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.

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 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.

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.

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.

Generalización diagnóstica fractal de la morfología cardiaca ventricular izquierda: anormalidades moderadas y severas a partir del ventriculograma / Fractal Diagnostic Generalization of Left Ventricular Cardiac Morphology: Moderate and Severe Anormalities from Ventriculography

Introducción: La irregularidad cardiaca es adecuadamente descrita mediante geometría fractal, la cual fue base para el desarrollo de un diagnóstico del ventriculograma izquierdo. Métodos: Se simularon la totalidad de permutaciones posibles de grados de similitud de las dimensiones fractales del ventrículo en sístole, diástole y totalidad, definidas entre los valores mínimos y máximos de los grados de similitud para anormalidad moderada y severa previamente establecidos. Resultados: Se estableció el número total de prototipos ventriculares entre anormalidad moderada y severa. El número total de prototipos de estructura ventricular posibles fue de 1614: 794 ventrículos con anonnalidad moderada y 820 con anonnalidad severa. Medidas previas de ventrículos con diagnóstico de anonnalidad moderada y severa se encontraron incluidas dentro de la generalización. Conclusiones: Se desarrolló una metodología geométrica objetiva y de ayuda diagnóstica a nivel clínico, que determinó todas las posibles estructuras ventriculares izquierdas con anonnalidad moderada y severa, independientemente de clasificaciones clínicas.

Introduction: The cardiac irregularity is adequately described by means of fractal geometry, which was the basis for the development of a diagnosis of left ventriculography. Methods: All possible pennutations of similarity degrees from fractal dimensions were done for the ventricle in systole. diastole and the totality. Pennutations were defined between the previously established mínimum and máximum valúes of similarity degrees for modérate and severe anonnality. Results: It was established the total number of possible ventricular prototypes between modérate and severe anonnality. The total number of possible ventricular structure prototypes is 1614: 794 of ventricles with modérate anonnality and 820 of ventricles with severe anonnality. Practical measures made previously were found within the generalization. Conclusions: It was developed an objective geometric methodology. which is of diagnostic aid in the clinical practice. It detennined all possible left ventricular structures with modérate and severe anonnality independent of clinical classifications.

Higuchi Fractal Analysis of Heart Rate Variability is Sensitive during Recovery from Exercise in Physically Active Men / Análise da variabilidade da frequência cardíaca pelo método da dimensão fractal de higuchi é sensível durante a recuperação após exercício em homens fisicamente ativos

OBJECTIVE: Nonlinear techniques to assess heart rate variability (HRV) have received much recent attention. We aimed to evaluate nonlinear HRV responses during recovery from exercise through the novel algorithm Higuchi Fractal Dimension. METHOD: We examined 35 healthy male volunteers aged between 18 and 35 years old. For the training of exercise intensity we used 60% of Vmax determined through a progressive test using the Conconi threshold. HRV was analyzed 10 minutes before and 10 minutes after exercise. We analyzed the geometric indices of HRV (SD1, a measure of short-term HRV and SD2, a measure of long-term HRV) and applied the Higuchi Fractal Dimension to RR intervals. RESULTS: During recovery from exercise the Poincaré plot indices SD1 and SD1/SD2 decreased while SD2 and SD2/SD1 increased (p<0.0001) compared to control at rest. All parameters of Higuchi Fractal Dimension analysis were lowered after exercise compared to control at rest (p<0.0001). CONCLUSION: Physical exercise acutely decreased the chaotic behavior of HRV as measured through the Higuchi Fractal Dimension analysis. Physiologically, this indicates that we detected complex changes in HRV immediately after exercise.

OBJETIVO: Métodos não-lineares para avaliar a variabilidade da freqüência cardíaca (VFC) têm recebido muita atenção recente. Nosso objetivo é analisar as respostas não-lineares da VFC durante a recuperação do exercício através do novo algoritmo da análise fractal da dimensão de Higuchi. MÉTODO: Foram examinados 35 voluntários saudáveis, com idade entre 18 e 35 anos. Para o treinamento de intensidade de exercício utilizamos 60% de Vmax determinado através de um teste progressivo utilizando o limiar de Conconi. A VFC foi analisada 10 minutos antes e 10 minutos após o exercício. Analisamos os índices geométricos de VFC (SD1, uma medida de VFC em curto prazo e SD2, uma medida de VFC em longo prazo) e aplicamos a Dimensão Fractal de Higuchi aos intervalos RR. RESULTADOS: Durante a recuperação do exercício, os índices de plot de Poincaré SD1 e SD1/SD2 diminuíram, enquanto que SD2 e SD2/SD1 aumentaram (p <0,0001) em relação ao repouso. Todos os parâmetros da análise da Dimensão Fractal de Higuchi foram reduzidos após o exercício em comparação com o controle em repouso (p <0,0001). CONCLUSÃO: O exercício físico diminuiu agudamente o comportamento complexo da VFC, conforme medido pela análise da Dimensão Fractal de Higuchi. Fisiologicamente, isso indica que detectamos alterações na complexidade da VFC imediatamente após o exercício.

Comparison of EEG complexity between rats under awaking and anesthesia / 临床麻醉学杂志

Objective To compare the EEG complexity between rats under awaking and differ-ent depth of anesthesia via analyzing sample entropy and fractal dimension.Methods Sixteen SD rats were intraperitoneally injected with urethane twice,first with 500 mg/kg and second with 800 mg/kg one hour later.The scalp EEG was collected in stage of awaking (W),light anesthesia (LA)and heavy anesthesia (HA).The sample entropy (SampEn)and fractal dimension (FD)were computed by MATLAB.The characteristic values were denoised by linear dynamic system method during the whole process.Results The value of SampEn and FD gradually dropped from awaking to heavy anes-thesia.The SampEn and FD in W was significantly higher than the value in LA or in HA (P <0.05). The SampEn and FD in HA was significantly lower than that in LA (P < 0.05 ).Conclusion The SampEn and FD of EEG could be used to monitor the depth of anesthesia.

Evaluation of hypoxic pulmonary vascular remodeling based on fractal theory / 实用放射学杂志

Objective To evaluate the relationship between the spatial structure of pulmonary vascular tree and oxygen partial pressure in patients with chronic obstructive pulmonary disease(COPD) by the fractal dimension method.Methods 106 patients with COPD and 100 healthy people without COPD as controls were included in this study.All of the patients underwent multidetector CT scan and blood gas analysis.The pulmonary vascular trees were generated using post-processing software,and the FD of the pulmonary vascular trees were determined with ImageJ software in a personal computer.The fractal dimension were evaluated in the two groups.The relationship between FD and oxygen partial pressure in patients with COPD was analyzed.Results The FD value of the patients with COPD was lower than that of the patients without COPD (t =5.21,P＜ 0.01).There was a significant correlation between FD and the PaO2 in patients with COPD (r=0.692,P＜ 0.01).Conclusion FD analysis can effectively evaluate the process of pulmonary vascular remodeling induced by hypoxia in patients with COPD,which may be used as an important index for quantitative evaluation of pulmonary vascular remodeling in the course of COPD.

Ley de Zipf/Mandelbrot y teoría de la probabilidad aplicadas a la caracterización de reacciones adversas a medicamentos en adultos mayores

Introducción. La ley de Zipf/Mandelbrot establece una auto-organización fractal de fenómenos como el lenguaje, el repertorio inmune B y T, la dinámica cardiaca fetal, entre otros. La teoría de la probabilidad ha permitido desarrollar predicciones en distintos campos de la medicina. Objetivo. Realizar una aplicación de la ley de Zipf/Mandelbrot y la teoría de probabilidad a la caracterización de reacciones adversas a medicamentos en pacientes adultos mayores. Materiales y métodos. Las tasas de incidencias de reacciones adversas a medicamentos (RAM) y problemas relacionados con medicamentos (PRM) en adultos mayores de 44 años en Bogotá, Colombia, de enero a diciembre de 2012 fueron analizadas mediante la ley Zipf-Mandelbrot, agrupando las edades por rangos cada 5 años. Adicionalmente, se evaluó la probabilidad del número de reportes de los 10 grupos farmacológicos que generan mayor número de RAM y PRM. Resultados. Las tasas de incidencia de RAM y PRM presentan un comportamiento fractal estadístico con dimensión fractal de 0,983 y un R2 de 0,8618. La probabilidad de los grupos farmacológicos varió entre 0,0383 para los anticonvulsivos e hipolipemiantes y 0,2743 para antibacterianos. Las probabilidades de los grupos farmacológicos evidencian diferencias de 10 en órdenes de magnitud respecto a la máxima probabilidad. Conclusión. La tasa de incidencia de RAM y PRM es caracterizada mediante la ley de Zipf/Mandelbrot; se encontró un comportamiento no equiprobable de la distribución de reportes por grupos farmacológicos, que podría evidenciar tendencias útiles en la vigilancia farmacológica.

Introduction. Zipf/Mandelbrot Law establishes a fractal auto-organization of phenomena such as language, the B and T immune repertoire and the fetal cardiac behavior, among other possible applications. Objective. The application of the probability theory has allowed the prediction of the cardiac behavior, epidemics and the union of peptides in molecular biology. Materials and methods. The adverse reactions rate to medications (ARM) and problems related to medications (PRM) in adults above 44 years of age in Bogotá, Colombia, from January to December, 2012, were analyzed by means of the Zipf- Mandelbrot law, separating the ages by ratios every 5 years. Additionally, the probability of the number of reports of the 19 pharmacological groups with higher ARM and PRM were assessed. Results. The ARM and PRM rates have a fractal statistic behavior with fractal dimension of 0,983 and a R2 of 0,8618. The probability of the pharmacological groups varied between 0,0383 for anticonvulsants and lipid-lowering medications and 0,2743 for anti-bacterial ones. The probabilities of the pharmacological groups show differences of 10 in magnitude orders in regard to the maximum probability. Conclusion. The incidence rate of RAM and PRM is characterized by Zipf/Mandelbrot law; It was found a not equiprobable behavior of the distribution of reports by pharmacological groups, which could show useful trends in pharmacological surveillance.

Introdução. A lei de Zipf/Mandelbrot estabelece uma auto-organização fractal de fenômenos como a linguagem, o repertório imune B e T, a dinâmica cardíaca fetal, entre outras aplicações. Objetivo. Aplicar a teoria da probabilidade há permitido desenvolver predições na dinâmica cardíaca, epidemias, e união de peptídeo em biologia molecular. Materiais e métodos. As taxas de incidências de reações adversas a medicamentos (RAM) e problemas relacionados com medicamentos (PRM) em adultos maiores de 44 anos em Bogotá, Colômbia, de Janeiro a dezembro de 2012 foram analisadas mediante a lei Zipf-Mandelbrot, agrupando as idades por faixa de cada 5 anos. Adicionalmente se avaliou a probabilidade do número de relatórios dos 10 grupos farmacológicos que geram maior número de RAM e PRM. Resultados. As taxas de incidência de RAM e PRM apresentam um comportamento fractal estatístico com dimensão fractal de 0,983 e um R2 de 0,8618. A probabilidade dos grupos farmacológicos variou entre 0,0383 para os anti-convulsivos e hipolipemiantes, e 0,2743 para antibacterianos. As probabilidades dos grupos farmacológicos evidenciam diferencias de 10 em ordens de magnitude com respeito à máxima probabilidade. Conclusão. A taxa de incidência de RAM e PRM avaliada em diferentes grupos de idade é caracterizada por um comportamento a escala de acordo com a lei de Zipf/Mandelbrot; se encontrou um comportamento não equiprovável da distribuição de relatórios por grupos farmacológicos. Este comportamento poderia evidenciar tendências úteis na vigilância farmacológica.

Chaotic analysis of heart rate dynamics after an exercise with flexible pole / Análise caótica da dinâmica da frequência cardíaca após exercício com barra flexível

INTRODUCTION: Exercises with a flexible pole have been applied in clinical practice for upper limb rehabilitation. Nevertheless, its acute effects on cardiac autonomic regulation are unclear. OBJECTIVE: To evaluate the acute effects of exercise with flexible pole on complex behavior of heart rate variability (HRV). METHOD: We investigated 32 healthy female volunteers aged between 18 and 25 years who performed a session of exercise with a flexible pole. HRV was analyzed 10 minutes before and 10 minutes immediately after the exercise. RESULTS: Exercises with a flexible pole did not significantly change time and frequency domain indices of HRV. Non-linear analysis of HRV through the Higuchi Fractal Dimension was not significantly changed during recovery from exercise compared to the control reading at rest. CONCLUSION: Exercises with the flexible pole were unable to acutely change chaotic behavior of heart rate dynamics. This is advantageous for assessments of levels of rehabilitative treatment required in such patients; and their susceptibility to dynamical diseases.

INTRODUÇÃO: Exercícios com uma barra flexível têm sido usados na prática clínica para a reabilitação do membro superior. No entanto, os seus efeitos agudos sobre a regulação autonômica cardíaca não estão bem esclarecidas. OBJETIVO: Avaliar os efeitos agudos do exercício com barra flexível sobre o comportamento complexo da variabilidade da frequência cardíaca (VFC). MÉTODO: Foram investigadas 32 voluntárias saudáveis com idades entre 18 e 25 anos que realizaram uma sessão de exercício com barra flexível. A VFC foi analisada 10 minutos antes e 10 minutos imediatamente depois do exercício. RESULTADOS: Os exercícios com a barra flexível não alteraram significativamente os domínios de tempo e frequência de VFC. Análise não-linear da VFC através da Dimensão Fractal Higuchi mostra que a mesma não foi significativamente alterada durante a recuperação do exercício em relação ao controle pré-exercício. CONCLUSÃO: O exercício com a barra flexível não alterou profundamente o comportamento caótico da dinâmica da frequência cardíaca. Isto é vantajoso para a avaliação de níveis de tratamento de reabilitação necessário em tais pacientes; e sua suscetibilidade a doenças dinâmicas.

Higuchi fractal dimension applied to RR intervals in children with Attention Deficit Hyperactivity Disorder

BACKGROUND: Attention deficit hyperactivity disorder (ADHD) is categorized by a lowered attention span, recklessness, and hyperactivity. Autonomic nervous system inequality has previously been studied using the same data by chaotic global techniques. We aim to compare the autonomic function of children with ADHD and controls by analyzing heart rate variability (HRV) METHODS: 28 children with ADHD (22 boys, mean age 10.0 years ± 1.9 years) and 28 controls (15 boys, mean age 9.9 years ± 1.8 years) rested in supine position with spontaneous breathing for 20 minutes. Heart rate was recorded beat by beat. HRV analysis was performed by Higuchi Fractal Dimension technique. RESULTS: ADHD promoted an increase in the Higuchi Fractal Dimension. The optimum value of Kmax was 10. CONCLUSION: ADHD significantly altered cardiac autonomic modulation as measured by the Higuchi fractal dimension of HRV. It can therefore be stated that ADHD has increased the complexity of the HRV signal through cardiac autonomic modulation.

INTRODUÇÃO: O transtorno de deficit de atenção e hiperatividade (TDAH) é caracterizado por um período reduzido de atenção, impulsividade e hiperatividade. O desequilíbrio na função do sistema nervoso autônomo (SNA) tem sido previamente estudado utilizando-se técnicas globais da teoria do caos. OBJETIVO: comparar a função autonômica de crianças com TDAH e controles por meio da análise da variabilidade da frequência cardíaca (VFC) MÉTODO: 28 crianças com TDAH (22 meninos, com média de idade de 10,0 anos ± 1,9 anos) e 28 controles (15 meninos, com média de idade de 9,9 anos ± 1,8 anos) permaneceram em decúbito dorsal, com respiração espontânea por 20 minutos. A frequência cardíaca foi registrada batimento a batimento e a análise da VFC foi realizada pela técnica de Dimensão Fractal Higuchi. RESULTADOS: TDAH promoveu um aumento na Dimensão Fractal Higuchi. O valor ideal de Kmax foi 10. CONCLUSÃO: O TDAH alterou significantemente a modulação autonômica cardíaca, como demonstrado pela Dimensão Fractal Higuchi da VFC. Assim, pode-se afirmar que crianças com TDAH apresentaram aumento das respostas caóticas neste tipo de análise da modulação autonômica cardíaca.

Crescimento vascular em membrana do saco vitelínico e desenvolvimento embrionário de codornas japonesas (Coturnix japonica) expostas a campo magnético de baixa frequência / Vascular growth in yolk sac membrane and embryonic development of Japanese quail (Coturnix japonica) exposed to low frequency magnetic field

O objetivo deste trabalho foi observar a influência do campo magnético (CM) de baixa frequência na membrana do saco vitelínico (MSV) e no desenvolvimento do embrião de codornas japonesas (Coturnix japonica) em 72 horas de incubação. Ovos fertilizados foram expostos a nove horas consecutivas de CM, sendo um grupo a partir das 48 horas e o outro a partir das 63 horas de incubação. A quantificação da vascularização da MSV foi determinada pela obtenção da dimensão fractal por meio dos métodos de box-counting e de dimensão de informação, enquanto o peso corporal e o percentual de comprimento cefálico dos embriões foram utilizados como parâmetros de desenvolvimento embrionário. O CM não causou diferenças significativas na densidade vascular da MSV nem no desenvolvimento embrionário, quando comparados ao grupo controle...

The aim of this study was to observe the influence of the low frequency magnetic field (MF) on the yolk sac membrane (YSM) and embryonic development of Japanese quail (Coturnix japonica) in 72 hours of incubation. Fertilized eggs were exposed to 9 consecutive hours of MF, with a group from 48 hours and the second group from 63 hours of incubation. The evaluation of YSM vascularization was determined by the fractal dimensions obtained through box-counting method and information dimension, while body weight of the embryo and percentage of cephalic length were used as parameters for embryo development. The MF caused no significant differences in vessel density in the YSM, nor in the embryonic development considering the body weight and percentage cephalic length, when were compared to the control group...

Generalización geométrica fractal de ventriculografías izquierdas normales y con disfunción leve / Fractal geometric generalization of normal left ventriculographies and with mild dysfunction

Introducción: la estructura cardiaca es por naturaleza, irregular, su adecuada caracterización se hace mediante la aplicación de la geometría fractal. Desde esta geometría se desarrolló un diagnóstico objetivo del ventriculograma izquierdo. Objetivo: desarrollar una generalización teórica de la dinámica ventricular izquierda en los estados de normalidad y enfermedad leve, a partir del diagnóstico matemático objetivo y reproducible desarrollado previamente. Se calcularon todas las posibles estructuras ventriculares durante la dinámica cardiaca a partir de los grados de similitud para casos que evolucionan entre normales y leves en busca de los prototipos matemáticos ventriculares de normalidad y enfermedad leve. Resultados: se estableció que la totalidad de posibles prototipos de la estructura ventricular para normalidad y enfermedad leve son 1345; 551 corresponden a normalidad y 794 a enfermedad leve. Al comparar los grados de similitud de ventrículos previamente medidos, con los prototipos obtenidos, se encontró que sus medidas estaban incluidas en la generalización. Conclusión: se desarrolló una nueva metodología de aplicación clínica reproducible y de ayuda diagnóstica objetiva, independiente de clasificaciones clínicas, con base en la generalización geométrica de la dinámica ventricular. (Acta Med Colomb 2014; 39: 131-136).

Introduction: Cardiac structure is irregular by nature; its proper characterization is done by application of fractal geometry. From this geometry an objective diagnosis of left ventriculogram was developed. Objective: to develop a theoretical generalization of left ventricular dynamics in states of normality and mild disease, from the objective and reproducible previously developed mathematical diagnosis. All possible ventricular structures were calculated during cardiac dynamics from the degrees of similarity for cases that evolve between normal and mild in search of mathematical prototypes of normality and mild disease. Results: It was established that all of the possible prototypes for normal ventricular structure and mild disease are 1345; 551 correspond to normality and 794 to mild disease. Comparing the degree of similarity of previously measured ventricles, with the obtained prototypes, it was found that its measures were included in the generalization. Conclusion: a new methodology for clinical application reproducible and of objective diagnostic aid independently of clinical classifications, based on the geometric generalization of ventricular dynamics, was developed. (Acta Med Colomb 2014; 39: 131-136).

Evolución de la dimensión fractal y correlación temporal de agregados eritrocitarios producidos por Ascaris lumbricoides / Evolution of the fractal dimension and time correlation of erythrocyte aggregates produced by Ascaris lumbricoides

Introducción: se ha demostrado que Ascaris lumbricoides capta ácido siálico eritrocitario. Objetivo: estudiar la evolución de la dimensión fractal y la correlación temporal de los agregados eritrocitarios producidos por incubación con el helminto. Métodos: se trabajó con extractos parasitarios y concentrados de larvas, que fueron incubados en partes iguales con eritrocitos grupo O, en medio salino y enzimático, durante 90 min (eritrocitos tratados). Las suspensiones de eritrocitos control se incubaron con igual volumen de buffer fosfato salino. Las muestras de eritrocitos fueron extraídas cada 10 min durante la incubación. Se aplicó análisis digital de imágenes para la toma de los datos, se calculó a posteriori el conteo de células aisladas utilizando la técnica de box-counting y se aplicó el método de May y Sugihara, realizando las comparaciones siguientes: control de sangre entera enfrentada a otra muestra control de igual característica; control enfrentado a eritrocitos tratados con concentrados de larvas y control enfrentado a eritrocitos tratados con extractos parasitarios. Resultados: el análisis de la dimensión fractal para eritrocitos controles en ambos medios mostró una evolución de tipo movimiento browniano. Los eritrocitos tratados con extractos parasitarios presentaron un movimiento caótico determinista en medio salino y browniano fraccionario en medio enzimático. La cinética de agregación de los eritrocitos tratados con concentrados de larvas presentó un comportamiento intermedio entre ambos. La correlación temporal indicó que la conducta del control fue aleatoria en ambos medios y que los eritrocitos tratados con extractos parasitarios presentaron un comportamiento caótico determinista en medio salino y débilmente autosemejante en medio enzimático. El control enfrentado a muestras tratadas con concentrados de larvas en ambos medios, tuvo una conducta intermedia entre la que presentaron los otros dos procesos. Conclusiones: los análisis matemáticos realizados han permitido caracterizar el proceso de agregación eritrocitaria producido por Ascaris lumbricoides.

Introduction: Ascaris lumbricoides has been shown to capture erythrocyte sialic acid. Objective: study the evolution of the fractal dimension and the time correlation of erythrocyte aggregates produced by incubation with this helminth. Methods: parasite extracts and larval concentrates were incubated in equal parts with group O erythrocytes in saline and enzymatic media for 90 minutes (treated erythrocytes). Control erythrocytes suspensions were incubated with an equal volume of saline phosphate buffer. Erythrocyte samples were extracted every 10 minutes during incubation. Digital image analysis was used for data collection. The count of isolated cells was estimated a posteriori using box-counting technique. The May & Sugihara method was used for the following comparisons: whole blood control vs. a control sample with the same characteristic; control vs. erythrocytes treated with larval concentrates, and control vs. erythrocytes treated with parasite extracts. Results: fractal dimension analysis of control erythrocytes revealed Brownian motion evolution in both media. Erythrocytes treated with parasite extracts showed deterministic chaotic motion in the saline medium and fractional Brownian motion in the enzymatic medium. The behavior of aggregation kinetics for erythrocytes treated with larval concentrates was intermediate between the two. Time correlation revealed random behavior by the control in both media. It also showed that erythrocytes treated with parasite extracts had deterministic chaotic behavior in the saline medium and weakly self-similar behavior in the enzymatic medium. When compared with samples treated with larval concentrates in both media, the behavior of the control was intermediate between that of the other two processes. Conclusions: the mathematical analyses conducted have allowed characterization of the process of erythrocyte aggregation performed by Ascaris lumbricoides.

Evidence of Fractality in a Pattern of Crystallization of Bovine Cervical Mucus Obtained at Oestrus / Evidencia de Fractalidad en un Patrón de Cristalización de Moco Cervical Bovino Obtenido en Estro

Fractality has emerged as a feature of the organization of some complex natural systems. Several biological secretions show fractal-like patterns for their crystallization phenomena but their presence in crystallizations of bovine cervical mucus (BCM) is yet unknown. In order to assess the fractality of BCM crystallization, samples of this fluid were taken from heifers at oestrus, their crystalline patterns photographed and its morphology analyzed. Among the many images obtained for BCM crystallizations, one of them had a highly symmetrical geometric arrangement, possessing three zones characterized by pine-like, arboriform structures, evidencing a remarkable similarity between them. Moreover, fractal dimensions obtained for these zones were statistically equal when analyzed by using specialized software. In summary, this brief communication shows, for the first time, that a pattern of crystallization of BCM at oestrus possesses a fractal-like organization.

La fractalidad ha surgido como una característica propia de algunos sistemas biológicos complejos. Varias secreciones biológicas presentan patrones de tipo fractal al cristalizar; no obstante, su presencia en las cristalizaciones de moco cervical bovino aún se desconoce. Con el objetivo de investigar la presencia de fractalidad en las cristalizaciones de moco cervical bovino, se obtuvieron muestras de este fluido de vaquillas en estro, fotografiándose los patrones cristalinos observados. Entre las típicas disposiciones similares a frondas de helechos observadas para la cristalización del moco cervical, se encontró una imagen con un arreglo geométrico altamente simétrico, constando de tres zonas caracterizadas por estructuras arborescentes similares a pinos, muy semejantes entre sí. Más aún, las dimensiones fractales obtenidas para esas zonas fueron estadísticamente iguales al ser dichas áreas analizadas con un programa computacional apropiado. En resumen, esta comunicación breve demuestra por primera vez que uno de los patrones de cristalización de moco cervical bovino en estro está caracterizado por una organización de tipo fractal.

Evaluación de la dimensión fractal reactiva de los glicinatos de magnesio, manganeso y zinc / Evaluation of the reactive fractal dimension of magnesium, manganese and zinc glycinates

Introducción: complejos de glicina con los cationes magnesio, manganeso y zinc podrían ser parte de una formulación de un suplemento nutricional que proporcione una adecuada absorción de los metales en el organismo sin generar molestias gastrointestinales. Objetivo: realizar una aproximación a la solubilidad de los complejos de glicina con los cationes magnesio, manganeso y zinc. Métodos: se efectuaron estudios de disolución y análisis de imagen. Se realizó la síntesis y la verificación de formación de los complejos por espectroscopia infrarroja, calorimetría de barrido diferencial, análisis termogravimétrico y difracción de rayos X de polvos. Resultados: se obtuvieron por análisis de imagen los descriptores: circularidad, diámetro de Feret y dimensión fractal; esta última se relacionó con el proceso de disolución en agua, para obtener dos propiedades relacionadas: la dimensión fractal superficial y la dimensión fractal reactiva. Conclusiones: los resultados muestran que el proceso de disolución de los glicinatos, se realiza a través de los poros o grietas de la superficie de las partículas de estos y que son aptos para su empleo en formulaciones nutricionales como fuentes de magnesio, manganeso y zinc.

Introduction: Complexes of glycine and cations magnesium, manganese and zinc, could be included in the formulation of a nutritional supplement that provides adequate absorption of these metals into the body without gastrointestinal disturbances. Objective: to study the solubility of complexes of glycine and cations manganese, zinc and magnesium. Methods: dissolution and image analysis studies were performed. The synthesis and verification of the formation of complexes were carried out by infrared spectroscopy, differential scanning calorimetry, thermal gravimetric analysis, and X-ray diffraction of dust. Results: the image analysis showed some descriptors such as circularity, the Ferret diameter and the fractal dimension. The latter was related to the water dissolution process in order to obtain two associated properties, that is, the surface fractal dimension and the reactive fractal dimension, Conclusions: these results showed that the dissolution of glycinates occurs through the pores or cracks found in their particle surfaces and that these complexes are suitable for use in nutritional formulations as sources of magnesium, manganese and zinc.

Fractal Dimension Analysis of MDCT Images for Quantifying the Morphological Changes of the Pulmonary Artery Tree in Patients with Pulmonary Hypertension

OBJECTIVE: The aim of this study was to use fractal dimension (FD) analysis on multidetector CT (MDCT) images for quantifying the morphological changes of the pulmonary artery tree in patients with pulmonary hypertension (PH). MATERIALS AND METHODS: Fourteen patients with PH and 17 patients without PH as controls were studied. All of the patients underwent contrast-enhanced helical CT and transthoracic echocardiography. The pulmonary artery trees were generated using post-processing software, and the FD and projected image area of the pulmonary artery trees were determined with ImageJ software in a personal computer. The FD, the projected image area and the pulmonary artery pressure (PAP) were statistically evaluated in the two groups. RESULTS: The FD, the projected image area and the PAP of the patients with PH were higher than those values of the patients without PH (p < 0.05, t-test). There was a high correlation of FD with the PAP (r = 0.82, p < 0.05, partial correlation analysis). There was a moderate correlation of FD with the projected image area (r = 0.49, p < 0.05, partial correlation analysis). There was a correlation of the PAP with the projected image area (r = 0.65, p < 0.05, Pearson correlation analysis). CONCLUSION: The FD of the pulmonary arteries in the PH patients was significantly higher than that of the controls. There is a high correlation of FD with the PAP.

Study on bone healing process following cyst enucleation using fractal analysis

INTRODUCTION: Bone regeneration of cystic defects of the jaws after a cyst treatment requires lengthy healing periods. Generally, the bony changes are observed periodically through a visual radiographic reading as well as by the clinical opinion and radiographic images (panorama, periapical view), but it is difficult to compare the objective bony changes using only the radiographic density. In addition, it is difficult to observe minute bony changes through a visual radiographic reading, which can lead to a subjective judgment. This study exmined the bone density after the enucleation of a jaw cyst by fractal analysis. MATERIALS AND METHODS: Eighteen patients with a cystic lesion on the jaw were assessed. Panoramic radiographs were taken preoperatively, immediately postoperatively, and 1, 3, 6 and 12 months after cyst enucleation. The images were analyzed by fractal analysis. RESULTS: The mean fractal dimensions increased immediately after surgery and 3, 6 and 12 months postoperatively. The postoperative 6 and 12 months fractal dimension was similar to the controls. CONCLUSION: Fractal analysis was used to overcome the limit of a subjective reading during an assessment of bone regeneration after cyst enucleation.

Can the fractal dimension be applied for the early diagnosis of non-proliferative diabetic retinopathy?

The fractal dimension has been employed as a useful parameter in the diagnosis of retinal disease. Avakian et al. (Curr Eye Res 2002; 24: 274-280), comparing the vascular pattern of normal patients with mild to moderate non-proliferative diabetic retinopathy (NPDR), found a significant difference between them only in the macular region. This significant difference in the box-counting fractal dimension of the macular region between normal and mild NPDR patients has been proposed as a method of precocious diagnosis of NPDR. The aim of the present study was to determine if fractal dimensions can really be used as a parameter for the early diagnosis of NPDR. Box-counting and information fractal dimensions were used to parameterize the vascular pattern of the human retina. The two methods were applied to the whole retina and to nine anatomical regions of the retina in 5 individuals with mild NPDR and in 28 diabetic but opthalmically normal individuals (controls), with age between 31 and 86 years. All images of retina were obtained from the Digital Retinal Images for Vessel Extraction (DRIVE) database. The results showed that the fractal dimension parameter was not sensitive enough to be of use for an early diagnosis of NPDR.