Refined Composite Multiscale Fuzzy Dispersion Entropy and Its Applications to Bearing Fault Diagnosis.

Rotary machines often exhibit nonlinear behavior due to factors such as nonlinear stiffness, damping, friction, coupling effects, and defects. Consequently, their vibration signals display nonlinear characteristics. Entropy techniques prove to be effective in detecting these nonlinear dynamic characteristics. Recently, an approach called fuzzy dispersion entropy (DE-FDE) was introduced to quantify the uncertainty of time series. FDE, rooted in dispersion patterns and fuzzy set theory, addresses the sensitivity of DE to its parameters. However, FDE does not adequately account for the presence of multiple time scales inherent in signals. To address this limitation, the concept of multiscale fuzzy dispersion entropy (MFDE) was developed to capture the dynamical variability of time series across various scales of complexity. Compared to multiscale DE (MDE), MFDE exhibits reduced sensitivity to noise and higher stability. In order to enhance the stability of MFDE, we propose a refined composite MFDE (RCMFDE). In comparison with MFDE, MDE, and RCMDE, RCMFDE's performance is assessed using synthetic signals and three real bearing datasets. The results consistently demonstrate the superiority of RCMFDE in detecting various patterns within synthetic and real bearing fault data. Importantly, classifiers built upon RCMFDE achieve notably high accuracy values for bearing fault diagnosis applications, outperforming classifiers based on refined composite multiscale dispersion and sample entropy methods.

Assessment and Comparison of Nonlinear Measures in Resting-State Magnetoencephalograms in Alzheimer's Disease and Mild Cognitive Impairment.

BACKGROUND: Nonlinear dynamical measures, such as fractal dimension (FD), entropy, and Lempel-Ziv complexity (LZC), have been extensively investigated individually for detecting information content in magnetoencephalograms (MEGs) from patients with Alzheimer's disease (AD). OBJECTIVE: To compare systematically the performance of twenty conventional and recently introduced nonlinear dynamical measures in studying AD versus mild cognitive impairment (MCI) and healthy control (HC) subjects using MEG. METHODS: We compared twenty nonlinear measures to distinguish MEG recordings from 36 AD (mean age = 74.06±6.95 years), 18 MCI (mean age = 74.89±5.57 years), and 26 HC subjects (mean age = 71.77±6.38 years) in different brain regions and also evaluated the effect of the length of MEG epochs on their performance. We also studied the correlation between these measures and cognitive performance based on the Mini-Mental State Examination (MMSE). RESULTS: The results obtained by LZC, zero-crossing rate (ZCR), FD, and dispersion entropy (DispEn) measures showed significant differences among the three groups. There was no significant difference between HC and MCI. The highest Hedge's g effect sizes for HC versus AD and MCI versus AD were respectively obtained by Higuchi's FD (HFD) and fuzzy DispEn (FuzDispEn) in the whole brain and was most prominent in left lateral. The results obtained by HFD and FuzDispEn had a significant correlation with the MMSE scores. DispEn-based techniques, LZC, and ZCR, compared with HFD, were less sensitive to epoch length in distinguishing HC form AD. CONCLUSIONS: FuzDispEn was the most consistent technique to distinguish MEG dynamical patterns in AD compared with HC and MCI.

Bidimensional ensemble entropy: Concepts and application to emphysema lung computerized tomography scans.

BACKGROUND AND OBJECTIVE: Bidimensional entropy algorithms provide meaningful quantitative information on image textures. These algorithms have the advantage of relying on well-known one-dimensional entropy measures dedicated to the analysis of time series. However, uni- and bidimensional algorithms require the adjustment of some parameters that influence the obtained results or even findings. To address this, ensemble entropy techniques have recently emerged as a solution for signal analysis, offering greater stability and reduced bias in data patterns during entropy estimation. However, such algorithms have not yet been extended to their two-dimensional forms. METHODS: We therefore propose six bidimensional algorithms, namely ensemble sample entropy, ensemble permutation entropy, ensemble dispersion entropy, ensemble distribution entropy, and two versions of ensemble fuzzy entropy based on different models or parameters initialization of an entropy algorithm. These new measures are first tested on synthetic images and further applied to a biomedical dataset. RESULTS: The results suggest that ensemble techniques are able to detect different levels of image dynamics and their degrees of randomness. These methods lead to more stable entropy values (lower coefficients of variations) for the synthetic data. The results also show that these new measures can obtain up to 92.7% accuracy and 88.4% sensitivity when classifying patients with pulmonary emphysema through a k-nearest neighbors algorithm. CONCLUSIONS: This is a further step towards the potential clinical deployment of bidimensional ensemble approaches to detect different levels of image dynamics and their successful performance on emphysema lung computerized tomography scans. These bidimensional ensemble entropy algorithms have potential to be used in various imaging applications thanks to their ability to distinguish more stable and less biased image patterns compared to their original counterparts.

Beta to theta power ratio in EEG periodic components as a potential biomarker in mild cognitive impairment and Alzheimer's dementia.

BACKGROUND: Alzheimer's dementia (AD) is associated with electroencephalography (EEG) abnormalities including in the power ratio of beta to theta frequencies. EEG studies in mild cognitive impairment (MCI) have been less consistent in identifying such abnormalities. One potential reason is not excluding the EEG aperiodic components, which are less associated with cognition than the periodic components. Here, we investigate whether aperiodic and periodic EEG components are disrupted differently in AD or MCI vs. healthy control (HC) individuals and whether a periodic based beta/theta ratio differentiates better MCI from AD and HC groups than a ratio based on the full spectrum. METHODS: Data were collected from 44 HC (mean age (SD) = 69.1 (5.3)), 114 MCI (mean age (SD) = 72.2 (7.5)), and 41 AD (mean age (SD) = 75.7 (6.5)) participants. Aperiodic and periodic components and full spectrum EEG were compared among the three groups. Receiver operating characteristic curves obtained via logistic regression classifications were used to distinguish the groups. Last, we explored the relationships between cognitive performance and the beta/theta ratios based on the full or periodic spectrum. RESULTS: Aperiodic EEG components did not differ among the three groups. In contrast, AD participants showed an increase in full spectrum and periodic relative powers for delta, theta, and gamma and a decrease for beta when compared to HC or MCI participants. As predicted, MCI group differed from HC participants on the periodic based beta/theta ratio (Bonferroni corrected p-value = 0.036) measured over the occipital region. Classifiers based on beta/theta power ratio in EEG periodic components distinguished AD from HC and MCI participants, and outperformed classifiers based on beta/theta power ratio in full spectrum EEG. Beta/theta ratios were comparable in their association with cognition. CONCLUSIONS: In contrast to a full spectrum EEG analysis, a periodic-based analysis shows that MCI individuals are different on beta/theta ratio when compared to healthy individuals. Focusing on periodic components in EEG studies with or without other biological markers of neurodegenerative diseases could result in more reliable findings to separate MCI from healthy aging, which would be valuable for designing preventative interventions.

EEG Entropy in REM Sleep as a Physiologic Biomarker in Early Clinical Stages of Alzheimer's Disease.

BACKGROUND: Alzheimer's disease (AD) is associated with EEG changes across the sleep-wake cycle. As the brain is a non-linear system, non-linear EEG features across behavioral states may provide an informative physiologic biomarker of AD. Multiscale fluctuation dispersion entropy (MFDE) provides a sensitive non-linear measure of EEG information content across a range of biologically relevant time-scales. OBJECTIVE: To evaluate MFDE in awake and sleep EEGs as a potential biomarker for AD. METHODS: We analyzed overnight scalp EEGs from 35 cognitively normal healthy controls, 23 participants with mild cognitive impairment (MCI), and 19 participants with mild dementia due to AD. We examined measures of entropy in wake and sleep states, including a slow-to-fast-activity ratio of entropy (SFAR-entropy). We compared SFAR-entropy to linear EEG measures including a slow-to-fast-activity ratio of power spectral density (SFAR-PSD) and relative alpha power, as well as to cognitive function. RESULTS: SFAR-entropy differentiated dementia from MCI and controls. This effect was greatest in REM sleep, a state associated with high cholinergic activity. Differentiation was evident in the whole brain EEG and was most prominent in temporal and occipital regions. Five minutes of REM sleep was sufficient to distinguish dementia from MCI and controls. Higher SFAR-entropy during REM sleep was associated with worse performance on the Montreal Cognitive Assessment. Classifiers based on REM sleep SFAR-entropy distinguished dementia from MCI and controls with high accuracy, and outperformed classifiers based on SFAR-PSD and relative alpha power. CONCLUSION: SFAR-entropy measured in REM sleep robustly discriminates dementia in AD from MCI and healthy controls.

Detection of Oculomotor Dysmetria From Mobile Phone Video of the Horizontal Saccades Task Using Signal Processing and Machine Learning Approaches.

Eye movement assessments have the potential to help in diagnosis and tracking of neurological disorders. Cerebellar ataxias cause profound and characteristic abnormalities in smooth pursuit, saccades, and fixation. Oculomotor dysmetria (i.e., hypermetric and hypometric saccades) is a common finding in individuals with cerebellar ataxia. In this study, we evaluated a scalable approach for detecting and quantifying oculomotor dysmetria. Eye movement data were extracted from iPhone video recordings of the horizontal saccade task (a standard clinical task in ataxia) and combined with signal processing and machine learning approaches to quantify saccade abnormalities. Entropy-based measures of eye movements during saccades were significantly different in 72 individuals with ataxia with dysmetria compared with 80 ataxia and Parkinson's participants without dysmetria. A template matching-based analysis demonstrated that saccadic eye movements in patients without dysmetria were more similar to the ideal template of saccades. A support vector machine was then used to train and test the ability of multiple signal processing features in combination to distinguish individuals with and without oculomotor dysmetria. The model achieved 78% accuracy (sensitivity= 80% and specificity= 76%). These results show that the combination of signal processing and machine learning approaches applied to iPhone video of saccades, allow for extraction of information pertaining to oculomotor dysmetria in ataxia. Overall, this inexpensive and scalable approach for capturing important oculomotor information may be a useful component of a screening tool for ataxia and could allow frequent at-home assessments of oculomotor function in natural history studies and clinical trials.

Bearing Fault Diagnosis Using Refined Composite Generalized Multiscale Dispersion Entropy-Based Skewness and Variance and Multiclass FCM-ANFIS.

Bearing vibration signals typically have nonlinear components due to their interaction and coupling effects, friction, damping, and nonlinear stiffness. Bearing faults affect the signal complexity at various scales. Hence, measuring signal complexity at different scales is helpful to diagnosis of bearing faults. Numerous studies have investigated multiscale algorithms; nevertheless, multiscale algorithms using the first moment lose important complexity data. Accordingly, generalized multiscale algorithms have been recently introduced. The present research examined the use of refined composite generalized multiscale dispersion entropy (RCGMDispEn) based on the second moment (variance) and third moment (skewness) along with refined composite multiscale dispersion entropy (RCMDispEn) in bearing fault diagnosis. Moreover, multiclass FCM-ANFIS, which is a combination of adaptive network-based fuzzy inference systems (ANFIS), was developed to improve the efficiency of rotating machinery fault classification. According to the results, it is recommended that generalized multiscale algorithms based on variance and skewness be examined for diagnosis, along with multiscale algorithms, and be used to achieve an improvement in the results. The simultaneous usage of the multiscale algorithm and generalized multiscale algorithms improved the results in all three real datasets used in this study.

Measures of resting state EEG rhythms for clinical trials in Alzheimer's disease: Recommendations of an expert panel.

The Electrophysiology Professional Interest Area (EPIA) and Global Brain Consortium endorsed recommendations on candidate electroencephalography (EEG) measures for Alzheimer's disease (AD) clinical trials. The Panel reviewed the field literature. As most consistent findings, AD patients with mild cognitive impairment and dementia showed abnormalities in peak frequency, power, and "interrelatedness" at posterior alpha (8-12 Hz) and widespread delta (< 4 Hz) and theta (4-8 Hz) rhythms in relation to disease progression and interventions. The following consensus statements were subscribed: (1) Standardization of instructions to patients, resting state EEG (rsEEG) recording methods, and selection of artifact-free rsEEG periods are needed; (2) power density and "interrelatedness" rsEEG measures (e.g., directed transfer function, phase lag index, linear lagged connectivity, etc.) at delta, theta, and alpha frequency bands may be use for stratification of AD patients and monitoring of disease progression and intervention; and (3) international multisectoral initiatives are mandatory for regulatory purposes.

A pilot protocol to assess the feasibility of a virtual multiple crossover, randomized controlled trial design using methylphenidate in mild cognitive impairment.

BACKGROUND: The conventional clinical trial design in Alzheimer's disease (AD) and AD-related disorders (ADRDs) is the parallel-group randomized controlled trial. However, in heterogeneous disorders like AD/ADRDs, this design requires large sample sizes to detect meaningful effects in an "average" patient. They are very costly and, despite many attempts, have not yielded new treatments for many years. An alternative, the multi-crossover, randomized control trial (MCRCT) is a design in which each patient serves as their own control across successive, randomized blocks of active treatment and placebo. This design overcomes many limitations of parallel-group trials, yielding an unbiased assessment of treatment effect at the individual level ("N-of-1") regardless of unique patient characteristics. The goal of the present study is to pilot a MCRCT of a potential symptomatic treatment, methylphenidate, for mild-stage AD/ADRDs, testing feasibility and compliance of participants in this design and efficacy of the drug using both standard and novel outcome measures suited for this design. METHODS: Ten participants with mild cognitive impairment or mild-stage dementia due to AD/ADRDs will undergo a 4-week lead-in period followed by three, month-long treatment blocks (2 weeks of treatment with methylphenidate, 2 weeks placebo in random order). This trial will be conducted entirely virtually with an optional in-person screening visit. The primary outcome of interest is feasibility as measured by compliance and retention, with secondary and exploratory outcomes including cognition as measured by neuropsychological assessment at the end of each treatment period and daily brain games played throughout the study, actigraphy, and neuropsychiatric and functional assessments. DISCUSSION: This pilot study will gauge the feasibility of conducting a virtual MCRCT for symptomatic treatment in early AD/ADRD. It will also compare home-based daily brain games with standard neuropsychological measures within a clinical trial for AD/ADRD. Particular attention will be paid to compliance, tolerability of drug and participation, learning effects, trends and stability of daily measures across blocks, medication carryover effects, and correlations between standard and brief daily assessments. These data will provide guidance for more efficient trial design and the use of potentially more robust, ecological outcome measures in AD/ADRD research. TRIAL REGISTRATION: ClinicalTrials.gov, NCT03811847 . Registered on 21 January 2019.

Bidimensional Multiscale Fuzzy Entropy and Its Application to Pseudoxanthoma Elasticum.

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 ( FuzEn2D) and its multiscale extension ( MSF2D) and then evaluated them on a set of synthetic images and texture datasets. Afterwards, we applied MSF2D to dermoscopic PXE images and compared the results to those obtained by bidimensional multiscale sample entropy ( MSE2D). RESULTS: The results for the synthetic images illustrate that FuzEn2D has the ability to quantify images irregularity. Moreover, FuzEn2D, compared with bidimensional sample entropy ( SampEn2D), leads to more stable results. The tests with the multiscale version show that MSF2D is a proper image complexity measure. When applied to the dermoscopic PXE images, the paired t-test illustrates a significant statistical difference between MSF2D of neck images with papules and normal skin images at a couple of scale factors. CONCLUSION: The results for the synthetic data illustrate that FuzEn2D is an image irregularity measure that overcomes SampEn2D in terms of reliability, especially for small-sized images, and stability of results. The results for the PXE dermoscopic images demonstrate the ability of MSF2D 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 MSF2D to serve as a possible tool helping medical doctors in PXE diagnosis.

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.

Amplitude- and Fluctuation-Based Dispersion Entropy.

Dispersion entropy (DispEn) is a recently introduced entropy metric to quantify the uncertainty of time series. It is fast and, so far, it has demonstrated very good performance in the characterisation of time series. It includes a mapping step, but the effect of different mappings has not been studied yet. Here, we investigate the effect of linear and nonlinear mapping approaches in DispEn. We also inspect the sensitivity of different parameters of DispEn to noise. Moreover, we develop fluctuation-based DispEn (FDispEn) as a measure to deal with only the fluctuations of time series. Furthermore, the original and fluctuation-based forbidden dispersion patterns are introduced to discriminate deterministic from stochastic time series. Finally, we compare the performance of DispEn, FDispEn, permutation entropy, sample entropy, and Lempel-Ziv complexity on two physiological datasets. The results show that DispEn is the most consistent technique to distinguish various dynamics of the biomedical signals. Due to their advantages over existing entropy methods, DispEn and FDispEn are expected to be broadly used for the characterization of a wide variety of real-world time series. The MATLAB codes used in this paper are freely available at http://dx.doi.org/10.7488/ds/2326.

The Influence of Synthesis Parameters on Vertically Aligned CNT Sheets: Empirical Modeling and Process Optimization Using Response Surface Methodology.

In the present work, vertically aligned carbon nanotube (VA-CNT) sheets were synthesized via pyrolysis of polybenzimidazole (PBI)-Kapton inside the pores of anodized aluminum oxide (AAO). The synthesized VA-CNT sheets were then evaluated for the desalination of salty water. The results indicated that the VA-CNT sheets were effective for application as an adsorbent for desalination of salty water due to their high adsorption capacity, with no loss of CNTs in the treated water. This study explored the impact of operating time and temperature on liquid adsorption performance through optimization and modeling methods. An empirical model was developed through the evolution of a full factorial design process which considered two significant factors for enhanced antibacterial efficiency and adsorption uptake. The highest antibacterial efficiency was achieved with carbon precursors synthesized at a higher temperature. However, optimal values were obtained for both antibacterial efficiency and adsorption uptake (NaCl) with a combination of CNT membranes. The best conditions for such a membrane were 800 °C and 18 min. Under these conditions, antibacterial efficiency, contact angle, carbon content, adsorption uptake (NaCl = 10,000) and adsorption uptake (NaCl = 20,000) were 90.079, 1.69256, 75.213, 76.2352 and 0.997, respectively.

Multiscale dispersion entropy for the regional analysis of resting-state magnetoencephalogram complexity in Alzheimer's disease.

Alzheimer's disease (AD) is a progressive and irreversible brain disorder of the nervous system affecting memory, thinking, and emotion. It is the most important cause of dementia and an influential social problem in all the world. The complexity of brain recordings has been successfully used to help to characterize AD. We have recently introduced multiscale dispersion entropy (MDE) as a very fast and powerful tool to quantify the complexity of signals. The aim of this study is to assess the ability of MDE, in comparison with multiscale permutation entropy (MPE) and multiscale entropy (MSE), to discriminate 36 AD patients from 26 elderly age-matched control subjects using resting-state magnetoencephalogram (MEG) recordings. The results showed that MDE, unlike MSE, does not lead to undefined values. Moreover, the differences between the MDE values for AD palatines versus controls were more significant than their corresponding MSE- and MPE-based values. In addition, the computation time for our recently developed MDE was considerably less than that for MSE and even MPE.

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 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 .

Refined Composite Multiscale Dispersion Entropy and its Application to Biomedical Signals.

OBJECTIVE: We propose a novel complexity measure to overcome the deficiencies of the widespread and powerful multiscale entropy (MSE), including, MSE values may be undefined for short signals, and MSE is slow for real-time applications. METHODS: We introduce multiscale dispersion entropy (DisEn-MDE) as a very fast and powerful method to quantify the complexity of signals. MDE is based on our recently developed DisEn, which has a computation cost of O(N), compared with O(N2) for sample entropy used in MSE. We also propose the refined composite MDE (RCMDE) to improve the stability of MDE. RESULTS: We evaluate MDE, RCMDE, and refined composite MSE (RCMSE) on synthetic signals and three biomedical datasets. The MDE, RCMDE, and RCMSE methods show similar results, although the MDE and RCMDE are faster, lead to more stable results, and discriminate different types of physiological signals better than MSE and RCMSE. CONCLUSION: For noisy short and long time series, MDE and RCMDE are noticeably more stable than MSE and RCMSE, respectively. For short signals, MDE and RCMDE, unlike MSE and RCMSE, do not lead to undefined values. The proposed MDE and RCMDE are significantly faster than MSE and RCMSE, especially for long signals, and lead to larger differences between physiological conditions known to alter the complexity of the physiological recordings. SIGNIFICANCE: MDE and RCMDE are expected to be useful for the analysis of physiological signals thanks to their ability to distinguish different types of dynamics. The MATLAB codes used in this paper are freely available at http://dx.doi.org/10.7488/ds/1982.

Amplitude-aware permutation entropy: Illustration in spike detection and signal segmentation.

BACKGROUND AND OBJECTIVE: Signal segmentation and spike detection are two important biomedical signal processing applications. Often, non-stationary signals must be segmented into piece-wise stationary epochs or spikes need to be found among a background of noise before being further analyzed. Permutation entropy (PE) has been proposed to evaluate the irregularity of a time series. PE is conceptually simple, structurally robust to artifacts, and computationally fast. It has been extensively used in many applications, but it has two key shortcomings. First, when a signal is symbolized using the Bandt-Pompe procedure, only the order of the amplitude values is considered and information regarding the amplitudes is discarded. Second, in the PE, the effect of equal amplitude values in each embedded vector is not addressed. To address these issues, we propose a new entropy measure based on PE: the amplitude-aware permutation entropy (AAPE). METHODS: AAPE is sensitive to the changes in the amplitude, in addition to the frequency, of the signals thanks to it being more flexible than the classical PE in the quantification of the signal motifs. To demonstrate how the AAPE method can enhance the quality of the signal segmentation and spike detection, a set of synthetic and realistic synthetic neuronal signals, electroencephalograms and neuronal data are processed. We compare the performance of AAPE in these problems against state-of-the-art approaches and evaluate the significance of the differences with a repeated ANOVA with post hoc Tukey's test. RESULTS: In signal segmentation, the accuracy of AAPE-based method is higher than conventional segmentation methods. AAPE also leads to more robust results in the presence of noise. The spike detection results show that AAPE can detect spikes well, even when presented with single-sample spikes, unlike PE. For multi-sample spikes, the changes in AAPE are larger than in PE. CONCLUSION: We introduce a new entropy metric, AAPE, that enables us to consider amplitude information in the formulation of PE. The AAPE algorithm can be used in almost every irregularity-based application in various signal and image processing fields. We also made freely available the Matlab code of the AAPE.

Dispersion entropy for the analysis of resting-state MEG regularity in Alzheimer's disease.

Alzheimer's disease (AD) is a progressive degenerative brain disorder affecting memory, thinking, behaviour and emotion. It is the most common form of dementia and a big social problem in western societies. The analysis of brain activity may help to diagnose this disease. Changes in entropy methods have been reported useful in research studies to characterize AD. We have recently proposed dispersion entropy (DisEn) as a very fast and powerful tool to quantify the irregularity of time series. The aim of this paper is to evaluate the ability of DisEn, in comparison with fuzzy entropy (FuzEn), sample entropy (SampEn), and permutation entropy (PerEn), to discriminate 36 AD patients from 26 elderly control subjects using resting-state magnetoencephalogram (MEG) signals. The results obtained by DisEn, FuzEn, and SampEn, unlike PerEn, show that the AD patients' signals are more regular than controls' time series. The p-values obtained by DisEn, FuzEn, SampEn, and PerEn based methods demonstrate the superiority of DisEn over PerEn, SampEn, and PerEn. Moreover, the computation time for the newly proposed DisEn-based method is noticeably less than for the FuzEn, SampEn, and PerEn based approaches.

MEMD-enhanced multivariate fuzzy entropy for the evaluation of complexity in biomedical signals.

Multivariate multiscale entropy (mvMSE) has been proposed as a combination of the coarse-graining process and multivariate sample entropy (mvSE) to quantify the irregularity of multivariate signals. However, both the coarse-graining process and mvSE may not be reliable for short signals. Although the coarse-graining process can be replaced with multivariate empirical mode decomposition (MEMD), the relative instability of mvSE for short signals remains a problem. Here, we address this issue by proposing the multivariate fuzzy entropy (mvFE) with a new fuzzy membership function. The results using white Gaussian noise show that the mvFE leads to more reliable and stable results, especially for short signals, in comparison with mvSE. Accordingly, we propose MEMD-enhanced mvFE to quantify the complexity of signals. The characteristics of brain regions influenced by partial epilepsy are investigated by focal and non-focal electroencephalogram (EEG) time series. In this sense, the proposed MEMD-enhanced mvFE and mvSE are employed to discriminate focal EEG signals from non-focal ones. The results demonstrate the MEMD-enhanced mvFE values have a smaller coefficient of variation in comparison with those obtained by the MEMD-enhanced mvSE, even for long signals. The results also show that the MEMD-enhanced mvFE has better performance to quantify focal and non-focal signals compared with multivariate multiscale permutation entropy.

Inspection of short-time resting-state electroencephalogram functional networks in Alzheimer's disease.

Functional connectivity has proven useful to characterise electroencephalogram (EEG) activity in Alzheimer's disease (AD). However, most current functional connectivity analyses have been static, disregarding any potential variability of the connectivity with time. In this pilot study, we compute short-time resting state EEG functional connectivity based on the imaginary part of coherency for 12 AD patients and 11 controls. We derive binary unweighted graphs using the cluster-span threshold, an objective binary threshold. For each short-time binary graph, we calculate its local clustering coefficient (Cloc), degree (K), and efficiency (E). The distribution of these graph metrics for each participant is then characterised with four statistical moments: mean, variance, skewness, and kurtosis. The results show significant differences between groups in the mean of K and E, and the kurtosis of Cloc and K. Although not significant when considered alone, the skewness of Cloc is the most frequently selected feature for the discrimination of subject groups. These results suggest that the variability of EEG functional connectivity may convey useful information about AD.