Two-dimensional multiscale entropy analysis: applications to image texture evaluation

Complexity measures, defined as measures of irregularity over time scales, are the subject of a growing number of studies as the information they reveal can find utility in a large field of applications. One of the most popular complexity measures is the multiscale entropy. Nevertheless, more and more algorithms dedicated to complexity analyses are proposed to improve the existing ones. However, such measures are available only for one-dimensional time series. For bidimensional data (images), no equivalent algorithm has been proposed to analyze irregularity over spatial scales. We herein introduce a new framework that extends the one-dimensional multiscale entropy (MSE1D) to the bidimensional case (MSE2D). Moreover, a variant of MSE2D is also ModMSE2D). The two new algorithms are tested as new texture analysis frameworks. They are applied to simulated and real data. Our results show that, compared with other existing texture analysis algorithms, MSE2D and ModMSE2D are suitable and powerful tools for image analysis and classification according to their texture patterns. While MSE2D is computationally faster than ModMSE2D, ModMSE2D is more robust to small image sizes. The two methods present interesting performances, and can be as useful as their unidimensional versions in two-dimensional applications

Bi-dimensional multiscale entropy: Relation with discrete Fourier transform and biomedical application

The multiscale entropy (MSE1D) 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 MSE1D has been proposed (MSE2D) to analyze images. The interpretation of MSE2D curves and the applications to real data are still emergent. Because the coarse-graining step in the MSE2D computation changes the frequency content of the image, we hypothesized a possible dependence between MSE2D 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 MSE2D is sensitive to both the amplitude and phase of the DFT; ii) MSE2D could find applications in the biomedical field. This work brings valuable information for MSE2D interpretation and opens possibilities to study images from an entropy point of view through spatial scales

Comparison between spectral analysis and symbolic dynamics for heart rate variability analysis in the rat

Spectral analysis of heart rate (HR) has been widely used to assess the autonomic cardiovascular control. A nonlinear approach, known as symbolic analysis, has been reported to be very useful to assess the autonomic control of cardiovascular system in humans, but very few studies reported on the differences between these two approaches on experimental models. Two distinct approaches were used to elicit autonomic changes in conscious Wistar rats: (1) pharmacological blockade of cardiac autonomic receptors with atenolol (ATE, N\u2009=\u20099) or methylatropine (ATR, N\u2009=\u20099) and (2) mild changes in arterial pressure (AP) induced by phenylephrine (PHE, N\u2009=\u20099) or sodium nitroprusside (NPS, N\u2009=\u20099). Series of cardiac interval (CI) and systolic AP (SAP) were assessed using spectral analysis and symbolic dynamics. Results show that, for spectral analysis, the power in high frequency band of CI and the power in low frequency band of SAP are the most reliable indices of vagal and sympathetic modulation, respectively. For symbolic analysis, results point 0V% and 1V% to be related to sympathetic and 2UV% to vagal modulation. Interestingly, the incidence of 1V patterns, hitherto with unknown meaning, was revealed the best index of sympathetic modulation in the rat and should be accounted for in the future studies

Two-dimensional dispersion entropy: an information-theoretic method for irregularity analysis of images

Two-dimensional sample entropy (SampEn2D) is a recently developed method in the field of information theory for evaluating the regularity or predictability of images. SampEn2D, though powerful, has two key limitations: (1) SampEn2D values are undefined for small-sized images; and (2) SampEn2D is computationally expensive for several real-world applications. To overcome these drawbacks, we introduce the two-dimensional dispersion entropy (DispEn2D) measure. To evaluate the ability of DispEn2D, in comparison with SampEn2D, we use various synthetic and real datasets. The results demonstrate that DispEn2D distinguishes different amounts of white Gaussian and salt and pepper noise. The periodic images, compared with their corresponding synthesized ones, have lower DispEn2D values. The results for Kylberg texture dataset show the ability of DispEn2D to differentiate various textures. Although the results based on DispEn2D and SampEn2D for both the synthetic and real datasets are consistent in that they lead to similar findings about the irregularity of images, DispEn2D has three main advantages over SampEn2D: (1) DispEn2D, unlike SampEn2D, does not lead to undefined values; (2) DispEn2D is noticeably quicker; and (3) The coefficient of variations and Mann–Whitney U test-based p-values for DispEn2D are considerably smaller, showing the more stability of the DispEn2D results. Overall, thanks to its successful performance and low computational time, DispEn2D opens up a new way to analyze the uncertainty of images

Multiscale entropy analysis of heart rate variability in heart failure, hypertensive and sinoaortic-denervated rats : Classical and refined approaches

The analysis of heart rate variability (HRV) by nonlinear methods has been gaining increasing interest due to their ability to quantify the complexity of cardiovascular regulation. In this study, multiscale entropy (MSE) and refined MSE (RMSE) were applied to track the complexity of HRV as a function of time scale in three pathological conscious animal models: rats with heart failure (HF), spontaneously hypertensive rats (SHR), and rats with sinoaortic denervation (SAD). Results showed that HF did not change HRV complexity, although there was a tendency to decrease the entropy in HF animals. On the other hand, SHR group was characterized by reduced complexity at long time scales, whereas SAD animals exhibited a smaller short- and long-term irregularity. We propose that short time scales (1 to 4), accounting for fast oscillations, are more related to vagal and respiratory control, whereas long time scales (5 to 20), accounting for slow oscillations, are more related to sympathetic control. The increased sympathetic modulation is probably the main reason for the lower entropy observed at high scales for both SHR and SAD groups, acting as a negative factor for the cardiovascular complexity. This study highlights the contribution of the multiscale complexity analysis of HRV for understanding the physiological mechanisms involved in cardiovascular regulation

Inversão da sacarose utilizando ácido cítrico e suco de limão para preparo de dieta energética de Apis mellifera Linnaeus, 1758 Inversion of the sucrose using citric acid and lemon juice for preparing energetic diet of Apis mellifera Linnaeus, 1758

Em época de escassez de néctar, pode-se fornecer ao enxame uma suplementação alimentar utilizando "açúcar invertido" que é obtido pela hidrólise da sacarose em meio ácido por aquecimento, formando uma mistura de glicose e frutose. O ácido normalmente utilizado em tal reação é o ácido cítrico, no entanto, diante da dificuldade de pequenos produtores apícolas em obterem tal produto comercialmente, uma alternativa seria substituí-lo pela utilização de suco de limões. Sendo assim, o objetivo deste trabalho foi quantificar a inversão da sacarose em dietas para operárias de Apis mellifera, empregando-se o ácido cítrico e sucos de limões. Prepararam-se 21 soluções aquosas de açúcar cristal na proporção de 100 g/100 mL, colocando-se em cada uma 1,0; 2,0; 3,0; 5,0; 10,0; 15,0 ou 20,0 mL de suco dos limões Galego [Citrus aurantifolia (C.) Swingle], Tahiti [Citrus latifolia Tanaka] ou Cravo [Citrus limonia (L.) Osbeck]. Além dessas, outras seis soluções aquosas de açúcar na mesma proporção foram preparadas adicionando-se 0,1; 0,16; 0,3; 0,5 e 0,7 g de ácido cítrico e uma para testemunha. Quantificou-se a inversão pelo método de Somogyi-Nelson. Para o limão Cravo foi encontrada a menor porcentagem de inversão. Em relação a adição de ácido cítrico, constatou-se que ao colocar 0,1 g, a inversão foi estimada em 12,2% enquanto que, com a adição de 0,16 g, a inversão seria de 18,8%. A quantidade máxima de ácido cítrico a ser adicionada foi estimada em 0,18 g adotando como critério o pH médio de 3,3 dos méis de abelhas africanizadas. Para os sucos dos limões Galego, Tahiti e Cravo, quando utilizados como substitutos do ácido cítrico, estimou-se a quantidade máxima a ser adicionada sendo igual a 2,1; 3,6 e 5,3 mL, respectivamente, para cada 100 g de açúcar em 100 mL de água, para o pH fixado em 3,3. Considerando-se a inversão e o pH, o suco do limão Tahiti forneceu melhores resultados.<br>In times of nectar shortage, food supplementation using "inverted sugar" obtained by sucrose hydrolysis in an acid environment by heating can be supplied to the hive, forming a glucose and fructose mixture. The acid usually used in such a reaction is the citric acid, however, due to the difficulty that small producers have to obtain the product commercially, an alternative would be to replace it with lemon juice. The objective of this work was to quantify the inversion of sucrose present in Apis mellifera worker diets by employing commercial citric acid and lemon juice. A total of 21 aqueous solutions of granulated sugar at the proportion of 100 g/100 mL were prepared, placing in each one 1.0; 2.0; 3.0; 5.0; 10.0; 15.0 or 20.0 mL of the juices of the Galego [Citrus aurantifolia (C.) Swingle], Tahiti [Citrus latifolia Tanaka] or Cravo [Citrus limonia (L.) Osbeck] lemon varieties. In addition to those, six other aqueous sucrose solutions were prepared by adding 0.0 (control); 0.16; 0.3; 0.5 and 0.7 g citric acid. Sucrose inversion was quantified by using the Somogyi-Nelson method. For the Cravo lemon, the lowest inversion rate was found. Regarding the addition of citric acid, it was estimated that in placing 0.1 g, the inversion was of 12.2% while with 0.16 g, an inversion of 18.8% sucrose present in the solution. The maximum amount of citric acid to be added was estimated to be 0.18 g, adopting as a criterion the mean pH of 3.3 in Africanized bee honey. If Galego, Tahiti and Cravo lemon juices are used as replacements for the citric acid, the maximum added amount should be 2.1, 3.6 and 5.3 mL, respectively, for each 100 g sugar/100 mL water, at fixed pH of 3.3. Considering the inversion rate and pH level recommended for the use of citric acid, Tahiti lemon juice provides better results

Global perspective of familial hypercholesterolaemia: a cross-sectional study from the EAS Familial Hypercholesterolaemia Studies Collaboration (FHSC)

Background The European Atherosclerosis Society Familial Hypercholesterolaemia Studies Collaboration (FHSC) global registry provides a platform for the global surveillance of familial hypercholesterolaemia through harmonisation and pooling of multinational data. In this study, we aimed to characterise the adult population with heterozygous familial hypercholesterolaemia and described how it is detected and managed globally. Methods Using FHSC global registry data, we did a cross-sectional assessment of adults (aged 18 years or older) with a clinical or genetic diagnosis of probable or definite heterozygous familial hypercholesterolaemia at the time they were entered into the registries. Data were assessed overall and by WHO regions, sex, and index versus non-index cases. Findings Of the 61 612 individuals in the registry, 42 167 adults (21 999 [53·6%] women) from 56 countries were included in the study. Of these, 31 798 (75·4%) were diagnosed with the Dutch Lipid Clinic Network criteria, and 35 490 (84·2%) were from the WHO region of Europe. Median age of participants at entry in the registry was 46·2 years (IQR 34·3–58·0); median age at diagnosis of familial hypercholesterolaemia was 44·4 years (32·5–56·5), with 40·2% of participants younger than 40 years when diagnosed. Prevalence of cardiovascular risk factors increased progressively with age and varied by WHO region. Prevalence of coronary disease was 17·4% (2·1% for stroke and 5·2% for peripheral artery disease), increasing with concentrations of untreated LDL cholesterol, and was about two times lower in women than in men. Among patients receiving lipid-lowering medications, 16 803 (81·1%) were receiving statins and 3691 (21·2%) were on combination therapy, with greater use of more potent lipid-lowering medication in men than in women. Median LDL cholesterol was 5·43 mmol/L (IQR 4·32–6·72) among patients not taking lipid-lowering medications and 4·23 mmol/L (3·20–5·66) among those taking them. Among patients taking lipid-lowering medications, 2·7% had LDL cholesterol lower than 1·8 mmol/L; the use of combination therapy, particularly with three drugs and with proprotein convertase subtilisin–kexin type 9 inhibitors, was associated with a higher proportion and greater odds of having LDL cholesterol lower than 1·8 mmol/L. Compared with index cases, patients who were non-index cases were younger, with lower LDL cholesterol and lower prevalence of cardiovascular risk factors and cardiovascular diseases (all p<0·001). Interpretation Familial hypercholesterolaemia is diagnosed late. Guideline-recommended LDL cholesterol concentrations are infrequently achieved with single-drug therapy. Cardiovascular risk factors and presence of coronary disease were lower among non-index cases, who were diagnosed earlier. Earlier detection and greater use of combination therapies are required to reduce the global burden of familial hypercholesterolaemia. Funding Pfizer, Amgen, Merck Sharp & Dohme, Sanofi–Aventis, Daiichi Sankyo, and Regeneron