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.

Dimensions of self-rated health in older adults

OBJECTIVE To analyze the association between negative self-rated health and indicators of health, wellbeing and sociodemographic variables in older adults. METHODS Cross-sectional study that used data from a population-based health survey with a probability cluster sample that was carried out in Campinas, SP, Southeastern Brazil,, in 2008 and 2009. The participants were older adults (≥ 60 years) and the dependent variable was self-rated health, categorized as: excellent, very good, good, bad and very bad. The adjusted prevalence ratios were estimated by means of Poisson multiple regression. RESULTS The highest prevalences of bad/very bad self-rated health were observed in the individuals who never attended school, in those with lower level of schooling, with monthly per capita family income lower than one minimum salary. Individuals who scored five or more in the physical health indicator also had bad self-rated health, as well as those who scored five or more in the Self-Reporting Questionnaire 20 and those who did not refer feeling happiness all the time. CONCLUSIONS The independent effects of material life conditions, physical and mental health and subjective wellbeing, observed in self-rated health, suggest that older adults can benefit by health policies supported by a global and integrative view of old age.

A Novel Algorithm to Quantify Coronary Remodeling Using Inferred Normal Dimensions

Background:Vascular remodeling, the dynamic dimensional change in face of stress, can assume different directions as well as magnitudes in atherosclerotic disease. Classical measurements rely on reference to segments at a distance, risking inappropriate comparison between dislike vessel portions.Objective:to explore a new method for quantifying vessel remodeling, based on the comparison between a given target segment and its inferred normal dimensions.Methods:Geometric parameters and plaque composition were determined in 67 patients using three-vessel intravascular ultrasound with virtual histology (IVUS-VH). Coronary vessel remodeling at cross-section (n = 27.639) and lesion (n = 618) levels was assessed using classical metrics and a novel analytic algorithm based on the fractional vessel remodeling index (FVRI), which quantifies the total change in arterial wall dimensions related to the estimated normal dimension of the vessel. A prediction model was built to estimate the normal dimension of the vessel for calculation of FVRI.Results:According to the new algorithm, “Ectatic” remodeling pattern was least common, “Complete compensatory” remodeling was present in approximately half of the instances, and “Negative” and “Incomplete compensatory” remodeling types were detected in the remaining. Compared to a traditional diagnostic scheme, FVRI-based classification seemed to better discriminate plaque composition by IVUS-VH.Conclusion:Quantitative assessment of coronary remodeling using target segment dimensions offers a promising approach to evaluate the vessel response to plaque growth/regression.

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.

Buccal apparatus and gastrointestinal tract dimensions associated to the diet of early life stages of Centropomus undecimalis (Centropomidae, Actinopterygii)

The present study aims to compare the buccal apparatus and gastrointestinal tract of early life stages of Centropomus undecimalis (Bloch, 1792), and relate them to its diet. A total of 190 individuals collected with a channel net in the Catuama estuary (07º40'9.9''S, 34º50'36.7''W), northern coast of the state of Pernambuco, were examined. Morphometrical and meristic data were analyzed for the two initial developmental periods (larval and juvenile). Their digestive tube was morphologically characterized and its content identified. The longest transverse axis of food items was measured, and compared to the standard length (SL) and mouth gape size (D) of the individuals. Body measurement regressions differed significantly (p<0.001) between larvae and juveniles. The stomachs with food content (n=118 individuals) presented a proportion of 62% full and 30% empty (being 8% damaged). They differed in relation to the fullness level and presented a coiled shape when empty. The number of food items in relation to SL and D did not present an evident correlation. Larvae (SL<10 mm) feed on small copepods, while juveniles (SL=11.1 to 64.7 mm) ingest larvae of various decapod species, showing a distinct diet between these initial developmental stages.

Influence of altitude, latitude and season of collection (Bergmann's Rule) on the dimensions of Lutzomyia intermedia (Lutz & Neiva, 1912) (diptera, psychodidae, phlebotominae)

The influence of altitude and latitude on some structure sizes of Lutzomyia intermedia was noted; several structures of insects collected in higher localities were greater, according to Bergmann's rule. This influence was more remarkable in two localities of the State of Espírito Santo, probably due to greater differences in altitude. Comparing insects from different latitudes, more differences were noted in comparisons of insects from low altitude localities than in those of material from higher altitudes. The small number of differences between insects collected in July and in December does not indicate a defined influence of season and temperature on the size of adults. The possible epidemiological implications of these variations are discussed.

Distinction of males of the Lutzomyia intermedia (Lutz & Neiva, 1912) species complex by ratios between dimensions and by an artificial neural network (Diptera: Psychodidae, Phlebotominae)

The females of the two species of the Lutzomyia intermedia complex can be easily distinguished, but the males of each species are quite similar. The ratios between the extra-genital and the genital structures of L. neivai are larger than those of L. intermedia s. s., according to ANOVA. An artificial neural network was trained with a set of 300 examples, randomly taken from a sample of 358 individuals. The input vectors consisted of several ratios between some structures of each insect. The model was tested on the remaining 58 insects, 56 of which (96.6%) were correctly identified. This ratio of success can be considered remarkable if one takes into account the difficulty of attaining comparable results using traditional statistical techniques.

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.

Content validation of the dimensions constituting non-adherence to treatment of arterial hypertension

The objective of the study was to validate the content of the dimensions that constituted nonadherence to treatment of arterial systemic hypertension. It was a methodological study of content validation. Initially an integrative review was conducted that demonstrated four dimensions of nonadherence: person, disease/treatment, health service, and environment. Definitions of these dimensions were evaluated by 17 professionals, who were specialists in the area, including: nurses, pharmacists and physicians. The Content Validity Index was calculated for each dimension (IVCi) and the set of the dimensions (IVCt), and the binomial test was conducted. The results permitted the validation of the dimensions with an IVCt of 0.88, demonstrating reasonable systematic comprehension of the phenomena of nonadherence.

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.

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.