Fractal Dimension in Quantifying Experimental-Pulmonary-Hypertension-Induced Cardiac Dysfunction in Rats

Abstract Background: Right-sided heart failure has high morbidity and mortality, and may be caused by pulmonary arterial hypertension. Fractal dimension is a differentiated and innovative method used in histological evaluations that allows the characterization of irregular and complex structures and the quantification of structural tissue changes. Objective: To assess the use of fractal dimension in cardiomyocytes of rats with monocrotaline-induced pulmonary arterial hypertension, in addition to providing histological and functional analysis. Methods: Male Wistar rats were divided into 2 groups: control (C; n = 8) and monocrotaline-induced pulmonary arterial hypertension (M; n = 8). Five weeks after pulmonary arterial hypertension induction with monocrotaline, echocardiography was performed and the animals were euthanized. The heart was dissected, the ventricles weighed to assess anatomical parameters, and histological slides were prepared and stained with hematoxylin/eosin for fractal dimension analysis, performed using box-counting method. Data normality was tested (Shapiro-Wilk test), and the groups were compared with non-paired Student t test or Mann Whitney test (p < 0.05). Results: Higher fractal dimension values were observed in group M as compared to group C (1.39 ± 0.05 vs. 1.37 ± 0.04; p < 0.05). Echocardiography showed lower pulmonary artery flow velocity, pulmonary acceleration time and ejection time values in group M, suggesting function worsening in those animals. Conclusion: The changes observed confirm pulmonary-arterial-hypertension-induced cardiac dysfunction, and point to fractal dimension as an effective method to evaluate cardiac morphological changes induced by ventricular dysfunction.

Four whole-istic aspects of schistosome granuloma biology: fractal arrangement, internal regulation, autopoietic component and closure

This paper centers on some whole-istic organizational and functional aspects of hepatic Schistosoma mansoni granuloma, which is an extremely complex system. First, it structurally develops a collagenic topology, originated bidirectionally from an inward and outward assembly of growth units. Inward growth appears to be originated from myofibroblasts derived from small portal vessel around intravascular entrapped eggs, while outward growth arises from hepatic stellate cells. The auto-assembly of the growth units defines the three-dimensional scaffold of the schistosome granulomas. The granuloma surface irregularity and its border presented fractal dimension equal to 1.58. Second, it is internally regulated by intricate networks of immuneneuroendocrine stimuli orchestrated by leptin and leptin receptors, substance P and Vasoactive intestinal peptide. Third, it can reach the population of ± 40,000 cells and presents an autopoietic component evidenced by internal proliferation (Ki-67+ Cells), and by expression of c-Kit+ Cells, leptin and leptin receptor (Ob-R), granulocyte-colony stimulating factor (G-CSF-R), and erythropoietin (Epo-R) receptors. Fourth, the granulomas cells are intimately connected by pan-cadherins, occludin and connexin-43, building a state of closing (granuloma closure). In conclusion, the granuloma is characterized by transitory stages in such a way that its organized structure emerges as a global property which is greater than the sum of actions of its individual cells and extracellular matrix components.

Pain intensity among institutionalized elderly: a comparison between numerical scales and verbal descriptors

AbstractOBJECTIVECorrelating two unidimensional scales for measurement of self-reported pain intensity for elderly and identifying a preference for one of the scales.METHODA study conducted with 101 elderly people living in Nursing Home who reported any pain and reached ( 13 the scores on the Mini-Mental State Examination. A Numeric Rating Scale - (NRS) of 11 points and a Verbal Descriptor Scale (VDS) of five points were compared in three evaluations: overall, at rest and during movement.RESULTSWomen were more representative (61.4%) and the average age was 77.0±9.1 years. NRS was completed by 94.8% of the elderly while VDS by 100%. The association between the mean scores of NRS with the categories of VDS was significant, indicating convergent validity and a similar metric between the scales.CONCLUSIONPain measurements among institutionalized elderly can be made by NRS and VDS; however, the preferred scale for the elderly was the VDS, regardless of gender.

A natureza fractal de ácidos húmicos

Dentre as ferramentas usadas para descrever a estrutura ramificada ou a superfície rugosa e distorcida de ácidos húmicos (AH), a geometria fractal aparece como uma das mais adequadas para explicar a conformação de partículas húmicas (agregados moleculares). Do ponto de vista experimental, a dimensão fractal (D) de sistemas naturais pode ser determinada a partir do monitoramento da luz transmitida, não espalhada e não absorvida (turbidimetria 'τ'). A presença de fractais implica que o sistema pode ser decomposto em partes, em que cada uma, subseqüentemente, é cópia do todo. A determinação do valor 'D' dessas partículas foi conseguida pela utilização de turbidimetria, em que suspensões de AH-comercial e de AH-Espodossolo foram analisadas por espectrofotometria UV-Vis. O fundamento matemático utilizado foi a lei de potência τ ∝ λβ, em que β < 3 indica a presença de fractal de massa (Dm); 3 < β < 4 indica fractal de superfície (Ds), e β ≅ 3 indica não-fractal (NF). A declividade das retas (β) por meio do gráfico (logτ vs logλ) permitiu a obtenção de 'D'. Segundo os resultados, partículas de AH em suspensões aquosas diluídas formam estruturas fractais, cuja geometria pode ser caracterizada por meio de turbidimetria. Entretanto, a faixa de comprimento de onda usada (400 a 550 nm) ainda é pequena para se afirmar sobre a natureza fractal de AH e determinar suas dimensões fractais com precisão.

Variabilidade espacial da agregação do solo avaliada pela geometria fractal e geoestatística

Este trabalho teve por objetivo explorar a aplicabilidade da teoria de fractais no estudo da variabilidade espacial em agregação de solo. A geometria de fractais tem sido proposta como um modelo para a distribuição de tamanho de partículas. A distribuição do tamanho de agregados do solo, expressos em termos de massa, é apresentada. Os parâmetros do modelo, tais como: a dimensão fractal D, medida representativa da fragmentação do solo (quanto maior seu valor, maior a fragmentação), e o tamanho do maior agregado R L foram definidos como ferramentas descritivas para a agregação do solo. Os agregados foram coletados em uma profundidade de 0-10 cm de um Latossolo Vermelho distrófico típico álico textura argilosa, em Angatuba, São Paulo. Uma grade regular de 100 x 100 m foi usada e a amostragem realizada em 76 pontos nos quais se determinou a distribuição de agregados por via úmida, usando água, álcool e benzeno como pré-tratamentos. Pelo exame de semivariogramas, constatou-se a ocorrência de dependência espacial. A krigagem ordinária foi usada como interpolador e mapas de contorno mostraram-se de grande utilidade na descrição da variabilidade espacial de agregação do solo.

Desenvolvimento de um modelo fractal para a estimativa da condutividade hidráulica de solos não saturados

Baseado nos conceitos da geometria fractal e nas leis de Laplace e de Poiseuille, foi criado um modelo geral para estimar a condutividade hidráulica de solos não saturados, utilizando a curva de retenção da água no solo, conforme representada por um modelo em potência. Considerando o fato de que este novo modelo da condutividade hidráulica introduz um parâmetro de interpolação ainda desconhecido, e que, por sua vez, depende das propriedades dos solos, a validação do modelo foi realizada, utilizando dois valores-limite fisicamente representativos. Para a aplicação do modelo, os parâmetros de forma da curva de retenção da água no solo foram escolhidos de maneira a se obter o modelo de van Genuchten. Com a finalidade de obter fórmulas algébricas da condutividade hidráulica, foram impostas relações entre seus parâmetros de forma. A comparação dos resultados obtidos com o modelo da condutividade e a curva experimental da condutividade dos dois solos, Latossolo Vermelho-Amarelo e Argissolo Amarelo, permitiu concluir que o modelo proposto é simples em sua utilização e é capaz de predizer satisfatoriamente a condutividade hidráulica dos solos não saturados.

Modeling water movement in horizontal columns using fractal theory

Fractal mathematics has been used to characterize water and solute transport in porous media and also to characterize and simulate porous media properties. The objective of this study was to evaluate the correlation between the soil infiltration parameters sorptivity (S) and time exponent (n) and the parameters dimension (D) and the Hurst exponent (H). For this purpose, ten horizontal columns with pure (either clay or loam) and heterogeneous porous media (clay and loam distributed in layers in the column) were simulated following the distribution of a deterministic Cantor Bar with fractal dimension H" 0.63. Horizontal water infiltration experiments were then simulated using Hydrus 2D software. The sorptivity (S) and time exponent (n) parameters of the Philip equation were estimated for each simulation, using the nonlinear regression procedure of the statistical software package SAS®. Sorptivity increased in the columns with the loam content, which was attributed to the relation of S with the capillary radius. The time exponent estimated by nonlinear regression was found to be less than the traditional value of 0.5. The fractal dimension estimated from the Hurst exponent was 17.5 % lower than the fractal dimension of the Cantor Bar used to generate the columns.

Selection of the most informative morphoagronomic descriptors for cassava germplasm

The objective of this work was to select the most informative morphoagronomic descriptors for cassava (Manihot esculenta) germplasm and to evaluate the ability of different methods to select the descriptors. Ninety-five accessions were characterized using 51 morphoagronomic descriptors. Data were subjected to a multiple correspondence analysis (MCA), whose information was used in the following four methods of descriptor selection: reverse order of the descriptor for the pth factorial axis of the MCA (Jolliffe); sequential, multiple correspondence analysis (SMCA); mean of the contribution orders of the descriptor in the first three factorial axes (C3PA); and C3PA method weighted by the respective eigenvalues of the full analysis (C3PAWeig). The correlations between the dissimilarity matrix with all descriptors and the most informative descriptors were high and significant (0.75, 0.77, 0.83, and 0.84 for C3PAWeig, C3PA, SMCA, and Jolliffe, respectively). The less informative descriptors were discarded, considering those common among the selection methods and relevant for the breeding interests. Therefore, 32 morphoagronomic descriptors with correlation between the dissimilarity matrices (r=0.81) were selected, due to their high capacity to discriminate cassava germplasm and to their ability to maintain some preliminary agronomic traits, useful for the initial characterization of the germplasm.

Dimensão fractal de ácidos húmicos em diferentes condições experimentais

The determination of fractal dimension (D) of humic particles was achieved by the turbidimetric technique where diluted suspensions of humic acids, in different experimental conditions, were analyzed by spectrophotometry UV-Vis. The slope of the lines (beta) was taken from the graphics (logtauvs loglambda) to obtain D. The results show that the values of D changed according to pH (3.0, 5.0 and 7.0), temperature (25 and 5 ºC) and shaking (magnetic and horizontal). In general, the value of D decreased with the increment of pH, increase of shaking and decrease of temperature.

GLOBAL AND LOCAL REACTIVITY DESCRIPTORS FOR PICLORAM HERBICIDE: A THEORETICAL QUANTUM STUDY

In this work, we studied the reactivity of picloram in the aqueous phase at the B3LYP/6-311++G(2d,2p) and MP2/6-311++G(2d,2p) levels of theory through global and local reactivity descriptors. The results obtained at the MP2 level indicate that the cationic form of picloram exhibits the highest hardness while the anionic form is the most nucleophilic. From the Fukui function values, the most reactive site for electrophilic and free radical attacks are on the nitrogen in the pyridine ring. The more reactive sites for nucleophilic attacks are located on the nitrogen atom of the amide group and on the carbon atoms located at positions 2 and 3 in the pyridine ring.

A geometria fractal da rede de drenagem da bacia hidrográfica do Caeté, Alfredo Wagner-SC

Os objetivos deste trabalho foram estimar e avaliar a dimensão fractal da rede de drenagem da bacia hidrográfica do Caeté, em Alfredo Wagner, SC, a partir de diferentes métodos, com o propósito de caracterizar as formas geomorfológicas irregulares. A rede de drenagem apresenta propriedades multifractais. As dimensões fractais para os segmentos individuais (df) e para a rede de drenagem inteira (Df) foram determinadas por métodos que se fundamentaram nas razões de Horton e pelo método da contagem de caixas (Box-Counting). A rede de drenagem tem característica de autoafinidade. A dimensão fractal proveniente da relação de parâmetros obtidos pelas Leis de Horton apresentou resultados dentro dos limiares da teoria da geometria fractal.

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.

Sensory descriptors of cocoa beans from cultivated trees of Soconusco, Chiapas, Mexico

The odor and taste profile of cocoa bean samples obtained from trees cultivated in southern Mexico were evaluated by trained panelists. Seven representative samples (groups) of a total of 45 were analyzed. Four attributes of taste (sweetness, bitterness, acidity and astringency), and nine of odor (chocolate, nutty, hazelnut, sweet, acidity, roasted, spicy, musty and off-odor) were evaluated. A sample (G7) with higher scores in sweet taste and sweet and nutty odors was detected, as well as a high association between these descriptors and the sample, analyzed through principal component analysis (PCA). Similarly, samples that showed high scores for non-desired odors in cocoas such as off-odor and musty were identified and related by PCA to roasted odor and astringent taste (G2 and G4). Based on this scores, the samples were listed in descending order by their sensory quality as G7> G5> G6> G3> G1> G4> G2.

Análise de políticas públicas: entre a modelagem e a realidade da política habitacional brasileira

Os desafios observados na implementação de políticas públicas têm fomentado uma série de debates no Brasil, entre os quais se destacam aqueles relacionados aos modelos teóricos de policy analysis e seus limites em face da visão multicêntrica e fractal das políticas públicas. Partindo de uma política setorial específica (habitacional), este artigo defende um posicionamento crítico em relação aos estudos monodisciplinares. Contudo, não se pode negar a complexidade dessa empreitada. Compreender os avanços da política habitacional da última década de forma interdisciplinar e integrada constitui uma tarefa intricada e desafiadora. Buscando avançar nesse campo, este artigo tem por objetivos avaliar os modelos teóricos de análise de políticas públicas e, a partir desses elementos, propor constructos com vistas a subsidiar futuros modelos teóricos de análise da política habitacional no Brasil.

O triunfo e a dor da beleza: comparando as estéticas recursiva, contrapontística e celular do ser

O principal argumento desenvolvido neste ensaio é o de que, para os Waiwai, o privilégio conferido à visibilidade lateral sugere idéias sobre um indivíduo fractal, associado ao poder recursivo, enquanto, para as sociedades do litoral da Guiana e dos Estados Unidos, o privilégio conferido à visibilidade axial sugere concepções sobre um indivíduo autônomo, associado a relações de poder contrapontísticas e celulares, respectivamente. Será argumentado que, ao contrário da situação dos Waiwai, de acordo com o objetivo de atingir maior eficiência no funcionamento de suas relações políticas com os cidadãos, o desejo do Estado moderno, expresso por meio do uso privilegiado da visibilidade axial, reduz a importância das relações laterais e produz indivíduos categorialmente isolados e solitários.