Aplicações médicas das abordagens complexas não lineares: a geometria fractal do EEG

Pós-graduação em Saúde Coletiva - FMB

Fractal sets and their applications in medicine

La geometria euclidea risulta spesso inadeguata a descrivere le forme della natura. I Frattali, oggetti interrotti e irregolari, come indica il nome stesso, sono più adatti a rappresentare la forma frastagliata delle linee costiere o altri elementi naturali. Lo strumento necessario per studiare rigorosamente i frattali sono i teoremi riguardanti la misura di Hausdorff, con i quali possono definirsi gli s-sets, dove s è la dimensione di Hausdorff. Se s non è intero, l'insieme in gioco può riconoscersi come frattale e non presenta tangenti e densità in quasi nessun punto. I frattali più classici, come gli insiemi di Cantor, Koch e Sierpinski, presentano anche la proprietà di auto-similarità e la dimensione di similitudine viene a coincidere con quella di Hausdorff. Una tecnica basata sulla dimensione frattale, detta box-counting, interviene in applicazioni bio-mediche e risulta utile per studiare le placche senili di varie specie di mammiferi tra cui l'uomo o anche per distinguere un melanoma maligno da una diversa lesione della cute.

Toward reduction of artifacts in fused images

Most fusion satellite image methodologies at pixel-level introduce false spatial details, i.e.artifacts, in the resulting fusedimages. In many cases, these artifacts appears because image fusion methods do not consider the differences in roughness or textural characteristics between different land covers. They only consider the digital values associated with single pixels. This effect increases as the spatial resolution image increases. To minimize this problem, we propose a new paradigm based on local measurements of the fractal dimension (FD). Fractal dimension maps (FDMs) are generated for each of the source images (panchromatic and each band of the multi-spectral images) with the box-counting algorithm and by applying a windowing process. The average of source image FDMs, previously indexed between 0 and 1, has been used for discrimination of different land covers present in satellite images. This paradigm has been applied through the fusion methodology based on the discrete wavelet transform (DWT), using the à trous algorithm (WAT). Two different scenes registered by optical sensors on board FORMOSAT-2 and IKONOS satellites were used to study the behaviour of the proposed methodology. The implementation of this approach, using the WAT method, allows adapting the fusion process to the roughness and shape of the regions present in the image to be fused. This improves the quality of the fusedimages and their classification results when compared with the original WAT method

Fractal scaling of apparent soil moisture estimated from vertical planes of Vertisol pit images

Image analysis could be a useful tool for investigating the spatial patterns of apparent soil moisture at multiple resolutions. The objectives of the present work were (i) to define apparent soil moisture patterns from vertical planes of Vertisol pit images and (ii) to describe the scaling of apparent soil moisture distribution using fractal parameters. Twelve soil pits (0.70 m long × 0.60 m width × 0.30 m depth) were excavated on a bare Mazic Pellic Vertisol. Six of them were excavated in April/2011 and six pits were established in May/2011 after 3 days of a moderate rainfall event. Digital photographs were taken from each Vertisol pit using a Kodak™ digital camera. The mean image size was 1600 × 945 pixels with one physical pixel ≈373 μm of the photographed soil pit. Each soil image was analyzed using two fractal scaling exponents, box counting (capacity) dimension (DBC) and interface fractal dimension (Di), and three prefractal scaling coefficients, the total number of boxes intercepting the foreground pattern at a unit scale (A), fractal lacunarity at the unit scale (Λ1) and Shannon entropy at the unit scale (S1). All the scaling parameters identified significant differences between both sets of spatial patterns. Fractal lacunarity was the best discriminator between apparent soil moisture patterns. Soil image interpretation with fractal exponents and prefractal coefficients can be incorporated within a site-specific agriculture toolbox. While fractal exponents convey information on space filling characteristics of the pattern, prefractal coefficients represent the investigated soil property as seen through a higher resolution microscope. In spite of some computational and practical limitations, image analysis of apparent soil moisture patterns could be used in connection with traditional soil moisture sampling, which always renders punctual estimates

Fractal scaling of apparent soil moisture estimated from vertical planesof Vertisol pit images

Image analysis could be a useful tool for investigating the spatial patterns of apparent soil moisture at multiple resolutions. The objectives of the present work were (i) to define apparent soil moisture patterns from vertical planes of Vertisol pit images and (ii) to describe the scaling of apparent soil moisture distribution using fractal parameters. Twelve soil pits (0.70 m long × 0.60 m width × 0.30 m depth) were excavated on a bare Mazic Pellic Vertisol. Six of them were excavated in April/2011 and six pits were established in May/2011 after 3 days of a moderate rainfall event. Digital photographs were taken from each Vertisol pit using a Kodak? digital camera. The mean image size was 1600 × 945 pixels with one physical pixel ?373 ?m of the photographed soil pit. Each soil image was analyzed using two fractal scaling exponents, box counting (capacity) dimension (DBC) and interface fractal dimension (Di), and three prefractal scaling coefficients, the total number of boxes intercepting the foreground pattern at a unit scale (A), fractal lacunarity at the unit scale (?1) and Shannon entropy at the unit scale (S1). All the scaling parameters identified significant differences between both sets of spatial patterns. Fractal lacunarity was the best discriminator between apparent soil moisture patterns. Soil image interpretation with fractal exponents and prefractal coefficients can be incorporated within a site-specific agriculture toolbox. While fractal exponents convey information on space filling characteristics of the pattern, prefractal coefficients represent the investigated soil property as seen through a higher resolution microscope. In spite of some computational and practical limitations, image analysis of apparent soil moisture patterns could be used in connection with traditional soil moisture sampling, which always renders punctual estimates.

Os fractais no urbanismo

Dissertação para obtenção do grau de Mestre em Arquitectura com Especialização em Urbanismo, apresentada na Universidade de Lisboa - Faculdade de Arquitectura.

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.

Comportements alimentaires de jeunes utilisateurs de boîte à lunch, selon des mères québécoises

Objectif. Étudier les comportements alimentaires des enfants utilisateurs de boîte à lunch tels que décrits par les mères, en s’inspirant des descripteurs de comportements alimentaires de Jean-Pierre Poulain. Méthodes. Des entrevues individuelles et de groupes eurent lieu avec 18 mères. Une analyse de données qualitatives a été réalisée en utilisant les dimensions de Poulain comme cadre de référence. Une considération additionnelle fut intégrée dans l’analyse, celle de la dimension matérielle de la boîte à lunch. Résultats. Dimension spatiale : Les repas ont lieu dans des classes ou dans de grandes salles communes. Dimension temporelle : Le moment et la durée de la consommation du repas varient selon différents facteurs. Le moment de préparation de la boîte est aussi d’intérêt. Environnement social : Les pairs et les médias ont une grande influence dans les comportements liés à la boîte à lunch. Logique de choix : La mère est le principal décideur et acteur à l’égard du contenu. Structure de la prise : Les mères précisent des contenus associés aux repas de la veille ou des mets froids. Des desserts et des à-côtés accompagnent le repas principal. L’étude de la dimension matérielle de la boîte révèle que la facilité d’entretien est le principal critère de choix des boîtes alors que l’apparence visuelle est celui de l’enfant. L’écologie devient de plus en plus une priorité. Conclusion. Cette nouvelle approche pour l’étude des comportements alimentaires du jeune utilisateur de boîte à lunch fournit aux intervenants une autre perspective selon laquelle étudier cette activité quotidienne et/ou élaborer des projets promotionnels en santé publique.

Medidas fractales de radiografías de tórax de pacientes con diferentes patologías

Introducción: La geometría fractal permite la descripción objetiva de objetos irregulares tales como las estructuras del cuerpo humano: Por ello, en este caso, se aplicó al desarrollo de una nueva metodología de caracterización de la cavidad cardiotorácica.Material y métodos: Estudio exploratorio descriptivo en el que se desarrolló una metodología de medición basada en la geometría fractal aplicada a 14 radiografías de tórax de sujetos con diferentes patologías. Se calcularon las dimensiones fractales de la cavidad torácica, la silueta cardíaca y la superposición de estas partes con el método de Box-Counting.Resultados: Se obtuvieron nuevas medidas morfométricas objetivas y reproducibles de placas de tórax a partir de dimensiones fractales.Conclusiones: La geometría fractal permite la caracterización matemática de placas de tórax de pacientes con diferentes patologías. Es posible que el desarrollo de esta metodología en posteriores investigaciones permita generar parámetros útiles de aplicación clínica, independientes de la experiencia del médico y de su observación subjetiva, de modo que garantice la reproducibilidad y objetividad de las medidas.

Geometria frattale: analisi della lacunarita cerebrale in MRI

La geometria frattale descrive la complessità strutturale di oggetti che presentano, entro certi limiti, invarianza a fattori di scala. Obiettivo di questa tesi è l’analisi di indici frattali della morfologia cerebrale e cerebellare da immagini di risonanza magnetica (MRI) pesate T1 e della loro correlazione con l’età. A tale scopo sono state analizzate la dimensione frattale (D0) e la lacunarità (λs), indice di eterogeneità strutturale, della sostanza grigia (GM) e bianca (WM), calcolate mediante algoritmi di box counting e di differential gliding box, implementati in linguaggio C++, e regressione lineare con scelta automatica delle scale spaziali. Gli algoritmi sono stati validati su fantocci 3D ed è stato proposto un metodo per compensare la dipendenza di λs dalle dimensioni dell’immagine e dalla frazione di immagine occupata. L’analisi frattale è stata applicata ad immagini T1 a 3T del dataset ICBM (International Consortium for Brain Mapping) composto da 86 soggetti (età 19-85 anni). D0 e λs sono state rispettivamente 2.35±0.02 (media±deviazione standard) e 0.41±0.05 per la GM corticale, 2.34±0.03 e 0.35±0.05 per la WM cerebrale, 2.19±0.05 e 0.17±0.02 per la GM cerebellare, 1.95±0.06 e 0.30±0.04 per la WM cerebellare. Il coefficiente di correlazione lineare tra età e D0 della GM corticale è r=−0.38 (p=0.003); tra età e λs, r=0.72 (p<0.001) (mostrando che l’eterogeneità strutturale aumenta con l’invecchiamento) e tra età e λs compensata rispetto al volume della GM cerebrale (GMV), r=0.51 (p<0.001), superiore in valore assoluto a quello tra età e GMV (r=−0.45, p<0.001). In un modello di regressione lineare multipla, dove l’età è stata modellata da D0, λ e GMV della GM corticale, λs è risultato l’unico predittore significativo (r parziale=0.62, p<0.001). La lacunarità λs è un indice sensibile alle variazioni strutturali dovute all’invecchiamento cerebrale e si candida come biomarcatore nella valutazione della complessità cerebrale nelle malattie neurodegenerative.

The fractal properties of the retinal vascular architecture

Purpose: The human retinal vasculature has been demonstrated to exhibit fractal, or statistically self similar properties. Fractal analysis offers a simple quantitative method to characterise the complexity of the branching vessel network in the retina. Several methods have been proposed to quantify the fractal properties of the retina. Methods: Twenty five healthy volunteers underwent retinal photography, retinal oximetry and ocular biometry. A robust method to evaluate the fractal properties of the retinal vessels is proposed; it consists of manual vessel segmentation and box counting of 50 degree retinal photographs centred on the fovea. Results: Data is presented on the associations between the fractal properties of the retinal vessels and various functional properties of the retina. Conclusion Fractal properties of the retina could offer a promising tool to assess the risk and prognostic factors that define retinal disease. Outstanding efforts surround the need to adopt a standardised protocol for assessing the fractal properties of the retina, and further demonstrate its association with disease processes.

Écoulements granulaires par avalanches : indices de fluidité, fractales et multifractales

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Écoulements granulaires par avalanches : indices de fluidité, fractales et multifractales

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Relación entre atrofia cortical difusa y desempeño cognitivo : estudio en población mayor de 60 años en un hospital universitario en la ciudad de Bogotá

El presente trabajo tuvo como objetivo evaluar la existencia de la relación entre la atrofia cortical difusa objetivada por neuroimagenes cerebrales y desempeños cognitivos determinados mediante la aplicación de pruebas neuropsicológicas que evalúan memoria de trabajo, razonamiento simbólico verbal y memoria anterógrada declarativa. Participaron 114 sujetos reclutados en el Hospital Universitario Mayor Méderi de la ciudad de Bogotá mediante muestreo de conveniencia. Los resultados arrojaron diferencias significativas entre los dos grupos (pacientes con diagnóstico de atrofia cortical difusa y pacientes con neuroimagenes interpretadas como dentro de los límites normales) en todas las pruebas neuropsicológicas aplicadas. Respecto a las variables demográficas se pudo observar que el grado de escolaridad contribuye como factor neuroprotector de un posible deterioro cognitivo. Tales hallazgos son importantes para determinar protocoles tempranos de detección de posible instalación de enfermedades neurodegenerativas primarias.