Refined Multiscale Fuzzy Entropy based on Standard Deviation for Biomedical Signal Analysis

Multiscale entropy (MSE) has been a prevalent algorithm to quantify the complexity of fluctuations in the local mean value of biomedical time series. Recent developments in the field have tried to improve the MSE by reducing its variability in large scale factors. On the other hand, there has been recent interest in using other statistical moments than the mean, i.e. variance, in the coarse-graining step of the MSE. Building on these trends, here we introduce the so-called refined composite multiscale fuzzy entropy based on the standard deviation (RCMFE{\sigma}) to quantify the dynamical properties of spread over multiple time scales. We demonstrate the dependency of the RCMFE{\sigma}, in comparison with other multiscale approaches, on several straightforward signal processing concepts using a set of synthetic signals. We also investigate the complementarity of using the standard deviation instead of the mean in the coarse-graining process using magnetoencephalograms in Alzheimer disease and publicly available electroencephalograms recorded from focal and non-focal areas in epilepsy. Our results indicate that RCMFE{\sigma} offers complementary information to that revealed by classical coarse-graining approaches and that it has superior performance to distinguish different types of physiological activity

Refined multiscale entropy using fuzzy metrics: validation and application to nociception assessmentt

The refined multiscale entropy (RMSE) approach is commonly applied to assess complexity as a function of the time scale. RMSE is normally based on the computation of sample entropy (SampEn) estimating complexity as conditional entropy. However, SampEn is dependent on the length and standard deviation of the data. Recently, fuzzy entropy (FuzEn) has been proposed, including several refinements, as an alternative to counteract these limitations. In this work, FuzEn, translated FuzEn (TFuzEn), translated-reflected FuzEn (TRFuzEn), inherent FuzEn (IFuzEn), and inherent translated FuzEn (ITFuzEn) were exploited as entropy-based measures in the computation of RMSE and their performance was compared to that of SampEn. FuzEn metrics were applied to synthetic time series of different lengths to evaluate the consistency of the different approaches. In addition, electroencephalograms of patients under sedation-analgesia procedure were analyzed based on the patient’s response after the application of painful stimulation, such as nail bed compression or endoscopy tube insertion. Significant differences in FuzEn metrics were observed over simulations and real data as a function of the data length and the pain responses. Findings indicated that FuzEn, when exploited in RMSE applications, showed similar behavior to SampEn in long series, but its consistency was better than that of SampEn in short series both over simulations and real data. Conversely, its variants should be utilized with more caution, especially whether processes exhibit an important deterministic component and/or in nociception prediction at long scalesPeer ReviewedPostprint (published version

Refined multiscale entropy using fuzzy metrics : validation and application to nociception assessment

The refined multiscale entropy (RMSE) approach is commonly applied to assess complexity as a function of the time scale. RMSE is normally based on the computation of sample entropy (SampEn) estimating complexity as conditional entropy. However, SampEn is dependent on the length and standard deviation of the data. Recently, fuzzy entropy (FuzEn) has been proposed, including several refinements, as an alternative to counteract these limitations. In this work, FuzEn, translated FuzEn (TFuzEn), translated-reflected FuzEn (TRFuzEn), inherent FuzEn (IFuzEn), and inherent translated FuzEn (ITFuzEn) were exploited as entropy-based measures in the computation of RMSE and their performance was compared to that of SampEn. FuzEn metrics were applied to synthetic time series of different lengths to evaluate the consistency of the different approaches. In addition, electroencephalograms of patients under sedation-analgesia procedure were analyzed based on the patient's response after the application of painful stimulation, such as nail bed compression or endoscopy tube insertion. Significant differences in FuzEn metrics were observed over simulations and real data as a function of the data length and the pain responses. Findings indicated that FuzEn, when exploited in RMSE applications, showed similar behavior to SampEn in long series, but its consistency was better than that of SampEn in short series both over simulations and real data. Conversely, its variants should be utilized with more caution, especially whether processes exhibit an important deterministic component and/or in nociception prediction at long scales

Entropy Analysis of Univariate Biomedical Signals:Review and Comparison of Methods

International audienc

Effects of repetitive SSVEPs on EEG complexity using multiscale inherent fuzzy entropy

© 2019 Elsevier B.V. Multiscale inherent fuzzy entropy is an objective measurement of electroencephalography (EEG) complexity, reflecting the habituation of brain systems. Entropy dynamics are generally believed to reflect the ability of the brain to adapt to a visual stimulus environment. In this study, we explored repetitive steady-state visual evoked potential (SSVEP)-based EEG complexity by assessing multiscale inherent fuzzy entropy with relative measurements. We used a wearable EEG device with Oz and Fpz electrodes to collect EEG signals from 40 participants under the following three conditions: a resting state (closed-eyes (CE) and open-eyes (OE) stimulation with five 15-Hz CE SSVEPs and stimulation with five 20-Hz OE SSVEPs. We noted monotonic enhancement of occipital EEG relative complexity with increasing stimulus times in CE and OE conditions. The occipital EEG relative complexity was significantly higher for the fifth SSVEP than for the first SSEVP (FDR-adjusted p < 0.05). Similarly, the prefrontal EEG relative complexity tended to be significantly higher in the OE condition compared to that in the CE condition (FDR-adjusted p < 0.05). The results also indicate that multiscale inherent fuzzy entropy is superior to other competing multiscale-based entropy methods. In conclusion, EEG relative complexity increases with stimulus times, a finding that reflects the strong habituation of brain systems. These results suggest that multiscale inherent fuzzy entropy is an EEG pattern with which brain complexity can be assessed using repetitive SSVEP stimuli

Entropy Measures in Machine Fault Diagnosis: Insights and Applications

Entropy, as a complexity measure, has been widely applied for time series analysis. One preeminent example is the design of machine condition monitoring and industrial fault diagnostic systems. The occurrence of failures in a machine will typically lead to non-linear characteristics in the measurements, caused by instantaneous variations, which can increase the complexity in the system response. Entropy measures are suitable to quantify such dynamic changes in the underlying process, distinguishing between different system conditions. However, notions of entropy are defined differently in various contexts (e.g., information theory and dynamical systems theory), which may confound researchers in the applied sciences. In this paper, we have systematically reviewed the theoretical development of some fundamental entropy measures and clarified the relations among them. Then, typical entropy-based applications of machine fault diagnostic systems are summarized. Further, insights into possible applications of the entropy measures are explained, as to where and how these measures can be useful towards future data-driven fault diagnosis methodologies. Finally, potential research trends in this area are discussed, with the intent of improving online entropy estimation and expanding its applicability to a wider range of intelligent fault diagnostic systems

Coarse-graining Approaches in Univariate Multiscale Sample and Dispersion Entropy

The evaluation of complexity in univariate signals has attracted considerable attention in recent years. This is often done using the framework of Multiscale Entropy, which entails two basic steps: coarse-graining to consider multiple temporal scales, and evaluation of irregularity for each of those scales with entropy estimators. Recent developments in the field have proposed modifications to this approach to facilitate the analysis of short-time series. However, the role of the downsampling in the classical coarse-graining process and its relationships with alternative filtering techniques has not been systematically explored yet. Here, we assess the impact of coarse-graining in multiscale entropy estimations based on both Sample Entropy and Dispersion Entropy. We compare the classical moving average approach with low-pass Butterworth filtering, both with and without downsampling, and empirical mode decomposition in Intrinsic Multiscale Entropy, in selected synthetic data and two real physiological datasets. The results show that when the sampling frequency is low or high, downsampling respectively decreases or increases the entropy values. Our results suggest that, when dealing with long signals and relatively low levels of noise, the refine composite method makes little difference in the quality of the entropy estimation at the expense of considerable additional computational cost. It is also found that downsampling within the coarse-graining procedure may not be required to quantify the complexity of signals, especially for short ones. Overall, we expect these results to contribute to the ongoing discussion about the development of stable, fast and robust-to-noise multiscale entropy techniques suited for either short or long recordings

Stratified Multivariate Multiscale Dispersion Entropy for Physiological Signal Analysis

Multivariate Entropy quantification algorithms are becoming a prominent tool for the extraction of information from multi-channel physiological time-series. However, in the analysis of physiological signals from heterogeneous organ systems, certain channels may overshadow the patterns of others, resulting in information loss. Here, we introduce the framework of Stratified Entropy to prioritize each channels' dynamics based on their allocation to respective strata, leading to a richer description of the multi-channel time-series. As an implementation of the framework, three algorithmic variations of the Stratified Multivariate Multiscale Dispersion Entropy are introduced. These variations and the original algorithm are applied to synthetic time-series, waveform physiological time-series, and derivative physiological data . Based on the synthetic time-series experiments, the variations successfully prioritize channels following their strata allocation while maintaining the low computation time of the original algorithm. In experiments on waveform physiological time-series and derivative physiological data, increased discrimination capacity was noted for multiple strata allocations in the variations when benchmarked to the original algorithm. This suggests improved physiological state monitoring by the variations. Furthermore, our variations can be modified to utilize a priori knowledge for the stratification of channels. Thus, our research provides a novel approach for the extraction of previously inaccessible information from multi-channel time series acquired from heterogeneous systems