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.

A self-attention model for cross-subject seizure detection.

Epilepsy is a neurological disorder characterized by recurring seizures, detected by electroencephalography (EEG). EEG signals can be detected by manual time-consuming analysis and recently by automatic detection. The latter poses a significant challenge due to the high dimensional and non-stationary nature of EEG signals. Recently, deep learning (DL) techniques have emerged as valuable tools for seizure detection. In this study, a novel data-driven model based on DL, incorporating a self-attention mechanism (SAT), is proposed. One notable advantage of the proposed method is its simplicity in application, as the raw signal data is directly fed into the suggested network without requiring expertise in signal processing. The model leverages a one-dimensional convolutional neural network (CNN) to extract relevant features from EEG signals. These features are then passed through a long short-term memory (LSTM) module to benefit from its memory capabilities, along with a SAT mechanism. The key contribution of this paper lies in the addition of the SAT layer to the LSTM encoder, enabling enhanced exploration of the latent mapping during the encoding step. Cross-subject experiments revealed good performance of this approach with F1-score of 97.8% and 92.7% for binary and five-class epileptic seizure recognition tasks, respectively, on the public UCI dataset, and 97.9% on the CHB-MIT database, surpassing state-of-the-art DL performance. Besides, the proposed method exhibits robustness to inter-subject variability.

Pulmonary embolism detection on venous thrombosis ultrasound images with bi-dimensional entropy measures: Preliminary results.

BACKGROUND: Venous thromboembolism (VTE) is a common health issue. A clinical expression of VTE is a deep vein thrombosis (DVT) that may lead to pulmonary embolism (PE), a critical illness. When DVT is suspected, an ultrasound exam is performed. However, the characteristics of the clot observed on ultrasound images cannot be linked with the presence of PE. Computed tomography angiography is the gold standard to diagnose PE. Nevertheless, the latter technique is expensive and requires the use of contrast agents. PURPOSE: In this article, we present an image processing method based on ultrasound images to determine whether PE is associated or not with lower limb DVT. In terms of medical equipment, this new approach (Doppler ultrasound image processing) is inexpensive and quite easy. METHODS: With the aim to help medical doctors in detecting PE, we herein propose to process ultrasound images of patients with DVT. After a first step based on histogram equalization, the analysis procedure is based on the use of bi-dimensional entropy measures. Two different algorithms are tested: the bi-dimensional dispersion entropy ( D i s p E n 2 D $DispEn_{2D}$ ) mesure and the bi-dimensional fuzzy entropy ( F u z E n 2 D $FuzEn_{2D}$ ) mesure. Thirty-two patients (12 women and 20 men, 67.63 ± 16.19 years old), split into two groups (16 with and 16 without PE), compose our database of around 1490 ultrasound images (split into seven different sizes from 32× 32 px to 128 × 128 px). p-values, computed with the Mann-Whitney test, are used to determine if entropy values of the two groups are statistically significantly different. Receiver operating characteristic (ROC) curves are plotted and analyzed for the most significant cases to define if entropy values are able to discriminate the two groups. RESULTS: p-values show that there are statistical differences between F u z E n 2 D $FuzEn_{2D}$  of patients with PE and patients without PE for 112× 112 px and 128× 128 px images. Area under the ROC curve (AUC) is higher than 0.7 (threshold for a fair test) for 112× 112 and 128× 128 images. The best value of AUC (0.72) is obtained for 112× 112 px images. CONCLUSIONS: Bi-dimensional entropy measures applied to ultrasound images seem to offer encouraging perspectives for PE detection: our first experiment, on a small dataset, shows that F u z E n 2 D $FuzEn_{2D}$  on 112× 112 px images is able to detect PE. The next step of our work will consist in testing this approach on a larger dataset and in integrating F u z E n 2 D $FuzEn_{2D}$  in a machine learning algorithm. Furthermore, this study could also contribute to PE risk prediction for patients with VTE.

Deep Learning and Entropy-Based Texture Features for Color Image Classification.

In the domain of computer vision, entropy-defined as a measure of irregularity-has been proposed as an effective method for analyzing the texture of images. Several studies have shown that, with specific parameter tuning, entropy-based approaches achieve high accuracy in terms of classification results for texture images, when associated with machine learning classifiers. However, few entropy measures have been extended to studying color images. Moreover, the literature is missing comparative analyses of entropy-based and modern deep learning-based classification methods for RGB color images. In order to address this matter, we first propose a new entropy-based measure for RGB images based on a multivariate approach. This multivariate approach is a bi-dimensional extension of the methods that have been successfully applied to multivariate signals (unidimensional data). Then, we compare the classification results of this new approach with those obtained from several deep learning methods. The entropy-based method for RGB image classification that we propose leads to promising results. In future studies, the measure could be extended to study other color spaces as well.

Colored Texture Analysis Fuzzy Entropy Methods with a Dermoscopic Application.

Texture analysis is a subject of intensive focus in research due to its significant role in the field of image processing. However, few studies focus on colored texture analysis and even fewer use information theory concepts. Entropy measures have been proven competent for gray scale images. However, to the best of our knowledge, there are no well-established entropy methods that deal with colored images yet. Therefore, we propose the recent colored bidimensional fuzzy entropy measure, FuzEnC2D, and introduce its new multi-channel approaches, FuzEnV2D and FuzEnM2D, for the analysis of colored images. We investigate their sensitivity to parameters and ability to identify images with different irregularity degrees, and therefore different textures. Moreover, we study their behavior with colored Brodatz images in different color spaces. After verifying the results with test images, we employ the three methods for analyzing dermoscopic images of malignant melanoma and benign melanocytic nevi. FuzEnC2D, FuzEnV2D, and FuzEnM2D illustrate a good differentiation ability between the two-similar in appearance-pigmented skin lesions. The results outperform those of a well-known texture analysis measure. Our work provides the first entropy measure studying colored images using both single and multi-channel approaches.

Overview on prediction, detection, and classification of atrial fibrillation using wavelets and AI on ECG.

Atrial fibrillation (AF) is the most common supraventricular cardiac arrhythmia, resulting in high mortality rates among affected patients. AF occurs as episodes coming from irregular excitations of the ventricles that affect the functionality of the heart and can increase the risk of stroke and heart attack. Early and automatic prediction, detection, and classification of AF are important steps for effective treatment. For this reason, it is the subject of intensive research in both medicine and engineering fields. The latter research focuses on three axes: prediction, classification, and detection. Knowing that AF is often asymptomatic and that its episodes are often very short, its automatic early detection is a very complicated but clinically important task to improve AF treatment and reduce the risks for the patients. This article is a review of publications from the past decade, focusing on AF episode prediction, detection, and classification using wavelets and artificial intelligence (AI). Forty-five articles were selected of which five are about AF in general, four articles compare accuracy, recall and precision between Fourier transform (FT) and wavelets transform (WT), and thirty-six are about detection, classification, and prediction of AF with WT: 15 are based on deep learning (DL) and 21 on conventional machine learning (ML). Of the thirty-six studies, thirty were published after 2015, confirming that this particular research area is very important and has great potential for future research.

Three-dimensional dispersion entropy for uterine fibroid texture quantification and post-embolization evaluation.

BACKGROUND AND OBJECTIVE: Uterine fibroids are benign tumors that could lead to symptoms complicating a patient's daily life. Those fibroids can be treated using uterine fibroid embolization (UFE), an effective non-surgical procedure. However, objectively quantifying the benefits of such a procedure, and the patient's quality of life, is rather challenging. METHODS: With a novel multiscale three-dimensional (3D) entropy-based texture analysis, the multiscale 3D dispersion entropy (MDispEn3D), this work aims to objectively quantify the evolution -  after UFE  -  of patients' health in terms of quality of life, symptoms severity, and sexual function. For this purpose, clinical data and magnetic resonance imaging (MRI) scans of fibroids are analyzed before UFE (D0), ten days after (D10), and six months after (M6). RESULTS: An inverse correlation is observed between MDispEn3D entropy values and both size and volume of fibroids. An inverse correlation is also observed between MDispEn3D at M6 and the scores of symptoms severity. Moreover, the patient age is found to be related to the relative difference of DispEn3D and MDispEn3D values, between D0 and M6, translating into an increasing entropy value. Furthermore, we show that history of fibroma plays a role in determining the obtained DispEn3D values at D0. Finally, we observe that the lower MDispEn3D values at D0, the larger the size of the fibroid at M6. CONCLUSIONS: The proposed MDispEn3D method - by quantifying fibroid texture - could assist the medical doctors in the prognosis of uterine fibroids and the patients' quality of life assessment post-UFE. It could therefore favor the choice of this treatment compared to other more invasive surgical treatments.

Multiscale Entropy Analysis of Short Signals: The Robustness of Fuzzy Entropy-Based Variants Compared to Full-Length Long Signals.

Multiscale entropy (MSE) analysis is a fundamental approach to access the complexity of a time series by estimating its information creation over a range of temporal scales. However, MSE may not be accurate or valid for short time series. This is why previous studies applied different kinds of algorithm derivations to short-term time series. However, no study has systematically analyzed and compared their reliabilities. This study compares the MSE algorithm variations adapted to short time series on both human and rat heart rate variability (HRV) time series using long-term MSE as reference. The most used variations of MSE are studied: composite MSE (CMSE), refined composite MSE (RCMSE), modified MSE (MMSE), and their fuzzy versions. We also analyze the errors in MSE estimations for a range of incorporated fuzzy exponents. The results show that fuzzy MSE versions-as a function of time series length-present minimal errors compared to the non-fuzzy algorithms. The traditional multiscale entropy algorithm with fuzzy counting (MFE) has similar accuracy to alternative algorithms with better computing performance. For the best accuracy, the findings suggest different fuzzy exponents according to the time series length.

Parameter Analysis of Multiscale Two-Dimensional Fuzzy and Dispersion Entropy Measures Using Machine Learning Classification.

Two-dimensional fuzzy entropy, dispersion entropy, and their multiscale extensions (MFuzzyEn2D and MDispEn2D, respectively) have shown promising results for image classifications. However, these results rely on the selection of key parameters that may largely influence the entropy values obtained. Yet, the optimal choice for these parameters has not been studied thoroughly. We propose a study on the impact of these parameters in image classification. For this purpose, the entropy-based algorithms are applied to a variety of images from different datasets, each containing multiple image classes. Several parameter combinations are used to obtain the entropy values. These entropy values are then applied to a range of machine learning classifiers and the algorithm parameters are analyzed based on the classification results. By using specific parameters, we show that both MFuzzyEn2D and MDispEn2D approach state-of-the-art in terms of image classification for multiple image types. They lead to an average maximum accuracy of more than 95% for all the datasets tested. Moreover, MFuzzyEn2D results in a better classification performance than that extracted by MDispEn2D as a majority. Furthermore, the choice of classifier does not have a significant impact on the classification of the extracted features by both entropy algorithms. The results open new perspectives for these entropy-based measures in textural analysis.

Evaluation of COVID-19 chest computed tomography: A texture analysis based on three-dimensional entropy.

Radiologists, and doctors in general, need relevant information for the quantification and characterization of pulmonary structures damaged by severe diseases, such as the Coronavirus disease 2019 (COVID-19). Texture-based analysis in scope of other pulmonary diseases has been used to screen, monitor, and provide valuable information for several kinds of diagnoses. To differentiate COVID-19 patients from healthy subjects and patients with other pulmonary diseases is crucial. Our goal is to quantify lung modifications in two pulmonary pathologies: COVID-19 and idiopathic pulmonary fibrosis (IPF). For this purpose, we propose the use of a three-dimensional multiscale fuzzy entropy (MFE3D) algorithm. The three groups tested (COVID-19 patients, IPF, and healthy subjects) were found to be statistically different for 9 scale factors ( p < 0.01 ). A complexity index (CI) based on the sum of entropy values is used to classify healthy subjects and COVID-19 patients showing an accuracy of 89.6 % , a sensitivity of 96.1 % , and a specificity of 76.9 % . Moreover, 4 different machine-learning models were also used to classify the same COVID-19 dataset for comparison purposes.

Machine learning for predictive data analytics in medicine: A review illustrated by cardiovascular and nuclear medicine examples.

The evidence-based medicine allows the physician to evaluate the risk-benefit ratio of a treatment through setting and data. Risk-based choices can be done by the doctor using different information. With the emergence of new technologies, a large amount of data is recorded offering interesting perspectives with machine learning for predictive data analytics. Machine learning is an ensemble of methods that process data to model a learning problem. Supervised machine learning algorithms consist in using annotated data to construct the model. This category allows to solve prediction data analytics problems. In this paper, we detail the use of supervised machine learning algorithms for predictive data analytics problems in medicine. In the medical field, data can be split into two categories: medical images and other data. For brevity, our review deals with any kind of medical data excluding images. In this article, we offer a discussion around four supervised machine learning approaches: information-based, similarity-based, probability-based and error-based approaches. Each method is illustrated with detailed cardiovascular and nuclear medicine examples. Our review shows that model ensemble (ME) and support vector machine (SVM) methods are the most popular. SVM, ME and artificial neural networks often lead to better results than those given by other algorithms. In the coming years, more studies, more data, more tools and more methods will, for sure, be proposed.

Three-Dimensional Multiscale Fuzzy Entropy: Validation and Application to Idiopathic Pulmonary Fibrosis.

Idiopathic Pulmonary Fibrosis (IPF) is a chronic, severe, and progressive lung disease with short life expectancy. Based on information theory and entropy measurement, a three-dimensional multiscale fuzzy entropy (MFE 3D) algorithm is proposed to identify IPF patients from their computed tomography (CT) volumetric data. First, the validation of the algorithm was performed by analyzing several volumetric synthetic noises (white, blue, brown, and pink), MIX(p) processes-based volumes, and texture-based volumes. The entropy values obtained by MFE 3D were consistent with the values obtained using the one, and two-dimensional versions, validating its use in biomedical data. Hence, MFE 3D was applied to CT scans to identify the existence of IPF within two different groups, one of healthy subjects (26) and another of IPF patients (26). Statistical differences were found (p < 0.05) between the entropy values of each group in 5 scale factors out of 10. These results demonstrate that MFE 3D could be an interesting metric to identify IPF in CT scans.

Age-related alterations on the capacities to navigate on a bike: use of a simulator and entropy measures.

Studying the impact of age is important to understand the phenomenon of aging and the disorders that are associated with it. In this work, we analyze age-related alterations on the capacities to navigate on a bike. For this purpose, we use CycléoONE, a bike simulator, and entropy measures. We thus record navigation data (handlebar angle and speed) during the ride. They are processed with two cross-distribution entropy methods (time-shift multiscale cross-distribution entropy and multiscale cross-distribution entropy). We also analyze the time series with a detrended cross-correlation analysis to determine which method can best underline age-related alterations. Our results show that methods based on cross-distribution entropy may be efficient to stress the decrease in navigation capacities with age. The results are very encouraging for our future goal of adding medical benefits to a leisure equipment. They also show the value of using virtual reality to study the impact of age. Graphical Abstract This study deals with the use of the signal processing methods (multiscale cross-entropy and multiscale cross-correlation) applied on naviagtion data, acquired with a bike simulator, to study the impact of age on two populations (young healthy subjects and older adults with loss of autonomy).

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.

Multichannel Time-Frequency Complexity Measures for the Analysis of Age-Related Changes in Neuromagnetic Resting-State Activity.

We propose new multichannel time-frequency complexity measures to evaluate differences on magnetoencephalograpy (MEG) recordings between healthy young and old subjects at rest at different spatial scales. After reviewing the Rényi and singular value decomposition entropies based on time-frequency representations, we introduce multichannel generalizations, using multilinear singular value decomposition for one of them. We test these quantities on synthetic data, illustrating how the introduced complexity measures focus on number of components, nonstationarity, and similarity across channels. Friedman tests are used to confirm the differences between young and old groups, and heterogeneity within groups. Experimental results show a consistent increase in complexity measures for the old group. When analyzing the topographical distribution of complexity values, we found clusters in the frontal sensors. The complexity measures here introduced seem to be a better indicator of the neurophysiologic changes of aging than power envelope connectivity. Here, we applied new multichannel time-frequency complexity measures to resting-state MEG recordings from healthy young and old subjects. We showed that these features are able to reveal regional clusters. The multichannel time-frequency complexities can be used to monitor the aging of subjects. They also allow a mutual information approach, and could be applied to a wider range of problems.

A New Mutual Information Measure to Estimate Functional Connectivity: Preliminary Study.

Functional Connectivity (FC) is a powerful tool to investigate brain networks both in rest and while performing tasks. Functional magnetic resonance imaging (fMRI) gave good spatial estimation of FC but lacked the temporal resolution. Electroencephalography (EEG) allows estimating FC with good temporal resolution. In this study we introduce a new method based on Mutual Information and Multivariate Improved Weighted Multi-scale Permutation Entropy to estimate FC of brain using EEG. We applied this method on resting-state EEG signals from healthy children. Using network measures of nodes and Wilcoxon signed-rank test, we identified the most important nodes in the estimated networks. Comparing the localization of those outstanding nodes with the regions involved in resting-state networks (RSNs) estimated from fMRI showed that our proposal is efficient in the identification of nodes belonging to RSNs and could be used as a general estimator for FC without having to band-pass the signals into frequency bands.

A Novel Multiscale Cross-Entropy Method Applied to Navigation Data Acquired with a Bike Simulator.

We present herein a new approach - the so-called time-shift multiscale cross-distribution entropy (TSMCDE) - to quantify the complexity between two sequences. By analyzing biomedical data, we reveal that TSMCDE over-performs other cross-entropy measures. Thus, TSMCDE, multiscale cross-sample entropy (MCSE), multiscale cross-distribution entropy (MCDE), and time-shift multiscale cross-sample entropy (TSMCSE) were applied to handlebar angle and speed time series recorded from a bike simulator. Twenty-four subjects divided into two groups (12 subjects each) participated to the study. The first group corresponds to young healthy subjects. The second group corresponds to older adults with loss of autonomy. Our results show that a link may exist between complexity and the age and physical state of a population. Moreover, TSMCDE leads to a better differentiation of the two groups than MCSE, MCDE, and TSMCSE. TSMCDE should now be tested on other types of data and on larger datasets to prove its usefulness and its efficiency.

Bidimensional Fuzzy Entropy: Principle Analysis and Biomedical Applications.

Since the 2010's, entropy measures have been extended from the 1D to the 2D case to deal with images and are forming potent bidimensional irregularity measures. In our work, we study a new 2D entropy measure - the so-called bidimensional fuzzy entropy (FuzEn2D) - that out-performs existing bidimensional entropy measures. We first assess its sensitivity to parameters, then analyze its behavior upon rotation and translation, and finally show its multiscale application in the biomedical field (dermoscopic images). To validate the output of the newly introduced FuzEn2D and its multiscale extension, a set of synthetic images based on several concepts in image processing (including power of noise and degree of randomness) and texture datasets are used. The results for synthetic images illustrate that FuzEn2D has low sensitivity to the chosen parameters and it is rotation and translation invariant. Moreover, it outperforms the already existing bidimensional entropy measures. Finally, we evaluate dermoscopic melanoma (malignant lesion) and melanocytic nevi (benign lesion) images and the results are found to be interesting for a potential diagnostic application.