Dimensão fractal na quantificação do grau de rejeição celular miocárdica pós-transplante cardíaco

INTRODUÇÃO: O termo fractal é derivado do latim fractus, que significa irregular ou quebrado, considerando a estrutura observada como tendo uma dimensão não-inteira. Há muitos estudos que empregaram a Dimensão Fractal (DF) como uma ferramenta de diagnóstico. Um dos métodos mais comuns para o seu estudo é a Box-plot counting (Método de contagem de caixas). OBJETIVO: O objetivo do estudo foi tentar estabelecer a contribuição da DF na quantificação da rejeição celular miocárdica após o transplante cardíaco. MÉTODOS: Imagens microscópicas digitalizadas foram capturadas na resolução 800x600 (aumento de 100x). A DF foi calculada com auxílio do software ImageJ, com adaptações. A classificação dos graus de rejeição foi de acordo com a Sociedade Internacional de Transplante Cardíaco e Pulmonar (ISHLT 2004). O relatório final do grau de rejeição foi confirmado e redefinido após exaustiva revisão das lâminas por um patologista experiente externo. No total, 658 lâminas foram avaliadas, com a seguinte distribuição entre os graus de rejeição (R): 335 (0R), 214 (1R), 70 (2R), 39 (3R). Os dados foram analisados estatisticamente com os testes Kruskal-Wallis e curvas ROC sendo considerados significantes valores de P < 0,05. RESULTADOS: Houve diferença estatística significativa entre os diferentes graus de rejeição com exceção da 3R versus 2R. A mesma tendência foi observada na aplicação da curva ROC. CONCLUSÃO: ADF pode contribuir para a avaliação da rejeição celular do miocárdio. Os valores mais elevados estiveram diretamente associados com graus progressivamente maiores de rejeição. Isso pode ajudar na tomada de decisão em casos duvidosos e naqueles que possam necessitar de intensificação da medicação imunossupressora.

Mass fractal characteristics of silica sonogels as determined by small-angle x-ray scattering and nitrogen adsorption

A sample series of silica sonogels was prepared using different water-tetraethoxysilane molar ratio (r(w)) in the gelation step of the process in order to obtain aerogels with different bulk densities after the supercritical drying. The samples were analyzed by means of small-angle x-ray-scattering (SAXS) and nitrogen-adsorption techniques. Wet sonogels exhibit mass fractal structure with fractal dimension D increasing from similar to2.1 to similar to2.4 and mass-fractal correlation length xi diminishing from similar to13 nm to similar to2 nm, as r(w) is changed in the nominal range from 66 to 6. The process of obtaining aerogels from sonogels and heat treatment at 500degreesC, in general, increases the mass-fractal dimension D, diminishes the characteristic length xi of the fractal structure, and shortens the fractal range at the micropore side for the formation of a secondary structured particle, apparently evolved from the original wet structure at a high resolution level. The overall mass-fractal dimension D of aerogels was evaluated as similar to2.4 and similar to2.5, as determined from SAXS and from pore-size distribution by nitrogen adsorption, respectively. The fine structure of the secondary particle developed in the obtaining of aerogels could be described as a surface-mass fractal, with the correlated surface and mass-fractal dimensions decreasing from similar to2.4 to similar to2.0 and from similar to2.7 to similar to2.5, respectively, as the aerogel bulk density increases from 0.25 (r(w)=66) up to 0.91 g/cm(3) (r(w)=6).

Mass fractal characteristics of wet sonogels as determined by small-angle x-ray scattering and differential scanning calorimetry

Low density silica sonogels were prepared from acid sonohydrolysis of tetraethoxysilane. Wet gels were studied by small-angle x-ray scattering (SAXS) and differential scanning calorimetry (DSC). The DSC tests were carried out under a heating rate of 2 degrees C/min from -120 degrees C up to 30 degrees C. Aerogels were obtained by CO(2) supercritical extraction and characterized by nitrogen adsorption and SAXS. The DSC thermogram displays two distinct endothermic peaks. The first, a broad peak extending from about -80 degrees C up to practically 0 degrees C, was associated to the melting of ice nanocrystals with a crystal size distribution with pore diameter ranging from 1 or 2 nm up to about 60 nm, as estimated from Thomson's equation. The second, a sharp peak with onset temperature close to 0 degrees C, was attributed to the melting of macroscopic crystals. The DSC incremental nanopore volume distribution is in reasonable agreement with the incremental pore volume distribution of the aerogel as determined from nitrogen adsorption. No macroporosity was detected by nitrogen adsorption, probably because the adsorption method applies stress on the sample during measurement, leading to a underestimation of pore volume, or because often positive curvature of the solid surface is in aerogels, making the nitrogen condensation more difficult. According to the SAXS results, the solid network of the wet gels behaves as a mass fractal structure with mass fractal dimension D=2.20 +/- 0.01 in a characteristic length scale below xi=7.9 +/- 0.1 nm. The mass fractal characteristics of the wet gels have also been probed from DSC data by means of an earlier applied modeling for generation of a mass fractal from the incremental pore volume distribution curves. The results are shown to be in interesting agreement with the results from SAXS.

Structural characteristics of gels prepared from sonohydrolysis and conventional hydrolysis of TEOS: an emphasis on the mass fractal as determined from the pore size distribution

Silica gels were preparated from fixed proportion mixtures of tetraethoxysilane, water and hydrocloric acid, using either ultrasound stimulation (US) or conventional method (CO) in the hydrolysis step of the process. Wet gets were obtained with the same silica volume concentration and density. According to small-angle X-ray scattering, the structure of the wet gels can be described as mass fractal structures with mass fractal dimension D = 2.20 in a length scale xi = 7.9 nm, in the case of wet gels US, and D = 2.26 in a length scale 6.9 nm, in the case of wet gels CO. The mass fractal characteristics of the wet gels US and CO account for the different structures evolved in the drying of the gels US and CO in the obtaining of xerogels and aerogels. The pore structure of the dried gels was studied by nitrogen adsorption as a function of the temperature. Aerogels (US and CO) present high porosity with pore size distribution (PSD) curves in the mesopore region while xerogels (US and CO) present minor porosity with PSD curves mainly in the micropore region. The dried gels US (aerogels and xerogels) generally present pore volume and specific surface area greater than the dried gels CO. The mass fractal structure of the aerogels has been studied from an approach based on the PSD curves exclusively. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Effect of tillage on fractal indices describing soil surface microrelief of a Brazilian Alfisol

Soil surface roughness is known to influence water infiltration, runoff and erosion. Soil surface roughness changes with management and weather and its mathematical description still remains an important issue. The main objective of this study was to investigate the effect of tillage on the two fractal indices, fractal dimension, D, and crossover length, 1, currently used in characterizing soil surface microrelief. The statistical index random roughness, RR, was also assessed. Field experiments were done on an Alfisol located at Rio Grande do Sul State (Brazil). Two tillage treatments (conventional versus direct drilling) were tested. The soil surface microrelief was assessed by point elevation measurements in 16 plots for each treatment. The sampling scheme was a square grid with 20 x 20 mm between point spacing and the plot size was 280 x 280 mm, so that each data set consisted of 225 individual elevation points. All indices were calculated after trend removal, both by slope correction, i.e., oriented microrelief, and by slope plus tillage marks correction, i.e., random microrelief. The implemented algorithm for estimating D and 1 consisted in evaluating the roughness around the local root mean square deviation (RMS) of the point elevation values. Irrespective of tillage treatment and detrending procedure, fractal behavior extended only over a bounded range of scales, from 40 to 100 mm, due to the experimental setup. In these conditions, assessing fractal indices was not always straightforward. The statistical index RR and the fractal index I were significantly different between tillage treatments for oriented and random surface conditions. D values of random soil surfaces were not affected by tillage treatment, whereas D values of oriented microrelief were significantly lower in the direct drilled plots. Removal of tillage marks trend resulted in a significant increase in D values. Within each tillage treatment, 1 and D were significantly correlated. (c) 2006 Elsevier B.V. All rights reserved.

Mass fractal characteristics of sonogels prepared from sonohydrolysis of tetraethoxysilane with additions of dimethylformamide

Wet silica gels with similar to 1.4 x 10(-3) mol SiO2/cm(3) and similar to 90 vol.% liquid phase were prepared from the sonohydrolysis of tetraethoxysilane (TEOS) with different additions of dimethylformamide (DMF). Aerogels were obtained by CO2 supercritical extraction. The samples were studied mainly by small-angle X-ray scattering (SAXS) and nitrogen adsorption. Wet gels exhibit a mass fractal structure with fractal dimension D increasing from 2.23 to 2.35 and characteristic length xi decreasing from similar to 9.4 nm to similar to 5.1 nm, as the DMF/TEOS molar ratio is increased from 0 to 4. The supercritical process apparently eliminates some porosity, shortening the fractality domain in the mesopore region and developing an apparent surface/mass fractal (with correlated mass fractal dimension D-m similar to 2.6 and surface fractal dimension D-s similar to 2.3) in the micropore region. The fundamental role of the DMF addition on the structure of the aerogels is to diminish the porosity and the pore mean size, without, however, modify substantially the specific surface area and the average size of the silica particle of the solid network. (c) 2006 Elsevier B.V. All rights reserved.

Comportamento fractal de tracos de fraturas na borda sul do macico granitico de itu, estado de Sao Paulo

Fractal geometry is relevant to understand and explain many natural complex geometries. Using the fractal set concept (fig. 1) many authors have shown that shorelines, landscapes and fractures follow a fractal behaviour. These authors have developed many methods, including the Cantor's Dust Method (CDM) (VELDE et al., 1992), a linear method of analysis adapted for the determination of two-dimensional phenomena. The Itu Granitic Complex (IGC) is a wide granitic body that that crops out at northwest of Cabreuva City, Sao Paulo State (fig. 2) and was affected in its south border by dextral Itu-Jundiuvira Shear Zone (IJSZ) that produced fractures and alignment of feldspars crystals. The different types of fractures (compression, distension and shear) was discriminated from the relationship between them and medium stress ellipsoid of IJSZ (fig. 3). A modified version of CDM was used to study a possible fractal behaviour of the fracture traces in the south border of IGC. The main modification was the use only one direction of analysis (NE/SW). Four parallel profiles were traced with lengths between 9.75km and 12.75km, each one them was divided into six classes of segments (x) with 375m, 500m, 750m, 1.000m, 1.250m and 1.500m. The parameter (N) is provided by he rate between profile length and choiced segment. For each x the number of intervals is counted with at least one event (fracture intersection) which supplied the parameter(n). The n/N rate provide the parameter (p) that represents the relationship between frequency of events and x. And finally the parameters p and x were plotted in a logarithmic graphics (fig. 4) that provide a line with such a declivity (1) which is related to effective dimension (De). In theory, granitics bodies are isotropics and they would have a same fractal dimension in all segments, but the logarithmic graphics (fig. 4) show that fracture traces of IGC has a fractal behaviour in a restrict interval. This fact probably occurs from the passage of a ductil-brittle deformation condition to a more brittle deformation condition of IGC.

Fractal approach to ac impedance spectroscopy studies of ceramic materials

A novel fractal model for grain boundary regions of ceramic materials was developed. The model considers laterally inhomogeneous distribution of charge carriers in the vicinity of grain boundaries as the main cause of the non-Debye behaviour and distribution of relaxation times in ceramic materials. Considering the equivalent circuit the impedance of the grain boundary region was expressed. It was shown that the impedance of the grain boundary region has the form of the Davidson-Cole equation. The fractal dimension of the inhomogeneous distribution of charge carriers in the region close to the grain boundaries could be calculated based on the relation ds = 1 + β, where β is the constant from the Davidson-Cole equation.

Análise espaço temporal da dimensão fractal de matas ciliares na alta bacia do rio Passa Cinco - centro Leste do Estado de São Paulo

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Síntese e caracterização de partículas de poli(álcool vinílico) utilizadas em aplicações biomédicas: contribuição da análise fractal e entropia de Shannon

Pós-graduação em Biofísica Molecular - IBILCE

Caracteres estruturais e dimensão fractal da folha de espécies de Arachis e sua relação com a cercosporiose

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Análise do comportamento fractal da propagação de trinca por fadiga em aço 300M e liga de alumínio AA7475

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Fractografia quantitativa: análise do comportamento fractal de fratura em compósitos carbono/epóxi, por processamento digital de imagens

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Fractografia quantitativa: análise do comportamento fractal da fratura por explosão hidrostática em cilindros de aço sem costura

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Fractografia quantitativa: relações entre tenacidade e o comportamento fractal em ligas metálicas

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)