Comparative study of approximate entropy and sample entropy robustness to spikes

Comparative analysis of resting-state EEG-based multiscale entropy between schizophrenia and bipolar disorder

BACKGROUND

Studies that use nonlinear methods to identify abnormal brain dynamics in patients with psychiatric disorders are limited. This study investigated brain dynamics based on EEG using multiscale entropy (MSE) analysis in patients with schizophrenia (SZ) and bipolar disorder (BD).

METHODS

The eyes-closed resting-state EEG data were collected from 51 patients with SZ, 51 patients with BD, and 51 healthy controls (HCs). Patients with BD were further categorized into type I (n = 23) and type II (n = 16), and then compared with patients with SZ. A sample entropy-based MSE was evaluated from the bilateral frontal, central, and parieto-occipital regions using 30-s artifact-free EEG data for each individual. Correlation analyses of MSE values and psychiatric symptoms were performed.

RESULTS

For patients with SZ, higher MSE values were observed at higher-scale factors (i.e., 41-70) across all regions compared with both HCs and patients with BD. Furthermore, there were positive correlations between the MSE values in the left frontal and parieto-occipital regions and PANSS scores. For patients with BD, higher MSE values were observed at middle-scale factors (i.e., 13-40) in the bilateral frontal and central regions compared with HCs. Patients with BD type I exhibited higher MSE values at higher-scale factors across all regions compared with those with BD type II. In BD type I, positive correlations were found between MSE values in all left regions and YMRS scores.

CONCLUSIONS

Patients with psychiatric disorders exhibited group-dependent MSE characteristics. These results suggest that MSE features may be useful biomarkers that reflect pathophysiological characteristics.

Immediate and long-term electrophysiological biomarkers of antidepressant-like behavioral effects after subanesthetic ketamine and medial prefrontal cortex deep brain stimulation treatment

Introduction

Both ketamine (KET) and medial prefrontal cortex (mPFC) deep brain stimulation (DBS) are emerging therapies for treatment-resistant depression, yet our understanding of their electrophysiological mechanisms and biomarkers is incomplete. This study investigates aperiodic and periodic spectral parameters, and the signal complexity measure sample entropy, within mPFC local field potentials (LFP) in a chronic corticosterone (CORT) depression model after ketamine and/or mPFC DBS.

Methods

Male rats were intraperitoneally administered CORT or vehicle for 21 days. Over the last 7 days, animals receiving CORT were treated with mPFC DBS, KET, both, or neither; then tested across an array of behavioral tasks for 9 days.

Results

We found that the depression-like behavioral and weight effects of CORT correlated with a decrease in aperiodic-adjusted theta power (5-10 Hz) and an increase in sample entropy during the administration phase, and an increase in theta peak frequency and a decrease in the aperiodic exponent once the depression-like phenotype had been induced. The remission-like behavioral effects of ketamine alone correlated with a post-treatment increase in the offset and exponent, and decrease in sample entropy, both immediately and up to eight days post-treatment. The remission-like behavioral effects of mPFC DBS alone correlated with an immediate decrease in sample entropy, an immediate and sustained increase in low gamma (20-50 Hz) peak width and aperiodic offset, and sustained improvements in cognitive function. Failure to fully induce remission-like behavior in the combinatorial treatment group correlated with a failure to suppress an increase in sample entropy immediately after treatment.

Conclusion

Our findings therefore support the potential of periodic theta parameters as biomarkers of depression-severity; and periodic low gamma parameters and cognitive measures as biomarkers of mPFC DBS treatment efficacy. They also support sample entropy and the aperiodic spectral parameters as potential cross-modal biomarkers of depression severity and the therapeutic efficacy of mPFC DBS and/or ketamine. Study of these biomarkers is important as objective measures of disease severity and predictive measures of therapeutic efficacy can be used to personalize care and promote the translatability of research across studies, modalities, and species.

Molecular basis underlying default mode network functional abnormalities in postpartum depression with and without anxiety

Although Postpartum depression (PPD) and PPD with anxiety (PPD-A) have been well characterized as functional disruptions within or between multiple brain systems, however, how to quantitatively delineate brain functional system irregularity and the molecular basis of functional abnormalities in PPD and PPD-A remains unclear. Here, brain sample entropy (SampEn), resting-state functional connectivity (RSFC), transcriptomic and neurotransmitter density data were used to investigate brain functional system irregularity, functional connectivity abnormalities and associated molecular basis for PPD and PPD-A. PPD-A exhibited higher SampEn in medial prefrontal cortex (MPFC) and posterior cingulate cortex (PPC) than healthy postnatal women (HPW) and PPD while PPD showed lower SampEn in PPC compared to HPW and PPD-A. The functional connectivity analysis with MPFC and PPC as seed areas revealed decreased functional couplings between PCC and paracentral lobule and between MPFC and angular gyrus in PPD compared to both PPD-A and HPW. Moreover, abnormal SampEn and functional connectivity were associated with estrogenic level and clinical symptoms load. Importantly, spatial association analyses between functional changes and transcriptome and neurotransmitter density maps revealed that these functional changes were primarily associated with synaptic signaling, neuron projection, neurotransmitter level regulation, amino acid metabolism, cyclic adenosine monophosphate (cAMP) signaling pathways, and neurotransmitters of 5-hydroxytryptamine (5-HT), norepinephrine, glutamate, dopamine and so on. These results reveal abnormal brain entropy and functional connectivities primarily in default mode network (DMN) and link these changes to transcriptome and neurotransmitters to establish the molecular basis for PPD and PPD-A for the first time. Our findings highlight the important role of DMN in neuropathology of PPD and PPD-A.

Impact of exposure to natural versus urban soundscapes on brain functional connectivity, BOLD entropy and behavior

BACKGROUND

Humans have been moving from rural to urban environments for decades. This process may have important consequences for our health and well-being. Most previous studies have focused on visual input, and the auditory domain has been understudied so far. Therefore, we set out to investigate the influence of exposure to natural vs urban soundscapes on brain activity and behavior.

METHODS

Resting-state fMRI data was acquired while participants (N = 35) listened to natural and urban soundscapes. Two affective questionnaires (the Positive and Negative Affect Schedule (PANAS) and the Perceived Stress Scale) and two cognitive tasks (dual n-back (DNB) and the backward digit-span (BDS)) were assessed before and after each soundscape condition. To quantify brain function we used complexity and network measures, namely brain entropy (BEN) and whole brain functional connectivity (FC). To study the link between brain and behavior, changes in BEN and whole brain FC were correlated to changes in cognitive performance and self-reported affect.

RESULTS

We found higher BEN when listening to urban sounds in posterior cingulate gyrus, cuneus and precuneus, occipital lobe/calcarine as compared to nature sounds, which was negatively correlated to (post-pre) differences in positive affect (PANAS) in the urban soundscape condition. In addition, we found higher FC between areas in the auditory, cinguloopercular, somatomotor hand and mouth networks when listening to nature as compared to urban sounds which was positively correlated to (post-pre) differences of the of the composite score of Digit span and N-back for nature soundscape.

CONCLUSIONS

This study provides a framework for the neural underpinnings of how natural versus urban soundscapes affect both whole brain FC and BEN and bear implications for the understanding of how the physical auditory environment affects brain function and subsequently observed behavior. Moreover, correlations with cognition and affect reveal the meaning that exposure to soundscapes may have on the human brain. To the best of our knowledge this is the first study to analyze BEN and whole brain FC at rest during exposure to nature and urban soundscapes and to explore their relationship to behavior.

Expecting the Unexpected: Entropy and Multifractal Systems in Finance

Entropy serves as a measure of chaos in systems by representing the average rate of information loss about a phase point's position on the attractor. When dealing with a multifractal system, a single exponent cannot fully describe its dynamics, necessitating a continuous spectrum of exponents, known as the singularity spectrum. From an investor's point of view, a rise in entropy is a signal of abnormal and possibly negative returns. This means he has to expect the unexpected and prepare for it. To explore this, we analyse the New York Stock Exchange (NYSE) U.S. Index as well as its constituents. Through this examination, we assess their multifractal characteristics and identify market conditions (bearish/bullish markets) using entropy, an effective method for recognizing fluctuating fractal markets. Our findings challenge conventional beliefs by demonstrating that price declines lead to increased entropy, contrary to some studies in the literature that suggest that reduced entropy in market crises implies more determinism. Instead, we propose that bear markets are likely to exhibit higher entropy, indicating a greater chance of unexpected extreme events. Moreover, our study reveals a power-law behaviour and indicates the absence of variance.

Electrocardiogram morphological arrhythmia classification using fuzzy entropy-based feature selection and optimal classifier

Electrocardiogram (ECG) signal analysis has become significant in recent years as cardiac arrhythmia shares a major portion of all mortality worldwide. To detect these arrhythmias, computer-assisted algorithms play a pivotal role as beat-by-beat monitoring of holter ECG signals is required. In this paper, a morphological arrhythmia classification algorithm has been proposed to classify seven different ECG beats, namely Normal Beat (N), Left Bundle Branch Block Beat (L), Right Bundle Branch Block Beat (R), Atrial Premature Contraction Beat (A), Premature Ventricular Contraction Beat (V), Fusion of Normal and Ventricle Beat (F) and Pace Beat (P). A novel feature set of 25 attributes has been extracted from each ECG beat and ranked using the Fuzzy Entropy-based feature selection (FEBFS) technique. In addition, two distinct classifiers, support vector machine with radial basis function as the kernel (SVM-RBF) and weighted K-nearest neighbor (WKNN), are used to categorize ECG beats, and their performances are also evaluated after adjusting vital parameters. The performance of classifiers is compared for four different ECG beat segmentation approaches and further analyzed using three similarity measurement techniques and two fuzzy entropy methods while feature selection. The classifier results are also cross-validated using a 10-fold cross-validation scheme, and the MIT-BIH Arrhythmia Database has been used to validate the proposed work. After selecting 21 highly ranked features, WKNN achieves the best results with the nearest neighbor value K = 3 and cityblock distance metrics, with Average Sensitivity (Sen) = 94.89%, Positive Predictivity (Ppre) = 97.13%, Specificity (Spe) = 99.72%, F1 Score = 95.95%, and Overall Accuracy (Acc) = 99.15%. The novelty of this work relies on formulating a unique feature set, including proposed symbolic features, followed by the FEBFS technique making this algorithm efficient and reliable for morphological arrhythmia classification. The above results demonstrate that the proposed algorithm performs better than many existing state-of-the-art works.

Entropy-based reliable non-invasive detection of coronary microvascular dysfunction using machine learning algorithm

PURPOSE

Coronary microvascular dysfunction (CMD) is emerging as an important cause of myocardial ischemia, but there is a lack of a non-invasive method for reliable early detection of CMD.

AIM

To develop an electrocardiogram (ECG)-based machine learning algorithm for CMD detection that will lay the groundwork for patient-specific non-invasive early detection of CMD.

METHODS

Vectorcardiography (VCG) was calculated from each 10-second ECG of CMD patients and healthy controls. Sample entropy (SampEn), approximate entropy (ApEn), and complexity index (CI) derived from multiscale entropy were extracted from ST-T segments of each lead in ECGs and VCGs. The most effective entropy subset was determined using the sequential backward selection algorithm under the intra-patient and inter-patient schemes, separately. Then, the corresponding optimal model was selected from eight machine learning models for each entropy feature based on five-fold cross-validations. Finally, the classification performance of SampEn-based, ApEn-based, and CI-based models was comprehensively evaluated and tested on a testing dataset to investigate the best one under each scheme.

RESULTS

ApEn-based SVM model was validated as the optimal one under the intra-patient scheme, with all testing evaluation metrics over 0.8. Similarly, ApEn-based SVM model was selected as the best one under the intra-patient scheme, with major evaluation metrics over 0.8.

CONCLUSIONS

Entropies derived from ECGs and VCGs can effectively detect CMD under both intra-patient and inter-patient schemes. Our proposed models may provide the possibility of an ECG-based tool for non-invasive detection of CMD.

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.

Evaluating EEG complexity metrics as biomarkers for depression

Nonlinear EEG analysis offers the potential for both increased diagnostic accuracy and deeper mechanistic understanding of psychopathology. EEG complexity measures have previously been shown to positively correlate with clinical depression. In this study, resting state EEG recordings were taken across multiple sessions and days with both eyes open and eyes closed conditions from a total of 306 subjects, 62 of which were in a current depressive episode, and 81 of which had a history of diagnosed depression but were not currently depressed. Three different EEG montages (mastoids, average, and Laplacian) were also computed. Higuchi fractal dimension (HFD) and sample entropy (SampEn) were calculated for each unique condition. The complexity metrics showed high internal consistency within session and high stability across days. Higher complexity was found in open-eye recordings compared to closed eyes. The predicted correlation between complexity and depression was not found. However, an unexpected sex effect was observed, in which males and females exhibited different topographic patterns of complexity.

Considerations for Applying Entropy Methods to Temporally Correlated Stochastic Datasets

The goal of this paper is to highlight considerations and provide recommendations for analytical issues that arise when applying entropy methods, specifically Sample Entropy (SampEn), to temporally correlated stochastic datasets, which are representative of a broad range of biomechanical and physiological variables. To simulate a variety of processes encountered in biomechanical applications, autoregressive fractionally integrated moving averaged (ARFIMA) models were used to produce temporally correlated data spanning the fractional Gaussian noise/fractional Brownian motion model. We then applied ARFIMA modeling and SampEn to the datasets to quantify the temporal correlations and regularity of the simulated datasets. We demonstrate the use of ARFIMA modeling for estimating temporal correlation properties and classifying stochastic datasets as stationary or nonstationary. We then leverage ARFIMA modeling to improve the effectiveness of data cleaning procedures and mitigate the influence of outliers on SampEn estimates. We also emphasize the limitations of SampEn to distinguish among stochastic datasets and suggest the use of complementary measures to better characterize the dynamics of biomechanical variables. Finally, we demonstrate that parameter normalization is not an effective procedure for increasing the interoperability of SampEn estimates, at least not for entirely stochastic datasets.

New Insights into Stroke from Continuous Passively Collected Temperature and Sleep Data Using Wrist-Worn Wearables

Actigraphy may provide new insights into clinical outcomes and symptom management of patients through passive, continuous data collection. We used the GENEActiv smartwatch to passively collect actigraphy, wrist temperature, and ambient light data from 27 participants after stroke or probable brain transient ischemic attack (TIA) over 42 periods of device wear. We computed 323 features using established algorithms and proposed 25 novel features to characterize sleep and temperature. We investigated statistical associations between the extracted features and clinical outcomes evaluated using clinically validated questionnaires to gain insight into post-stroke recovery. We subsequently fitted logistic regression models to replicate clinical diagnosis (stroke or TIA) and disability due to stroke. The model generalization performance was assessed using a leave-one-subject-out cross validation method with the selected feature subsets, reporting the area under the curve (AUC). We found that several novel features were strongly correlated (|r|>0.3) with stroke symptoms and mental health measures. Using selected novel features, we obtained an AUC of 0.766 to estimate diagnosis and an AUC of 0.749 to estimate whether disability due to stroke was present. Collectively, these findings suggest that features extracted from the temperature smartwatch sensor may reveal additional clinically useful information over and above existing actigraphy-based features.

Slope Entropy Normalisation by Means of Analytical and Heuristic Reference Values

Slope Entropy (SlpEn) is a very recently proposed entropy calculation method. It is based on the differences between consecutive values in a time series and two new input thresholds to assign a symbol to each resulting difference interval. As the histogram normalisation value, SlpEn uses the actual number of unique patterns found instead of the theoretically expected value. This maximises the information captured by the method but, as a consequence, SlpEn results do not usually fall within the classical [0,1] interval. Although this interval is not necessary at all for time series classification purposes, it is a convenient and common reference framework when entropy analyses take place. This paper describes a method to keep SlpEn results within this interval, and improves the interpretability and comparability of this measure in a similar way as for other methods. It is based on a max-min normalisation scheme, described in two steps. First, an analytic normalisation is proposed using known but very conservative bounds. Afterwards, these bounds are refined using heuristics about the behaviour of the number of patterns found in deterministic and random time series. The results confirm the suitability of the approach proposed, using a mixture of the two methods.

Temporal complexity of EEG encodes human alertness

OBJECTIVE

Automatic human alertness monitoring has recently become an important research topic with important applications in many areas such as the detection of drivers' fatigue, monitoring of monotonous tasks that require a high level of alertness such as traffic control and nuclear power plant monitoring, and sleep staging. In this study, we propose that balanced dynamics of Electroencephalography (EEG) (so called EEG temporal complexity) is a potentially useful feature for identifying human alertness states. Recently, a new signal entropy measure, called Range Entropy (RangeEn), was proposed to overcome some limitations of two of the most widely used entropy measures, namely Approximate Entropy (ApEn) and Sample Entropy (SampEn), and showed its relevance for the study of time domain EEG complexity. In this paper, we investigated whether the RangeEn holds discriminating information associated with human alertness states, namely Awake, Drowsy, and Sleep and compare its performance against those of SampEn and ApEn.

APPROACH

We used EEG data from 60 healthy subjects of both sexes and different ages acquired during whole night sleeps. Using a 30-second sliding window, we computed the three entropy measures of EEG and performed statistical analyses to evaluate the ability of these entropy measures to discriminate among the different human alertness states.

MAIN RESULTS

Although the three entropy measures contained useful information about human alertness, RangeEn showed a higher discriminative capability compared to ApEn and SampEn especially when using EEG within the Beta frequency band.

SIGNIFICANCE

Our findings highlight the EEG temporal complexity evolution through the human alertness states. This relationship can potentially be exploited for the development of automatic human alertness monitoring systems and diagnostic tools for different neurological and sleep disorders, including insomnia.

Reliable Detection of Myocardial Ischemia Using Machine Learning Based on Temporal-Spatial Characteristics of Electrocardiogram and Vectorcardiogram

Background: Myocardial ischemia is a common early symptom of cardiovascular disease (CVD). Reliable detection of myocardial ischemia using computer-aided analysis of electrocardiograms (ECG) provides an important reference for early diagnosis of CVD. The vectorcardiogram (VCG) could improve the performance of ECG-based myocardial ischemia detection by affording temporal-spatial characteristics related to myocardial ischemia and capturing subtle changes in ST-T segment in continuous cardiac cycles. We aim to investigate if the combination of ECG and VCG could improve the performance of machine learning algorithms in automatic myocardial ischemia detection. Methods: The ST-T segments of 20-second, 12-lead ECGs, and VCGs were extracted from 377 patients with myocardial ischemia and 52 healthy controls. Then, sample entropy (SampEn, of 12 ECG leads and of three VCG leads), spatial heterogeneity index (SHI, of VCG) and temporal heterogeneity index (THI, of VCG) are calculated. Using a grid search, four SampEn and two features are selected as input signal features for ECG-only and VCG-only models based on support vector machine (SVM), respectively. Similarly, three features (S I , THI, and SHI, where S I is the SampEn of lead I) are further selected for the ECG + VCG model. 5-fold cross validation was used to assess the performance of ECG-only, VCG-only, and ECG + VCG models. To fully evaluate the algorithmic generalization ability, the model with the best performance was selected and tested on a third independent dataset of 148 patients with myocardial ischemia and 52 healthy controls. Results: The ECG + VCG model with three features (S I ,THI, and SHI) yields better classifying results than ECG-only and VCG-only models with the average accuracy of 0.903, sensitivity of 0.903, specificity of 0.905, F1 score of 0.942, and AUC of 0.904, which shows better performance with fewer features compared with existing works. On the third independent dataset, the testing showed an AUC of 0.814. Conclusion: The SVM algorithm based on the ECG + VCG model could reliably detect myocardial ischemia, providing a potential tool to assist cardiologists in the early diagnosis of CVD in routine screening during primary care services.

Discriminating Bacterial Infection from Other Causes of Fever Using Body Temperature Entropy Analysis

Body temperature is usually employed in clinical practice by strict binary thresholding, aiming to classify patients as having fever or not. In the last years, other approaches based on the continuous analysis of body temperature time series have emerged. These are not only based on absolute thresholds but also on patterns and temporal dynamics of these time series, thus providing promising tools for early diagnosis. The present study applies three time series entropy calculation methods (Slope Entropy, Approximate Entropy, and Sample Entropy) to body temperature records of patients with bacterial infections and other causes of fever in search of possible differences that could be exploited for automatic classification. In the comparative analysis, Slope Entropy proved to be a stable and robust method that could bring higher sensitivity to the realm of entropy tools applied in this context of clinical thermometry. This method was able to find statistically significant differences between the two classes analyzed in all experiments, with sensitivity and specificity above 70% in most cases.

Short duration Vectorcardiogram based inferior myocardial infarction detection: class and subject-oriented approach

Myocardial infarction (MI) happens when blood stops circulating to an explicit segment of the heart causing harm to the heart muscles. Vectorcardiography (VCG) is a technique of recording direction and magnitude of the signals that are produced by the heart in a 3-lead representation. In this work, we present a technique for detection of MI in the inferior portion of heart using short duration VCG signals. The raw signal was pre-processed using the median and Savitzky-Golay (SG) filter. The Stationary Wavelet Transform (SWT) was used for time-invariant decomposition of the signal followed by feature extraction. The selected features using minimum-redundancy-maximum-relevance (mRMR) based feature selection method were applied to the supervised classification methods. The efficacy of the proposed method was assessed under both class-oriented and a more real-life subject-oriented approach. An accuracy of 99.14 and 89.37% were achieved respectively. Results of the proposed technique are better than existing state-of-art methods and used VCG segment is shorter. Thus, a shorter segment and a high accuracy can be helpful in the automation of timely and reliable detection of MI. The satisfactory performance achieved in the subject-oriented approach shows reliability and applicability of the proposed technique.

Measures of repolarization variability predict ventricular arrhythmogenesis in heptanol-treated Langendorff-perfused mouse hearts

BACKGROUND

Time-domain and non-linear methods can be used to quantify beat-to-beat repolarization variability but whether measures of repolarization variability can predict ventricular arrhythmogenesis in mice have never been explored.

METHODS

Left ventricular monophasic action potentials (MAPs) were recorded during constant right ventricular 8 ​Hz pacing in Langendorff-perfused mouse hearts, in the presence or absence of the gap junction and sodium channel inhibitor heptanol (0.1, 0.5, 1 or 2 ​mM).

RESULTS

Under control conditions, mean action potential duration (APD) was 39.4 ​± ​8.1 ​ms. Standard deviation (SD) of APDs was 0.3 ​± ​0.2 ​ms, coefficient of variation was 0.9 ​± ​0.8% and the root mean square (RMS) of successive differences in APDs was 0.15 ​± ​0.14 ​ms. Poincaré plots of APDn+1 against APDn revealed ellipsoid morphologies with a SD along the line-of-identity (SD2) to SD perpendicular to the line-of-identity (SD1) ratio of 4.6 ​± ​2.1. Approximate and sample entropy were 0.61 ​± ​0.12 and 0.76 ​± ​0.26, respectively. Detrended fluctuation analysis revealed short- and long-term fluctuation slopes of 1.49 ​± ​0.27 and 0.81 ​± ​0.36, respectively. Heptanol at 2 ​mM induced ventricular tachycardia in five out of six hearts. None of the above parameters were altered by heptanol during which reproducible electrical activity was observed (KW-ANOVA, P ​> ​0.05). Contrastingly, SD2/SD1 decreased to 2.03 ​± ​0.41, approximate and sample entropy increased to 0.82 ​± ​0.12 and 1.45 ​± ​0.34, and short-term fluctuation slope decreased to 0.82 ​± ​0.19 during the 20-s period preceding spontaneous ventricular tachy-arrhythmias (n ​= ​6, KW-ANOVA, P ​< ​0.05).

CONCLUSION

Measures of repolarization variability, such as SD2/SD1, entropy, and fluctuation slope are altered preceding the occurrence of ventricular arrhythmogenesis in mouse hearts. Changes in these variables may allow detection of impending arrhythmias for early intervention.

Entropy Analysis in Gait Research: Methodological Considerations and Recommendations

The usage of entropy analysis in gait research has grown considerably the last two decades. The present paper reviews the application of different entropy analyses in gait research and provides recommendations for future studies. While single-scale entropy analysis such as approximate and sample entropy can be used to quantify regularity/predictability/probability, they do not capture the structural richness and component entanglement characterized by a complex system operating across multiple spatial and temporal scales. Thus, for quantification of complexity, either multiscale entropy or refined composite multiscale entropy is recommended. For both single- and multiscale-scale entropy analyses, care should be made when selecting the input parameters of tolerance window r, vector length m, time series length N and number of scales. This selection should be based on the proposed research question and the type of data collected and not copied from previous studies. Parameter consistency should be investigated and published along with the main results to ensure transparency and enable comparisons between studies. Furthermore, since the interpretation of the absolute size of both single- and multiscale entropy analyses outcomes is not straightforward, comparisons should always be made with a control condition or group.

Assessment of Outliers and Detection of Artifactual Network Segments Using Univariate and Multivariate Dispersion Entropy on Physiological Signals

Network physiology has emerged as a promising paradigm for the extraction of clinically relevant information from physiological signals by moving from univariate to multivariate analysis, allowing for the inspection of interdependencies between organ systems. However, for its successful implementation, the disruptive effects of artifactual outliers, which are a common occurrence in physiological recordings, have to be studied, quantified, and addressed. Within the scope of this study, we utilize Dispersion Entropy (DisEn) to initially quantify the capacity of outlier samples to disrupt the values of univariate and multivariate features extracted with DisEn from physiological network segments consisting of synchronised, electroencephalogram, nasal respiratory, blood pressure, and electrocardiogram signals. The DisEn algorithm is selected due to its efficient computation and good performance in the detection of changes in signals for both univariate and multivariate time-series. The extracted features are then utilised for the training and testing of a logistic regression classifier in univariate and multivariate configurations in an effort to partially automate the detection of artifactual network segments. Our results indicate that outlier samples cause significant disruption in the values of extracted features with multivariate features displaying a certain level of robustness based on the number of signals formulating the network segments from which they are extracted. Furthermore, the deployed classifiers achieve noteworthy performance, where the percentage of correct network segment classification surpasses 95% in a number of experimental setups, with the effectiveness of each configuration being affected by the signal in which outliers are located. Finally, due to the increase in the number of features extracted within the framework of network physiology and the observed impact of artifactual samples in the accuracy of their values, the implementation of algorithmic steps capable of effective feature selection is highlighted as an important area for future research.

Relative Consistency of Sample Entropy Is Not Preserved in MIX Processes

Relative consistency is a notion related to entropic parameters, most notably to Approximate Entropy and Sample Entropy. It is a central characteristic assumed for e.g., biomedical and economic time series, since it allows the comparison between different time series at a single value of the threshold parameter r. There is no formal proof for this property, yet it is generally accepted that it is true. Relative consistency in both Approximate Entropy and Sample entropy was first tested with the M I X process. In the seminal paper by Richman and Moorman, it was shown that Approximate Entropy lacked the property for cases in which Sample Entropy did not. In the present paper, we show that relative consistency is not preserved for M I X processes if enough noise is added, yet it is preserved for another process for which we define a sum of a sinusoidal and a stochastic element, no matter how much noise is present. The analysis presented in this paper is only possible because of the existence of the very fast NCM algorithm for calculating correlation sums and thus also Sample Entropy.

Nonlinear analysis of EEG complexity in episode and remission phase of recurrent depression

OBJECTIVES

Biomarkers of major depressive disorder (MDD), its phases and forms have long been sought. Objectives were to examine whether the complexity of EEG activity, measured by Higuchi's fractal dimension (HFD) and sample entropy (SampEn), differs between healthy subjects, patients in remission, and in episode phase of the recurrent depression and whether the changes are differentially distributed between hemispheres and cortical regions.

METHODS

Resting state EEG with eyes closed was recorded from 22 patients suffering from recurrent depression (11 in remission, 11 in the episode), and 20 age and sex-matched healthy control subjects. Artifact-free EEG epochs were analyzed by in-house developed programs running HFD and SampEn algorithms.

RESULTS

Depressed patients had higher HFD and SampEn complexity compared to healthy subjects. The complexity was higher in patients who were in remission than in those in the acute episode. Altered complexity was present in the frontal and centro-parietal regions when compared to control group. The complexity in frontal and parietal regions differed between the two phases of depressive disorder.

CONCLUSIONS

Complexity measures of EEG distinguish between the healthy controls, patients in remission and episode. Further studies are needed to establish whether these measures carry a potential to aid clinically relevant decisions about depression.

Impact of observational error on heart rate variability analysis

An observational error of heart rate variability (HRV) may arise from many factors, such as a limited sampling frequency, QRS complexes detection process, preprocessing procedures and others. In our study, we focused on the first two origins of measurement error. We introduced a model of observational error and suggested universal descriptors for the assessment of its resultant magnitude in terms of time, frequency as well as nonlinear parameters. For this purpose, we applied Monte Carlo simulations which showed that the most sensitive to observational error are: pNN50 (the proportion of pairs of successive RR intervals that differ by more than 50 ms) and markers obtained from frequency analysis. On the other hand, the most resistant are other time domain parameters as well as the short and long-term slopes of Detrended Fluctuation Analysis (DFA). We postulate that the observational error should be considered in population studies, when different recorders are used in the research centres. Additionally, in the case of patients with similar etiology of disease but with different heart rhythms abnormalities the scatter of HRV parameters will also be observed due to the subject's the time series variability.

Using the Information Provided by Forbidden Ordinal Patterns in Permutation Entropy to Reinforce Time Series Discrimination Capabilities

Despite its widely tested and proven usefulness, there is still room for improvement in the basic permutation entropy (PE) algorithm, as several subsequent studies have demonstrated in recent years. Some of these new methods try to address the well-known PE weaknesses, such as its focus only on ordinal and not on amplitude information, and the possible detrimental impact of equal values found in subsequences. Other new methods address less specific weaknesses, such as the PE results' dependence on input parameter values, a common problem found in many entropy calculation methods. The lack of discriminating power among classes in some cases is also a generic problem when entropy measures are used for data series classification. This last problem is the one specifically addressed in the present study. Toward that purpose, the classification performance of the standard PE method was first assessed by conducting several time series classification tests over a varied and diverse set of data. Then, this performance was reassessed using a new Shannon Entropy normalisation scheme proposed in this paper: divide the relative frequencies in PE by the number of different ordinal patterns actually found in the time series, instead of by the theoretically expected number. According to the classification accuracy obtained, this last approach exhibited a higher class discriminating power. It was capable of finding significant differences in six out of seven experimental datasets-whereas the standard PE method only did in four-and it also had better classification accuracy. It can be concluded that using the additional information provided by the number of forbidden/found patterns, it is possible to achieve a higher discriminating power than using the classical PE normalisation method. The resulting algorithm is also very similar to that of PE and very easy to implement.

The successful discrimination of depression from EEG could be attributed to proper feature extraction and not to a particular classification method

Reliable diagnosis of depressive disorder is essential for both optimal treatment and prevention of fatal outcomes. This study aimed to elucidate the effectiveness of two non-linear measures, Higuchi's Fractal Dimension (HFD) and Sample Entropy (SampEn), in detecting depressive disorders when applied on EEG. HFD and SampEn of EEG signals were used as features for seven machine learning algorithms including Multilayer Perceptron, Logistic Regression, Support Vector Machines with the linear and polynomial kernel, Decision Tree, Random Forest, and Naïve Bayes classifier, discriminating EEG between healthy control subjects and patients diagnosed with depression. This study confirmed earlier observations that both non-linear measures can discriminate EEG signals of patients from healthy control subjects. The results suggest that good classification is possible even with a small number of principal components. Average accuracy among classifiers ranged from 90.24 to 97.56%. Among the two measures, SampEn had better performance. Using HFD and SampEn and a variety of machine learning techniques we can accurately discriminate patients diagnosed with depression vs controls which can serve as a highly sensitive, clinically relevant marker for the diagnosis of depressive disorders.

Augmentation of Dispersion Entropy for Handling Missing and Outlier Samples in Physiological Signal Monitoring

Entropy quantification algorithms are becoming a prominent tool for the physiological monitoring of individuals through the effective measurement of irregularity in biological signals. However, to ensure their effective adaptation in monitoring applications, the performance of these algorithms needs to be robust when analysing time-series containing missing and outlier samples, which are common occurrence in physiological monitoring setups such as wearable devices and intensive care units. This paper focuses on augmenting Dispersion Entropy (DisEn) by introducing novel variations of the algorithm for improved performance in such applications. The original algorithm and its variations are tested under different experimental setups that are replicated across heart rate interval, electroencephalogram, and respiratory impedance time-series. Our results indicate that the algorithmic variations of DisEn achieve considerable improvements in performance while our analysis signifies that, in consensus with previous research, outlier samples can have a major impact in the performance of entropy quantification algorithms. Consequently, the presented variations can aid the implementation of DisEn to physiological monitoring applications through the mitigation of the disruptive effect of missing and outlier samples.

Detection of stretch reflex onset based on empirical mode decomposition and modified sample entropy

Background

Accurate spasticity assessment provides an objective evaluation index for the rehabilitation treatment of patients with spasticity, and the key is detecting stretch reflex onset. The surface electromyogram of patients with spasticity is prone to false peaks, and its data length is unstable. These conditions decrease signal differences before and after stretch reflex onset. Therefore, a method for detecting stretch reflex onset based on empirical mode decomposition denoising and modified sample entropy recognition is proposed in this study.

Results

The empirical mode decomposition algorithm is better than the wavelet threshold algorithm in denoising surface electromyogram signal. Without adding Gaussian white noise to the electromyogram signal, the stretch reflex onset recognition rate of the electromyogram signal before and after empirical mode decomposition denoising was increased by 56%. In particular, the recognition rate of stretch reflex onset under the optimal parameter of the modified sample entropy can reach up to 100% and the average recognition rate is 93%.

Conclusions

The empirical mode decomposition algorithm can eliminate the baseline activity of the surface electromyogram signal before stretch reflex onset and effectively remove noise from the signal. The identification of stretch reflex onset using combined empirical mode decomposition and modified sample entropy is better than that via modified sample entropy alone, and stretch reflex onset can be accurately determined.

A New Physically Meaningful Threshold of Sample Entropy for Detecting Cardiovascular Diseases

Sample Entropy (SampEn) is a popular method for assessing the regularity of physiological signals. Prior to the entropy calculation, certain common parameters need to be initialized: Embedding dimension m, tolerance threshold r and time series length N. Nevertheless, the determination of these parameters is usually based on expert experience. Improper assignments of these parameters tend to bring invalid values, inconsistency and low statistical significance in entropy calculation. In this study, we proposed a new tolerance threshold with physical meaning (rp), which was based on the sampling resolution of physiological signals. Statistical significance, percentage of invalid entropy values and ROC curve were used to evaluate the proposed rp against the traditional threshold (rt). Normal sinus rhythm (NSR), congestive heart failure (CHF) as well as atrial fibrillation (AF) RR interval recordings from Physionet were used as the test data. The results demonstrated that the proposed rp had better stability than rt, hence more adaptive to detect cardiovascular diseases of CHF and AF.

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

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

Quantification of Beat-To-Beat Variability of Action Potential Durations in Langendorff-Perfused Mouse Hearts

Background: Beat-to-beat variability in action potential duration (APD) is an intrinsic property of cardiac tissue and is altered in pro-arrhythmic states. However, it has never been examined in mice.

Methods: Left atrial or ventricular monophasic action potentials (MAPs) were recorded from Langendorff-perfused mouse hearts during regular 8 Hz pacing. Time-domain, frequency-domain and non-linear analyses were used to quantify APD variability.

Results: Mean atrial APD (90% repolarization) was 23.5 ± 6.3 ms and standard deviation (SD) was 0.9 ± 0.5 ms (n = 6 hearts). Coefficient of variation (CoV) was 4.0 ± 1.9% and root mean square (RMS) of successive differences in APDs was 0.3 ± 0.2 ms. The peaks for low- and high-frequency were 0.7 ± 0.5 and 2.7 ± 0.9 Hz, respectively, with percentage powers of 39.0 ± 20.5 and 59.3 ± 22.9%. Poincaré plots of APD_n+1 against APD_n revealed ellipsoid shapes. The ratio of the SD along the line-of-identity (SD2) to the SD perpendicular to the line-of-identity (SD1) was 8.28 ± 4.78. Approximate and sample entropy were 0.57 ± 0.12 and 0.57 ± 0.15, respectively. Detrended fluctuation analysis revealed short- and long-term fluctuation slopes of 1.80 ± 0.15 and 0.85 ± 0.29, respectively. When compared to atrial APDs, ventricular APDs were longer (ANOVA, P < 0.05), showed lower mean SD and CoV but similar RMS of successive differences in APDs and showed lower SD2 (P < 0.05). No difference in the remaining parameters was observed.

Conclusion: Beat-to-beat variability in APD is observed in mouse hearts during regular pacing. Atrial MAPs showed greater degree of variability than ventricular MAPs. Non-linear techniques offer further insights on short-term and long-term variability and signal complexity.

Characterization of Artifact Influence on the Classification of Glucose Time Series Using Sample Entropy Statistics

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

Sample Entropy Analysis of Noisy Atrial Electrograms during Atrial Fibrillation

Most cardiac arrhythmias can be classified as atrial flutter, focal atrial tachycardia, or atrial fibrillation. They have been usually treated using drugs, but catheter ablation has proven more effective. This is an invasive method devised to destroy the heart tissue that disturbs correct heart rhythm. In order to accurately localise the focus of this disturbance, the acquisition and processing of atrial electrograms form the usual mapping technique. They can be single potentials, double potentials, or complex fractionated atrial electrogram (CFAE) potentials, and last ones are the most effective targets for ablation. The electrophysiological substrate is then localised by a suitable signal processing method. Sample Entropy is a statistic scarcely applied to electrograms but can arguably become a powerful tool to analyse these time series, supported by its results in other similar biomedical applications. However, the lack of an analysis of its dependence on the perturbations usually found in electrogram data, such as missing samples or spikes, is even more marked. This paper applied SampEn to the segmentation between non-CFAE and CFAE records and assessed its class segmentation power loss at different levels of these perturbations. The results confirmed that SampEn was able to significantly distinguish between non-CFAE and CFAE records, even under very unfavourable conditions, such as 50% of missing data or 10% of spikes.

Reliability of the Parabola Approximation Method in Heart Rate Variability Analysis Using Low-Sampling-Rate Photoplethysmography

Photoplethysmographic signals are useful for heart rate variability analysis in practical ambulatory applications. While reducing the sampling rate of signals is an important consideration for modern wearable devices that enable 24/7 continuous monitoring, there have not been many studies that have investigated how to compensate the low timing resolution of low-sampling-rate signals for accurate heart rate variability analysis. In this study, we utilized the parabola approximation method and measured it against the conventional cubic spline interpolation method for the time, frequency, and nonlinear domain variables of heart rate variability. For each parameter, the intra-class correlation, standard error of measurement, Bland-Altman 95% limits of agreement and root mean squared relative error were presented. Also, elapsed time taken to compute each interpolation algorithm was investigated. The results indicated that parabola approximation is a simple, fast, and accurate algorithm-based method for compensating the low timing resolution of pulse beat intervals. In addition, the method showed comparable performance with the conventional cubic spline interpolation method. Even though the absolute value of the heart rate variability variables calculated using a signal sampled at 20 Hz were not exactly matched with those calculated using a reference signal sampled at 250 Hz, the parabola approximation method remains a good interpolation method for assessing trends in HRV measurements for low-power wearable applications.

Noise Robustness Analysis of Performance for EEG-Based Driver Fatigue Detection Using Different Entropy Feature Sets

Driver fatigue is an important factor in traffic accidents, and the development of a detection system for driver fatigue is of great significance. To estimate and prevent driver fatigue, various classifiers based on electroencephalogram (EEG) signals have been developed; however, as EEG signals have inherent non-stationary characteristics, their detection performance is often deteriorated by background noise. To investigate the effects of noise on detection performance, simulated Gaussian noise, spike noise, and electromyogram (EMG) noise were added into a raw EEG signal. Four types of entropies, including sample entropy (SE), fuzzy entropy (FE), approximate entropy (AE), and spectral entropy (PE), were deployed for feature sets. Three base classifiers (K-Nearest Neighbors (KNN), Support Vector Machine (SVM), and Decision Tree (DT)) and two ensemble methods (Bootstrap Aggregating (Bagging) and Boosting) were employed and compared. Results showed that: (1) the simulated Gaussian noise and EMG noise had an impact on accuracy, while simulated spike noise did not, which is of great significance for the future application of driver fatigue detection; (2) the influence on noise performance was different based on each classifier, for example, the robust effect of classifier DT was the best and classifier SVM was the weakest; (3) the influence on noise performance was also different with each feature set where the robustness of feature set FE and the combined feature set were the best; and (4) while the Bagging method could not significantly improve performance against noise addition, the Boosting method may significantly improve performance against superimposed Gaussian and EMG noise. The entropy feature extraction method could not only identify driver fatigue, but also effectively resist noise, which is of great significance in future applications of an EEG-based driver fatigue detection system.

Dedicated Entropy Measures for Early Assessment of Pregnancy Progression From Single-Channel Electrohysterography

OBJECTIVE

Preterm birth is a large-scale clinical problem involving over 10% of infants. Diagnostic means for timely risk assessment are lacking and the underlying physiological mechanisms unclear. To improve the evaluation of pregnancy before term, we introduce dedicated entropy measures derived from a single-channel electrohysterogram (EHG).

METHODS

The estimation of approximate entropy (ApEn) and sample entropy (SampEn) is adjusted to monitor variations in the regularity of single-channel EHG recordings, reflecting myoelectrical changes due to pregnancy progression. In particular, modifications in the tolerance metrics are introduced for improving robustness to EHG amplitude fluctuations. An extensive database of 58 EHG recordings with 4 monopolar channels in women presenting with preterm contractions was manually annotated and used for validation. The methods were tested for their ability to recognize the onset of labor and the risk of preterm birth. Comparison with the best single-channel methods according to the literature was performed.

RESULTS

The reference methods were outperformed. SampEn and ApEn produced the best prediction of delivery, although only one channel showed a significant difference () between labor and nonlabor. The modified ApEn produced the best prediction of preterm delivery, showing statistical significance () in three channels. These results were also confirmed by the area under the receiver operating characteristic curve and fivefold cross validation.

CONCLUSION

The use of dedicated entropy estimators improves the diagnostic value of EHG analysis earlier in pregnancy.

SIGNIFICANCE

Our results suggest that changes in the EHG might manifest early in pregnancy, providing relevant prognostic opportunities for pregnancy monitoring by a practical single-channel solution.

Noisy EEG signals classification based on entropy metrics. Performance assessment using first and second generation statistics

This paper evaluates the performance of first generation entropy metrics, featured by the well known and widely used Approximate Entropy (ApEn) and Sample Entropy (SampEn) metrics, and what can be considered an evolution from these, Fuzzy Entropy (FuzzyEn), in the Electroencephalogram (EEG) signal classification context. The study uses the commonest artifacts found in real EEGs, such as white noise, and muscular, cardiac, and ocular artifacts. Using two different sets of publicly available EEG records, and a realistic range of amplitudes for interfering artifacts, this work optimises and assesses the robustness of these metrics against artifacts in class segmentation terms probability. The results show that the qualitative behaviour of the two datasets is similar, with SampEn and FuzzyEn performing the best, and the noise and muscular artifacts are the most confounding factors. On the contrary, there is a wide variability as regards initialization parameters. The poor performance achieved by ApEn suggests that this metric should not be used in these contexts.

Improvement in Neural Respiratory Drive Estimation From Diaphragm Electromyographic Signals Using Fixed Sample Entropy

Diaphragm electromyography is a valuable technique for the recording of electrical activity of the diaphragm. The analysis of diaphragm electromyographic (EMGdi) signal amplitude is an alternative approach for the quantification of the neural respiratory drive (NRD). The EMGdi signal is, however, corrupted by electrocardiographic (ECG) activity, and this presence of cardiac activity can make the EMGdi interpretation more difficult. Traditionally, the EMGdi amplitude has been estimated using the average rectified value (ARV) and the root mean square (RMS). In this study, surface EMGdi signals were analyzed using the fixed sample entropy (fSampEn) algorithm, and compared to the traditional ARV and RMS methods. The fSampEn is calculated using a tolerance value fixed and independent of the standard deviation of the analysis window. Thus, this method quantifies the amplitude of the complex components of stochastic signals (such as EMGdi), and being less affected by changes in amplitude due to less complex components (such as ECG). The proposed method was tested in synthetic and recorded EMGdi signals. fSampEn was less sensitive to the effect of cardiac activity on EMGdi signals with different levels of NRD than ARV and RMS amplitude parameters. The mean and standard deviation of the Pearson's correlation values between inspiratory mouth pressure (an indirect measure of the respiratory muscle activity) and fSampEn, ARV, and RMS parameters, estimated in the recorded EMGdi signal at tidal volume (without inspiratory load), were 0.38±0.12, 0.27±0.11 , and 0.11±0.13, respectively. Whereas at 33 cmH2O (maximum inspiratory load) were 0.83±0.02, 0.76±0.07, and 0.61±0.19 , respectively. Our findings suggest that the proposed method may improve the evaluation of NRD.

Selection of entropy-measure parameters for knowledge discovery in heart rate variability data

Background

Heart rate variability is the variation of the time interval between consecutive heartbeats. Entropy is a commonly used tool to describe the regularity of data sets. Entropy functions are defined using multiple parameters, the selection of which is controversial and depends on the intended purpose. This study describes the results of tests conducted to support parameter selection, towards the goal of enabling further biomarker discovery.

Methods

This study deals with approximate, sample, fuzzy, and fuzzy measure entropies. All data were obtained from PhysioNet, a free-access, on-line archive of physiological signals, and represent various medical conditions. Five tests were defined and conducted to examine the influence of: varying the threshold value r (as multiples of the sample standard deviation σ, or the entropy-maximizing r_Chon), the data length N, the weighting factors n for fuzzy and fuzzy measure entropies, and the thresholds r_F and r_L for fuzzy measure entropy. The results were tested for normality using Lilliefors' composite goodness-of-fit test. Consequently, the p-value was calculated with either a two sample t-test or a Wilcoxon rank sum test.

Results

The first test shows a cross-over of entropy values with regard to a change of r. Thus, a clear statement that a higher entropy corresponds to a high irregularity is not possible, but is rather an indicator of differences in regularity. N should be at least 200 data points for r = 0.2 σ and should even exceed a length of 1000 for r = r_Chon. The results for the weighting parameters n for the fuzzy membership function show different behavior when coupled with different r values, therefore the weighting parameters have been chosen independently for the different threshold values. The tests concerning r_F and r_L showed that there is no optimal choice, but r = r_F = r_L is reasonable with r = r_Chon or r = 0.2σ.

Conclusions

Some of the tests showed a dependency of the test significance on the data at hand. Nevertheless, as the medical conditions are unknown beforehand, compromises had to be made. Optimal parameter combinations are suggested for the methods considered. Yet, due to the high number of potential parameter combinations, further investigations of entropy for heart rate variability data will be necessary.

Evidence towards improved estimation of respiratory muscle effort from diaphragm mechanomyographic signals with cardiac vibration interference using sample entropy with fixed tolerance values

The analysis of amplitude parameters of the diaphragm mechanomyographic (MMGdi) signal is a non-invasive technique to assess respiratory muscle effort and to detect and quantify the severity of respiratory muscle weakness. The amplitude of the MMGdi signal is usually evaluated using the average rectified value or the root mean square of the signal. However, these estimations are greatly affected by the presence of cardiac vibration or mechanocardiographic (MCG) noise. In this study, we present a method for improving the estimation of the respiratory muscle effort from MMGdi signals that is robust to the presence of MCG. This method is based on the calculation of the sample entropy using fixed tolerance values (fSampEn), that is, with tolerance values that are not normalized by the local standard deviation of the window analyzed. The behavior of the fSampEn parameter was tested in synthesized mechanomyographic signals, with different ratios between the amplitude of the MCG and clean mechanomyographic components. As an example of application of this technique, the use of fSampEn was explored also in recorded MMGdi signals, with different inspiratory loads. The results with both synthetic and recorded signals indicate that the entropy parameter is less affected by the MCG noise, especially at low signal-to-noise ratios. Therefore, we believe that the proposed fSampEn parameter could improve estimates of respiratory muscle effort from MMGdi signals with the presence of MCG interference.

Influence of QRS complex detection errors on entropy algorithms. Application to heart rate variability discrimination

Signal entropy measures such as approximate entropy (ApEn) and sample entropy (SampEn) are widely used in heart rate variability (HRV) analysis and biomedical research. In this article, we analyze the influence of QRS detection errors on HRV results based on signal entropy measures. Specifically, we study the influence that QRS detection errors have on the discrimination power of ApEn and SampEn using the cardiac arrhythmia suppression trial (CAST) database. The experiments assessed the discrimination capability of ApEn and SampEn under different levels of QRS detection errors. The results demonstrate that these measures are sensitive to the presence of ectopic peaks: from a successful classification rate of 100%, down to a 75% when spikes are present. The discriminating capability of the metrics degraded as the number of misdetections increased. For an error rate of 2% the segmentation failed in a 12.5% of the experiments, whereas for a 5% rate, it failed in a 25%.

The appropriate use of approximate entropy and sample entropy with short data sets

Approximate entropy (ApEn) and sample entropy (SampEn) are mathematical algorithms created to measure the repeatability or predictability within a time series. Both algorithms are extremely sensitive to their input parameters: m (length of the data segment being compared), r (similarity criterion), and N (length of data). There is no established consensus on parameter selection in short data sets, especially for biological data. Therefore, the purpose of this research was to examine the robustness of these two entropy algorithms by exploring the effect of changing parameter values on short data sets. Data with known theoretical entropy qualities as well as experimental data from both healthy young and older adults was utilized. Our results demonstrate that both ApEn and SampEn are extremely sensitive to parameter choices, especially for very short data sets, N ≤ 200. We suggest using N larger than 200, an m of 2 and examine several r values before selecting your parameters. Extreme caution should be used when choosing parameters for experimental studies with both algorithms. Based on our current findings, it appears that SampEn is more reliable for short data sets. SampEn was less sensitive to changes in data length and demonstrated fewer problems with relative consistency.

Central tendency measure and wavelet transform combined in the non-invasive analysis of atrial fibrillation recordings

Background

Atrial fibrillation (AF) is the most common supraventricular arrhythmia in the clinical practice, being the subject of intensive research.

Methods

The present work introduces two different Wavelet Transform (WT) applications to electrocardiogram (ECG) recordings of patients in AF. The first one predicts spontaneous termination of paroxysmal AF (PAF), whereas the second one deals with the prediction of electrical cardioversion (ECV) outcome in persistent AF patients. In both cases, the central tendency measure (CTM) from the first differences scatter plot was applied to the AF wavelet decomposition. In this way, the wavelet coefficients vector CTM associated to the AF frequency scale was used to assess how atrial fibrillatory (f) waves variability can be related to AF events.

Results

Structural changes into the f waves can be assessed by combining WT and CTM to reflect atrial activity organization variation. This fact can be used to predict organization-related events in AF. To this respect, results in the prediction of PAF termination regarding sensitivity, specificity and accuracy were 100%, 91.67% and 96%, respectively. On the other hand, for ECV outcome prediction, 82.93% sensitivity, 90.91% specificity and 85.71% accuracy were obtained. Hence, CTM has reached the highest diagnostic ability as a single predictor published to date.

Conclusions

Results suggest that CTM can be considered as a promising tool to characterize non-invasive AF signals. In this sense, therapeutic interventions for the treatment of paroxysmal and persistent AF patients could be improved, thus, avoiding useless procedures and minimizing risks.