DistEn, considered a measure of cardiovascular complexity, differs substantially from SampEn or Fuzzy Entropy (FuzzyEn), both measures of HRV randomness. This work aims to compare DistEn, SampEn, and FuzzyEn analyzing postural changes (expected to modify the HRV randomness through a sympatho/vagal shift without affecting the cardiovascular complexity) and low-level spinal cord injuries (SCI, whose impaired integrative regulation may alter the system complexity without affecting the HRV spectrum). We recorded RR intervals in able-bodied (AB) and SCI participants in supine and sitting postures, evaluating DistEn, SampEn, and FuzzyEn over 512 beats. The significance of "case" (AB vs. SCI) and "posture" (supine vs. sitting) was assessed by longitudinal analysis. Multiscale DistEn (mDE), SampEn (mSE), and FuzzyEn (mFE) compared postures and cases at each scale between 2 and 20 beats. Unlike SampEn and FuzzyEn, DistEn is affected by the spinal lesion but not by the postural sympatho/vagal shift. The multiscale approach shows differences between AB and SCI sitting participants at the largest mFE scales and between postures in AB participants at the shortest mSE scales. Thus, our results support the hypothesis that DistEn measures cardiovascular complexity while SampEn/FuzzyEn measure HRV randomness, highlighting that together these methods integrate the information each of them provides.

ComEDA: A new tool for stress assessment based on electrodermal activity

Non-specific sympathetic arousal responses to different stressful elicitations can be easily recognized from the analysis of physiological signals. However, neural patterns of sympathetic arousal during physical and mental fatigue are clearly not unitary. In the context of physiological monitoring through wearable and non-invasive devices, electrodermal activity (EDA) is the most effective and widely used marker of sympathetic activation. This study presents ComEDA, a novel approach for the characterization of complex dynamics of EDA. ComEDA overcomes the methodological limitations related to the application of nonlinear analysis to EDA dynamics, is not parameter-sensitive and is suitable for the analysis of ultra-short time series. We validated the proposed algorithm using synthetic series of white noise and 1/f noise, varying the number of samples from 50 to 5000. By applying our approach, we were able to discriminate a statistically significant increase of complexity in the 1/f noise with respect to white noise, obtaining p-values in the range [4.35 × 10-6, 0.03] after the Mann-Whitney test. Then, we tested ComEDA on both EDA signal and its tonic and phasic components, acquired from healthy subjects during four experimental protocols: two inducing a sympathetic activation through physical efforts and two based on mentally stressful tasks. Results are encouraging and promising, outperforming state of the art metrics such as the Sample Entropy. ComEDA shows good performance not only in discriminating between stressful tasks and resting state (p-value < 0.01 after the Wilcoxon non-parametric statistical test applied to EDA signals of all the four datasets), but also in differentiating different trends of complexity of EDA dynamics when induced by physical and mental stressors. These findings suggest future applications to automatically detect and selectively identify threats due to overwhelming stress impacting both physical and mental health or in the field of telemedicine to monitor autonomic diseases correlated to atypical sympathetic activation. The Matlab code implementing the ComEDA algorithm is available online.

Multivariate Pattern Analysis of Entropy estimates in Fast- and Slow-Wave Functional Near Infrared Spectroscopy: A Preliminary Cognitive Stress study

Functional near infrared spectroscopy (fNIRS) is a modality that can measure shallow cortical brain signals and also contains pulsatile oscillations that originate from heartbeat dynamics. In particular, while fNIRS slow waves (0 Hz to 0.6 Hz) refer to the standard hemodynamic signal, fast-wave (0.8 Hz to 3 Hz) fNIRS signals refer to cardiac oscillations. Using a cognitive stress experiment paradigm with mental arithmetic, the aim of this study was to assess differences in cortical activity when using slow-wave or fast-wave fNIRS signals. Furthermore, we aimed to see whether fNIRS fast and slow waves provide different information to discriminate mental arithmetic tasks from baseline. We used data from 10 healthy subjects from an open dataset performing mental arithmetic tasks and assessed fNIRS signals using mean values in the time domain, as well as complexity estimates including sample, fuzzy, and distribution entropy. A searchlight representational similarity analysis with pairwise t-test group analysis was performed to compare the representational dissimilarity matrices of each searchlight center. We found significant representational differences between fNIRS fast and slow waves for all complexity estimates, at different brain regions. On the other hand, no statistical differences were observed for mean values. We conclude that entropy analysis of fNIRS data may be more sensitive than traditional methods like mean analysis at detecting the additional information provided by fast-wave signals for discriminating mental arithmetic tasks and warrants further research.

Wearable Electrocardiogram Quality Assessment Using Wavelet Scattering and LSTM

As the fast development of wearable devices and Internet of things technologies, real-time monitoring of ECG signals is quite critical for cardiovascular diseases. However, dynamic ECG signals recorded in free-living conditions suffered from extremely serious noise pollution. Presently, most algorithms for ECG signal evaluation were designed to divide signals into acceptable and unacceptable. Such classifications were not enough for real-time cardiovascular disease monitoring. In the study, a wearable ECG quality database with 50,085 recordings was built, including A/B/C (or high quality/medium quality/low quality) three quality grades (A: high quality signals can be used for CVD detection; B: slight contaminated signals can be used for heart rate extracting; C: heavily polluted signals need to be abandoned). A new SQA classification method based on a three-layer wavelet scattering network and transfer learning LSTM was proposed in this study, which can extract more systematic and comprehensive characteristics by analyzing the signals thoroughly and deeply. Experimental results (mACC = 98.56%, mF₁ = 98.55%, Se_A = 97.90%, Se_B = 98.16%, Se_C = 99.60%, +P_A = 98.52%, +P_B = 97.60%, +P_C = 99.54%, F_1A = 98.20%, F_1B = 97.90%, F_1C = 99.60%) and real data validations proved that this proposed method showed the high accuracy, robustness, and computationally efficiency. It has the ability to evaluate the long-term dynamic ECG signal quality. It is advantageous to promoting cardiovascular disease monitoring by removing contaminating signals and selecting high-quality signal segments for further analysis.

Heart rate variability as a biomarker in patients with Chronic Chagas Cardiomyopathy with or without concomitant digestive involvement and its relationship with the Rassi score

Background

Dysautonomia plays an ancillary role in the pathogenesis of Chronic Chagas Cardiomyopathy (CCC), but is the key factor causing digestive organic involvement. We investigated the ability of heart rate variability (HRV) for death risk stratification in CCC and compared alterations of HRV in patients with isolated CCC and in those with the mixed form (CCC + digestive involvement). Thirty-one patients with CCC were classified into three risk groups (low, intermediate and high) according to their Rassi score. A single-lead ECG was recorded for a period of 10–20 min, RR series were generated and 31 HRV indices were calculated. The HRV was compared among the three risk groups and regarding the associated digestive involvement. Four machine learning models were created to predict the risk class of patients.

Results

Phase entropy is decreased and the percentage of inflection points is increased in patients from the high-, compared to the low-risk group. Fourteen patients had the mixed form, showing decreased triangular interpolation of the RR histogram and absolute power at the low-frequency band. The best predictive risk model was obtained by the support vector machine algorithm (overall F1-score of 0.61).

Conclusions

The mixed form of Chagas' disease showed a decrease in the slow HRV components. The worst prognosis in CCC is associated with increased heart rate fragmentation. The combination of HRV indices enhanced the accuracy of risk stratification. In patients with the mixed form of Chagas disease, a higher degree of sympathetic autonomic denervation may be associated with parasympathetic impairment.

On the Possibility of Designing an Advanced Sensor with Particle Sizing Using Dynamic Light Scattering Time Series Spectral Entropy and Artificial Neural Network

Dynamic Light Scattering is a well-established technique used in particle sizing. An alternative procedure for Dynamic Light Scattering time series processing based on spectral entropy computation and Artificial Neural Networks is described. An error analysis of the proposed method was carried out and the results on both the simulated and on the experimental DLS time series are presented in detail. The results reveal the possibility of designing an advanced sensor capable of detecting particles with a size bigger than a threshold using this alternative for processing the DLS time series.

Heart Rate Variability Analysis for Seizure Detection in Neonatal Intensive Care Units

In Neonatal Intensive Care Units (NICUs), the early detection of neonatal seizures is of utmost importance for a timely clinical intervention. Over the years, several neonatal seizure detection systems were proposed to detect neonatal seizures automatically and speed up seizure diagnosis, most based on the EEG signal analysis. Recently, research has focused on other possible seizure markers, such as electrocardiography (ECG). This work proposes an ECG-based NSD system to investigate the usefulness of heart rate variability (HRV) analysis to detect neonatal seizures in the NICUs. HRV analysis is performed considering time-domain, frequency-domain, entropy and multiscale entropy features. The performance is evaluated on a dataset of ECG signals from 51 full-term babies, 29 seizure-free. The proposed system gives results comparable to those reported in the literature: Area Under the Receiver Operating Characteristic Curve = 62%, Sensitivity = 47%, Specificity = 67%. Moreover, the system’s performance is evaluated in a real clinical environment, inevitably affected by several artefacts. To the best of our knowledge, our study proposes for the first time a multi-feature ECG-based NSD system that also offers a comparative analysis between babies suffering from seizures and seizure-free ones.

Automated Detection of Sudden Cardiac Death by Discrete Wavelet Transform of Electrocardiogram Signal

Sudden cardiac death (SCD) results in millions of deaths annually; as it is a fatal heart abnormality, early prediction of SCD could save peoples’ lives to the greatest extent. Symmetry and asymmetry play an important role in many fields. Electrocardiograms (ECG) as a noninvasive process for acquiring the electrical activity of the heart, has both asymmetric and non-stationary characteristics; it is frequently employed to diagnose and evaluate the heart’s condition. In this work, we have detected SCD 14 min (separately for each one-minute interval) prior to its occurrence by analyzing ECG signals using discrete wavelet transform (DWT) and locality preserving projection (LPP). In the experiment, we have performed DWT on ECG signals to obtain coefficients, then LPP as a reduction methodology was used to cut down these obtained coefficients. Then, the acquired LPP features were ranked using various methods, including the T-test, Bhattacharyya, Wilcoxon, and entropy. At last, the highly ranked LPP features were subjected to decision tree, k-nearest neighbor (KNN), and support vector machine classifiers for distinguishing normal from SCD ECG signals. Our proposed technique has achieved a highest accuracy of 97.6% for the detection of SCD 14 min prior using the KNN classifier, compared to the existing works. Our proposed method is capable of predicting the people at risk of developing SCD 14 min before its onset, and, hence, clinicians would have enough time to provide treatment in intensive care units (ICU) for a subject at risk of SCD. Thus, this proposed technique as a useful tool can increase the survival rate of many cardiac patients.

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.

Denoising and Feature Extraction for Space Infrared Dim Target Recognition Utilizing Optimal VMD and Dual-Band Thermometry

Space target feature extraction and space infrared target recognition are important components of space situational awareness (SSA). However, owing to far imaging distance between the space target and infrared detector, the infrared signal of the target received by the detector is dim and easily contaminated by noise. To effectively improve the accuracy of feature extraction and recognition, it is essential to suppress the noise of the infrared signal. Hence, a novel denoising and extracting feature method combinating optimal variational mode decomposition (VMD) and dual-band thermometry (DBT) is proposed. It takes the mean weighted fuzzy-distribution entropy (FuzzDistEn) of the band-limited intrinsic mode functions (BLIMFs) as the optimization index of dragonfly algorithm (DA) to obtain the optimal parameters (K, α) of VMD. Then the VMD is utilized to decompose the noisy signal to obtain a series of BLIMFs and the Pearson correlation coefficient (PCC) is proposed to determine the effective modes to reconstructe the denoising signal. Finally, based on the denoising signal, the feature of temperature and emissivity-area product are calculated using the DBT. The simulation and experiment results show that the proposed method has better noise reduction performance compared with the other denoising methods, and the accuracy of feature extraction is improved at different noise equivalent irradiance. This provides more accurate feature of temerpature and emissivity-area product for space infrared dim target recognition.

A Multiscale Partition-Based Kolmogorov–Sinai Entropy for the Complexity Assessment of Heartbeat Dynamics

Background: Several methods have been proposed to estimate complexity in physiological time series observed at different time scales, with a particular focus on heart rate variability (HRV) series. In this frame, while several complexity quantifiers defined in the multiscale domain have already been investigated, the effectiveness of a multiscale Kolmogorov–Sinai (K-S) entropy has not been evaluated yet for the characterization of heartbeat dynamics. Methods: The use of the algorithmic information content, which is estimated through an effective compression algorithm, is investigated to quantify multiscale partition-based K-S entropy on publicly available experimental HRV series gathered from young and elderly subjects undergoing a visual elicitation task (Fantasia). Moreover, publicly available HRV series gathered from healthy subjects, as well as patients with atrial fibrillation and congestive heart failure in unstructured conditions have been analyzed as well. Results: Elderly people are associated with a lower HRV complexity and a more predictable cardiovascular dynamics, with significantly lower partition-based K-S entropy than the young adults. Major differences between these groups occur at partitions greater than six. In case of partition cardinality greater than 5, patients with congestive heart failure show a minimal predictability, while atrial fibrillation shows a higher variability, and hence complexity, which is actually reduced by the time coarse-graining procedure. Conclusions: The proposed multiscale partition-based K-S entropy is a viable tool to investigate complex cardiovascular dynamics in different physiopathological states.

Correlation between heart rate variability and polysomnography-derived scores of obstructive sleep apnea

Obstructive sleep apnea (OSA) is one of the most common sleep disorders and affects nearly a billion people worldwide. Furthermore, it is estimated that many patients with OSA are underdiagnosed, which contributes to the development of comorbidities, such as cardiac autonomic imbalance, leading to high cardiac risk. Heart rate variability (HRV) is a non-invasive, widely used approach to evaluating neural control of the heart. This study evaluates the relationship between HRV indices and the presence and severity of OSA. We hypothesize that HRV, especially the nonlinear methods, can serve as an easy-to-collect marker for OSA early risk stratification. Polysomnography (PSG) exams of 157 patients were classified into four groups: OSA-free (N = 26), OSA-mild (N = 39), OSA-moderate (N = 37), and OSA-severe (N = 55). The electrocardiogram was extracted from the PSG recordings, and a 15-min beat-by-beat series of RR intervals were generated every hour during the first 6 h of sleep. Linear and nonlinear HRV approaches were employed to calculate 32 indices of HRV. Specifically, time- and frequency-domain, symbolic analysis, entropy measures, heart rate fragmentation, acceleration and deceleration capacities, asymmetry measures, and fractal analysis. Results with indices of sympathovagal balance provided support to reinforce previous knowledge that patients with OSA have sympathetic overactivity. Nonlinear indices showed that HRV dynamics of patients with OSA display a loss of physiologic complexity that could contribute to their higher risk of development of cardiovascular disease. Moreover, many HRV indices were found to be linked with clinical scores of PSG. Therefore, a complete set of HRV indices, especially the ones obtained by the nonlinear approaches, can bring valuable information about the presence and severity of OSA, suggesting that HRV can be helpful for in a quick diagnosis of OSA, and supporting early interventions that could potentially reduce the development of comorbidities.

EntropyHub: An open-source toolkit for entropic time series analysis

An increasing number of studies across many research fields from biomedical engineering to finance are employing measures of entropy to quantify the regularity, variability or randomness of time series and image data. Entropy, as it relates to information theory and dynamical systems theory, can be estimated in many ways, with newly developed methods being continuously introduced in the scientific literature. Despite the growing interest in entropic time series and image analysis, there is a shortage of validated, open-source software tools that enable researchers to apply these methods. To date, packages for performing entropy analysis are often run using graphical user interfaces, lack the necessary supporting documentation, or do not include functions for more advanced entropy methods, such as cross-entropy, multiscale cross-entropy or bidimensional entropy. In light of this, this paper introduces EntropyHub, an open-source toolkit for performing entropic time series analysis in MATLAB, Python and Julia. EntropyHub (version 0.1) provides an extensive range of more than forty functions for estimating cross-, multiscale, multiscale cross-, and bidimensional entropy, each including a number of keyword arguments that allows the user to specify multiple parameters in the entropy calculation. Instructions for installation, descriptions of function syntax, and examples of use are fully detailed in the supporting documentation, available on the EntropyHub website- www.EntropyHub.xyz. Compatible with Windows, Mac and Linux operating systems, EntropyHub is hosted on GitHub, as well as the native package repository for MATLAB, Python and Julia, respectively. The goal of EntropyHub is to integrate the many established entropy methods into one complete resource, providing tools that make advanced entropic time series analysis straightforward and reproducible.

Performance Analysis of Entropy Methods in Detecting Epileptic Seizure from Surface Electroencephalograms

Physiological signals like Electrocardiography (ECG) and Electroencephalography (EEG) are complex and nonlinear in nature. To retrieve diagnostic information from these, we need the help of nonlinear methods of analysis. Entropy estimation is a very popular approach in the nonlinear category, where entropy estimates are used as features for signal classification and analysis. In this study, we analyze and compare the performances of four entropy methods; namely Distribution entropy (DistEn), Shannon entropy (ShanEn), Renyi entropy (RenEn) and LempelZiv complexity (LempelZiv) as classification features to detect epileptic seizure (ES) from surface Electroencephalography (sEEG) signal. Experiments were conducted on sEEG data from 23 subjects, obtained from the CHB-MIT database of PhysioNet. ShanEn, RenEn and LempelZiv entropy are found to be potential features for accurate and consistent detection of ES from sEEG, across multiple channels and subjects.

Prediction of epileptic seizures based on multivariate multiscale modified-distribution entropy

Epilepsy is a common neurological disease that affects a wide range of the world population and is not limited by age. Moreover, seizures can occur anytime and anywhere because of the sudden abnormal discharge of brain neurons, leading to malfunction. The seizures of approximately 30% of epilepsy patients cannot be treated with medicines or surgery; hence these patients would benefit from a seizure prediction system to live normal lives. Thus, a system that can predict a seizure before its onset could improve not only these patients' social lives but also their safety. Numerous seizure prediction methods have already been proposed, but the performance measures of these methods are still inadequate for a complete prediction system. Here, a seizure prediction system is proposed by exploring the advantages of multivariate entropy, which can reflect the complexity of multivariate time series over multiple scales (frequencies), called multivariate multiscale modified-distribution entropy (MM-mDistEn), with an artificial neural network (ANN). The phase-space reconstruction and estimation of the probability density between vectors provide hidden complex information. The multivariate time series property of MM-mDistEn provides more understandable information within the multichannel data and makes it possible to predict of epilepsy. Moreover, the proposed method was tested with two different analyses: simulation data analysis proves that the proposed method has strong consistency over the different parameter selections, and the results from experimental data analysis showed that the proposed entropy combined with an ANN obtains performance measures of 98.66% accuracy, 91.82% sensitivity, 99.11% specificity, and 0.84 area under the curve (AUC) value. In addition, the seizure alarm system was applied as a postprocessing step for prediction purposes, and a false alarm rate of 0.014 per hour and an average prediction time of 26.73 min before seizure onset were achieved by the proposed method. Thus, the proposed entropy as a feature extraction method combined with an ANN can predict the ictal state of epilepsy, and the results show great potential for all epilepsy patients.

A Comprehensive Review of Techniques for Processing and Analyzing Fetal Heart Rate Signals

The availability of standardized guidelines regarding the use of electronic fetal monitoring (EFM) in clinical practice has not effectively helped to solve the main drawbacks of fetal heart rate (FHR) surveillance methodology, which still presents inter- and intra-observer variability as well as uncertainty in the classification of unreassuring or risky FHR recordings. Given the clinical relevance of the interpretation of FHR traces as well as the role of FHR as a marker of fetal wellbeing autonomous nervous system development, many different approaches for computerized processing and analysis of FHR patterns have been proposed in the literature. The objective of this review is to describe the techniques, methodologies, and algorithms proposed in this field so far, reporting their main achievements and discussing the value they brought to the scientific and clinical community. The review explores the following two main approaches to the processing and analysis of FHR signals: traditional (or linear) methodologies, namely, time and frequency domain analysis, and less conventional (or nonlinear) techniques. In this scenario, the emerging role and the opportunities offered by Artificial Intelligence tools, representing the future direction of EFM, are also discussed with a specific focus on the use of Artificial Neural Networks, whose application to the analysis of accelerations in FHR signals is also examined in a case study conducted by the authors.

Multiscale Entropy Analysis of Heart Rate Variability in Neonatal Patients with and without Seizures

The complex physiological dynamics of neonatal seizures make their detection challenging. A timely diagnosis and treatment, especially in intensive care units, are essential for a better prognosis and the mitigation of possible adverse effects on the newborn's neurodevelopment. In the literature, several electroencephalographic (EEG) studies have been proposed for a parametric characterization of seizures or their detection by artificial intelligence techniques. At the same time, other sources than EEG, such as electrocardiography, have been investigated to evaluate the possible impact of neonatal seizures on the cardio-regulatory system. Heart rate variability (HRV) analysis is attracting great interest as a valuable tool in newborns applications, especially where EEG technologies are not easily available. This study investigated whether multiscale HRV entropy indexes could detect abnormal heart rate dynamics in newborns with seizures, especially during ictal events. Furthermore, entropy measures were analyzed to discriminate between newborns with seizures and seizure-free ones. A cohort of 52 patients (33 with seizures) from the Helsinki University Hospital public dataset has been evaluated. Multiscale sample and fuzzy entropy showed significant differences between the two groups (p-value < 0.05, Bonferroni multiple-comparison post hoc correction). Moreover, interictal activity showed significant differences between seizure and seizure-free patients (Mann-Whitney Test: p-value < 0.05). Therefore, our findings suggest that HRV multiscale entropy analysis could be a valuable pre-screening tool for the timely detection of seizure events in newborns.

Detection of Coronary Artery Disease Using Multi-Domain Feature Fusion of Multi-Channel Heart Sound Signals

Heart sound signals reflect valuable information about heart condition. Previous studies have suggested that the information contained in single-channel heart sound signals can be used to detect coronary artery disease (CAD). But accuracy based on single-channel heart sound signal is not satisfactory. This paper proposed a method based on multi-domain feature fusion of multi-channel heart sound signals, in which entropy features and cross entropy features are also included. A total of 36 subjects enrolled in the data collection, including 21 CAD patients and 15 non-CAD subjects. For each subject, five-channel heart sound signals were recorded synchronously for 5 min. After data segmentation and quality evaluation, 553 samples were left in the CAD group and 438 samples in the non-CAD group. The time-domain, frequency-domain, entropy, and cross entropy features were extracted. After feature selection, the optimal feature set was fed into the support vector machine for classification. The results showed that from single-channel to multi-channel, the classification accuracy has increased from 78.75% to 86.70%. After adding entropy features and cross entropy features, the classification accuracy continued to increase to 90.92%. The study indicated that the method based on multi-domain feature fusion of multi-channel heart sound signals could provide more information for CAD detection, and entropy features and cross entropy features played an important role in it.

Automated Classification of Mental Arithmetic Tasks Using Recurrent Neural Network and Entropy Features Obtained from Multi-Channel EEG Signals

The automated classification of cognitive workload tasks based on the analysis of multi-channel EEG signals is vital for human–computer interface (HCI) applications. In this paper, we propose a computerized approach for categorizing mental-arithmetic-based cognitive workload tasks using multi-channel electroencephalogram (EEG) signals. The approach evaluates various entropy features, such as the approximation entropy, sample entropy, permutation entropy, dispersion entropy, and slope entropy, from each channel of the EEG signal. These features were fed to various recurrent neural network (RNN) models, such as long-short term memory (LSTM), bidirectional LSTM (BLSTM), and gated recurrent unit (GRU), for the automated classification of mental-arithmetic-based cognitive workload tasks. Two cognitive workload classification strategies (bad mental arithmetic calculation (BMAC) vs. good mental arithmetic calculation (GMAC); and before mental arithmetic calculation (BFMAC) vs. during mental arithmetic calculation (DMAC)) are considered in this work. The approach was evaluated using the publicly available mental arithmetic task-based EEG database. The results reveal that our proposed approach obtained classification accuracy values of 99.81%, 99.43%, and 99.81%, using the LSTM, BLSTM, and GRU-based RNN classifiers, respectively for the BMAC vs. GMAC cognitive workload classification strategy using all entropy features and a 10-fold cross-validation (CV) technique. The slope entropy features combined with each RNN-based model obtained higher classification accuracy compared with other entropy features for the classification of the BMAC vs. GMAC task. We obtained the average classification accuracy values of 99.39%, 99.44%, and 99.63% for the classification of the BFMAC vs. DMAC tasks, using the LSTM, BLSTM, and GRU classifiers with all entropy features and a hold-out CV scheme. Our developed automated mental arithmetic task system is ready to be tested with more databases for real-world applications.

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.

Gait Stability Measurement by Using Average Entropy

Gait stability has been measured by using many entropy-based methods. However, the relation between the entropy values and gait stability is worth further investigation. A research reported that average entropy (AE), a measure of disorder, could measure the static standing postural stability better than multiscale entropy and entropy of entropy (EoE), two measures of complexity. This study tested the validity of AE in gait stability measurement from the viewpoint of the disorder. For comparison, another five disorders, the EoE, and two traditional metrics methods were, respectively, used to measure the degrees of disorder and complexity of 10 step interval (SPI) and 79 stride interval (SI) time series, individually. As a result, every one of the 10 participants exhibited a relatively high AE value of the SPI when walking with eyes closed and a relatively low AE value when walking with eyes open. Most of the AE values of the SI of the 53 diseased subjects were greater than those of the 26 healthy subjects. A maximal overall accuracy of AE in differentiating the healthy from the diseased was 91.1%. Similar features also exists on those 5 disorder measurements but do not exist on the EoE values. Nevertheless, the EoE versus AE plot of the SI also exhibits an inverted U relation, consistent with the hypothesis for physiologic signals.

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.

Short-Term HRV Analysis Using Nonparametric Sample Entropy for Obstructive Sleep Apnea

Obstructive sleep apnea (OSA) is associated with reduced heart rate variability (HRV) and autonomic nervous system dysfunction. Sample entropy (SampEn) is commonly used for regularity analysis. However, it has limitations in processing short-term segments of HRV signals due to the extreme dependence of its functional parameters. We used the nonparametric sample entropy (NPSampEn) as a novel index for short-term HRV analysis in the case of OSA. The manuscript included 60 6-h electrocardiogram recordings (20 healthy, 14 mild-moderate OSA, and 26 severe OSA) from the PhysioNet database. The NPSampEn value was compared with the SampEn value and frequency domain indices. The empirical results showed that NPSampEn could better differentiate the three groups (p < 0.01) than the ratio of low frequency power to high frequency power (LF/HF) and SampEn. Moreover, NPSampEn (83.3%) approached a higher OSA screening accuracy than the LF/HF (73.3%) and SampEn (68.3%). Compared with SampEn (|r| = 0.602, p < 0.05), NPSampEn (|r| = 0.756, p < 0.05) had a significantly stronger association with the apnea-hypopnea index (AHI). Hence, NPSampEn can fully overcome the influence of individual differences that are prevalent in biomedical signal processing, and might be useful in processing short-term segments of HRV signal.

Resting Heartbeat Complexity Predicts All-Cause and Cardiorespiratory Mortality in Middle- to Older-Aged Adults From the UK Biobank

Background

Spontaneous heart rate fluctuations contain rich information related to health and illness in terms of physiological complexity, an accepted indicator of plasticity and adaptability. However, it is challenging to make inferences on complexity from shorter, more practical epochs of data. Distribution entropy (DistEn) is a recently introduced complexity measure that is designed specifically for shorter duration heartbeat recordings. We hypothesized that reduced DistEn predicted increased mortality in a large population cohort.

Method and Results

The prognostic value of DistEn was examined in 7631 middle‐older–aged UK Biobank participants who had 2‐minute resting ECGs conducted (mean age, 59.5 years; 60.4% women). During a median follow‐up period of 7.8 years, 451 (5.9%) participants died. In Cox proportional hazards models with adjustment for demographics, lifestyle factors, physical activity, cardiovascular risks, and comorbidities, for each 1‐SD decrease in DistEn, the risk increased by 36%, 56%, and 73% for all‐cause, cardiovascular, and respiratory disease–related mortality, respectively. These effect sizes were equivalent to the risk of death from being >5 years older, having been a former smoker, or having diabetes mellitus. Lower DistEn was most predictive of death in those <55 years with a prior myocardial infarction, representing an additional 56% risk for mortality compared with older participants without prior myocardial infarction. These observations remained after controlling for traditional mortality predictors, resting heart rate, and heart rate variability.

Conclusions

Resting heartbeat complexity from short, resting ECGs was independently associated with mortality in middle‐ to older‐aged adults. These risks appear most pronounced in middle‐aged participants with prior MI, and may uniquely contribute to mortality risk screening.

Entropy Profiling: A Reduced-Parametric Measure of Kolmogorov-Sinai Entropy from Short-Term HRV Signal

Entropy profiling is a recently introduced approach that reduces parametric dependence in traditional Kolmogorov-Sinai (KS) entropy measurement algorithms. The choice of the threshold parameter r of vector distances in traditional entropy computations is crucial in deciding the accuracy of signal irregularity information retrieved by these methods. In addition to making parametric choices completely data-driven, entropy profiling generates a complete profile of entropy information as against a single entropy estimate (seen in traditional algorithms). The benefits of using "profiling" instead of "estimation" are: (a) precursory methods such as approximate and sample entropy that have had the limitation of handling short-term signals (less than 1000 samples) are now made capable of the same; (b) the entropy measure can capture complexity information from short and long-term signals without multi-scaling; and (c) this new approach facilitates enhanced information retrieval from short-term HRV signals. The novel concept of entropy profiling has greatly equipped traditional algorithms to overcome existing limitations and broaden applicability in the field of short-term signal analysis. In this work, we present a review of KS-entropy methods and their limitations in the context of short-term heart rate variability analysis and elucidate the benefits of using entropy profiling as an alternative for the same.

PyBioS: A freeware computer software for analysis of cardiovascular signals

BACKGROUND AND OBJECTIVE

Several software applications have been proposed in the past years as computational tools for assessing biomedical signals. Many of them are focused on heart rate variability series only, with their strengths and limitations depending on the necessity of the user and the scope of the application. Here, we introduce new software, named PyBioS, intended for the analysis of cardiovascular signals, even though any type of biomedical signal can be used. PyBioS has some functionalities that differentiate it from the other software.

METHODS

PyBioS was developed in Python language with an intuitive, user-friendly graphical user interface. The basic steps for using PyBioS comprise the opening or creation (simulation) of signals, their visualization, preprocessing and analysis. Currently, PyBioS has 8 preprocessing tools and 15 analysis methods, the later providing more than 50 metrics for analysis of the signals' dynamics.

RESULTS

The possibility to create simulated signals and save the preprocessed signals is a strength of PyBioS. Besides, the software allows batch processing of files, making the analysis of a large amount of data easy and fast. Finally, PyBioS has plenty of analysis methods implemented, with the focus on nonlinear and complexity analysis of signals and time series.

CONCLUSIONS

Although PyBioS is not intended to overcome all the necessities from users, it has useful functionalities that may be helpful in many situations. Moreover, PyBioS is continuously under improvement and several simulated signals, tools and analysis methods are still to be implemented. Also, a new module is being implemented on it to provide machine learning algorithms for classification and regression of data extracted from the biomedical signals.

Age-related alterations on the capacities to navigate on a bike: use of a simulator and entropy measures

Studying the impact of age is important to understand the phenomenon of aging and the disorders that are associated with it. In this work, we analyze age-related alterations on the capacities to navigate on a bike. For this purpose, we use CycléoONE, a bike simulator, and entropy measures. We thus record navigation data (handlebar angle and speed) during the ride. They are processed with two cross-distribution entropy methods (time-shift multiscale cross-distribution entropy and multiscale cross-distribution entropy). We also analyze the time series with a detrended cross-correlation analysis to determine which method can best underline age-related alterations. Our results show that methods based on cross-distribution entropy may be efficient to stress the decrease in navigation capacities with age. The results are very encouraging for our future goal of adding medical benefits to a leisure equipment. They also show the value of using virtual reality to study the impact of age. Graphical Abstract This study deals with the use of the signal processing methods (multiscale cross-entropy and multiscale cross-correlation) applied on naviagtion data, acquired with a bike simulator, to study the impact of age on two populations (young healthy subjects and older adults with loss of autonomy).

On the Use of Fuzzy and Permutation Entropy in Hand Gesture Characterization from EMG Signals: Parameters Selection and Comparison

The surface electromyography signal (sEMG) is widely used for gesture characterization; its reliability is strongly connected to the features extracted from sEMG recordings. This study aimed to investigate the use of two complexity measures, i.e., fuzzy entropy (FEn) and permutation entropy (PEn) for hand gesture characterization. Fourteen upper limb movements, sorted into three sets, were collected on ten subjects and the performances of FEn and PEn for gesture descriptions were analyzed for different computational parameters. FEn and PEn were able to properly cluster the expected numbers of gestures, but computational parameters were crucial for ensuring clusters’ separability and proper gesture characterization. FEn and PEn were also compared with other eighteen classical time and frequency domain features through the minimum redundancy maximum relevance algorithm and showed the best predictive importance scores in two gesture sets; they also had scores within the subset of the best five features in the remaining one. Further, the classification accuracies of four different feature sets presented remarkable increases when FEn and PEn are included as additional features. Outcomes support the use of FEn and PEn for hand gesture description when computational parameters are properly selected, and they could be useful in supporting the development of robotic arms and prostheses myoelectric control.

Development of Automated Sleep Stage Classification System Using Multivariate Projection-Based Fixed Boundary Empirical Wavelet Transform and Entropy Features Extracted from Multichannel EEG Signals

The categorization of sleep stages helps to diagnose different sleep-related ailments. In this paper, an entropy-based information–theoretic approach is introduced for the automated categorization of sleep stages using multi-channel electroencephalogram (EEG) signals. This approach comprises of three stages. First, the decomposition of multi-channel EEG signals into sub-band signals or modes is performed using a novel multivariate projection-based fixed boundary empirical wavelet transform (MPFBEWT) filter bank. Second, entropy features such as bubble and dispersion entropies are computed from the modes of multi-channel EEG signals. Third, a hybrid learning classifier based on class-specific residuals using sparse representation and distances from nearest neighbors is used to categorize sleep stages automatically using entropy-based features computed from MPFBEWT domain modes of multi-channel EEG signals. The proposed approach is evaluated using the multi-channel EEG signals obtained from the cyclic alternating pattern (CAP) sleep database. Our results reveal that the proposed sleep staging approach has obtained accuracies of 91.77%, 88.14%, 80.13%, and 73.88% for the automated categorization of wake vs. sleep, wake vs. rapid eye movement (REM) vs. Non-REM, wake vs. light sleep vs. deep sleep vs. REM sleep, and wake vs. S1-sleep vs. S2-sleep vs. S3-sleep vs. REM sleep schemes, respectively. The developed method has obtained the highest overall accuracy compared to the state-of-art approaches and is ready to be tested with more subjects before clinical application.

Intrinsic Complexity of Sympathetic and Parasympathetic Dynamics from HRV series: a Preliminary Study on Postural Changes

The analysis of complex heartbeat dynamics has been widely used to characterize heartbeat autonomic control in healthy and pathological conditions. However, underlying physiological correlates of complexity measurements from heart rate variability (HRV) series have not been identified yet. To this extent, we investigated intrinsic irregularity and complexity of cardiac sympathetic and vagal activity time series during postural changes. We exploited our recently proposed HRV-based, time-varying Sympathetic and Parasympathetic Activity Indices (SAI and PAI) and performed Sample Entropy, Fuzzy Entropy, and Distribution Entropy calculations on publicly-available heartbeat series gathered from 10 healthy subjects undergoing resting state and passive slow tilt sessions. Results show significantly higher entropy values during the upright position than resting state in both SAI and PAI series. We conclude that an increase in HRV complexity resulting from postural changes may derive from sympathetic and vagal activities with higher complex dynamics.

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.

Development and validation of a sample entropy-based method to identify complex patient-ventilator interactions during mechanical ventilation

Patient-ventilator asynchronies can be detected by close monitoring of ventilator screens by clinicians or through automated algorithms. However, detecting complex patient-ventilator interactions (CP-VI), consisting of changes in the respiratory rate and/or clusters of asynchronies, is a challenge. Sample Entropy (SE) of airway flow (SE-Flow) and airway pressure (SE-Paw) waveforms obtained from 27 critically ill patients was used to develop and validate an automated algorithm for detecting CP-VI. The algorithm's performance was compared versus the gold standard (the ventilator's waveform recordings for CP-VI were scored visually by three experts; Fleiss' kappa = 0.90 (0.87-0.93)). A repeated holdout cross-validation procedure using the Matthews correlation coefficient (MCC) as a measure of effectiveness was used for optimization of different combinations of SE settings (embedding dimension, m, and tolerance value, r), derived SE features (mean and maximum values), and the thresholds of change (Th) from patient's own baseline SE value. The most accurate results were obtained using the maximum values of SE-Flow (m = 2, r = 0.2, Th = 25%) and SE-Paw (m = 4, r = 0.2, Th = 30%) which report MCCs of 0.85 (0.78-0.86) and 0.78 (0.78-0.85), and accuracies of 0.93 (0.89-0.93) and 0.89 (0.89-0.93), respectively. This approach promises an improvement in the accurate detection of CP-VI, and future study of their clinical implications.

Towards a Universal Measure of Complexity

Recently, it has been argued that entropy can be a direct measure of complexity, where the smaller value of entropy indicates lower system complexity, while its larger value indicates higher system complexity. We dispute this view and propose a universal measure of complexity that is based on Gell-Mann's view of complexity. Our universal measure of complexity is based on a non-linear transformation of time-dependent entropy, where the system state with the highest complexity is the most distant from all the states of the system of lesser or no complexity. We have shown that the most complex is the optimally mixed state consisting of pure states, i.e., of the most regular and most disordered which the space of states of a given system allows. A parsimonious paradigmatic example of the simplest system with a small and a large number of degrees of freedom is shown to support this methodology. Several important features of this universal measure are pointed out, especially its flexibility (i.e., its openness to extensions), suitability to the analysis of system critical behaviour, and suitability to study the dynamic complexity.

fNIRS Complexity Analysis for the Assessment of Motor Imagery and Mental Arithmetic Tasks

Conventional methods for analyzing functional near-infrared spectroscopy (fNIRS) signals primarily focus on characterizing linear dynamics of the underlying metabolic processes. Nevertheless, linear analysis may underrepresent the true physiological processes that fully characterizes the complex and nonlinear metabolic activity sustaining brain function. Although there have been recent attempts to characterize nonlinearities in fNIRS signals in various experimental protocols, to our knowledge there has yet to be a study that evaluates the utility of complex characterizations of fNIRS in comparison to standard methods, such as the mean value of hemoglobin. Thus, the aim of this study was to investigate the entropy of hemoglobin concentration time series obtained from fNIRS signals and perform a comparitive analysis with standard mean hemoglobin analysis of functional activation. Publicly available data from 29 subjects performing motor imagery and mental arithmetics tasks were exploited for the purpose of this study. The experimental results show that entropy analysis on fNIRS signals may potentially uncover meaningful activation areas that enrich and complement the set identified through a traditional linear analysis.

Complexity Analysis on Functional-Near Infrared Spectroscopy Time Series: a Preliminary Study on Mental Arithmetic

It is well known that physiological systems show complex and nonlinear behaviours. In spite of that, functional near-infrared spectroscopy (fNIRS) is usually analyzed in the time and frequency domains with the assumption that metabolic activity is generated from a linear system. To leverage the full information provided by fNIRS signals, in this study we investigate topological entropy in fNIRS series collected from 10 healthy subjects during mental mental arithmetic task. While sample entropy and fuzzy entropy were used to estimate time series irregularity, distribution entropy was used to estimate time series complexity. Our findings show that entropy estimates may provide complementary characterization of fNIRS dynamics with respect to reference time domain measurements. This finding paves the way to further investigate functional activation in fNIRS in different case studies using nonlinear and complexity system theory.