Multivariate Multiscale Dispersion Entropy of Biomedical Times Series

Due to the non-linearity of numerous physiological recordings, non-linear analysis of multi-channel signals has been extensively used in biomedical engineering and neuroscience. Multivariate multiscale sample entropy (MSE–mvMSE) is a popular non-linear metric to quantify the irregularity of multi-channel time series. However, mvMSE has two main drawbacks: (1) the entropy values obtained by the original algorithm of mvMSE are either undefined or unreliable for short signals (300 sample points); and (2) the computation of mvMSE for signals with a large number of channels requires the storage of a huge number of elements. To deal with these problems and improve the stability of mvMSE, we introduce multivariate multiscale dispersion entropy (MDE–mvMDE), as an extension of our recently developed MDE, to quantify the complexity of multivariate time series. We assess mvMDE, in comparison with the state-of-the-art and most widespread multivariate approaches, namely, mvMSE and multivariate multiscale fuzzy entropy (mvMFE), on multi-channel noise signals, bivariate autoregressive processes, and three biomedical datasets. The results show that mvMDE takes into account dependencies in patterns across both the time and spatial domains. The mvMDE, mvMSE, and mvMFE methods are consistent in that they lead to similar conclusions about the underlying physiological conditions. However, the proposed mvMDE discriminates various physiological states of the biomedical recordings better than mvMSE and mvMFE. In addition, for both the short and long time series, the mvMDE-based results are noticeably more stable than the mvMSE- and mvMFE-based ones. For short multivariate time series, mvMDE, unlike mvMSE, does not result in undefined values. Furthermore, mvMDE is faster than mvMFE and mvMSE and also needs to store a considerably smaller number of elements. Due to its ability to detect different kinds of dynamics of multivariate signals, mvMDE has great potential to analyse various signals

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

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

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Multivariate permutation entropy, a Cartesian graph product approach

Entropy metrics are nonlinear measures to quantify the complexity of time series. Among them, permutation entropy is a common metric due to its robustness and fast computation. Multivariate entropy metrics techniques are needed to analyse data consisting of more than one time series. To this end, we present a multivariate permutation entropy, $MPE_G$, using a graph-based approach. Given a multivariate signal, the algorithm $MPE_G$ involves two main steps: 1) we construct an underlying graph G as the Cartesian product of two graphs G1 and G2, where G1 preserves temporal information of each times series together with G2 that models the relations between different channels, and 2) we consider the multivariate signal as samples defined on the regular graph G and apply the recently introduced permutation entropy for graphs. Our graph-based approach gives the flexibility to consider diverse types of cross channel relationships and signals, and it overcomes with the limitations of current multivariate permutation entropy.Comment: 5 pages, 4 figures, 2 table

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

A noise-robust Multivariate Multiscale Permutation Entropy for two-phase flow characterisation

Using a graph-based approach, we propose a multiscale permutation entropy to explore the complexity of multivariate time series over multiple time scales. This multivariate multiscale permutation entropy (MPEG) incorporates the interaction between channels by constructing an underlying graph for each coarse-grained time series and then applying the recent permutation entropy for graph signals. Given the challenge posed by noise in real-world data analysis, we investigate the robustness to noise of MPEG using synthetic time series and demonstrating better performance than similar multivariate entropy metrics. Two-phase flow data is an important industrial process characterised by complex, dynamic behaviour. MPEG characterises the flow behaviour transition of two-phase flow by incorporating information from different scales. The experimental results show that MPEG is sensitive to the dynamic of flow patterns, allowing us to distinguish between different flow patterns

Multiscale Fluctuation Dispersion Entropy of EEG as a Physiological Biomarker of Schizotypy

Altered electroencephalography (EEG) activity in schizotypal individuals is a powerful indicator of proneness towards psychosis. This alteration is beyond decreased alpha power often measured in resting state EEG. Multiscale fluctuation dispersion entropy (MFDE) measures the non-linear complexity of the fluctuations of EEGs and is a more effective approach compared to the traditional linear power spectral density (PSD) measures of EEG activity in patients with neurodegenerative disorders. In this study, we applied MFDE to EEG signals to distinguish high schizotypy (HS) and low schizotypy (LS) individuals. The study includes several trials from 29 participants psychometrically classified as HS (n=19) and LS (n=10). After preprocessing, MFDE was computed in frontal, parietal, central, temporal and occipital regions for each participant at multiple time scales. Statistical analysis and machine learning algorithms were used to calculate the differences in MFDE measures between the HS and LS groups. Our findings revealed significant differences in MFDE measures between LS and HS individuals in the delta frequency band (at time scale 100 ms). HS individuals exhibited increased complexity and irregularity compared to LS individuals in the delta frequency band particularly in the occipital region. Furthermore, the MFDE measures resulted in high accuracy (96.55%) in discriminating between HS and LS individuals and outperformed the models based on power spectrum, demonstrating the potential of MFDE as a neurophysiological marker for schizotypy traits. The increased non-linear fluctuation in delta frequency band in the occipital region of HS individuals implies the changes in cognitive functions, such as memory and attention, and has significant potential as a biomarker for schizotypy and proneness towards psychosis

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

Dispersion Entropy: A Measure of Electrohysterographic Complexity for Preterm Labor Discrimination

[EN] Although preterm labor is a major cause of neonatal death and often leaves health sequels in the survivors, there are no accurate and reliable clinical tools for preterm labor prediction. The Electrohysterogram (EHG) has arisen as a promising alternative that provides relevant information on uterine activity that could be useful in predicting preterm labor. In this work, we optimized and assessed the performance of the Dispersion Entropy (DispEn) metric and compared it to conventional Sample Entropy (SampEn) in EHG recordings to discriminate term from preterm deliveries. For this, we used the two public databases TPEHG and TPEHGT DS of EHG recordings collected from women during regular checkups. The 10th, 50th and 90th percentiles of entropy metrics were computed on whole (WBW) and fast wave high (FWH) EHG bandwidths, sweeping the DispEn and SampEn internal parameters to optimize term/preterm discrimination. The results revealed that for both the FWH and WBW bandwidths the best separability was reached when computing the 10th percentile, achieving a p-value (0.00007) for DispEn in FWH, c = 7 and m = 2, associated with lower complexity preterm deliveries, indicating that DispEn is a promising parameter for preterm labor prediction.This work was supported by the Spanish ministry of economy and competitiveness, the European Regional Development Fund (MCIU/AEI/FEDER, UE RTI2018-094449-A-I00-AR) and the Generalitat Valenciana (AICO/2019/220).Nieto-Del-Amor, F.; Ye Lin, Y.; Garcia-Casado, J.; Díaz-Martínez, MDA.; González Martínez, M.; Monfort-Ortiz, R.; Prats-Boluda, G. (2021). Dispersion Entropy: A Measure of Electrohysterographic Complexity for Preterm Labor Discrimination. SCITEPRESS. 260-267. https://doi.org/10.5220/0010316602600267S26026