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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., Competing Interests: Declaration of competing interest None., (Copyright © 2024. Published by Elsevier Inc.)

Automatic identification of negative stress is an unresolved challenge that has received great attention in the last few years. Many studies have analyzed electroencephalographic (EEG) recordings to gain new insights about how the brain reacts to both short- and long-term stressful stimuli. Although most of them have only considered linear methods, the heterogeneity and complexity of the brain has recently motivated an increasing use of nonlinear metrics. Nonetheless, brain dynamics reflected in EEG recordings often exhibit a multiscale nature and no study dealing with this aspect has been developed yet. Hence, in this work two nonlinear indices for quantifying regularity and predictability of time series from several time scales are studied for the first time to discern between visually elicited emotional states of calmness and negative stress. The obtained results have revealed the maximum discriminant ability of 86.35% for the second time scale, thus suggesting that brain dynamics triggered by negative stress can be more clearly assessed after removal of some fast temporal oscillations. Moreover, both metrics have also been able to report complementary information for some brain areas.

The multiscale entropy (MSE 1D ) measure is now widely used to quantify the complexity of time series. The development of complexity measures for images is also a long-standing goal. Recently, the bi-dimensional version of MSE 1D has been proposed (MSE 2D ) to analyze images. The interpretation of MSE 2D curves and the applications to real data are still emergent. Because the coarse-graining step in the MSE 2D computation changes the frequency content of the image, we hypothesized a possible dependence between MSE 2D and the discrete Fourier transform (DFT). To analyze this dependence, synthetic as well as biomedical images are analyzed. Our results reveal that i) the profile of MSE 2D is sensitive to both the amplitude and phase of the DFT; ii) MSE 2D could find applications in the biomedical field. This work brings valuable information for MSE 2D interpretation and opens possibilities to study images from an entropy point of view through spatial scales., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

Objective: Vagus nerve stimulation (VNS) is an adjunctive treatment in drug-resistant epilepsy. The alterations in heart rate dynamics through VNS are not well understood. This study aimed to determine changes in heart rhythm complexity in association with VNS and to relate the findings to the outcome of VNS treatment in patients with drug-resistant epilepsy., Methods: We prospectively analyzed 32 patients with drug-resistant epilepsy, who underwent VNS implantation, and 32 age- and sex-matched healthy control subjects. The interictal heartbeat intervals were analyzed using the heart rhythm complexity with multiscale entropy (MSE) and traditional heart rate variability (HRV) analyses based on ambulatory 24-hour electrocardiograms (ECGs)., Results: Patients had significantly decreased complexity indices (Slope 5, Area 1-5, Area 6-15, Area 6-20) on MSE analysis and decreased HRV measurements (standard deviation of the heartbeat interval (SDNN), square root of the mean of sum of squares of the differences between adjacent RR intervals (RMSSD), pNN50, very low frequency (VLF), low frequency (LF), high frequency (HF), total power (TP)) in time and frequency domain analyses. After one year of VNS treatment in patients with drug-resistant epilepsy, there was a trend in an elevated MSE profile with significant higher values between the scales 1 and 9. Vagus nerve stimulation induces a more significant increase of MSE in VNS responders than those in the nonresponders. The conventional HRV measurements did not change., Conclusion: Our results suggest that heart rhythm complexity is impaired in patients with drug-resistant epilepsy, and this is at least partially reversed by VNS treatment. Furthermore, VNS-induced effects on heart rate complexity may be associated with the therapeutic response to VNS in patients with drug-resistant epilepsy., (Copyright © 2018 Elsevier Inc. All rights reserved.)

Movement complexity can be defined as the capability of using different strategies to accomplish a specific task and is expected to increase with maturation, reaching its highest level in adulthood.Multiscale Entropy (MSE) has been proposed to estimate complexity on different kinematic signals, at different time scales. When applied on trunk acceleration data during natural walking (NW) at different ages, MSE decreased from childhood to adulthood, apparently contradicting the premises. On the contrary, authors hypothesised that this decrease was dependent on the specific task analysed and resulted from the concurrent increase in gait automaticity.This work aims to test this hypothesis, applying MSE on a non-paradigmatic task (tandem walking, TW), in order to exclude aspects related to automaticity.MSE was estimated on trunk acceleration data, collected on children, adolescents, and young adults during TW and NW. As hypothesized, MSE increased significantly with age in TW and decreased in NW on the sagittal plane. Assuming the development of complexity in TW as reference, MSE in NW showed a reduction to half of the complexity of TW with maturation on the sagittal plane. These results indicate MSE as sensitive to differences in performance due to maturation and to expected changes in complexity related to the specific performed task.

A wobble board (WB) is a balance rehabilitation tool that is used in physiotherapy to improve strength and stability. The WB tested in this study includes a sensory module for measuring patients' tilt and rotation during stance. The aim of this study was to assess the reliability and validity of a balance measurement using a WB. Thirty healthy young adults participated in this study. The participants stood on the WB to simultaneously record the tilt of the WB and the center of pressure data using a force plate. The data were recorded during five measurement sessions on various days, with four trials each. Sways, velocities and indexes of complexity (CI) were computed. For reliability assessment, we used intra-class correlation coefficients within and between sessions; for validity, we computed Spearman correlation coefficients. The velocities and CI showed good intra-session reliability, and the sways showed mostly poor intra-session reliability. The results of inter-session reliability showed good to excellent reliability for CI, poor reliability for sways and poor to good reliability for velocities. The Spearman correlation coefficient showed excellent agreement between the mean velocities computed from the force plate and the WB. Our results confirm that the WB tested is suitable for stability assessment in young adults., (Copyright © 2017 IPEM. Published by Elsevier Ltd. All rights reserved.)

Multiscale approximate entropy (MAE) is used to quantify the complexity of a time series as a function of time scale τ. Approximate entropy (ApEn) tolerance threshold selection 'r' is based on either: (1) arbitrary selection in the recommended range (0.1-0.25) times standard deviation of time series (2) or finding maximum ApEn (ApEnmax) i.e., the point where self-matches start to prevail over other matches and choosing the corresponding 'r' (rmax) as threshold (3) or computing rchon by empirically finding the relation between rmax, SD1/SD2 ratio and N using curve fitting, where, SD1 and SD2 are short-term and long-term variability of a time series respectively. None of these methods is gold standard for selection of 'r'. In our previous study [1], an adaptive procedure for selection of 'r' is proposed for approximate entropy (ApEn). In this paper, this is extended to multiple time scales using MAEbin and multiscale cross-MAEbin (XMAEbin). We applied this to simulations i.e. 50 realizations (n = 50) of random number series, fractional Brownian motion (fBm) and MIX (P) [1] series of data length of N = 300 and short term recordings of HRV and SBPV performed under postural stress from supine to standing. MAEbin and XMAEbin analysis was performed on laboratory recorded data of 50 healthy young subjects experiencing postural stress from supine to upright. The study showed that (i) ApEnbin of HRV is more than SBPV in supine position but is lower than SBPV in upright position (ii) ApEnbin of HRV decreases from supine i.e. 1.7324 ± 0.112 (mean ± SD) to upright 1.4916 ± 0.108 due to vagal inhibition (iii) ApEnbin of SBPV increases from supine i.e. 1.5535 ± 0.098 to upright i.e. 1.6241 ± 0.101 due sympathetic activation (iv) individual and cross complexities of RRi and systolic blood pressure (SBP) series depend on time scale under consideration (v) XMAEbin calculated using ApEnmax is correlated with cross-MAE calculated using ApEn (0.1-0.26) in steps of 0.02 at each time scale in supine and upright position and is concluded that ApEn0.26 has highest correlation at most scales (vi) choice of 'r' is critical in interpreting interactions between RRi and SBP and in ascertaining true complexity of the individual RRi and SBP series.

Multiscale entropy (MSE) has been applied in biomechanics to evaluate gait stability during human gait and was found to be a promising method for evaluating fall risk in elderly and/or pathologic subjects. The hypothesis of this work is that gait complexity is a relevant parameter of gait development during life, decreasing from immature to mature gait and then increasing again during old age. In order to verify this hypothesis, MSE was applied on trunk acceleration data collected during gait of subjects of different ages: toddlers at the onset of walking, pre-scholar and scholar children, adolescents, young adults, adults and elderlies. MSE was estimated by calculating sample entropy (SEN) on raw unfiltered data of L5 acceleration along the three axes, using values of τ ranging from 1 to 6. In addition, other performance parameters (cadence, stride time variability and harmonic ratio) were evaluated. The results followed the hypothesized trend when MSE was applied on the vertical and/or anteroposterior axis of trunk acceleration: an age effect was found and adult SEN values were significantly different from children ones. From young adults to elderlies a slight increase in SEN values was shown although not statistically significant. While performance gait parameters showed adolescent gait similar to the one of adults, SEN highlighted that their gait maturation is not complete yet. In conclusion, present results suggest that the complexity of gait, evaluated on the sagittal plane, can be used as a characterizing parameter of the maturation of gait control., (Copyright © 2016 Elsevier B.V. All rights reserved.)

The multiscale entropy (MSE) is a novel method for quantifying the intrinsic dynamical complexity of physiological systems over several scales. To evaluate this method as a promising way to explore the neural mechanisms in ADHD, we calculated the MSE in EEG activity during the designed task. EEG data were collected from 13 outpatient boys with a confirmed diagnosis of ADHD and 13 age- and gender-matched normal control children during their doing multi-source interference task (MSIT). We estimated the MSE by calculating the sample entropy values of delta, theta, alpha and beta frequency bands over twenty time scales using coarse-grained procedure. The results showed increased complexity of EEG data in delta and theta frequency bands and decreased complexity in alpha frequency bands in ADHD children. The findings of this study revealed aberrant neural connectivity of kids with ADHD during interference task. The results showed that MSE method may be a new index to identify and understand the neural mechanism of ADHD., (Copyright © 2016 Elsevier Inc. All rights reserved.)

Compared with the traditional AC grid, the flexible DC grid has the advantages of low wire loss and large transmission capacity, but it is difficult to extract fault signals and diagnose various faults. Therefore, a fault detection method based on complete ensemble empirical mode decomposition with adaptive noise analysis (CEEMDAN) multiscale entropy (MSE) and genetic algorithm optimization support vector machine (GA-SVM) is proposed. Firstly, CEEMDAN is used to decompose the extracted fault line mode voltage signal into several intrinsic mode function (IMF). The IMF containing more fault information is selected to reconstruct the denoising signal. The MSE of the reconstructed signal is calculated and input into the GA-SVM classifier as the fault feature, and the fault line mode voltage signals of different fault types under different operating conditions are classified and recognized. A large number of simulation results prove that the proposed method has strong anti-interference ability and high reliability, and has high classification accuracy in the case of small sample data. Compared with Linear-SVM, PSO-SVM, KNN and Fine Tree intelligent algorithms, the proposed method shows a significantly improved accuracy, 93.8888% on average. [ABSTRACT FROM AUTHOR]

Entropy measures are increasingly being used to analyze the structure of neural activity observed by functional magnetic resonance imaging (fMRI), with resting‐state networks (RSNs) being of interest for their reproducible descriptions of the brain's functional architecture. Temporal correlations have shown a dichotomy among these networks: those that engage with the environment, known as extrinsic, which include the visual and sensorimotor networks; and those associated with executive control and self‐referencing, known as intrinsic, which include the default mode network and the frontoparietal control network. While these inter‐voxel temporal correlations enable the assessment of synchrony among the components of individual networks, entropic measures introduce an intra‐voxel assessment that quantifies signal features encoded within each blood oxygen level‐dependent (BOLD) time series. As a result, this framework offers insights into comprehending the representation and processing of information within fMRI signals. Multiscale entropy (MSE) has been proposed as a useful measure for characterizing the entropy of neural activity across different temporal scales. This measure of temporal entropy in BOLD data is dependent on the length of the time series; thus, high‐quality data with fine‐grained temporal resolution and a sufficient number of time frames is needed to improve entropy precision. We apply MSE to the Midnight Scan Club, a highly sampled and well‐characterized publicly available dataset, to analyze the entropy distribution of RSNs and evaluate its ability to distinguish between different functional networks. Entropy profiles are compared across temporal scales and RSNs. Our results have shown that the spatial distribution of entropy at infra‐slow frequencies (0.005–0.1 Hz) reproduces known parcellations of RSNs. We found a complexity hierarchy between intrinsic and extrinsic RSNs, with intrinsic networks robustly exhibiting higher entropy than extrinsic networks. Finally, we found new evidence that the topography of entropy in the posterior cerebellum exhibits high levels of entropy comparable to that of intrinsic RSNs. [ABSTRACT FROM AUTHOR]

Multiscale entropy-based methods have made great progress in the field of health condition monitoring and fault diagnosis of machines due to their powerful feature representation capabilities. However, existing multiscale entropy methods suffer from three major obstacles: high fluctuation under large scale-factor, loss of high-frequency information, and poor robustness to noises. Thus, this work proposes a symbol-scale analysis method to deal with the above problems. In one aspect, to capture fault features from the time series over multiple time scales, time-delay process of different intervals is utilized to obtain long-term features and short-term features. In the other aspect, symbol-scale analysis introduces a symbolization procedure and maps time series into a corresponding sequence of symbols to overcome the limitation of weak fault extraction under a low-signal-to-noise ratio environment. Moreover, the symbol-scale entropy approach is developed by integrating with diversity entropy, called symbol-scale diversity entropy. The effectiveness of the proposed strategy is intensively validated using two simulated signals and experimental cases. Results demonstrate its advantages in dynamic change tracking ability and calculation efficiency by comparing it with other state-of-the-art entropy methods. Apart from diversity entropy, the versatility of incorporating the proposed symbol-scale analysis and other entropy methods is also verified using experimental data. [ABSTRACT FROM AUTHOR]

Two-phase flow in channels of small dimensions is often a non-stationary process, the nature of such flow is oscillatory. Due to small channel dimensions, high heat flux, parallel channels interactions, pressure and temperature oscillations, the character of the phenomena occurring during boiling is complex. The changes of the measured signals are observed in different time scales. In order to examine in detail two-phase flow parameters changes, many acquisition devices are often installed. This solution becomes challenging concerning mini and microchannel heat-exchangers due to space limitation and modifications of an experimental setup. This paper presents a novel application of multiscale entropies for spatial and temporal analysis of two-phase flow based on only one registered parameter. This analysis is performed based on pixel brightness changes in photo frames registered by a high speed camera during two-phase flow. The spatial changes of pixel brightness are observed on single frames and temporal changes are examined using a set of frames (in time). The Composite Multiscale Sample Entropy is applied to identify two-phase flow patterns and to analyze the complexity of phase distribution. Using Multivariate Multiscale Sample Entropy the most rapid changes of phase distribution in a multichannel heat exchanger are determined. [ABSTRACT FROM AUTHOR]

In this paper, we explore the use of multiscale bubble entropy and power metric for feature extraction procedure and extend it with MLA and stability analysis to design a reliable multichannel seizure detection technique. First, we represent the multichannel EEG signal in 2D matrix form and then apply AM FM model to exploit the decomposed form of EEG. Thereafter, we construct the complexity coefficient using multiscale bubble entropy analysis from decomposed EEG wave. Then, second feature set is formed by using simple and efficient power procedure to obtain absolute power index and relative power index. Using two machine learning approaches, classification performance of proposed approach is explored to correctly identify the epileptic seizures. To show the robustness of multiscale bubble entropy, the stability analysis is performed with normal EEG dataset. Experimental results demonstrate that our proposed technique can effectively detect the epileptic seizures and achieve a superior classification performance with the ANN classifier compared to KNN classifier. This method provides higher discriminating capability with greater stability, so that they could detect wider range of seizure and thus help advance the current diagnosis system. [ABSTRACT FROM AUTHOR]

Spinal cord injury (SCI) causes a disruption of autonomic nervous regulation to the cardiovascular system, leading to various cardiovascular and microvascular diseases. Exercise training is an effective intervention for reducing risk for microvascular diseases in healthy people. However, the effectiveness of exercise training on improving microvascular function in people with SCI is largely unknown. The purpose of this study was to compare blood flow oscillations in people with spinal cord injury and different physical activity levels to determine if such a lifestyle might influence skin blood flow. A total of 37 participants were recruited for this study, including 12 athletes with SCI (ASCI), 9 participants with SCI and a sedentary lifestyle (SSCI), and 16 healthy able-bodied controls (AB). Sacral skin blood flow (SBF) in response to local heating at 42 °C for 50 min was measured using laser Doppler flowmetry. The degree of the regularity of blood flow oscillations (BFOs) was quantified using a multiscale entropy approach. The results showed that BFO was significantly more irregular in ASCI and AB compared to SSCI during the maximal vasodilation period. Our results also demonstrate that the difference in the regularity of BFOs between original SBF signal and phase-randomized surrogate time series was larger in ASCI and AB compared to SSCI. Our findings indicate that SCI causes a loss of complexity of BFOs and exercise training may improve complexity in people with SCI. This study demonstrates that multiscale entropy is a sensitive method for detecting differences between different categories of people with SCI and might be able to detect effects of exercise training related to skin blood flow. [ABSTRACT FROM AUTHOR]

Beginning in 1998, a network of electronic random number generators located around the world has continuously recorded samples of truly random bits. The resulting data were used to explore a hypothesis that predicts the emergence of anomalous structure in randomness correlated with events that attract widespread human attention. A formal experiment testing this hypothesis from 1998 to 2015 found a highly significant deviation from chance expectation. However, the duration of the selected events comprised less than 5% of all data available through 2022, so the present analysis examined the full database to see if emergence of nonrandom structure was limited to those events, or if it was reflective of a persistent, if subtle, relationship between collective mind and matter. Two analytical methods were used to study emergent structure in time-series data: Multiscale entropy and a novel deconvolution technique. Both methods provided evidence consistent with the hypothesis, suggesting that some aspect of collective consciousness appears to be anomalously associated with aspects of the physical world. [ABSTRACT FROM AUTHOR]

Inverters and converters contain more and more power electronics switches which may subsequently affect their reliability. Therefore, fault detection and location are essential to improve their reliability and to ensure continuous operation. In this paper, an  A C − D C − A C  converter with three-phase inverter is investigated under permanent, single and multiple open-circuit fault scenarios. Many entropies and multiscale entropies are then proposed to evaluate the complexity of the output currents by quantifying their entropies over a range of temporal scales. Among the multitude of entropies, only some entropies are able to differentiate healthy from open-circuit faulty conditions. Moreover, the simulation results show that these entropies are able to detect and locate the arms of the bridge with open-circuit faults. [ABSTRACT FROM AUTHOR]

Distribution Entropy (DistEn) has been introduced as an alternative to Sample Entropy (SampEn) to assess the heart rate variability (HRV) on much shorter series without the arbitrary definition of distance thresholds. However, DistEn, considered a measure of cardiovascular complexity, differs substantially from SampEn or Fuzzy Entropy (FuzzyEn), both measures of HRV randomness. This work aims to compare DistEn, SampEn, and FuzzyEn analyzing postural changes (expected to modify the HRV randomness through a sympatho/vagal shift without affecting the cardiovascular complexity) and low-level spinal cord injuries (SCI, whose impaired integrative regulation may alter the system complexity without affecting the HRV spectrum). We recorded RR intervals in able-bodied (AB) and SCI participants in supine and sitting postures, evaluating DistEn, SampEn, and FuzzyEn over 512 beats. The significance of "case" (AB vs. SCI) and "posture" (supine vs. sitting) was assessed by longitudinal analysis. Multiscale DistEn (mDE), SampEn (mSE), and FuzzyEn (mFE) compared postures and cases at each scale between 2 and 20 beats. Unlike SampEn and FuzzyEn, DistEn is affected by the spinal lesion but not by the postural sympatho/vagal shift. The multiscale approach shows differences between AB and SCI sitting participants at the largest mFE scales and between postures in AB participants at the shortest mSE scales. Thus, our results support the hypothesis that DistEn measures cardiovascular complexity while SampEn/FuzzyEn measure HRV randomness, highlighting that together these methods integrate the information each of them provides. [ABSTRACT FROM AUTHOR]

A physiological system encompasses numerous components that function at various time scales. To characterize the scale-dependent feature, the multiscale entropy (MSE) analysis has been proposed to describe the complex processes on multiple time scales. However, MSE analysis uses the relative scale factors to reveal the time-related dynamics, which may cause in-comparability of results from diverse studies with inconsistent sampling rates. In this study, in addition to the conventional MSE with relative scale factors, we also expressed MSE with absolute time scales (MaSE). We compared the effects of sampling rates on MSE and MaSE of simulated and real EEG time series. The results show that the previously found phenomenon (down-sampling can increase sample entropy) is just the projection of the compressing effect of down-sampling on MSE. And we have also shown the compressing effect of down-sampling on MSE does not change MaSE's profile, despite some minor right-sliding. In addition, by analyzing a public EEG dataset of emotional states, we have demonstrated improved classification rate after choosing appropriate sampling rate. We have finally proposed a working strategy to choose an appropriate sampling rate, and suggested using MaSE to avoid confusion caused by sampling rate inconsistency. This novel study may apply to a broad range of studies that would traditionally utilize sample entropy and MSE to analyze the complexity of an underlying dynamic process. [ABSTRACT FROM AUTHOR]

Mental fatigue (MF) jeopardizes performance and safety through a variety of cognitive impairments and according to the complexity loss theory, should represent "complexity loss" in electroencephalogram (EEG). However, the studies are few and inconsistent concerning the relationship between MF and loss of complexity, probably because of the susceptibility of brain waves to noise. In this study, MF was induced in thirteen male college students by a simulated flight task. Before and at the end of the task, spontaneous EEG and auditory steady-state response (ASSR) were recorded and instantaneous frequency variation (IFV) in alpha rhythm was extracted and analyzed by multiscale entropy (MSE) analysis. The results show that there were significant differences in IFV in alpha rhythm either from spontaneous EEG or from ASSR for all subjects. Therefore, the proposed method can be effective in revealing the complexity loss caused by MF in spontaneous EEG and ASSR, which may serve as a promising analyzing method to mark mild mental impairments. [ABSTRACT FROM AUTHOR]

The Multiscale Entropy (MSE) is an effective measure to quantify the dynamical complexity of complex systems, which has many successful applications in physiological and physical fields. It uses different scales to mean-coarse-grain the original series, and then calculates the sample entropy for each coarse-grained series. Inspired by the MSE, we in this paper propose the Multi-Moment Multiscale Local Sample Entropy (MMMLSE), which considers both mean-coarse-grained and standard-deviation-coarse-grained characteristics of the original series for each scale, to quantify the dynamical complexity of complex systems. We use simulated data (1 / f noise, white noise and logistic map) to test the performance of our proposed method, with results showing that the MMMLSE can accurately and effectively characterize these complex systems. The ability to preserve nonlinear dynamics of the proposed method is also proved by surrogate data and nonlinearity test experiment. Furthermore, we apply the MMMLSE to analyze physiological signals, and the MMMLSE reveals that the ill individuals have lower dynamical complexity at larger scales than the healthy ones, and the elder individuals have lower dynamical complexity at larger scales than the younger ones, which are consistent with the reality. [ABSTRACT FROM AUTHOR]

Photovoltaic (PV) system diagnosis is a growing research domain likewise solar energy's ongoing significant expansion. Indeed, efficient Fault Detection and Diagnosis (FDD) tools are crucial to guarantee reliability, avoid premature aging and improve the profitability of PV plants. In this paper, an on-line diagnosis method using the PV plant electrical output is presented. This entirely signal-based method combines variational mode decomposition (VMD) and multiscale dispersion entropy (MDE) for the purpose of detecting and isolating faults in a real grid-connected PV plant. The present method seeks a low-cost design, an ease of implementation and a low computation cost. Taking into account the innovation of applying these techniques to PV FDD, the VMD and MDE procedures as well as parameters identification are carefully detailed. The proposed FFD approach performance is assessed on a real rooftop PV plant with experimentally induced faults, and the first results reveal the MDE approach has good suitability for PV plants diagnosis. [ABSTRACT FROM AUTHOR]

In order to accurately diagnose the fault type of power transformer, this paper proposes a transformer fault diagnosis method based on the combination of time-shift multiscale bubble entropy (TSMBE) and stochastic configuration network (SCN). Firstly, bubble entropy is introduced to overcome the shortcomings of traditional entropy models that rely too heavily on hyperparameters. Secondly, on the basis of bubble entropy, a tool for measuring signal complexity, TSMBE, is proposed. Then, the TSMBE of the transformer vibration signal is extracted as a fault feature. Finally, the fault feature is inputted into the stochastic configuration network model to achieve an accurate identification of different transformer state signals. The proposed method was applied to real power transformer fault cases, and the research results showed that TSMBE-SCN achieved 99.01%, 99.1%, 99.11%, 99.11%, 99.14% and 99.02% of the diagnostic rates under different folding numbers, respectively, compared with conventional diagnostic models MBE-SCN, TSMSE-SCN, MSE-SCN, TSMDE-SCN and MDE-SCN. This comparison shows that TSMBE-SCN has a strong competitive advantage, which verifies that the proposed method has a good diagnostic effect. This study provides a new method for power transformer fault diagnosis, which has good reference value. [ABSTRACT FROM AUTHOR]

Background: Patients with generalized epilepsy who had lateralized EEG abnormalities after corpus callosotomy (CC) occasionally undergo subsequent surgeries to control intractable epilepsy. Objectives: This study evaluated retrospectively the combination of EEG multiscale entropy (MSE) and FDG-PET for identifying lateralization of the epileptogenic zone after CC. Methods: This study included 14 patients with pharmacoresistant epilepsy who underwent curative epilepsy surgery after CC. Interictal scalp EEG and FDG-PET obtained after CC were investigated to determine (1) whether the MSE calculated from the EEG and FDG-PET findings was lateralized to the surgical side, and (2) whether the lateralization was associated with seizure outcomes. Results: Seizure reduction rate was higher in patients with lateralized findings to the surgical side than those without (MSE: p < 0.05, FDG-PET: p < 0.05, both: p < 0.01). Seizure free rate was higher in patients with lateralized findings in both MSE and FDG-PET than in those without (p < 0.05). Conclusions: This study demonstrated that patients with lateralization of MSE and FDG-PET to the surgical side had better seizure outcomes. The combination of MSE and conventional FDG-PET may help to select surgical candidates for additional surgery after CC with good postoperative seizure outcomes. [ABSTRACT FROM AUTHOR]

Inverters and converters contain more and more power electronics switches which may subsequently affect their reliability. Therefore, fault detection and location are essential to improve their reliability and to ensure continuous operation. In this paper, an AC−DC−AC converter with three-phase inverter is investigated under permanent, single and multiple open-circuit fault scenarios. Many entropies and multiscale entropies are then proposed to evaluate the complexity of the output currents by quantifying their entropies over a range of temporal scales. Among the multitude of entropies, only some entropies are able to differentiate healthy from open-circuit faulty conditions. Moreover, the simulation results show that these entropies are able to detect and locate the arms of the bridge with open-circuit faults.

The complex physiological dynamics of neonatal seizures make their detection challenging. A timely diagnosis and treatment, especially in intensive care units, are essential for a better prognosis and the mitigation of possible adverse effects on the newborn's neurodevelopment. In the literature, several electroencephalographic (EEG) studies have been proposed for a parametric characterization of seizures or their detection by artificial intelligence techniques. At the same time, other sources than EEG, such as electrocardiography, have been investigated to evaluate the possible impact of neonatal seizures on the cardio-regulatory system. Heart rate variability (HRV) analysis is attracting great interest as a valuable tool in newborns applications, especially where EEG technologies are not easily available. This study investigated whether multiscale HRV entropy indexes could detect abnormal heart rate dynamics in newborns with seizures, especially during ictal events. Furthermore, entropy measures were analyzed to discriminate between newborns with seizures and seizure-free ones. A cohort of 52 patients (33 with seizures) from the Helsinki University Hospital public dataset has been evaluated. Multiscale sample and fuzzy entropy showed significant differences between the two groups (p-value < 0.05, Bonferroni multiple-comparison post hoc correction). Moreover, interictal activity showed significant differences between seizure and seizure-free patients (Mann-Whitney Test: p-value < 0.05). Therefore, our findings suggest that HRV multiscale entropy analysis could be a valuable pre-screening tool for the timely detection of seizure events in newborns. [ABSTRACT FROM AUTHOR]

The mild cognitive impairment (MCI) stage plays an essential role in preventing the progression of older adults to Alzheimer's disease. In this study, neurofeedback training (NFT) is applied to improve MCI brain cognitive function. To assess the improvement effect, a novel algorithm called Weighted Multiple Multiscale Entropy (WMMSE) is proposed to extract and analyze the electroencephalogram (EEG) features of patients with MCI. To overcome the information loss problem of traditional multiscale entropy (MSE), WMMSE fully considered the correlation of the sequence and the contribution of each sequence to the total entropy. The experimental group composed of 39 patients with MCI was subjected to NFT for 10 days during two sessions. The control group included 21 patients with MCI without any intervention. The Lempel-Ziv complexity (LZC) was used for primary assessment, and WMMSE was used to accurately analyze the effect of NFT. The results show that the WMMSE values of F4, C3, C4, O1, and T5 channels post-NFT are higher compared with pre-NFT and significant differences (P < 0.05). Moreover, the cognitive subscale of the Montreal Cognitive Assessment (MoCA) results shows that the post-NFT score is higher than the pre-NFT in the vast majority of the patients with MCI and significant differences (P < 0.05). When compared with the control group, the WMMSE values of the experimental group increased in each channel. Therefore, the NFT intervention method contributes to brain cognitive functional recovery, and WMMSE can be used as a biomarker to evaluate the state of MCI brain cognitive function. [ABSTRACT FROM AUTHOR]

Multiscale entropy is a popular and valuable methodology for analyzing hydrological complexity. However, some errors and limitations remain in its use and interpretation. This study identified three key issues, incorrect mapping of entropy values with frequency signals, an insufficient time scale range, and an unclear relationship between features in the multiscale entropy curve and hydrological interpretation. To address these issues, we focused on the sediment concentration and runoff in the Yanhe Watershed and conducted in-depth explorations using refined composite multiscale entropy (RCMFE) and three other methods, power spectrum density analysis, wavelet transform, and surrogate analysis. The results indicate that the entropy at each scale is influenced by signals with time scales equal to or greater than its own scale and that its variation is controlled by the overall signal dispersion. The RCMFE method demonstrated suitability for the complexity analysis of sediment and runoff sequences with short-length data. To effectively capture hydrological complexity, attention to the scale range issue is crucial, ensuring that the richness of complex features at larger scales in multiscale entropy curves is not overlooked. Interpretation of the local minima and maxima in the multiscale entropy curve is highlighted. Local minima signify high periodic patterns and predictability, whereas the first peak, typically occurring at approximately 2–3 months, is a valuable indicator of the overall complexity of the hydrological series. Linear characteristics were found to contribute significantly to the hydrological complexity, with stronger linear correlations resulting in an overall increase, lower local minima, and increased volatility in the multiscale entropy curve. The notable reduction in the hydrological complexity of the Yanhe Watershed calls for ecological sustainability and sustainable soil and water conservation efforts. • RCMFE is suitable for the complexity analysis of hydrological sequences. • Clarify the incorrect mapping of entropy values with frequency signals. • Extending scale range is crucial for capturing hydrological complexity. • Local minima and maxima in RCMFE indicate periodicity and complexity, respectively. • Yanhe Watershed shows significant reduction in hydrological complexity. [ABSTRACT FROM AUTHOR]

Research has shown multiscale entropy, brain signal behavior across time scales, to reliably increase at lower time scales with time-on-task fatigue. However, multiscale entropy has not been examined in short vigilance tasks (i.e., ≤ 10 min). Addressing this gap, we examine multiscale entropy during a 10-minute Psychomotor Vigilance Test (PVT). Thirty-four participants provided neural data while completing the PVT. We compared the first 2 min of the task to the 7th and 8th minutes to avoid end-spurt effects. Results suggested increased multiscale entropy at lower time scales later compared to earlier in the task, suggesting multiscale entropy is a strong marker of time-on-task fatigue onset during short vigils. Separate analyses for Fast and Slow performers reveal differential entropy patterns, particularly over visual cortices. Here, observed brain-behavior linkage between entropy and reaction time for slow performers suggests that entropy assays over sensory cortices might have predictive value for fatigue onset or shifts from on- to off-task states. • We present novel findings describing differential multiscale entropy changes across time in a brief psychomotor vigilance test. • One brain-behavior linkage, with slow (poorly motivated) performers exhibiting strong positive relationships between reaction times and entropy, together with different entropy patterns than fast (motivated) performers at occipital cortices, suggests entropy assays at this location may be predictive of fatigue onset and/or a shift from on- to off-task states in future work and in computational modeling of fatigue onset. [ABSTRACT FROM AUTHOR]

We review the literature to argue the importance of the occurrence of crucial events in the dynamics of physiological processes. Crucial events are interpreted as short time intervals of turbulence, and the time distance between two consecutive crucial events is a waiting time distribution density with an inverse power law (IPL) index μ, with μ < 3 generating non-stationary behavior. The non-stationary condition is characterized by two regimes of the IPL index: (a) perennial non-stationarity, with 1 < μ < 2 and (b) slow evolution toward the stationary regime, with 2 < μ < 3. Human heartbeats and brain dynamics belong to the latter regime, with healthy physiological processes tending to be closer to the border with the perennial non-stationary regime with μ = 2. The complexity of cognitive tasks is associated with the mental effort required to address a difficult task, which leads to an increase of μ with increasing task difficulty. On this basis we explore the conjecture that disease evolution leads the IPL index μ moving from the healthy condition μ = 2 toward the border with Gaussian statistics with μ = 3, as the disease progresses. Examining heart rate time series of patients affected by diabetes-induced autonomic neuropathy of varying severity, we find that the progression of cardiac autonomic neuropathy (CAN) indeed shifts μ from the border with perennial variability, μ = 2, to the border with Gaussian statistics, μ = 3 and provides a novel, sensitive index for assessing disease progression. We find that at the Gaussian border, the dynamical complexity of crucial events is replaced by Gaussian fluctuation with long-time memory. [ABSTRACT FROM AUTHOR]

Visual short-term memory (VSTM) is an important cognitive function that acts as a temporary storage for visual information. Previous studies have shown that VSTM capacity can be modulated by the location of one’s hands, where hand proximity enhances neural processing and memory of nearby visual stimuli. The present study used traditional event-related potentials (ERP) along with multiscale entropy (MSE) analysis to shed light on the neural mechanism(s) behind such near-hand effect. Participants’ electroencephalogram (EEG) data were recorded as they performed a VSTM task with their hands either proximal or distal to the display. ERP analysis showed altered memory processing in the 400–700 ms time window during memory retrieval period. Importantly, MSE analysis also showed significant EEG difference between hand proximal and distal conditions between scales 10 to 20, and such difference is clustered around the right parietal cortex – a region that is involved in VSTM processing and bimodal hand-eye integration. The implications of higher MSE time scale in the parietal cortex are discussed in the context of signal complexity and its possible relation to cognitive processing. To our knowledge, this study provides the first investigation using MSE to characterize the temporal characteristics and signal complexity behind the effect of hand proximity.

Visual short-term memory (VSTM) is an important cognitive function that acts as a temporary storage for visual information. Previous studies have shown that VSTM capacity can be modulated by the location of one's hands, where hand proximity enhances neural processing and memory of nearby visual stimuli. The present study used traditional event-related potentials (ERP) along with multiscale entropy (MSE) analysis to shed light on the neural mechanism(s) behind such near-hand effect. Participants' electroencephalogram (EEG) data were recorded as they performed a VSTM task with their hands either proximal or distal to the display. ERP analysis showed altered memory processing in the 400–700 ms time window during memory retrieval period. Importantly, MSE analysis also showed significant EEG difference between hand proximal and distal conditions between scales 10 to 20, and such difference is clustered around the right parietal cortex – a region that is involved in VSTM processing and bimodal hand-eye integration. The implications of higher MSE time scale in the parietal cortex are discussed in the context of signal complexity and its possible relation to cognitive processing. To our knowledge, this study provides the first investigation using MSE to characterize the temporal characteristics and signal complexity behind the effect of hand proximity. [ABSTRACT FROM AUTHOR]

Objective: We propose a new bidimensional entropy measure and its multiscale form and evaluate their behavior using various synthetic and real images. The bidimensional multiscale measure finds application in helping clinicians for pseudoxanthoma elasticum (PXE) detection in dermoscopic images. Method: We developed bidimensional fuzzy entropy ($FuzEn_{2D}$) and its multiscale extension ($MSF_{2D}$) and then evaluated them on a set of synthetic images and texture datasets. Afterwards, we applied $ MSF_{2D}$ to dermoscopic PXE images and compared the results to those obtained by bidimensional multiscale sample entropy ($MSE_{2D}$). Results: The results for the synthetic images illustrate that $FuzEn_{2D}$ has the ability to quantify images irregularity. Moreover, $FuzEn_{2D}$ , compared with bidimensional sample entropy ($SampEn_{2D}$), leads to more stable results. The tests with the multiscale version show that $ MSF_{2D}$ is a proper image complexity measure. When applied to the dermoscopic PXE images, the paired t-test illustrates a significant statistical difference between $ MSF_{2D}$ of neck images with papules and normal skin images at a couple of scale factors. Conclusion: The results for the synthetic data illustrate that $FuzEn_{2D}$ is an image irregularity measure that overcomes $SampEn_{2D}$ in terms of reliability, especially for small-sized images, and stability of results. The results for the PXE dermoscopic images demonstrate the ability of $MSF_{2D}$ to recognize dermoscopic images of normal zones from PXE papules zones with a large effect size. Significance: This work introduces new image irregularity and complexity measures and shows the potential for $ MSF_{2D}$ to serve as a possible tool helping medical doctors in PXE diagnosis. [ABSTRACT FROM AUTHOR]

The characterization of irregular patterns in images has become a focal point in numerous studies due to its relevance in various applications. In particular, images depicting natural phenomena exhibit intricate patterns with unique irregularities, such as self-similarity and scaling. The classification of these phenomena based on their patterns has been an ongoing endeavor within the field of complex systems. However, existing techniques for characterizing these complex phenomena typically assume isotropic variability patterns, which is not always feasible. To address these limitations, this paper introduces a novel algorithm, called the maximum angular multiscale entropy (MAMSE), based on the multiscale entropy method. The MAMSE algorithm overcomes the challenges posed by anisotropic fractal properties and is tested on synthetic images featuring both isotropic irregularities and anisotropic fractal properties. The experimental results reveal a new concept of angular self-similarity enabled by MAMSE, which proves instrumental in effectively distinguishing between groups of oil spill and low-wind conditions images. Comparative analysis with the two-dimensional multiscalar entropy algorithm demonstrates the superior performance and efficiency of MAMSE, yielding better and faster results. • Using MAMSE algorithm, we can observe how the isotropy of the image changes with the scale. • Angular self-similarity is not always observed in real images, as we will see for satellite images. • Fractal images show lower entropy values than the random images. • The MAMSE algorithm can be up to 102x faster when compared to two-dimensional multiscale entropy. [ABSTRACT FROM AUTHOR]

Background: Postural stability depends on the integration of the multisensory system to produce motor outputs. When visual and somatosensory input is reliable, this reduces reliance on the vestibular system. Despite this, vestibular loss can still cause severe postural dysfunction. Training one or more of the three sensory systems through vestibular habituation and adaptation can alter sensory weighting and change postural behavior.Aim: The purpose of this study was to assess sensory reweighting of postural control processing after combined vestibular activation with voluntary weight shift training in healthy adults.Methods: Thirty-three healthy individuals (18-35 y.o.) were randomly assigned to one of three groups: No training (control), visual feedback weight shift training (WST) coupled with an active horizontal headshake (HS) activity to elicit a vestibular perturbation, or the same WST without HS (NoHS). Training was performed 2x/day, every other day (M, W, F), totaling six sessions. Pre- and post- assessments on the Sensory Organization Test (SOT) were performed. Separate between- and within- repeated measures ANOVAs were used to analyze the six SOT equilibrium scores, composite scores, sensory ratios and center of pressure (COP) variables by comparing baseline to post-training. Alpha level was set at p < .05.Results: There was a significant group x session x condition change (p = .012) in the COP multiscale entropy (MSE) velocity sway in the HS group during SOT conditions 5 and 6. Similarly, COP medio-lateral standard deviation sway (ML Std) showed group x session x visual condition (p = .028), due to HS in condition 6 relative to other two groups.Conclusion: Postural training can alter sensory organization after a visual feedback-vestibular activation training protocol, suggesting a possible sensory reweighting through vestibular adaptation and/or habituation.Significance: Translating these findings into a vestibular-impaired population can stimulate the design of a rehabilitation balance protocol. [ABSTRACT FROM AUTHOR]

Dynamic changes in the regularity of interictal gamma oscillations (GOs, 30–70 Hz) on intracranial electroencephalography (EEG) reflect focal ictogenesis with epileptogenic neuronal synchronization in focal cortical dysplasia (FCD). We investigated whether the regularity of interictal GOs is a biomarker of the seizure onset zone (SOZ) using multiscale entropy analysis. We quantified the regularity of interictal GOs using intracranial EEG data from 1164 electrodes in 13 patients with FCD who were seizure-free postoperatively. The regularity of interictal GOs was quantified as entropy values. Low entropy represents high regularity. We standardized entropy values using Z values for each SOZ, resection area (RA), and the region outside the RA. The cutoff Z values, sensitivity, and specificity for detecting each area were calculated using area under the receiver operating characteristics curves (AUCs). Low Z values represent higher regularity of GOs. The cutoff Z value of ≤− 2.09 for the SOZ had a sensitivity of 100% and specificity of 97.1% (AUC = 0.992 ± 0.002). The cutoff Z value of ≤− 0.12 for the RA had a sensitivity of 54.2% and specificity of 73.8% (AUC = 0.673 ± 0.019). The cutoff Z value of ≥− 0.11 for the region outside the RA had a sensitivity of 73.8% and specificity of 54.2% (AUC = 0.673 ± 0.019). Low entropy of interictal GOs was a reliable biomarker for the SOZ. Maintained high entropy of interictal GOs may be an auxiliary biomarker for nonepileptogenic regions. Low entropy of interictal GOs may be a biomarker for the SOZ in FCD type II. • We analyzed intracranial EEG in focal cortical dysplasia type II. • We evaluated the irregularity of interictal gamma oscillations (GOs). • The most reduction of irregularity of interictal GOs may be a biomarker for SOZ. • The irregularity of interictal GOs maintained in the nonepileptogenic region. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of topological entropy of a discrete dynamical system given by a continuous map f : X → X , where X is metric and compact, with respect to observations of its orbits given by a continuous map φ : X → R k. We apply our definitions to obtain an upper bound of multiscale entropy, which has been used in time series analysis. [ABSTRACT FROM AUTHOR]

Entropy is a powerful tool for quantification of the brain function and its information processing capacity. This is evident in its broad domain of applications that range from functional interactivity between the brain regions to quantification of the state of consciousness. A number of previous reviews summarized the use of entropic measures in neuroscience. However, these studies either focused on the overall use of nonlinear analytical methodologies for quantification of the brain activity or their contents pertained to a particular area of neuroscientific research. The present study aims at complementing these previous reviews in two ways. First, by covering the literature that specifically makes use of entropy for studying the brain function. Second, by highlighting the three fields of research in which the use of entropy has yielded highly promising results: the (altered) state of consciousness, the ageing brain, and the quantification of the brain networks’ information processing. In so doing, the present overview identifies that the use of entropic measures for the study of consciousness and its (altered) states led the field to substantially advance the previous findings. Moreover, it realizes that the use of these measures for the study of the ageing brain resulted in significant insights on various ways that the process of ageing may affect the dynamics and information processing capacity of the brain. It further reveals that their utilization for analysis of the brain regional interactivity formed a bridge between the previous two research areas, thereby providing further evidence in support of their results. It concludes by highlighting some potential considerations that may help future research to refine the use of entropic measures for the study of brain complexity and its function. The present study helps realize that (despite their seemingly differing lines of inquiry) the study of consciousness, the ageing brain, and the brain networks’ information processing are highly interrelated. Specifically, it identifies that the complexity, as quantified by entropy, is a fundamental property of conscious experience, which also plays a vital role in the brain’s capacity for adaptation and therefore whose loss by ageing constitutes a basis for diseases and disorders. Interestingly, these two perspectives neatly come together through the association of entropy and the brain capacity for information processing.

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Multiscale entropy (MSE) analysis was introduced in the 2002 to evaluate the complexity of a time series by quantifying its entropy over a range of temporal scales. The algorithm has been successfully applied in different research fields. Since its introduction, a number of modifications and refinements have been proposed, some aimed at increasing the accuracy of the entropy estimates, others at exploring alternative coarse-graining procedures. In this review, we first describe the original MSE algorithm. Then, we review algorithms that have been introduced to improve the estimation of MSE. We also report a recent generalization of the method to higher moments.

We introduce a generalization of multiscale entropy (MSE) analysis. The method is termed MSEn, where the subscript denotes the moment used to coarse-grain a time series. MSEμ, described previously, uses the mean value (first moment). Here, we focus on MSEσ2 , which uses the second moment, i.e., the variance. MSEσ2 quantifies the dynamics of the volatility (variance) of a signal over multiple time scales. We use the method to analyze the structure of heartbeat time series. We find that the dynamics of the volatility of heartbeat time series obtained from healthy young subjects is highly complex. Furthermore, we find that the multiscale complexity of the volatility, not only the multiscale complexity of the mean heart rate, degrades with aging and pathology. The “bursty” behavior of the dynamics may be related to intermittency in energy and information flows, as part of multiscale cycles of activation and recovery. Generalized MSE may also be useful in quantifying the dynamical properties of other physiologic and of non-physiologic time series.

The effect of an orthostatic stress on cardiovascular and respiratory complexity was investigated to detect impaired autonomic regulation in patients with vasovagal syncope (VVS). A total of 16 female patients and 12 age-matched healthy female subjects were enrolled in a passive 70° head-up tilt test. Also, 12 age-matched healthy male subjects were enrolled to study gender differences. Analysis was performed dynamically using various short-term (5 min) windows shifted by 1 min as well as by 20 min of orthostatic phase (OP) to evaluate local and global complexity. Complexity was determined over multiple time scales by the established method of refined composite multiscale entropy (RCMSE) and by a new proposed method of multiscale entropy based on symbolic dynamics (MSE-SD). Concerning heart rate variability (HRV) during OP, both methods revealed the highest complexity for female controls followed by lower complexity in male controls (p < 0.01) and by the lowest complexity in female patients (p < 0.01). For blood pressure variability (BPV), no gender differences in controls were shown by any method. However, MSE-SD demonstrated highly significantly increased BPV complexity in patients during OP (p < 0.01 on 4 time-scales after 7 min, p < 0.001 on 5 time-scales after 11 min) while RCMSE did not reveal considerable differences (p < 0.05 on 2 time scales after 7 min). Respiratory complexity was further increased in patients primary shown by MSE-SD. Findings indicated impaired autonomic regulation in VVS patients characterized by predominantly increased BPV complexity accompanied with decreased HRV complexity. In addition, results suggested extending the concept of complexity loss with disease. [ABSTRACT FROM AUTHOR]

Aimed at the non-stationary and nonlinear characteristics of wind turbine vibration signals, a novel fault diagnosis method based on integral extension load mean decomposition multiscale entropy and least squares support vector machine was proposed in this paper. At first, the raw vibration signals monitored from the wind turbine were divided into groups for the pre-process. Then the signals were processed in groups with integral extension load mean decomposition method and Product Functions were obtained. The characteristic parameters were achieved by multiscale entropy method of processing main Product Functions, which described the signal characteristics. Finally, the characteristic parameters were entered into least squares support vector machine, and least squares support vector machine was trained. Next the trained least squares support vector machine was tested and the pattern was classified. The method can not only extract characteristic parameters effectively, but also classify the fault type accurately. The effectiveness and availability of the proposed method were proved in the wind turbine measured data experiment. [ABSTRACT FROM AUTHOR]

Diabetic foot ulcer (DFU) is a common complication of diabetes mellitus, while tissue ischemia caused by impaired vasodilatory response to plantar pressure is thought to be a major factor of the development of DFUs, which has been assessed using various measures of skin blood flow (SBF) in the time or frequency domain. These measures, however, are incapable of characterizing nonlinear dynamics of SBF, which is an indicator of pathologic alterations of microcirculation in the diabetic foot. This study recruited 18 type 2 diabetics with peripheral neuropathy and eight healthy controls. SBF at the first metatarsal head in response to locally applied pressure and heating was measured using laser Doppler flowmetry. A multiscale entropy algorithm was utilized to quantify the regularity degree of the SBF responses. The results showed that during reactive hyperemia and thermally induced biphasic response, the regularity degree of SBF in diabetics underwent only small changes compared to baseline and significantly differed from that in controls at multiple scales (p < 0.05). On the other hand, the transition of regularity degree of SBF in diabetics distinctively differed from that in controls (p < 0.05). These findings indicated that multiscale entropy could provide a more comprehensive assessment of impaired microvascular reactivity in the diabetic foot compared to other entropy measures based on only a single scale, which strengthens the use of plantar SBF dynamics to assess the risk for DFU. [ABSTRACT FROM AUTHOR]

To achieve an effective feature extraction for power transformer vibration signals, the authors propose a method for signal feature extraction based on empirical wavelet transform (EWT) and multiscale entropy (MSE). First, transformer vibration signals are decomposed into several empirical wavelet functions (EWFs) with the method of EWT. Then, the frequency characteristics of signals are demonstrated in the time‐frequency representation by applying a Hilbert transform to each EWF component. Finally, in order to quantify the extracted features, the MSEs of components being highly correlated with the original signals are calculated to construct the eigenvectors of transformer vibration signals. Several experiments are presented showing the effectiveness of this method compared with the classic empirical mode decomposition method. [ABSTRACT FROM AUTHOR]

Pulse oximetry is routinely used for monitoring patients' oxygen saturation levels with little regard to the variability of this physiological variable. There are few published studies on oxygen saturation variability (OSV), with none describing the variability and its pattern in a healthy adult population. The aim of this study was to characterize the pattern of OSV using several parameters; the regularity (sample entropy analysis), the self-similarity [detrended fluctuation analysis (DFA)] and the complexity [multiscale entropy (MSE) analysis]. Secondly, to determine if there were any changes that occur with age. The study population consisted of 36 individuals. The “young” population consisted of 20 individuals [Mean (±1 SD) age = 21.0 (±1.36 years)] and the “old” population consisted of 16 individuals [Mean (±1 SD) age = 50.0 (±10.4 years)]. Through DFA analysis, OSV was shown to exhibit fractal-like patterns. The sample entropy revealed the variability to be more regular than heart rate variability and respiratory rate variability. There was also a significant inverse correlation between mean oxygen saturation and sample entropy in healthy individuals. Additionally, the MSE analysis described a complex fluctuation pattern, which was reduced with age (p < 0.05). These findings suggest partial “uncoupling” of the cardio-respiratory control system that occurs with aging. Overall, this study has characterized OSV using pre-existing tools. We have showed that entropy analysis of pulse oximetry signals carries information about body oxygenation. This may have the potential to be used in clinical practice to detect differences in diseased patient subsets.

Multiscale entropy (MSE) has been a prevalent algorithm to quantify the complexity of biomedical time series. Recent developments in the field have tried to alleviate the problem of undefined MSE values for short signals. Moreover, there has been a 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 (RCMFEσ) and mean (RCMFEμ) to quantify the dynamical properties of spread and mean, respectively, over multiple time scales. We demonstrate the dependency of the RCMFEσ and RCMFEμ, in comparison with other multiscale approaches, on several straightforward signal processing concepts using a set of synthetic signals. The results evidenced that the RCMFEσ and RCMFEμ values are more stable and reliable than the classical multiscale entropy ones. We also inspect the ability of using the standard deviation as well as the mean in the coarse-graining process using magnetoencephalograms in Alzheimer's disease and publicly available electroencephalograms recorded from focal and non-focal areas in epilepsy. Our results indicated that when the RCMFEμ cannot distinguish different types of dynamics of a particular time series at some scale factors, the RCMFEσ may do so, and vice versa. The results showed that RCMFEσ-based features lead to higher classification accuracies in comparison with the RCMFEμ-based ones. We also made freely available all the Matlab codes used in this study at http://dx.doi.org/10.7488/ds/1477 . [ABSTRACT FROM AUTHOR]