Trabecular Characteristics of Hypertrophic Cardiomyopathy Based on Cardiac Magnetic Resonance Fractal Analysis:A Preliminary Study / 中国医学影像学杂志

Purpose To evaluate the feasibility of cardiac magnetic resonance fractal analysis in evaluating left ventricular trabecular complexity in hypertrophic cardiomyopathy(HCM),and to study the degree of left ventricular trabecular complexity in HCM and the relationship between excessive trabecular complexity and cardiac function.Materials and Methods From August 2020 to December 2022,a total of 80 patients with HCM from the Second Affiliated Hospital of Nanchang University were retrospectively analyzed.Additionally,80 healthy volunteers were recruited as the control group.Left ventricular functional parameters and fractal dimension(FD)of left ventricular trabecular myocardium were measured.The differences of mean global FD,max basal FD and max apical FD were compared between the HCM group and the control group,the correlation between FDs and cardiac function parameters was evaluated.The diagnostic efficiency of mean global FD,max apical FD and max basal FD was analyzed via receiver operating characteristic curve.Results The mean global FD of HCM group was significantly higher than that of normal group,and the difference was statistically significant(1.303±0.047 vs.1.229±0.026;t=-12.387,P<0.001).Mean global FD showed the best performance in differentiating HCM from normal control group.The optimal cut-off value for the diagnosis of HCM was 1.251,with the area under curve of 0.933(95%CI 0.896-0.969).Mean global FD was positively correlated with maximum wall thickness and left ventricular mass index(r=0.686,0.687,P<0.001),and max apical FD was positively correlated with left ventricular ejection fraction(r=0.520,P<0.001).Conclusion The FD obtained by cardiac magnetic resonance fractal analysis technique is reproducible and has definite value in the diagnosis of HCM,with association with the structure and function of left heart.

Fractal dimension approach for quantitative analysis radiograph in periapical inflammation: A systematic review

Background and Objective@#Periapical inflammation on visual interpretation, especially in conditions of early inflammation, is very dependent on visual acuity. Visual ability can only detect if the inflammatory condition in the periapical area is more than 30%. This study reviewed the use of fractal dimension (FD) for quantitative assessment radiographs in periapical inflammation.@*Methods@#The search was performed using PubMed, Web of Science, and Scopus databases. The inclusion criteria were clinical research, the area was in the periapical inflammation, used the periapical radiograph, measured the fractal dimension in human bone, the article studies were in the English language. There was no restriction for publication date.@*Results@#Five articles were found in which fractal dimension was applied for the assessment of periapical lesions visually indiscernible in radiographs, for evaluation of apical inflammation, for imaging diagnosis of the periapical lesion, for analysis of trabecular bone, and for analysis of trabecular bone structure around the bone of periapical inflammation. Various sizes and sites of the regions of interest were used to evaluate the bone structure of periapical inflammation with fractal dimension.@*Conclusion@#Fractal dimension in Dentistry has been widely applied to the study of images. Periapical radiographs were the most frequently used. The Image J software and the fractal analysis method were extensively adopted in the studies reviewed herein. Further studies are encouraged to improve the use of fractal dimension in assessing quantitative radiographs in periapical inflammation.

Correlation study of retinal vascular morphological parameters with ischemic stroke / 中华眼底病杂志

Objective:To observe the morphological characteristics of retinal vessels in patients with ischemic stroke, and to preliminary analyze the correlation between retinal vascular morphological parameters and ischemic stroke.Methods:A retrospective study. From May 2015 to May 2017, 73 patients with ischemic stroke (ischemic stroke group) confirmed by examination at the Beijing Friendship Hospital, Capital Medical University were included in this study. In addition, 146 patients were included in the control group. A total of 146 patients with acute stroke who were excluded by head CT and/or magnetic resonance imaging were selected as the control group. Fundus images of patients were collected by nonmydriatic fundus camera. Retinal vascular parameters were measured by artificial intelligence fundus image analysis system, included retinal artery and vein caliber as well as vascular curvature, branching angle, fractal dimension, and density. The morphological characteristics of retinal vessels were compared between the control and ischemic stroke groups, and correlation between the retinal vascular parameters and ischemic stroke was analyzed using binary logistic regression.Results:Compared with the control group, the ischemic stroke group had thinner retinal artery caliber, smaller retinal vascular fractal dimension, and lower retinal vascular density; moreover, these differences were statistically significant ( t=3.232, 3.502, 3.280; P<0.05). Vascular fractal dimension [odds ratio ( OR)=0.291, 95% confidence interval ( CI) 0.160-0.528] and retinal artery caliber ( OR=0.924, 95% CI 0.870-0.981) were strongly correlated with ischemic stroke ( P<0.01). Conclusion:Compared with the control group, the retinal artery caliber, fractal dimension and retinal vascular density in ischemic stroke group are smaller; decreased retinal artery caliber and fractal dimension are correlated with ischemic stroke.

Fractal evaluation in retinographies of individuals with different grades of diabetic retinopathy / Avaliação fractal de retinografias de indivíduos com diferentes graus de retinopatia diabética

ABSTRACT Purpose To evaluate the retinal blood vascular network of the retinographies of patients with different grades of diabetic retinopathy. Methods Ninety Retinographies (MESSIDOR database) were used, with different grades of diabetic retinopathy divided into 4 groups: no retinopathy (n=23), grade one (n=20), grade two (n=20) and grade three (n=27) diabetic retinopathy. The grades of diabetic retinopathy were classified according to the number of microaneurysms, number of hemorrhages and the presence of neovascularization. The images were skeletonized and quantified by fractal methods: dimension of box-counting (Dbc) and information (Dinf). Results The means of Dbc values of groups were around 1.25, without statistically significant difference in the dimension values between groups for whole retina. There was also no statistical difference in Dinf values between groups, whose means ranged between 1.294 ± 0.013 (group of grade 1) and 1.3 ± 0.017 (group of grade 3). The retinographies were divided into regions of equal areas. The fractal values of some retinal regions showed statistical differences, but these differences were not enough to show the sensitivity of fractal methods in identifying diabetic retinopathy. Conclusion The fractal methods were not able to identify the different grades of diabetic retinopathy in retinographies.

RESUMO Objetivo Avaliar a rede vascular sanguínea da retina a partir de retinografias de pacientes com diferentes graus de retinopatia diabética. Métodos Foram utilizadas 90 retinografias (banco de dados MESSIDOR), com diferentes graus de retinopatia diabética divididas em quatro grupos: sem retinopatia (n=23), retinopatia diabética de grau um (n=20), grau dois (n=20) e grau três (n=27). Os graus de retinopatia foram classificados conforme o número de microaneurismas, número de hemorragias e presença de neovascularização. As imagens foram esqueletizadas e quantificadas pelos métodos fractais: dimensão da contagem de caixas e informação. Resultados As médias dos valores das dimensões de contagem de caixas para todos os grupos foram próximas a 1,25, sem diferença estatisticamente significativa nos valores das dimensões entre os grupos para retina inteira. Também não houve diferença estatística nos valores da dimensão de informação entre os grupos, cujas médias variaram entre 1,294 ± 0,013 (grupo do grau 1) e 1,3 ± 0,017 (grupo do grau 3). As imagens retinianas foram divididas em regiões de áreas iguais. Os valores fractais de algumas regiões retinais mostraram diferenças estatísticas, mas estas não foram suficientes para mostrar a sensibilidade dos métodos fractais na identificação da retinopatia diabética. Conclusão Os métodos fractais não foram capazes de identificar os diferentes graus de retinopatia diabética em retinografias.

Complexus cordis / Complexus cordis

Resumen El estudio científico del corazón nos ha permitido conocer su estructura y función profundamente, mediante la fragmentación y el análisis de sus partes, atendiendo a las pautas del método que tantos logros nos ha dado. Sin embargo, al momento de volver a ensamblar esos fragmentos analizados nos percatamos de que algo falta; simplemente la suma de las partes no hace al todo. Es así que, desde hace décadas, numerosos científicos han estudiado estrategias novedosas que permitan entender los fenómenos naturales desde modelos más incluyentes, abiertos e integradores, que atiendan con cercanía a las interacciones más que a los componentes. De esta manera, observamos que muchas variables suelen transgredir el plano convencional y parten hacia la no linealidad y la fractalidad, formando un tejido complejo que mantendrá su estructura mientras termodinámicamente sea viable. Así, en este documento se muestra la manera en que el estudio no lineal de la dinámica compleja cardiovascular comienza a darnos luz en muchas de las preguntas que a diario se plantea el cardiólogo clínico.

Abstract The science-based study of the heart has allowed us to know its structure and function deeply, through the fragmentation and analysis of its parts, following the guidelines that so many achievements have given to us. However, at the time of reassembling those analyzed fragments, we realize that something is missing; the simply sum of the parts is not equal to everything. Thus, for decades, numerous scientists have studied novel strategies that allow us understanding, every natural phenomena from a more inclusive, open and integrative models, which closely address to interactions rather than components. In this way, we can observe how, the behavior of many variables usually transgress the conventional plane and moves towards non-linearity and fractality, making a complex tissue that will maintain its structure while thermodynamically viable. Thus, this document shows the way how, the non-linear study of complex cardiovascular dynamics, begins to give us answers to many questions that the clinical cardiologist poses every day.

Caracterización geométrica de los eritrocitos nucleados de tilapia roja (Oreochromis spp) / Geometric characterization of nucleated erythrocytes of red tilapia (Oreochromis spp)

RESUMEN Introducción. En hematología, el estudio de las alteraciones de la morfología eritrocitaria contribuye con el diagnóstico de la normalidad o anormalidad de estas estructuras, sin embargo, el carácter cualitativo de los criterios diagnósticos dificulta su interpretación y alcance. Objetivo. Caracterizar los eritrocitos nucleados de tilapia roja (Oreochromis spp), en el contexto de la geometría fractal y euclidiana. Metodología. Se tomaron 50 eritrocitos nucleados de 20 extendidos de sangre de tilapia roja. Posteriormente todos los contornos del núcleo y el citoplasma de los eritrocitos fueron delineados, para superponer dos rejillas, una con el doble tamaño que la otra, para calcular mediante el método de Box Counting la dimensión fractal de cada eritrocito delineado. Adicionalmente fue calculada la superficie de estas dos partes del eritrocito. Resultados: Los resultados de este estudio revelaron que los valores de la dimensión fractal no permiten hacer comparaciones entre eritrocitos nucleados. Por su parte, la superposición de rejillas de 5x5 y 10x10 píxeles permitió observar que los valores de ocupación del citoplasma y el núcleo permiten hacer comparaciones entre los eritrocitos nucleados, junto con los valores de la superficie de estas dos partes del eritrocito nucleado. Conclusión: Los eritrocitos nucleados de tilapia roja pueden ser caracterizados mediante la medición de los valores espacios ocupados por su citoplasma y el núcleo, junto con los valores de la superficie de cada una de estas dos partes del eritrocito.

ABSTRACT Introduction. In hematology, the study of erythrocyte morphology alterations contributes to the diagnosis of normality or abnormality of these structures. However, the qualitative nature of the diagnostic criteria makes their interpretation and scope difficult. Objective. Characterize the nucleated erythrocytes of red tilapia (Oreochromis spp) in the context of fractal and Euclidean geometry. Methodology. Fifty nucleated erythrocytes were taken from twenty red tilapia blood smears. Subsequently, all the contours of the nucleus and the cytoplasm of the erythrocytes were delineated to superimpose two grids, one twice the size of the other, to calculate the fractal dimension of each delineated erythrocyte using the Box Counting method. Additionally, the surface of these two parts of the erythrocyte was calculated. Results: This study revealed that the fractal dimension values do not allow comparisons between nucleated erythrocytes. The superposition of 5x5 and 10x10 pixel grids allowed us to observe that the occupancy values of the cytoplasm and the nucleus allow comparisons between the nucleated erythrocytes, together with the values of the surface of these two parts of the nucleated erythrocyte. Conclusion: Red tilapia nucleated erythrocytes can be characterized by measuring the values of the spaces occupied by their cytoplasm and nucleus, together with the values of the surface of each of these two parts of the erythrocyte.

Fractal features of soil texture and physical attributes in indian dark earth under different uses in Western Amazon / Características fractais da textura e atributos físicos do solo em áreas com terra preta de índio sob diferentes usos na Amazônia Ocidental

Studying particle size distribution is important to understand soil structure and formation processes. This research aimed to assess the fractal dimension of soil texture in Indian Dark Earth (IDE) areas in southern Amazonas state under different land uses, as follows: two areas in the municipality of Apuí, one growing cocoa and the other coffee; a grassland area in the municipality of Manicoré; and a forest area in the municipality of Novo Aripuanã. A sampling grid containing 88 collection points (intersecting points on the grid) was established in each area, measuring 80 x 42 m for the cocoa and coffee-growing sites, and 80 x 56 m and 60 x 42 m for the grassland and forest areas, respectively. Soil samples were collected in soil core and as clumps at a depth of 0.0-0.20m to determine the structural physical properties and texture of the soil. The following physical attributes were assessed: texture (PSD), bulk density (BD), macroporosity (Macro), microporosity (Micro), total porosity (TP) and aggregate stability (GMD and WMD). The fractal dimension (D) of the soil texture was determined, followed by analysis of variance and comparison of the means using Tukey's test (p≤0.05). Pearson's correlation was applied to assess the correlation between variables. There was a significant difference between the IDEs studied, with a higher D value in the cocoa-growing area in relation to the other sites. Additionally, the larger the clay fraction, the higher the D value. Fractal dimension (D) showed a positive correlation with sand, clay, BD, Macro, GMD and WMD, and a negative correlation with silt, micro, TP. Based on the D values obtained, the ADE cultivated with cocoa showed superior quality in relation to the other areas studied.KEYWORDS: Fractal dimension. Soil physics. Soil use. INTRODUCTION Applications of fractal geometry in soil science have shown that soil exhibits fractal characteristics, being a porous medium having different particle compositions, with irregular shape and self-similar structure (TYLER; WHEATCRAFT, 1989; KRAVCHENKO; ZHANG, 1998). Fractal geometry, proposed and established by Mandelbrot (1982), is a method for describing systems with non-characteristic scales and self-similarity. In recent years, this theory has been used to quantitatively describe the particle size distribution of soil, attracting the interest of pedologists worldwide (DENG et al., 2017). Particle size distribution is one of the most important physical characteristics of soil because of its significant influence on water flow and soil erosion (XU; LI; LI, 2013). In this respect, broad and precise knowledge of particle size distribution is vital to understanding soil structures and formation, since it is closely related to soil erosion, organic matter content and moisture content (DU et al., 2017). Deng et al. (2017) studied the fractal features of soil particle size distribution and found an association between fractal dimensions and the physical and chemical properties of the soil analyzed, indicating that the lower the fractal dimension, the worse the soil physical and chemical properties. Recently, the fractal method was applied to estimate soil structure and proved to be an efficient tool in analyzing soil Received: 01/04/2019 Accepted: 30/01/2020

Estudar a distribuição do tamanho das partículas é importante para entender a estrutura do solo e os processos de formação. Esta pesquisa teve como objetivo avaliar a dimensão fractal da textura do solo em áreas de Terra Preta de Índio (TPI) no sul do Estado do Amazonas sob diferentes usos da terra: duas áreas no município de Apuí, uma com cultivo de cacau e outra de café; uma área de pastagem no município de Manicoré; e uma área florestal no município de Novo Aripuanã. Uma malha de amostragem contendo 88 pontos de coleta (pontos de interseção na grade) foi estabelecida em cada área, medindo 80 x 42 m para as áreas de cacau e café, e 80 x 56 m e 60 x 42 m para as áreas de pastagem e floresta, respectivamente. Amostras de solo foram coletadas em torrões a uma profundidade de 0,0-0,20 m para determinar as propriedades físicas estruturais e a textura do solo. Os seguintes atributos físicos foram avaliados: textura, densidade do solo (DS), macroporosidade (Macro), microporosidade (Micro), porosidade total (PT) e estabilidade de agregados (DMG e DMP). Determinou-se a dimensão fractal da textura do solo (D), seguida da análise de variância e comparação das médias pelo teste de Tukey (p≤0,05). A correlação de Pearson foi aplicada para avaliar a correlação entre as variáveis. Houve uma diferença significativa entre as TPIs estudadas, com um maior valor D na área de cultivo de cacau em relação aos outros locais. Além disso, quanto maior a fração argila, maior o valor de D. A dimensão fractal (D) apresentou correlação positiva com areia, argila, DS, Macro, DMG e DMP, e correlação negativa com silte, micro, PT. Com base nos valores de D obtidos, as TPIs cultivadas com cacau apresentaram qualidade superior em relação às demais áreas estudadas.PALAVRAS-CHAVES: Dimensão Fractal. Física do solo. Uso do solo. REFERENCES ALVARENGA, R. C.; FERNANDES, B.; SILVA, T. C. A.; RESENDE, M. Estabilidade de agregados de um Latossolo Roxo sob diferentes métodos de preparo do solo e de manejo da palha do milho. Revista Brasileira de Ciência do Solo, Viçosa, v. 10, n. 2, p. 273-277, 1986.

Comportamiento estocástico de la COVID-19 en la República Bolivariana de Venezuela. ¿Persistencia o antipersistencia en los contagios? / Stochastic behavior of covid-19 in the Bolivarian Republic of Venezuela: persistence or antipersistence in infections?

La novedosa pandemia por coronavirus, etiquetada por la Organización Mundial de la Salud OMS, 2020) como la covid-19, se reportó por primera vez en Wuhan, China, el 31 de diciembre de 2019 y a la fecha, según estimaciones de la misma OMS (2020), en la medida en que se ha extendido a nivel planetario, ha infectado a más de 9,2 millones de personas, de las cuales se reportan más de 500.000 fallecidos y 5.2 millones de pacientes recuperados. En este estudio, aplicaremos el exponente de Hurst (1951) asociado con la estadística fractal para simular la propagación de la covid-19, considerando series temporales de fluctuaciones de nuevos casos diarios de la enfermedad, disponibles a través de un sitio web de referencia de la República Bolivariana de Venezuela, como lo es el Observatorio Nacional de Ciencia, Tecnología e Innovación (ONCTI). Se parte de la hipótesis de que la propagación de la covid-19, puede analizarse en función de las fluctuaciones del crecimiento de nuevos casos diarios de contagio. Para ello, se empleó un método de rango reescalado R/S que permitió calcular el Exponente de Hurst, parámetro estocástico cuyo valor permitió inferir sobre la presencia de correlaciones de largo alcance en la transmisión del virus entre la población. Estudiaremos los efectos de correlación en la propagación de COVID-19 en Venezuela mediante el análisis de las series temporales de nuevos casos después del decreto de Alerta dictado por el Ejecutivo Nacional que convocó a la ciudadanía a "quedarse en casa" mediante una cuarentena social obligatoria. Simularemos el comportamiento a mediano plazo (180 días) considerando las fluctuaciones de los nuevos casos de contagio diarios sobre la base de dos factores: los casos de contagio importados y los contagios comunitarios. En consecuencia, inicialmente examinaremos el origen de correlaciones con grandes fluctuaciones, y posteriormente analizaremos en base a las series de tiempo de nuevos casos diarios de la covid-19 en Venezuela, para luego establecer las correlaciones de largo alcance e inferir sobre la posible la persistencia o antipersistencia de la misma(AU)

The novel coronavirus pandemic, labeled by the World Health Organization (WHO) as Covid-19, was first reported in Wuhan, China, on December 31, 2019. To date, according to the WHO's estimates, it has infected more than 9.2 million people, of whom more than 500,000 are reported dead, and 5.2 million patients have recovered. To deepen in its study, we apply the Hurst exponent, associated with fractal statistics to simulate the spread of Covid-19, considering time series of fluctuations of new daily cases, which are available in a site reference website of the Bolivarian Republic of Venezuela, such as the National Observatory for Science, Technology, and Innovation (ONCTI). This work starts from the hypothesis that the spread of Covid-19 can be analyzed based on the fluctuations in the increase of new daily cases. For this, an R / S rescaled range method was used that allowed calculating the Hurst Exponent, a stochastic parameter whose value allowed inferring the presence of long-range correlations in the virus transmission among the population. We will study the correlation effects in the spread of COVID-19 in Venezuela by analyzing the time series of new cases after the alert decree issued by the Executive branch, which called on citizens to "stay at home" through a mandatory social quarantine. Consequently, initially, we will examine the origin of correlations with large fluctuations, followed by an analysis based on the time series of new daily cases of Covid-19 in Venezuela, in order to establish the long-range correlations and infer about the possible persistence or anti persistence of it(AU)

Efecto del patrón de flujo sobre las pérdidas de presión para flujo bifásico a través de lechos porosos bajo perspectiva fractal / Flow pattern effect on the pressure drop of biphasic flow through porous media from a fractal dimension perspective

Resumen La descripción del comportamiento de un flujo bifásico, a través de lechos porosos, por medio de modelos, basados en las ecuaciones de fenómenos de transporte, se dificulta debido a la irregularidad geométrica de los canales que se forman entre las partículas sólidas que constituyen el lecho. Los modelos deterministas desarrollados para flujos monofásicos requieren del ajuste de constantes empíricas y no pueden extrapolarse a flujos bifásicos, donde el patrón de flujo generado en el sistema influye significativamente sobre el comportamiento del flujo total y las pérdidas de presión por fricción. Por lo anterior, en este trabajo se presenta un modelo para describir el comportamiento del flujo bifásico en función del patrón de flujo y de la morfología, las dimensiones y las condiciones de operación del lecho poroso, cuya obtención se basó en un formalismo, empleando conjuntamente las ecuaciones de conservación de la cantidad de movimiento, la geometría fractal y el cálculo diferencial fraccional. El modelo predice que, para una misma composición del flujo bifásico, el patrón de flujo influye significativamente sobre las pérdidas de presión por fricción, habiendo un incremento cuando una de las fases se encuentra dispersa en el seno de la otra. Por otro lado, el incremento de la dimensión fractal de los poros causa a su vez un incremento de las pérdidas de presión por fricción. El modelo presenta limitaciones asociadas a las consideraciones establecidas durante su obtención, de tal manera que sólo es válido cuando los efectos de la tensión superficial son más significativos que los gravitatorios, despreciándose los efectos de esos últimos sobre el patrón de flujo, así como para el estado estacionario.

Abstract The description of the behavior of a biphasic flow through porous beds by means of models based on the equations of transport phenomena is made difficult due to the geometric irregularity of the channels that are formed between the solid particles that make up the bed. Deterministic models developed for single-phase flows require the adjustment of empirical constants and cannot be extrapolated to biphasic flows, where the flow pattern generated in the system significantly influences the behavior of the total flow and the frictional pressure losses. Therefore, in this paper, we present a model to describe the behavior of the biphasic flow in relation to the flow pattern and the morphology, dimensions, and operating conditions of the porous bed, whose obtainment was based on a hierarchy that used the equations for conservation of momentum, fractal geometry and fractional differential calculus jointly. The model predicts that, for the same composition of the biphasic flow, the flow pattern significantly influences friction pressure losses, with an increase when one of the phases is dispersed within the other. On the other hand, the increase in the fractal dimension of the pores, in turn, causes an increase in pressure loss due to friction. The model has limitations associated with the considerations established during its collection, since it is only valid when the effects of surface tension are more significant than the gravitational effects, the effects of the latter being disregarded on the flow pattern, as well as for the stationary state.

Effect of ethanol to material ratio on ethanol precipitation and sediment morphology of Shuanghuanglian preparation / 中草药

Objective: The effect of ethanol to material ratio on ethanol precipitation and sediment morphology of Shuanghuanglian preparation (SHLP) were researched, and the feasibility of comprehensive evaluation of ethanol precipitation sediment fractal dimension was discussed. Methods: For the SHLP ethanol precipitation process, HPLC and gravimetric analysis were used to investigate the effects of ethanol to material ratio on the overall retention of the index components and the liquid content of the filter cake. The direct observation, atomic force microscope observation and "area-perimeter" calculation method were used to investigate the influence of ethanol to material ratio on the apparent morphology, micro-morphology and fractal dimension of the precipitate. At the same time, Pearson correlation analysis method was used to investigate the correlation between the fractal dimension and the above evaluation index of ethanol precipitation effect. Results: With the increase of the ethanol to material ratio, the comprehensive retention of the index components and the fractal dimension of the ethanol precipitation precipitates was gradually increased, while the liquid content of the filter cake was gradually decreased. Therefore, the fractal dimension of sediment was positively correlated with the comprehensive retention rate of index components, but negatively correlated with the liquid content of the filter cake. Conclusion: The fractal dimension of ethanol precipitation sediment can be used as comprehensive evaluation index for reflecting the ethanol precipitation effect in the SHLP ethanol precipitation process, which can provide a reference for the visualized fine control research of the subsequent SHLP ethanol precipitation process.

Means of communication for visually impaired people. Fractalyphlotechnologies of data communication

This article describes technical means of data communication for blind and visually impaired people. Radically new method of haptic and fingerspelling data coding is proposed based on fractal self-similarity of binary code. It would be possible to develop numerous typhlo-appliances at reasonable and low price, thus simplifying teaching Braille system both in conventional, manual, and computer variants. Coding of typhlodata on the basis of fractal self-similarity is referred to as fractal Braille. On the basis of fractal self-similarity of binary code, the concept of haptic and fingerspelling alphabet has been developed which combines essentially different methods of data coding in a single morphological base.

Evaluación física de la dinámica cardiaca durante 18 horas mediante una ley matemática / Physical evaluation of cardiac dynamics for 18 hours by a mathematical law

Resumen OBJETIVO: Evaluar la dinámica cardiaca durante 18 horas mediante una ley matemática desarrollada en el contexto de la teoría de los sistemas no lineales y la geometría fractal, aplicada originalmente para evaluar la dinámica en 21 horas. MATERIAL Y MÉTODO: Estudio retrospectivo en el que se realizó una inducción matemática con ocho registros electrocardiográficos continuos y ambulatorios con dinámicas normales y patológicas, efectuado de enero a diciembre de 2017. Se tomaron las cifras de la frecuencia cardiaca de cada registro y con ella se simuló una secuencia durante 18 horas para construir el atractor de la dinámica cardiaca. Se calculó la dimensión fractal de cada atractor y su ocupación espacial, para luego aplicar parámetros que diferenciaban entre dinámicas cardiacas normales de enfermas agudas. Se realizó este mismo procedimiento con 32 dinámicas cardiacas normales y con diferentes afecciones cardiacas, determinando su diagnóstico matemático en 18 horas y calculando sensibilidad, especificidad y coeficiente Kappa. RESULTADOS: Se diferenciaron sujetos con dinámicas cardiacas caóticas normales de agudas mediante los espacios de ocupación de los atractores evaluados con la ley matemática en 18 horas, que mostraron valores en la rejilla Kp entre 258 y 366 en normalidad y 43 y 195 en enfermedad aguda. CONCLUSIÓN: La ley desarrollada permitió diagnosticar en 18 horas, aun en casos en que las dinámicas cardiacas no mostraran manifestaciones clínicas.

Abstract OBJECTIVE: To evaluate the cardiac dynamic for 18 hours through a mathematical law developed in the context of nonlinear systems theory and fractal geometry that originally evaluated the dynamics in 21 hours. MATERIAL AND METHOD: A retrospective study was done performing a mathematical induction with 8 normal and pathological continuous and ambulatory electrocardiographic records from January to December 2017. From each registry, values of heart rate frequency were taken to simulate a sequence for 18 hours to build the attractor of the cardiac dynamic. Then, the fractal dimension of the attractors as well as their occupation spaces were calculated to later apply parameters that differentiated between normal cardiac dynamics from the pathological ones. The same procedure was performed with 32 normal and pathological cardiac dynamics, determining its mathematical diagnosis in 18 hours, calculating its sensibility, specificity and Kappa coefficient. RESULTS: Subjects with normal chaotic dynamics were differentiated from the acute ones through occupation spaces calculated from the attractors evaluated with the mathematical law in 18 hours, which presented values in the Kp grid between 258 to 366 for normality and 43 to 195 for acute disease. CONCLUSION: The developed law allowed to diagnose in 18 hours even in cases where the abnormal cardiac dynamics presented no clinical manifestations.

Ley exponencial de la dinámica cardiaca caótica aplicada a 18 horas / Exponential law of chaotic cardiac dynamics applied to 18 hours

Resumen Introducción: La aplicación de una ley exponencial para los sistemas dinámicos caóticos cardiacos ha sido reducida a 18 horas para el análisis del Holter, cuantificando las dinámicas cardiacas normales y patológicas, así como la evolución entre estos estados. Metodología: Se analizaron 80 registros electrocardiográficos, 15 con dinámicas normales y 65 con diferentes patologías. Se construyó un atractor caótico para cada dinámica cardiaca a partir de la simulación de la secuencia de las frecuencias cardiacas durante 18 horas, posteriormente se halló la dimensión fractal de cada atractor y su ocupación espacial. Los parámetros diferenciadores de la ley caótica exponencial fueron aplicados diferenciando dinámicas cardiacas normales de aquellas patológicas, finalmente se calculó la sensibilidad, especificidad y coeficiente Kappa. Resultados: Las dinámicas normales presentaron espacios de ocupación por encima de 200 en la rejillla Kp, y para la rejilla Kg por encima de 67. Para los casos de enfermedad aguda los valores en las rejillas Kp y Kg estuvieron por debajo de 73 y 22 respectivamente. Los valores de sensibilidad y especificidad fueron de 100% y el coeficiente Kappa fue de 1. Conclusión: La aplicación de la ley exponencial durante 18 horas mostro que fue posible caracterizar matemáticamente las dinámicas cardiacas, permitiendo reducir el tiempo de evaluación.

Abstract Introduction: The application of an exponential law for chaotic dynamic cardiac systems has been reduced to 18 hours for Holter analysis, quantifying normal and pathological cardiac dynamics, as well as the evolution between these states. Methodology: 80 electrocardiographic records were analyzed, 15 with normal dynamics and 65 with different pathologies. A chaotic attractor was constructed for each cardiac dynamic based on the simulation of the cardiac frequency sequence for 18 hours, after the fractal dimension of each attractor and its spatial occupation were found. The differentiating parameters of the chaotic exponential law were applied differentiating normal cardiac dynamics from those pathological, finally the sensitivity, specificity and Kappa coefficient were calculated. Results: The normal dynamics presented occupancy spaces above 200 in the Kp grid, and for the Kg grid above 67. In the cases of acute disease, the values in the Kp and Kg grids were below 73 and 22 respectively. The values of sensitivity and specificity were 100% and the Kappa coefficient was 1. Conclusion: The application of the exponential law for 18 hours showed that it was possible to characterize mathematically the cardiac dynamics, allowing reducing the time of evaluation.

Analysis of characteristics and influencing factors of fine particulate matters and submicron particulate matters in printing shop / 中华预防医学杂志

Objective@#To analyze the physical characteristics of fine particulate matters (PM2.5) and submicron particulate matters (PM1), and investigate the factors influencing the emission peak of printer particles.@*Methods@#A 12-hour particle concentration monitoring for PM2.5 and PM1 was conducted in a printing shop on January 5th, 2018. PM2.5 in the air was analyzed after the monitoring process to figure out morphological characteristics and element composition of printer particles. Besides, experiments were carried out in an enclosed space to detect the number concentration peaks of PM1 during every printing process. Influencing factors investigated in this study were printer types, toner coverages and interval time between different printing processes.@*Results@#The 12-hour particles concentration monitoring showed that the number concentration of PM1 and the mass concentration of PM2.5 were 7.510×104 pt/cm3 and 96.85 μg/m3. The diameter of most PM2.5 was less than 100 nm, with a fractal dimension of 2.591. Most PM2.5 appeared as regular spheres with typical agglomeration phenomenon, while some were in rhabditiform or irregular shapes. Element analysis showed that PM2.5 was mainly composed of C, O, Si, Ca, with less metallic element. The PM1 emission peak values of three printers were 3.60×104, 3.43×104, 0.31×104 pt/cm3, respectively and the difference was not statistically significant (χ2=5.42, P>0.05). When the page coverage rate was 0%, 2.5%, 5%, 10%, 20% and 50%, the PM1 emission peak value of printer A was 6.74×104, 4.62×104, 3.82×104, 2.82×104, 1.00×104 and 1.08×104 pt/cm3, and the difference was also not statistically significant (χ2=7.01, P>0.05). The natural logarithm of PM1 emission peak value in printing work was associated with the resting time before printing and the change value of heating roller temperature (r value was 0.83 and 0.89, respectively, all P values<0.05).@*Conclusion@#PM2.5 and PM1 in the printing shop stayed at a high level. Particles appeared as various shapes and element compositions were complex. The temperature change of heating roller was one of most important factors that lead to the increased number concentration peak of PM1.

Establishment of Determination of Fractal Dimension of Ethanol-precipitated Flocs of Two Root Medicinal Herbs / 中国实验方剂学杂志

Objective: To establish a method for the determination of fractal dimension of ethanol precipitation flocs in two kinds of root medicinal herbs (Astragali Radix and Isatidis Radix). Method: The ethanol-precipitated flocs of Astragali Radix and Isatidis Radix were taken as the research objects. Firstly, the original microscopic images of the ethanol precipitation flocs were binarized by Ostu algorithm. Secondly, the influence of sampling volume, dilution multiple, image magnification ratio and number of image acquisition sites on fractal dimension was investigated using perimeter-area method. Result: The ethanol precipitation flocs of Astragali Radix and Isatidis Radix had fractal characteristics. At the same time, the stable and reliable fractal dimension of the flocs could be obtained when the sampling volume was 600-800 μL, the sample was diluted to 5-20 times, the microscopic image was enlarged to 200 times or 400 times, and four different image acquisition sites were selected. Conclusion: The established method is stable and feasible, which can provide reference for the fractal theory of ethanol precipitation flocs of root medicinal herbs.

Effect of Fractal Tones on the Improvement of Tinnitus Handicap Inventory Functional Scores among Chronic Tinnitus Patients: An Open-label Pilot Study

Abstract Introduction Music-based sound therapies become recently a trend in the treatment of tinnitus. Few publications have studied the therapeutic use of fractal tones to treat chronic tinnitus. Objective The aim of this study was to determine the benefits of using fractal tones as a unique sound therapy for chronic tinnitus sufferers. Methods Twelve participants were recruited; however, six could not be assigned. At baseline and at 1, 3 and 6 months, the participants were provided with the Tinnitus Handicap Inventory (THI) and Hearing Handicap Inventory for Adults (HHIA) questionnaires, and their visual analog scale score was recorded. Tinnitus pitch and loudness matching was performed before fitting and after 6 months of use. Results The visual analog scale (VAS) score, pitch and loudness matching and minimal masking levels did not result in significant improvement at the end of the treatment. The mean THI measured at baseline was 45, and the final one was 25. A paired sample t-test showed that this 20-point difference was statistically significant. Conclusions We measured the benefits of using fractal tone therapy for the treatment of chronic tinnitus and found that most of the benefits were in the THI functional domain, which includes concentration, reading, attention, consciousness, sleep, social activities, and household tasks. For all patients with bothersome chronic tinnitus and high scores on the THI functional scale, fractal tones should be considered a promising initial sound therapy strategy. The findings from this open-label pilot study are preliminary, and further trials are needed before these results can be generalized to a larger tinnitus population.

Evaluación del comportamiento cardíaco mediante una metodología diagnóstica basada en sistemas dinámicos en 16 horas / Evaluation of the cardiac behaviour with a diagnostic methodology sustained in dynamical systems in 16 hours

Antecedentes: Con conceptos provenientes de la teoría de sistemas dinámicos y la geometría fractal, se ha logrado caracterizar el comportamiento de la dinámica cardíaca, dando resultados objetivos y estableciendo distinciones entre estados de normalidad y enfermedad. Objetivo: Aplicar una ley matemática exponencial de la dinámica cardíaca, inscrita en el contexto de los sistemas dinámicos y la geometría fractal, para evidenciar su utilidad diagnóstica en 16 horas. Materiales y métodos: Fueron empleados 200 Holters y registros electrocardiográficos continuos, entre normales y con diferentes alteraciones cardíacas. Se simuló una secuencia de frecuencias cardíacas en 16 y 21 horas, con la cual se construyó el atractor de cada dinámica. También se calculó la dimensión fractal y la ocupación de los atractores en el espacio fractal. Se estableció el diagnóstico físico-matemático en 16 y 21 horas y la subsecuente validación estadística. Resultados: Fueron obtenidos valores en la rejilla Kp entre 44 y 198 para estados patológicos y entre 221 y 377 para estados de normalidad en 16 horas, la sensibilidad y especificidad fue del 100% y el coeficiente Kappa de 1. Conclusión: Se logró diferenciar de manera adecuada estados normales de patológicos mediante la ley exponencial aplicada en registros de 16 horas

Background: With concepts derived from dynamical systems theory and fractal geometry, it has been possible to characterize the behavior of the cardiac dynamics, giving objective results and estabishing distinctions between states of normality and disease. Objective: To apply an exponential mathematical law of cardiac dynamics, inscribed in the context of dynamical systems and fractal geometry, to demonstrate its diagnostic utility in the context of a reduction in the evaluation time, originally of 21 hours. Materials and methods: There were used 200 Holters and cotinuous electrocardiographic records, between normal and with different cardiac alterations. A sequence of heart rates was simulated in 16 and 21 hours, with which the attractor of each dynamic was constructed. There were also calculated the fractal dimension and the occupation of the attractors in the fractal space. The physical-mathematical diagnosis was establishd at 16 and 21 hours, and the staqtistical validation was performed. Results: Values obtained in the Kp grid were between 44 y 198 for pathological sttes, and between 221 and 377 for normal states in 16 hours. The sensitivity and specificity was 100% and the Kappa coefficient was 1. Conclusion: It was possible to differentiate adequately normal states of pathological by means fo the exponential law applied in registers of 16 hours

Diagnostic methodology of cardiac dynamics based on the Zipf-Mandelbrot law: evaluation with 50 patients / Metodología diagnóstica de la dinámica cardiaca basada en ley de Zipf-Mandelbrot: evaluación con 50 pacientes

Abstract: Objective: Zipf-Mandelbrot law has been used to assess the complexity of cardiac systems. The objective of this work is to corroborate the clinical applicability of a diagnostic methodology developed from Zipf-Mandelbrot law, in the differentiation of normality and acute cardiac disease. Material and methods: there were taken 50 continuous electrocardiographic Holter monitoring records, 20 normal and 30 with acute alterations of the cardiac dynamics. The frequencies of occurrence of heart rates in ranges of 15 lat/min were organized hierarchically to demonstrate the hyperbolic behavior of dynamics and to apply the Zipf-Mandelbrot law. A linearization was performed and the statistical fractal dimension of each dynamic was obtained, giving rise to the mathematical diagnosis. Sensitivity, specificity and Kappa coefficient were calculated. Results: The values of the statistical fractal dimension of the acute cardiac dynamics were between 0.7123 and 0.9327, whereas for the normal dynamics were found between 0.4253 and 0.6698, evidencing quantitative differences between states of normality and disease. Sensitivity and specificity values of 100% were found and the kappa coefficient was 1. Conclusions: The clinical and diagnostic utility of the mathematical methodology based on Zipf-Mandelbrot law was verified, observing a decrease of dynamics complexity in cases of acute heart disease.(AU)

Resumen: Objetivo: La ley de Zipf-Mandelbrot ha sido utilizada con el fin de evaluar la complejidad de los sistemas cardiacos. El objetivo de este trabajo es corroborar la aplicabilidad clínica de una metodología diagnóstica desarrollada a partir de la ley de Zipf-Mandelbrot, en la diferenciación de normalidad y enfermedad cardiaca aguda. Material y métodos: Se tomaron 50 Holter cardiacos (monitoreo electrocardiográfico continuo ambulatorio), 20 normales y 30 con alteraciones agudas de la dinámica cardiaca. Se organizaron jerárquicamente las frecuencias de aparición de frecuencias cardiacas en rangos de a 15 lat/min, para evidenciar el comportamiento hiperbólico de las dinámicas y aplicar la ley de Zipf-Mandelbrot. Se realizó una linealización y se obtuvo la dimensión fractal estadística de cada dinámica, dando lugar al diagnóstico matemático. Fueron calculadas la sensibilidad, especificidad y el coeficiente Kappa. Resultados: Los valores de la dimensión fractal estadística de las dinámicas cardiacas agudas se encontraron entre 0.7123 y 0.9327, mientras que para las dinámicas normales se hallaron entre 0.4253 y 0.6698, evidenciando diferencias cuantitativas entre estados de normalidad y enfermedad. Se encontraron valores de sensibilidad y especificidad del 100% y el coeficiente kappa fue de 1. Conclusiones: Fue comprobada la utilidad clínica y diagnóstica de la metodología matemática basada en la ley de Zipf-Mandelbrot, observando un decremento de la complejidad de la dinámica en casos de enfermedad cardiaca aguda.(AU)

Fractal Characterization and Classification Characteristics of the Artificial Joint Wear Particles / 医用生物力学

Objective To study the morphology and fractal characterization of UHMWPE wear particles by simulation experiment on knee joint, analyze the classification characteristics of wear particles and discuss the correlation between fractal dimension and wear state. Methods The knee joint simulator was used to realize the knee joint wear motion. The forged CoCrMo alloy and UHMWPE were selected as artificial joint prosthesis materials. The wear particle extraction was based on ISO 17853. The automatic extraction and fractal identification system of wear particles were used to investigate fractal characteristics of wear particles. Three kinds of models were established to classify and recognize wear particles, by using the meshing method, cluster analysis and genetic simulated annealing algorithm, respectively. Results The fractal characteristics of UHMWPE single wear particles was very obvious. The fractal dimension calculated by radar fractal method decreased, during the transition from the larger size of strip debris to the smaller size of roundness debris, and the fractal dimension D of spherical debris was close to zero. The weighted sum of squared error values of fractal dimension for wear particle population classification was the smallest by the model of genetic simulated annealing algorithm, and the clustering feature was very obvious. When the wear cycles were low, the large fractal dimension of strip, needle and fibrous abrasive debris with larger fractal dimension had the largest proportion, and the main abrasion modes were the ploughing and spalling wears. With the extension of wear period, the proportion of wear particles with large fractal dimension decreased, and the proportion of flaky, blocky and near-spherical wear particles with low fractal dimension increased clearly. The wear mechanism changed to the fatigue and adhesive wear, and the wear state transited to the composite wear period. During the stable wear period, the proportion of all kinds of abrasive grains changed little. Due to the increase in the number of small particles, the fractal dimension decreased in stable wear state. Conclusions Based on the improved radar graph method, the fractal dimension of wear particles with different profiles could be obtained by automatic extraction and fractal identification system of wear particles. The research findings can be used in shape extraction, fractal dimension calculation and parameter statistics, as well as providing a new digital analysis tool for identification and diagnosis for wear particles of artificial prosthesis.

A new method of synthesizing personalized tinnitus rehabilitation sound based on iterative function system algorithm / 生物医学工程学杂志

Tinnitus is a common clinical symptom. Researches have shown that fractal sound can effectively treat tinnitus. But current fractal sound is usually synthesized based on constant notes via fractal algorithm, which lead to monotony of synthesized fractal sound. So it is difficult to achieve personalized match. Clinical datas have confirmed that it is common to match tinnitus sound with nature sound and it has a good effect on regulating negative emotion and relieving tinnitus via some natural sound. Therefore, a new method of personalized synthesizing tinnitus rehabilitation sound based on iterative function system (IFS) fractal algorithm is proposed in this paper. This method firstly generates personalized audio library based on natural sound, then tinnitus rehabilitation sound is synthesized via IFS fractal algorithm. Simulation results show that rehabilitation sound in this paper can meet the basic requirements of tinnitus therapy sound and can match tinnitus sound by controlling personalized audio library. So it has reference significance to the treatment of tinnitus sound therapy.