Interpretation of the approximate entropy using fixed tolerance values as a measure of amplitude variations in biomedical signals

Physiological Signal Analysis and Stress Classification from VR Simulations Using Decision Tree Methods

Stress is induced in response to any mental, physical or emotional change associated with our daily experiences. While short term stress can be quite beneficial, prolonged stress is detrimental to the heart, muscle tissues and immune system. In order to be proactive against these symptoms, it is important to assess the impact of stress due to various activities, which is initially determined through the change in the sympathetic (SNS) and parasympathetic (PNS) nervous systems. After acquiring physiological data wirelessly through captive electrocardiogram (ECG), galvanic skin response (GSR) and respiration (RESP) sensors, 21 time, frequency, nonlinear, GSR and respiration features were manually extracted from 15 subjects ensuing a baseline phase, virtual reality (VR) roller coaster simulation, color Stroop task and VR Bubble Bloom game. This paper presents a comprehensive physiological analysis of stress from an experiment involving a VR video game Bubble Bloom to manage stress levels. A personalized classification and regression tree (CART) model was developed using a novel Gini index algorithm in order to effectively classify binary classes of stress. A novel K-means feature was derived from 11 other features and used as an input in the Decision Tree (DT) algorithm, strong learners Ensemble Gradient Boosting (EGB) and Extreme Gradient Boosting (XGBoost (XGB)) embedded in a pipeline to classify 5 classes of stress. Results obtained indicate that heart rate (HR), approximate entropy (ApEN), low frequency and high frequency ratio (LF/HF), low frequency (LF), standard deviation (SD1), GSR and RESP all reduced and high frequency (HF) increased following the VR Bubble Bloom game phase. The personalized CART model was able to classify binary stress with 87.75% accuracy. It proved to be more effective than other related studies. EGB was able to classify binary stress with 100% accuracy, which outperformed every other related study. XGBoost and DT were able to classify five classes of stress with 72.22% using the novel K-means feature. This feature produced less error and better model performance in comparison to using all the features. Results substantiate that our proposed methods were more effective for stress classification than most related studies.

Multiscale Entropy Algorithms to Analyze Complexity and Variability of Trunk Accelerations Time Series in Subjects with Parkinson's Disease

The aim of this study was to assess the ability of multiscale sample entropy (MSE), refined composite multiscale entropy (RCMSE), and complexity index (CI) to characterize gait complexity through trunk acceleration patterns in subjects with Parkinson's disease (swPD) and healthy subjects, regardless of age or gait speed. The trunk acceleration patterns of 51 swPD and 50 healthy subjects (HS) were acquired using a lumbar-mounted magneto-inertial measurement unit during their walking. MSE, RCMSE, and CI were calculated on 2000 data points, using scale factors (τ) 1-6. Differences between swPD and HS were calculated at each τ, and the area under the receiver operating characteristics, optimal cutoff points, post-test probabilities, and diagnostic odds ratios were calculated. MSE, RCMSE, and CIs showed to differentiate swPD from HS. MSE in the anteroposterior direction at τ4 and τ5, and MSE in the ML direction at τ4 showed to characterize the gait disorders of swPD with the best trade-off between positive and negative posttest probabilities and correlated with the motor disability, pelvic kinematics, and stance phase. Using a time series of 2000 data points, a scale factor of 4 or 5 in the MSE procedure can yield the best trade-off in terms of post-test probabilities when compared to other scale factors for detecting gait variability and complexity in swPD.

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

BACKGROUND

We developed CEPS as an open access MATLAB^® GUI (graphical user interface) for the analysis of Complexity and Entropy in Physiological Signals (CEPS), and demonstrate its use with an example data set that shows the effects of paced breathing (PB) on variability of heart, pulse and respiration rates. CEPS is also sufficiently adaptable to be used for other time series physiological data such as EEG (electroencephalography), postural sway or temperature measurements.

METHODS

Data were collected from a convenience sample of nine healthy adults in a pilot for a larger study investigating the effects on vagal tone of breathing paced at various different rates, part of a development programme for a home training stress reduction system.

RESULTS

The current version of CEPS focuses on those complexity and entropy measures that appear most frequently in the literature, together with some recently introduced entropy measures which may have advantages over those that are more established. Ten methods of estimating data complexity are currently included, and some 28 entropy measures. The GUI also includes a section for data pre-processing and standard ancillary methods to enable parameter estimation of embedding dimension m and time delay τ ('tau') where required. The software is freely available under version 3 of the GNU Lesser General Public License (LGPLv3) for non-commercial users. CEPS can be downloaded from Bitbucket. In our illustration on PB, most complexity and entropy measures decreased significantly in response to breathing at 7 breaths per minute, differentiating more clearly than conventional linear, time- and frequency-domain measures between breathing states. In contrast, Higuchi fractal dimension increased during paced breathing.

CONCLUSIONS

We have developed CEPS software as a physiological data visualiser able to integrate state of the art techniques. The interface is designed for clinical research and has a structure designed for integrating new tools. The aim is to strengthen collaboration between clinicians and the biomedical community, as demonstrated here by using CEPS to analyse various physiological responses to paced breathing.

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.

Effects of online-bandwidth visual feedback on unilateral force control capabilities

Purpose

The purpose of this study was to examine how different threshold ranges of online-bandwidth visual feedback influence unilateral force control capabilities in healthy young women.

Methods

Twenty-five right-handed young women (mean±standard deviation age = 23.6±1.5 years) participated in this study. Participants unilaterally executed hand-grip force control tasks with their dominant and non-dominant hands, respectively. Each participant completed four experimental blocks in a different order of block presentation for each hand condition: (a) 10% of maximum voluntary contraction (MVC) with ±5% bandwidth threshold range (BTR), (b) 10% of MVC with ±10% BTR, (c) 40% of MVC with ±5% BTR, and (d) 40% of MVC with ±10% BTR. Outcome measures on force control capabilities included: (a) force accuracy, (b) force variability, (c) force regularity, and (d) the number of times and duration out of BTR.

Results

The non-dominant hand showed significant improvements in force control capabilities, as indicated by higher force accuracy, less force variability, and decreased force regularity from ±10% BTR to ±5% BTR during higher targeted force level task. For both hands, the number of times and duration out of BTR increased from ±10% BTR to ±5% BTR.

Conclusions

The current findings suggested that the narrow threshold range of online-bandwidth visual feedback effectively revealed transient improvements in unilateral isometric force control capabilities during higher targeted force level tasks.

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

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

The complexity of hemodynamic response to the tilt test with and without nitroglycerine provocation in patients with vasovagal syncope

The paper presents a comparison of vasovagal syndrome occurrence in a head up tilt table test between patients with a positive result of passive tilt test and those with a positive result after pharmacological provocation. The study group consisted of 80 patients: 57 patients who experienced syncope in the passive phase of the test (43 women (aged: 35.6 ± 16.2) and 14 men (aged: 41.7 ± 15.6) and 23 patients who experienced syncope after pharmacological provocation (17 women (age: 32.3 ± 12) and 6 men (age: 43 ± 15). The main investigation was based on the assessment of monitored signals complexity: heart rate, blood pressure and stroke volume. The analysis of complexity in chosen measurement phases was performed with Sample Entropy. The investigation showed that the reactions of autonomic nervous system during tilt test and before syncope are similar for positive result of passive tilt test and positive result of tilt test with provocation. The differences in supine position occurred only in analysis based on impedance measurement (SV: p = 0.01). Significant differences were denoted for all signals just before the syncope (RRI, sBP, dBP: p = 0,00001 and SV: p = 0.01). In analysis of signals complexity the significant differences occurred just before the syncope for Sample Entropy of blood pressure (SampEn (sBP): p = 0.0008, SampEn (dBP): p = 0,0001).

Estimation of Complexity of Sampled Biomedical Continuous Time Signals Using Approximate Entropy

Non-linear analysis found many applications in biomedicine. Approximate entropy (ApEn) is a popular index of complexity often applied to biomedical data, as it provides quite stable indications when processing short and noisy epochs. However, ApEn strongly depends on parameters, which were chosen in the literature in wide ranges. This paper points out that ApEn depends on sampling rate of continuous time signals, embedding dimension, tolerance (under which a match is identified), epoch duration and low frequency trends. Moreover, contradicting results can be obtained changing parameters. This was found both in simulations and in experimental EEG. These limitations of ApEn suggest the introduction of an alternative index, here called modified ApEn, which is based on the following principles: oversampling is compensated, self-recurrences are ignored, a fixed percentage of recurrences is selected and low frequency trends are removed. The modified index allows to get more stable measurements of the complexity of the tested simulated data and EEG. The final conclusions are that, in order to get a reliable estimation of complexity using ApEn, parameters should be chosen within specific ranges, data must be sampled close to the Nyquist limit and low frequency trends should be removed. Following these indications, different studies could be more easily compared, interpreted and replicated. Moreover, the modified ApEn can be an interesting alternative, which extends the range of parameters for which stable indications can be achieved.

Effect of parameter selection on entropy calculation for long walking trials

It is sometimes difficult to obtain uninterrupted data sets that are long enough to perform nonlinear analysis, especially in pathological populations. It is currently unclear as to how many data points are needed for reliable entropy analysis. The aims of this study were to determine the effect of changing parameter values of m, r, and N on entropy calculations for long gait data sets using two different modes of walking (i.e., overground versus treadmill). Fourteen young adults walked overground and on a treadmill at their preferred walking speed for one-hour while step time was collected via heel switches. Approximate (ApEn) and sample entropy (SampEn) were calculated using multiple parameter combinations of m, N, and r. Further, r was tested under two cases r*standard deviation and r constant. ApEn differed depending on the combination of r, m, and N. ApEn demonstrated relative consistency except when m=2 and the smallest r values used (rSD=0.015*SD, 0.20*SD; rConstant=0 and 0.003). For SampEn, as r increased, SampEn decreased. When r was constant, SampEn demonstrated excellent relative consistency for all combinations of r, m, and N. When r constant was used, overground walking was more regular than treadmill. However, treadmill walking was found to be more regular when using rSD for both ApEn and SampEn. For greatest relative consistency of step time data, it was best to use a constant r value and SampEn. When using entropy, several r values must be examined and reported to ensure that results are not an artifact of parameter choice.

Entropy change of biological dynamics in COPD

In this century, the rapid development of large data storage technologies, mobile network technology, and portable medical devices makes it possible to measure, record, store, and track analysis of large amount of data in human physiological signals. Entropy is a key metric for quantifying the irregularity contained in physiological signals. In this review, we focus on how entropy changes in various physiological signals in COPD. Our review concludes that the entropy change relies on the types of physiological signals under investigation. For major physiological signals related to respiratory diseases, such as airflow, heart rate variability, and gait variability, the entropy of a patient with COPD is lower than that of a healthy person. However, in case of hormone secretion and respiratory sound, the entropy of a patient is higher than that of a healthy person. For mechanomyogram signal, the entropy increases with the increased severity of COPD. This result should give valuable guidance for the use of entropy for physiological signals measured by wearable medical device as well as for further research on entropy in COPD.

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.

An approach to absence epileptic seizures detection using Approximate Entropy

Epilepsy is one of the most common chronic neurological diseases and the most common neurological chronic disease of childhood. The electroencephalogram (EEG) signal provides significant information neurologists take into consideration in the investigation and analysis of epileptic seizures. The Approximate Entropy (ApEn) is a formulated statistical parameter commonly used to quantify the regularity of a time series data of physiological signals. In this paper ApEn is used in order to detect the onset of epileptic seizures. The results show that the method provides promising results towards efficient detection of onset and ending of seizures, based on analyzing the corresponding EEG signals. ApEn parameters affect the method's behavior, suggesting that a more detailed study and a consistent methodology of their determination should be established. A preliminary analysis for the proper determination of these parameters is performed towards improving the results.

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.