A review on sample entropy applications for the non-invasive analysis of atrial fibrillation electrocardiograms

A transcutaneous acupoint electrical simulation glove for relieving the mental fatigue of crane drivers in real building environment

In the field of construction, the lifting environment of precast parts is more complex, which leads to the driver's fatigue. When the tower crane driver appears driving fatigue, it will appear slow operation response, hoisting precast parts appear abnormal swing, which will endanger the safety of on-site operators. Therefore, this study developed a kind of transcutaneous acupoint electrical stimulation gloves. When the crane driver wears this kind of glove, the good contraction of the glove can make the stimulation electrode closely fit with the three points, so as to perform electrical stimulation on the Neìguān point (PC6), Láogóng point (PC8) and Hégŭ point (L14) of the palm to relieve the driver's driving fatigue. In this study, non-periodic transcutaneous acupoint electrical stimulation (NPTAES) was used to stimulate human acupuncture points. This is different from the traditional periodic transcutaneous acupoint electrical stimulation (PTAES) method for relieving mental fatigue. In addition, this study used hilbert marginal spectral entropy (HMSE) to calculate the heart rate variability (HRV) characteristics of the subjects, so as to detect and analyze the driving fatigue of the drivers. At the same time, the drivers' blinking frequency and electroencephalogram (EEG) characteristics were analyzed comprehensively. The results show that: The NPTAES method used in this study is superior to the PTAES method in alleviating driving fatigue and greatly improves the efficiency of tower crane drivers. Compared to other methods, the HMSE method proposed in this study, when analyzing signals, stronger ability to characterize signal characteristics.

Novel Entropy-Based Metrics for Long-Term Atrial Fibrillation Recurrence Prediction Following Surgical Ablation: Insights from Preoperative Electrocardiographic Analysis

Atrial fibrillation (AF) is a prevalent cardiac arrhythmia often treated concomitantly with other cardiac interventions through the Cox-Maze procedure. This highly invasive intervention is still linked to a long-term recurrence rate of approximately 35% in permanent AF patients. The aim of this study is to preoperatively predict long-term AF recurrence post-surgery through the analysis of atrial activity (AA) organization from non-invasive electrocardiographic (ECG) recordings. A dataset comprising ECGs from 53 patients with permanent AF who had undergone Cox-Maze concomitant surgery was analyzed. The AA was extracted from the lead V1 of these recordings and then characterized using novel predictors, such as the mean and standard deviation of the relative wavelet energy (RWEm and RWEs) across different scales, and an entropy-based metric that computes the stationary wavelet entropy variability (SWEnV). The individual predictors exhibited limited predictive capabilities to anticipate the outcome of the procedure, with the SWEnV yielding a classification accuracy (Acc) of 68.07%. However, the assessment of the RWEs for the seventh scale (RWEs7), which encompassed frequencies associated with the AA, stood out as the most promising individual predictor, with sensitivity (Se) and specificity (Sp) values of 80.83% and 67.09%, respectively, and an Acc of almost 75%. Diverse multivariate decision tree-based models were constructed for prediction, giving priority to simplicity in the interpretation of the forecasting methodology. In fact, the combination of the SWEnV and RWEs7 consistently outperformed the individual predictors and excelled in predicting post-surgery outcomes one year after the Cox-Maze procedure, with Se, Sp, and Acc values of approximately 80%, thus surpassing the results of previous studies based on anatomical predictors associated with atrial function or clinical data. These findings emphasize the crucial role of preoperative patient-specific ECG signal analysis in tailoring post-surgical care, enhancing clinical decision making, and improving long-term clinical outcomes.

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.

Cardiac arrhythmia detection using cross-sample entropy measure based on short and long RR interval series

Background

Accurate arrhythmia (atrial fibrillation (AF) and congestive heart failure (CHF)) detection is still a challenge in the biomedical signal-processing field. Different linear and nonlinear measures of the electrocardiogram (ECG) signal analysis are used to fix this problem.

Methods

Sample entropy (SampEn) is used as a nonlinear measure based on single series to detect healthy and arrhythmia subjects. To follow this measure, the proposed work presents a nonlinear technique, namely, the cross-sample entropy (CrossSampEn) based on two series to quantify healthy and arrhythmia subjects.

Results

The research work consists of 10 records of normal sinus rhythm, 20 records of Fantasia (old group), 10 records of AF, and 10 records of CHF. The method of CrossSampEn has been proposed to obtain the irregularity between two same and different R-R (R peak to peak) interval series of different data lengths. Unlike the SampEn technique, the CrossSampEn technique never awards a 'not defined' value for very short data lengths and was found to be more consistent than SampEn. One-way ANOVA test has validated the proposed algorithm by providing a large F value and p < .0001. The proposed algorithm is also verified by simulated data.

Conclusions

It is concluded that different RR interval series of approximate 1500 data points and same RR interval series of approximate 1000 data points are required for health-status detection with embedded dimensions, M = 2 and threshold, r = .2. Also, CrossSampEn has been found more consistent than Sample entropy algorithm.

From mechanisms to markers: novel noninvasive EEG proxy markers of the neural excitation and inhibition system in humans

Brain function is a product of the balance between excitatory and inhibitory (E/I) brain activity. Variation in the regulation of this activity is thought to give rise to normal variation in human traits, and disruptions are thought to potentially underlie a spectrum of neuropsychiatric conditions (e.g., Autism, Schizophrenia, Downs' Syndrome, intellectual disability). Hypotheses related to E/I dysfunction have the potential to provide cross-diagnostic explanations and to combine genetic and neurological evidence that exists within and between psychiatric conditions. However, the hypothesis has been difficult to test because: (1) it lacks specificity-an E/I dysfunction could pertain to any level in the neural system- neurotransmitters, single neurons/receptors, local networks of neurons, or global brain balance - most researchers do not define the level at which they are examining E/I function; (2) We lack validated methods for assessing E/I function at any of these neural levels in humans. As a result, it has not been possible to reliably or robustly test the E/I hypothesis of psychiatric disorders in a large cohort or longitudinal patient studies. Currently available, in vivo markers of E/I in humans either carry significant risks (e.g., deep brain electrode recordings or using Positron Emission Tomography (PET) with radioactive tracers) and/or are highly restrictive (e.g., limited spatial extent for Transcranial Magnetic Stimulation (TMS) and Magnetic Resonance Spectroscopy (MRS). More recently, a range of novel Electroencephalography (EEG) features has been described, which could serve as proxy markers for E/I at a given level of inference. Thus, in this perspective review, we survey the theories and experimental evidence underlying 6 novel EEG markers and their biological underpinnings at a specific neural level. These cheap-to-record and scalable proxy markers may offer clinical utility for identifying subgroups within and between diagnostic categories, thus directing more tailored sub-grouping and, therefore, treatment strategies. However, we argue that studies in clinical populations are premature. To maximize the potential of prospective EEG markers, we first need to understand the link between underlying E/I mechanisms and measurement techniques.

Evaluation of Fast Sample Entropy Algorithms on FPGAs: From Performance to Energy Efficiency

Entropy is one of the most fundamental notions for understanding complexity. Among all the methods to calculate the entropy, sample entropy (SampEn) is a practical and common method to estimate time-series complexity. Unfortunately, SampEn is a time-consuming method growing in quadratic times with the number of elements, which makes this method unviable when processing large data series. In this work, we evaluate hardware SampEn architectures to offload computation weight, using improved SampEn algorithms and exploiting reconfigurable technologies, such as field-programmable gate arrays (FPGAs), a reconfigurable technology well-known for its high performance and power efficiency. In addition to the fundamental disclosed straightforward SampEn (SF) calculation method, this study evaluates optimized strategies, such as bucket-assist (BA) SampEn and lightweight SampEn based on BubbleSort (BS-LW) and MergeSort (MS-LW) on an embedded CPU, a high-performance CPU and on an FPGA using simulated data and real-world electrocardiograms (ECG) as input data. Irregular storage space and memory access of enhanced algorithms is also studied and estimated in this work. These fast SampEn algorithms are evaluated and profiled using metrics such as execution time, resource use, power and energy consumption based on input data length. Finally, although the implementation of fast SampEn is not significantly faster than versions running on a high-performance CPU, FPGA implementations consume one or two orders of magnitude less energy than a high-performance CPU.

Thermal Aging Evaluation of XLPE Power Cable by Using Multidimensional Characteristic Analysis of Leakage Current

Thermal aging is a common form of cable deterioration. In this paper, the effect of thermal aging on cables is evaluated by analyzing the harmonic characteristics in cable leakage currents. Cable samples were first fabricated and subjected to accelerated thermal aging tests at 120 °C. The experimental circuits were built to test the dielectric loss factor and the AC leakage current of the cable at different aging times. Then, the improved variational modal decomposition (VMD) algorithm was used for the time–frequency analysis of the leakage current, and the relationship between thermal aging and leakage current harmonics was investigated. Thermal aging was discovered to increase the capacitance and dielectric loss factor of the cable as well as generate harmonics in the leakage current, with harmonics at 150, 450, and 650 Hz being particularly sensitive to thermal aging. The multidimensional characteristic parameters such as the time-domain, frequency-domain, and relative energy and the sample entropy of the leakage current harmonics were calculated. The results demonstrated thermal aging increased the relative energy and power spectrum energy of the harmonics and increased the disorder of the harmonic sequence.

Multiscale partition-based Kolmogorov-Sinai Entropy: a preliminary HRV study on Heart Failure vs. Atrial Fibrillation

Several approaches for estimating complexity in physiological time series at various time scales have recently been developed, with a special focus on heart rate variability (HRV) series. While numerous multiscale complexity quantifiers have been investigated, a multiscale Kolmogorov-Sinai (K-S) entropy for the characterization of cardiovascular dynamics still has to be properly assessed. In this pilot study, we investigate the Algorithmic Information Content, which is calculated using an effective compression algorithm, to quantify multiscale partition- based K-S entropy on experimental HRV series. Data were gathered from publicly available datasets comprising long-term, unstructured recordings from 10 healthy subjects, as well as 10 patients with congestive heart failure (CHF) and 10 patients with atrial fibrillation. Results show that multiple time scales and domain partitions statistically discern healthy vs. pathological cardiovascular dynamics. We conclude that the proposed multiscale partition-based K-S entropy may constitute a viable tool for the complexity assessment of cardiovascular variability series.

Ultra-Short-Term Wind Speed Forecasting Using the Hybrid Model of Subseries Reconstruction and Broad Learning System

The traditional decomposition–combination wind speed forecasting model has high complexity and a long calculation time. As a result, an ultra-short-term wind speed hybrid forecasting model based on a broad learning system (BLS) that combines improved variational mode decomposition (EPSO-VMD, EVMD) and subseries reconstruction (SR) is proposed in this work. The values of K and α in the EVMD are determined by minimum mean envelope entropy (MMEE) and enhanced particle swarm optimization (EPSO), and EVMD is used to decompose the original wind speed data. SR is applied to recombine the subseries obtained by EVMD to improve the forecasting efficiency. The sample entropy (SE) is used to quantify the subseries’ complexity, and they are then adaptively divided into high-entropy and low-entropy subseries. Adjacent high-entropy subseries of approximate entropy values are merged to obtain a new group of reconstructed high-entropy subseries, while the low-entropy subseries merge into a new subseries as well. Then, the forecasting results of the reconstructed high- and low-entropy subseries are calculated via the BLS and ARIMA models. Numerical simulation results show that the proposed method is more effective than traditional methods.

Extended ECG Improves Classification of Paroxysmal and Persistent Atrial Fibrillation Based on P- and f-Waves

Background

The standard 12-lead ECG has been shown to be of value in characterizing atrial conduction properties. The added value of extended ECG recordings (longer recordings from more sites) has not been systematically explored yet.

Objective

The aim of this study is to employ an extended ECG to identify characteristics of atrial electrical activity related to paroxysmal vs. persistent atrial fibrillation (AF).

Methods

In 247 participants scheduled for AF ablation, an extended ECG was recorded (12 standard plus 3 additional leads, 5 min recording, no filtering). For patients presenting in sinus rhythm (SR), the signal-averaged P-wave and the spatiotemporal P-wave variability was analyzed. For patients presenting in AF, f-wave properties in the QRST (the amplitude complex of the ventricular electrical activity: Q-, R-, S-, and T-wave)-canceled ECG were determined.

Results

Significant differences between paroxysmal (N = 152) and persistent patients with AF (N = 95) were found in several P-wave and f-wave parameters, including parameters that can only be calculated from an extended ECG. Furthermore, a moderate, but significant correlation was found between echocardiographic parameters and P-wave and f-wave parameters. There was a moderate correlation of left atrial (LA) diameter with P-wave energy duration (r = 0.317, p < 0.001) and f-wave amplitude in lead A3 (r = -0.389, p = 0.002). The AF-type classification performance significantly improved when parameters calculated from the extended ECG were taken into account [area under the curve (AUC) = 0.58, interquartile range (IQR) 0.50-0.64 for standard ECG parameters only vs. AUC = 0.76, IQR 0.70-0.80 for extended ECG parameters, p < 0.001].

Conclusion

The P- and f-wave analysis of extended ECG configurations identified specific ECG features allowing improved classification of paroxysmal vs. persistent AF. The extended ECG significantly improved AF-type classification in our analyzed data as compared to a standard 10-s 12-lead ECG. Whether this can result in a better clinical AF type classification warrants further prospective study.

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.

Refined Multiscale Entropy Analysis of Wrist Pulse for Gender Difference in Traditional Chinese Medicine among Young Individuals

Pulse signal analysis plays an important role in promoting the objectification of traditional Chinese medicine (TCM). Like electrocardiogram (ECG) signals, wrist pulse signals are mainly caused by cardiac activities and are valuable in analyzing cardiac diseases. A large number of studies have reported ECG signals can distinguish gender characteristics of normal healthy subjects using entropy complexity measures, consistently showing more complexity in females than males. No research up to date, however, has been found on examining gender differences with wrist pulse signals of healthy subjects on entropy complexity measures. This paper is aimed to fill in the research gap, which could, in turn, provide a deeper insight into the pulse signal and might identify potential differences between ECG signals and pulse signals. In particular, several complementary entropy measures with corresponding refined composite multiscale versions are established to perform the analysis for the filtered TCM pulse signals. Experimental results reveal that regardless of entropy measures used, there is no statistically significant gender difference in terms of entropy complexity, indicating that the pulse signal holds less gender characteristics than the ECG signal. In view of these findings, wrist pulse signals could be likely to provide different pieces of information to ECG signals. The present study is the first to quantitatively evaluate gender differences in healthy pulse signals with measures of entropy complexity and more importantly; we expect this study could make contribution to the ongoing pulse intelligent diagnosis and objective analysis, further facilitating the modernization of TCM pulse diagnosis.

Determination of Parameters for an Entropy-Based Atrial Fibrillation Detector

Entropy algorithm is an important nonlinear method for cardiovascular disease detection due to its power in analyzing short-term time series. In previous a study, we proposed a new entropy-based atrial fibrillation (AF) detector, i.e., Entropy_AF, which showed a high classification accuracy in identifying AF and non-AF rhythms. As a variation of entropy measures, Entropy_AF has two parameters that need to be initialized before the calculation: (1) tolerance threshold r and (2) similarity weight n. In this study, a comprehensive analysis for the two parameters determination was presented, aiming to achieve a high detection accuracy for AF events. Data were from the MIT-BIH AF database. RR interval recordings were segmented using a 30-beat time window. The parameters r and n were initialized from a relatively small value, then gradually increased, and finally the best parameter combination was determined using grid searching. AUC (area under curve) values from the receiver operator characteristic curve (ROC) were compared under different parameter combinations of parameters r and n, and the results demonstrated that the selection of these two parameters plays an important role in AF/non-AF classification. Small values of parameters r and n can lead to a better detection accuracy than other selections. The best AUC value for AF detection was 98.15%, and the corresponding parameter combinations for Entropy_AF were as follows: r = 0.01, n = 0.0625, 0.125, 0.25, or 0.5; r = 0.05 and n = 0.0625, 0.125, or 0.25; and r = 0.10 and n = 0.0625 or 0.125.

A Review of Shannon and Differential Entropy Rate Estimation

In this paper, we present a review of Shannon and differential entropy rate estimation techniques. Entropy rate, which measures the average information gain from a stochastic process, is a measure of uncertainty and complexity of a stochastic process. We discuss the estimation of entropy rate from empirical data, and review both parametric and non-parametric techniques. We look at many different assumptions on properties of the processes for parametric processes, in particular focussing on Markov and Gaussian assumptions. Non-parametric estimation relies on limit theorems which involve the entropy rate from observations, and to discuss these, we introduce some theory and the practical implementations of estimators of this type.

Atrial Fibrillation Prediction from Critically Ill Sepsis Patients

Sepsis is defined by life-threatening organ dysfunction during infection and is the leading cause of death in hospitals. During sepsis, there is a high risk that new onset of atrial fibrillation (AF) can occur, which is associated with significant morbidity and mortality. Consequently, early prediction of AF during sepsis would allow testing of interventions in the intensive care unit (ICU) to prevent AF and its severe complications. In this paper, we present a novel automated AF prediction algorithm for critically ill sepsis patients using electrocardiogram (ECG) signals. From the heart rate signal collected from 5-min ECG, feature extraction is performed using the traditional time, frequency, and nonlinear domain methods. Moreover, variable frequency complex demodulation and tunable Q-factor wavelet-transform-based time-frequency methods are applied to extract novel features from the heart rate signal. Using a selected feature subset, several machine learning classifiers, including support vector machine (SVM) and random forest (RF), were trained using only the 2001 Computers in Cardiology data set. For testing the proposed method, 50 critically ill ICU subjects from the Medical Information Mart for Intensive Care (MIMIC) III database were used in this study. Using distinct and independent testing data from MIMIC III, the SVM achieved 80% sensitivity, 100% specificity, 90% accuracy, 100% positive predictive value, and 83.33% negative predictive value for predicting AF immediately prior to the onset of AF, while the RF achieved 88% AF prediction accuracy. When we analyzed how much in advance we can predict AF events in critically ill sepsis patients, the algorithm achieved 80% accuracy for predicting AF events 10 min early. Our algorithm outperformed a state-of-the-art method for predicting AF in ICU patients, further demonstrating the efficacy of our proposed method. The annotations of patients' AF transition information will be made publicly available for other investigators. Our algorithm to predict AF onset is applicable for any ECG modality including patch electrodes and wearables, including Holter, loop recorder, and implantable devices.

The Systematic Bias of Entropy Calculation in the Multi-Scale Entropy Algorithm

Entropy indicates irregularity or randomness of a dynamic system. Over the decades, entropy calculated at different scales of the system through subsampling or coarse graining has been used as a surrogate measure of system complexity. One popular multi-scale entropy analysis is the multi-scale sample entropy (MSE), which calculates entropy through the sample entropy (SampEn) formula at each time scale. SampEn is defined by the “logarithmic likelihood” that a small section (within a window of a length m) of the data “matches” with other sections will still “match” the others if the section window length increases by one. “Match” is defined by a threshold of r times standard deviation of the entire time series. A problem of current MSE algorithm is that SampEn calculations at different scales are based on the same matching threshold defined by the original time series but data standard deviation actually changes with the subsampling scales. Using a fixed threshold will automatically introduce systematic bias to the calculation results. The purpose of this paper is to mathematically present this systematic bias and to provide methods for correcting it. Our work will help the large MSE user community avoiding introducing the bias to their multi-scale SampEn calculation results.

Real-Time Heart Arrhythmia Detection Using Apache Spark Structured Streaming

One of the major causes of death in the world is cardiac arrhythmias. In the field of healthcare, physicians use the patient's electrocardiogram (ECG) records to detect arrhythmias, which indicate the electrical activity of the patient's heart. The problem is that the symptoms do not always appear and the physician may be mistaken in the diagnosis. Therefore, patients need continuous monitoring through real-time ECG analysis to detect arrhythmias in a timely manner and prevent an eventual incident that threatens the patient's life. In this research, we used the Structured Streaming module built top on the open-source Apache Spark platform for the first time to implement a machine learning pipeline for real-time cardiac arrhythmias detection and evaluate the impact of using this new module on classification performance metrics and the rate of delay in arrhythmia detection. The ECG data collected from the MIT/BIH database for the detection of three class labels: normal beats, RBBB, and atrial fibrillation arrhythmias. We also developed three decision trees, random forest, and logistic regression multiclass classifiers for data classification where the random forest classifier showed better performance in classification than the other two classifiers. The results show previous results in performance metrics of the classification model and a significant decrease in pipeline runtime by using more class labels compared to previous studies.

An efficient approach for Paroxysmal Atrial Fibrillation events prediction using Extreme Learning Machine

Paroxysmal Atrial Fibrillation (PAF) is a special class of Atrial Fibrillation. Predicting PAF events from electrocardiogram (ECG) signal streams plays a vital role in generating real-time alerts for cardiac disorders. These alerts are extremely important to cardiologists in taking precautions to prevent their patients from having a stroke. In this study, an effective predictive approach to PAF events using the Extreme Learning Machine classification technique is proposed. Besides, we propose a feature extraction method that integrates new ECG signal features to its time-domain ones. The new features are based on the construction of sparse vectors for peaks in ECG signals that provide high overlap between similar ECGs. The proposed prediction approach with the new ECG features representation were evaluated on a real PAF dataset using the five-fold cross-validation method. Experiments show promising results for predicting PAF in terms of accuracy and execution time compared to other existing studies. The proposed approach achieved classification accuracy of 97% for non-streaming ECG signals mode and 94.4% for streaming mode.

Demonstration of the potential of white-box machine learning approaches to gain insights from cardiovascular disease electrocardiograms

We present the results from a white-box machine learning approach to detect cardiac arrhythmias using electrocardiographic data. A C5.0 is trained to recognize four classes using common features. The four classes are (i) atrial fibrillation and atrial flutter, (ii) tachycardias (iii), sinus bradycardia and (iv) sinus rhythm. Data from 10,646 subjects, 83% of whom have at least one arrhythmia and 17% of whom exhibit a normal sinus rhythm, are used. The C5.0 is trained using 10-fold cross-validation and is able to achieve a balanced accuracy of 95.35%. By using the white-box machine learning approach, a clear and comprehensible tree structure can be revealed, which has selected the 5 most important features from a total of 24 features. These 5 features are ventricular rate, RR-Interval variation, atrial rate, age and difference between longest and shortest RR-Interval. The combination of ventricular rate, RR-Interval variation and atrial rate is especially relevant to achieve classification accuracy, which can be disclosed through the tree. The tree assigns unique values to distinguish the classes. These findings could be applied in medicine in the future. It can be shown that a white-box machine learning approach can reveal granular structures, thus confirming known linear relationships and also revealing nonlinear relationships. To highlight the strength of the C5.0 with respect to this structural revelation, the results of further white-box machine learning and black-box machine learning algorithms are presented.

Right Atrial Complexity Evolves With Stepwise Left-Sided Persistent Atrial Fibrillation Substrate Ablation and Predicts Outcomes

OBJECTIVES

This study sought to study the relation between outcomes of modified stepwise atrial fibrillation (AF) substrate ablation and dynamic electrogram characteristics in the coronary sinus (CS) and right atrium (RA).

BACKGROUND

Identifying patients with persistent AF who will benefit from limited lesion sets versus those requiring extensive substrate modification is challenging.

METHODS

We studied 70 patients undergoing persistent AF ablation, 43 with acute success (successful ablation [sABL], AF termination, or noninducibility) and 27 with failure (failed ablation [fABL], no termination, or induced AF of >5 minutes). Dominant frequency (DF) and sample entropy (SampEn, increasing with signal complexity) were measured on 30-second recordings of wide-coverage simultaneous RA and CS electrograms during baseline AF and induced AF post-pulmonary vein isolation and after left-sided electrogram-guided ablation steps (on the CS with or without the left atrium [LA]).

RESULTS

At baseline AF, patients with sABL exhibited lower RA SampEn (p = 0.023) and lower CS DF (p = 0.030) compared to fABL. A positive RA-to-CS SampEn gradient predicted ablation failure (48% vs. 19% for patients in fABL vs. sABL; p = 0.015). A positive RA-to-CS DF gradient developed in patients with fABL after extra-pulmonary vein substrate modification, unlike patients with sABL (p = 0.0008). At 24 months, 76% of patients were AF free, and 68% were arrhythmia free. sABL was associated with fewer AF recurrences (hazard ratio: 0.31; 95% confidence interval: 0.12-0.84; p = 0.021). A negative RA-to-CS SampEn gradient at baseline was associated with freedom from AF (-0.14 ± 0.19 vs. 0.04 ± 0.18; p = 0.002).

CONCLUSIONS

RA greater than CS electrogram complexity gradients at baseline or developing during ablation are associated with unfavorable acute and long-term outcomes of persistent AF ablation. These parameters allow monitoring of the effects of left-sided substrate ablation and, therefore, a rational choice of additional RA substrate modification.

A hybrid air pollutant concentration prediction model combining secondary decomposition and sequence reconstruction

Acid rain is a serious threat to terrestrial ecosystems. To provide more accurate early warning information for acid rain prevention, urban planning, and travel planning, a novel air pollutant prediction model was proposed in this paper to predict NO₂ and SO₂. First, the data were decomposed into several sub-sequences by a complete ensemble empirical mode decomposition with adaptive noise. Second, the subsequences are reconstructed by variational mode decomposition and sample entropy. Then, the new subsequences are predicted by the extreme learning machine combined with the whale optimization algorithm. The empirical analysis was carried out through 8 data sets. According to the experimental results, three main conclusions can be drawn. First, the proposed model in this paper has excellent prediction performance and robustness. In all the comparison experiments, the R² and RMSE of the proposed model are the best among all the models. Second, data preprocessing is very necessary. After adding the decomposition algorithm, the average improvement levels of R² and RMSE were 897.57% and 50.78%, respectively. Third, the re-decomposition of IMF1 is an effective method to improve prediction accuracy. After the re-decomposition of IMF1, R² can be improved by 13.64% on average on the original basis, and RMSE can be reduced by 31.99% on average. The results of this study can provide a valuable reference for the research of air pollutant prediction. In future work, the application of the proposed model in other air pollutants or other regions can be explored.

Atrial Fibrillation Detection During Sepsis: Study on MIMIC III ICU Data

Sepsis is defined by life-threatening organ dysfunction during infection and is one of the leading causes of critical illness. During sepsis, there is high risk that new-onset of atrial fibrillation (AF) can occur, which is associated with significant morbidity and mortality. As a result, computer aided automated and reliable detection of new-onset AF during sepsis is crucial, especially for the critically ill patients in the intensive care unit (ICU). In this paper, a novel automated and robust two-step algorithm to detect AF from ICU patients using electrocardiogram (ECG) signals is presented. First, several statistical parameters including root mean square of successive differences, Shannon entropy, and sample entropy were calculated from the heart rate for the screening of possible AF segments. Next, Poincaré plot-based features along with P-wave characteristics were used to reduce false positive detection of AF, caused by the premature atrial and ventricular beats. A subset of the Medical Information Mart for Intensive Care (MIMIC) III database containing 198 subjects was used in this study. During the training and validation phases, both the simple thresholding as well as machine learning classifiers achieved very high segment-wise AF classification performance. Finally, we tested the performance of our proposed algorithm using two independent test data sets and compared the performance with two state-of-the-art methods. The algorithm achieved an overall 100% sensitivity, 98% specificity, 98.99% accuracy, 98% positive predictive value, and 100% negative predictive value on the subject-wise AF detection, thus showing the efficacy of our proposed algorithm in critically ill sepsis patients. The annotations of the data have been made publicly available for other investigators.

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.

Assessment of Airflow and Oximetry Signals to Detect Pediatric Sleep Apnea-Hypopnea Syndrome Using AdaBoost

The reference standard to diagnose pediatric Obstructive Sleep Apnea (OSA) syndrome is an overnight polysomnographic evaluation. When polysomnography is either unavailable or has limited availability, OSA screening may comprise the automatic analysis of a minimum number of signals. The primary objective of this study was to evaluate the complementarity of airflow (AF) and oximetry (SpO₂) signals to automatically detect pediatric OSA. Additionally, a secondary goal was to assess the utility of a multiclass AdaBoost classifier to predict OSA severity in children. We extracted the same features from AF and SpO₂ signals from 974 pediatric subjects. We also obtained the 3% Oxygen Desaturation Index (ODI) as a common clinically used variable. Then, feature selection was conducted using the Fast Correlation-Based Filter method and AdaBoost classifiers were evaluated. Models combining ODI 3% and AF features outperformed the diagnostic performance of each signal alone, reaching 0.39 Cohens's kappa in the four-class classification task. OSA vs. No OSA accuracies reached 81.28%, 82.05% and 90.26% in the apnea-hypopnea index cutoffs 1, 5 and 10 events/h, respectively. The most relevant information from SpO₂ was redundant with ODI 3%, and AF was complementary to them. Thus, the joint analysis of AF and SpO₂ enhanced the diagnostic performance of each signal alone using AdaBoost, thereby enabling a potential screening alternative for OSA in children.

Atrial Fibrillation Detection in ICU Patients: A Pilot Study on MIMIC III Data

Atrial fibrillation (AF) is the most prevalent arrhythmia, resulting in varying and irregular heartbeats. AF increases risk for numerous cardiovascular diseases including stroke, heart failure and as a result, computer aided efficient monitoring of AF is crucial, especially for intensive care unit (ICU) patients. In this paper, we present an automated and robust algorithm to detect AF from ICU patients using electrocardiogram (ECG) signals. Several statistical parameters including root mean square of successive differences, Shannon entropy, Sample entropy and turning point ratio are calculated from the heart rate. A subset of the Medical Information Mart for Intensive Care (MIMIC) III database containing 36 subjects is used in this study. We compare the AF detection performance of several classifiers for both the training and blinded test data. Using the support vector machine classifier with radial basis kernel, the proposed method achieves 99.95% cross-validation accuracy on the training data and 99.88% sensitivity, 99.65% specificity and 99.75% accuracy on the blinded test data.

Distality of Attentional Focus and Its Role in Postural Balance Control

The role of attentional focusing in motor tasks has been highlighted frequently. The "internal-external" dimension has emerged, but also the spatial distance between body and attended location. In two experiments, an extended attentional focus paradigm was introduced to investigate distality effects of attentional foci on balance performance. First, the distality of the coordinates of the point of focus was varied between a proximal and distal position on an artificial tool attached to the body. Second, the distance of the displayed effect on the wall was varied between a 2.5 and 5 m condition. Subjects were instructed to focus on controlling either a proximal or distal spot on a tool attached to their head, represented by two laser pointers. Subsequently, they needed to visually track their own body-movement effect of one of the laser pointers at a wall while completing various single leg stance tasks. Center of pressure (COP) sway was analyzed using a linear method (classic sway variables) as well as a non-linear method (multiscale entropy). In addition, laser trajectories were videotaped and served as additional performance outcome measure. Experiment 1 revealed differences in balance performance under proximal compared to distal attentional focus conditions. Moreover, experiment 2 yielded differences in balance-related sway measures and laser data between the 2.5 and 5 m condition of the visually observable movement effect. In conclusion, varying the distality of the point of focus between proximal and distal impacted balance performance. However, this effect was not consistent across all balance tasks. Relevantly, the distality of the movement effect shows a significant effect on balance plus laser performance with advantages in more distal conditions. This research emphasizes the importance of the spatial distality of movement effects for human behavior.

Classification of autism spectrum disorder based on sample entropy of spontaneous functional near infra-red spectroscopy signal

OBJECTIVES

To assess the possibility of distinguishing autism spectrum disorder (ASD) based on the characteristic of spontaneous hemodynamic fluctuations and to explore the location of abnormality in the brain.

METHODS

Using the sample entropy (SampEn) of functional near-infrared spectroscopy (fNIRS) from bilateral inferior frontal gyrus (IFG) and temporal cortex (TC) on 25 children with ASD and 22 typical development (TD) children, the pattern of mind-wandering was assessed. With the SampEn as feature variables, a machine learning classifier was applied to mark ASD and locate the abnormal area in the brain.

RESULTS

The SampEn was generally lower for ASD than TD, indicating the fNIRS series from ASD was unstable, had low fluctuation, and high self-similarity. The classification between ASD and TD could reach 97.6% in accuracy.

CONCLUSIONS

The SampEn of fNIRS could accurately distinguish ASD. The abnormality in terms of the SampEn occurs more frequently in IFG than TC, and more frequently in the left than in the right hemisphere.

SIGNIFICANCE

The results of this study may help to understand the cortical mechanism of ASD and provide a fNIRS-based diagnosis for ASD.

Uncertainty of financial time series based on discrete fractional cumulative residual entropy

Cumulative residual entropy (CRE) is a measure of uncertainty and departs from other entropy in that it is established on cumulative residual distribution function instead of density function. In this paper, we prove some important properties of discrete CRE and propose fractional multiscale cumulative residual entropy (FMCRE) as a function of fractional order α, which combines CRE with fractional calculus, probability of permutation ordinal patterns, and multiscale to overcome the limitation of CRE. After adding amplitude information through weighted permutation ordinal patterns, we get fractional weighted multiscale cumulative residual entropy (FWMCRE). FMCRE and FWMCRE extend CRE into a continuous family and can be used in more situations with a suitable parameter. Moreover, they can capture long-range phenomena more clearly and have higher sensitivity to the signal evolution. Results from simulated data verify that FMCRE and FWMCRE can identify time series accurately and have immunity to noise. We confirm that the length of time series has little effect on the accuracy of distinguishing data, and even short series can get results exactly. Finally, we apply FMCRE and FWMCRE on stock data and confirm that they can be used as metrics to measure uncertainty of the system as well as distinguishing signals. FWMCRE can also track changes in stock markets and whether adding amplitude information must be decided by the characteristics of data.

Heart Rate Dynamics in Patients with Obstructive Sleep Apnea: Heart Rate Variability and Entropy

Background: Obstructive sleep apnea (OSA), a highly prevalent sleep disorder, is closely related to cardiovascular disease (CVD). Our previous work demonstrated that Shannon entropy of the degree distribution (E_DD), obtained from the network domain of heart rate variability (HRV), might be a potential indicator for CVD. Method: To investigate the potential association between OSA and E_DD, OSA patients and healthy controls (HCs) were identified from a sleep study database. Then E_DD was calculated from electrocardiogram (ECG) signals during sleep, followed by cross-sectional comparisons between OSA patients and HCs, and longitudinal comparisons from baseline to follow-up visits. Furthermore, for OSA patients, the association between E_DD and OSA severity, measured by apnea-hypopnea index (AHI), was also analyzed. Results: Compared with HCs, OSA patients had significantly increased E_DD during sleep. A positive correlation between E_DD and the severity of OSA was also observed. Although the value of E_DD became larger with aging, it was not OSA-specified. Conclusion: Increased E_DD derived from ECG signals during sleep might be a potential dynamic biomarker to identify OSA patients from HCs, which may be used in screening OSA with high risk before polysomnography is considered.

Interpretation of Entropy Algorithms in the Context of Biomedical Signal Analysis and Their Application to EEG Analysis in Epilepsy

Biomedical signals are measurable time series that describe a physiological state of a biological system. Entropy algorithms have been previously used to quantify the complexity of biomedical signals, but there is a need to understand the relationship of entropy to signal processing concepts. In this study, ten synthetic signals that represent widely encountered signal structures in the field of signal processing were created to interpret permutation, modified permutation, sample, quadratic sample and fuzzy entropies. Subsequently, the entropy algorithms were applied to two different databases containing electroencephalogram (EEG) signals from epilepsy studies. Transitions from randomness to periodicity were successfully detected in the synthetic signals, while significant differences in EEG signals were observed based on different regions and states of the brain. In addition, using results from one entropy algorithm as features and the k-nearest neighbours algorithm, maximum classification accuracies in the first EEG database ranged from 63% to 73.5%, while these values increased by approximately 20% when using two different entropies as features. For the second database, maximum classification accuracy reached 62.5% using one entropy algorithm, while using two algorithms as features further increased that by 10%. Embedding entropies (sample, quadratic sample and fuzzy entropies) are found to outperform the rest of the algorithms in terms of sensitivity and show greater potential by considering the fine-tuning possibilities they offer. On the other hand, permutation and modified permutation entropies are more consistent across different input parameter values and considerably faster to calculate.

Mechanical Fault Diagnosis of a DC Motor Utilizing United Variational Mode Decomposition, SampEn, and Random Forest-SPRINT Algorithm Classifiers

Traditional fault diagnosis methods of DC (direct current) motors require establishing accurate mathematical models, effective state and parameter estimations, and appropriate statistical decision-making methods. However, these preconditions considerably limit traditional motor fault diagnosis methods. To address this issue, a new mechanical fault diagnosis method was proposed. Firstly, the vibration signals of motors were collected by the designed acquisition system. Subsequently, variational mode decomposition (VMD) was adopted to decompose the signal into a series of intrinsic mode functions and extract the characteristics of the vibration signals based on sample entropy. Finally, a united random forest improvement based on a SPRINT algorithm was employed to identify vibration signals of rotating machinery, and each branch tree was trained by applying different bootstrap sample sets. As the results reveal, the proposed fault diagnosis method is featured with good generalization performance, as the recognition rate of samples is more than 90%. Compared with the traditional neural network, data-heavy parameter optimization processes are avoided in this method. Therefore, the VMD-SampEn-RF-based method proposed in this paper performs well in fault diagnosis of DC motors, providing new ideas for future fault diagnoses of rotating machinery.

A Fetal ECG Monitoring System Based on the Android Smartphone

In this paper, a fetal electrocardiogram (ECG) monitoring system based on the Android smartphone was proposed. We designed a portable low-power fetal ECG collector, which collected maternal abdominal ECG signals in real time. The ECG data were sent to a smartphone client via Bluetooth. Smartphone app software was developed based on the Android system. The app integrated the fast fixed-point algorithm for independent component analysis (FastICA) and the sample entropy algorithm, for the sake of real-time extraction of fetal ECG signals from the maternal abdominal ECG signals. The fetal heart rate was computed using the extracted fetal ECG signals. Experimental results showed that the FastICA algorithm can extract a clear fetal ECG, and the sample entropy can correctly determine the channel where the fetal ECG is located. The proposed fetal ECG monitoring system may be feasible for non-invasive, real-time monitoring of fetal ECGs.

Time-Shift Multiscale Fuzzy Entropy and Laplacian Support Vector Machine Based Rolling Bearing Fault Diagnosis

Multiscale entropy (MSE), as a complexity measurement method of time series, has been widely used to extract the fault information hidden in machinery vibration signals. However, the insufficient coarse graining in MSE will result in fault pattern information missing and the sample entropy used in MSE at larger factors will fluctuate heavily. Combining fractal theory and fuzzy entropy, the time shift multiscale fuzzy entropy (TSMFE) is put forward and applied to the complexity analysis of time series for enhancing the performance of MSE. Then TSMFE is used to extract the nonlinear fault features from vibration signals of rolling bearing. By combining TSMFE with the Laplacian support vector machine (LapSVM), which only needs very few marked samples for classification training, a new intelligent fault diagnosis method for rolling bearing is proposed. Also the proposed method is applied to the experiment data analysis of rolling bearing by comparing with the existing methods and the analysis results show that the proposed fault diagnosis method can effectively identify different states of rolling bearing and get the highest recognition rate among the existing methods.

Health Degradation Monitoring and Early Fault Diagnosis of a Rolling Bearing Based on CEEMDAN and Improved MMSE

Rolling bearings play a crucial role in rotary machinery systems, and their operating state affects the entire mechanical system. In most cases, the fault of a rolling bearing can only be identified when it has developed to a certain degree. At that moment, there is already not much time for maintenance, and could cause serious damage to the entire mechanical system. This paper proposes a novel approach to health degradation monitoring and early fault diagnosis of rolling bearings based on a complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and improved multivariate multiscale sample entropy (MMSE). The smoothed coarse graining process was proposed to improve the conventional MMSE. Numerical simulation results indicate that CEEMDAN can alleviate the mode mixing problem and enable accurate intrinsic mode functions (IMFs), and improved MMSE can reflect intrinsic dynamic characteristics of the rolling bearing more accurately. During application studies, rolling bearing signals are decomposed by CEEMDAN to obtain IMFs. Then improved MMSE values of effective IMFs are computed to accomplish health degradation monitoring of rolling bearings, aiming at identifying the early weak fault phase. Afterwards, CEEMDAN is performed to extract the fault characteristic frequency during the early weak fault phase. The experimental results indicate the proposed method can obtain a better performance than other techniques in objective analysis, which demonstrates the effectiveness of the proposed method in practical application. The theoretical derivations, numerical simulations, and application studies all confirmed that the proposed health degradation monitoring and early fault diagnosis approach is promising in the field of prognostic and fault diagnosis of rolling bearings.

Spasticity assessment based on the Hilbert-Huang transform marginal spectrum entropy and the root mean square of surface electromyography signals: a preliminary study

BACKGROUND

Most of the objective and quantitative methods proposed for spasticity measurement are not suitable for clinical application, and methods for surface electromyography (sEMG) signal processing are mainly limited to the time-domain. This study aims to quantify muscle activity in the time-frequency domain, and develop a practical clinical method for the objective and reliable evaluation of the spasticity based on the Hilbert-Huang transform marginal spectrum entropy (HMSEN) and the root mean square (RMS) of sEMG signals.

METHODS

Twenty-six stroke patients with elbow flexor spasticity participated in the study. The subjects were tested at sitting position with the upper limb stretched towards the ground. The HMSEN of the sEMG signals obtained from the biceps brachii was employed to facilitate the stretch reflex onset (SRO) detection. Then, the difference between the RMS of a fixed-length sEMG signal obtained after the SRO and the RMS of a baseline sEMG signal, denoted as the RMS difference (RMSD), was employed to evaluate the spasticity level. The relations between Modified Ashworth Scale (MAS) scores and RMSD were investigated by Ordinal Logistic Regression (OLR). Goodness-of-fit of the OLR was obtained with Hosmer-Lemeshow test.

RESULTS

The HMSEN based method can precisely detect the SRO, and the RMSD scores and the MAS scores were fairly well related (test: χ2 = 8.8060, p = 0.2669; retest: χ2 = 1.9094, p = 0.9647). The prediction accuracies were 85% (test) and 77% (retest) when using RMSD for predicting MAS scores. In addition, the test-retest reliability was high, with an interclass correlation coefficient of 0.914 and a standard error of measurement of 1.137. Bland-Altman plots also indicated a small bias.

CONCLUSIONS

The proposed method is manually operated and easy to use, and the HMSEN based method is robust in detecting SRO in clinical settings. Hence, the method is applicable to clinical practice. The RMSD can assess spasticity in a quantitative way and provide greater resolution of spasticity levels compared to the MAS in clinical settings. These results demonstrate that the proposed method could be clinically more useful for the accurate and reliable assessment of spasticity and may be an alternative clinical measure to the MAS.

Entropy measures, entropy estimators, and their performance in quantifying complex dynamics: Effects of artifacts, nonstationarity, and long-range correlations

Entropy measures are widely applied to quantify the complexity of dynamical systems in diverse fields. However, the practical application of entropy methods is challenging, due to the variety of entropy measures and estimators and the complexity of real-world time series, including nonstationarities and long-range correlations (LRC). We conduct a systematic study on the performance, bias, and limitations of three basic measures (entropy, conditional entropy, information storage) and three traditionally used estimators (linear, kernel, nearest neighbor). We investigate the dependence of entropy measures on estimator- and process-specific parameters, and we show the effects of three types of nonstationarities due to artifacts (trends, spikes, local variance change) in simulations of stochastic autoregressive processes. We also analyze the impact of LRC on the theoretical and estimated values of entropy measures. Finally, we apply entropy methods on heart rate variability data from subjects in different physiological states and clinical conditions. We find that entropy measures can only differentiate changes of specific types in cardiac dynamics and that appropriate preprocessing is vital for correct estimation and interpretation. Demonstrating the limitations of entropy methods and shedding light on how to mitigate bias and provide correct interpretations of results, this work can serve as a comprehensive reference for the application of entropy methods and the evaluation of existing studies.