A Phase Space Box-counting based Method for Arrhythmia Prediction from Electrocardiogram Time Series

Arrhythmia is one kind of cardiovascular diseases that give rise to the number of deaths and potentially yields immedicable danger. Arrhythmia is a life threatening condition originating from disorganized propagation of electrical signals in heart resulting in desynchronization among different chambers of the heart. Fundamentally, the synchronization process means that the phase relationship of electrical activities between the chambers remains coherent, maintaining a constant phase difference over time. If desynchronization occurs due to arrhythmia, the coherent phase relationship breaks down resulting in chaotic rhythm affecting the regular pumping mechanism of heart. This phenomenon was explored by using the phase space reconstruction technique which is a standard analysis technique of time series data generated from nonlinear dynamical system. In this project a novel index is presented for predicting the onset of ventricular arrhythmias. Analysis of continuously captured long-term ECG data recordings was conducted up to the onset of arrhythmia by the phase space reconstruction method, obtaining 2-dimensional images, analysed by the box counting method. The method was tested using the ECG data set of three different kinds including normal (NR), Ventricular Tachycardia (VT), Ventricular Fibrillation (VF), extracted from the Physionet ECG database. Statistical measures like mean (μ), standard deviation (σ) and coefficient of variation (σ/μ) for the box-counting in phase space diagrams are derived for a sliding window of 10 beats of ECG signal. From the results of these statistical analyses, a threshold was derived as an upper bound of Coefficient of Variation (CV) for box-counting of ECG phase portraits which is capable of reliably predicting the impeding arrhythmia long before its actual occurrence. As future work of research, it was planned to validate this prediction tool over a wider population of patients affected by different kind of arrhythmia, like atrial fibrillation, bundle and brunch block, and set different thresholds for them, in order to confirm its clinical applicability.

The relationship between interimplant distances and vascularization of the interimplant bone

Background Long-term success of the implant restorations is based upon the biology and vasculature of the bone surrounding the implants, especially for the bone between two implants. Purpose The aim of this study was to evaluate how loaded implants placed 2 or 3 mm apart influence bone vessel organization. Material and methods Six mongrel dogs were used for the study. The four mandibular premolars were extracted and 3 months later, four 4.5 x 10 mm implants were placed on each side of the mandible. The implants were placed so that two adjacent implants were 2 mm (group 1) or 3 mm (group 2) distant from each other. After 12 weeks, the implants were loaded with provisional prostheses, then metallic crowns were placed 4 weeks later. Both temporary and metallic restorations were made so that the distance between the contact point and the bone crest was 5 mm. The animals were sacrificed after 8 weeks. The hemi-mandibles were removed and prepared for analysis. The interimplant bone vasculature of the two groups was studied using scanning electron microscopic images fractal analysis. The fractal dimension (D(f)) was calculated using the box-counting method. Results The values of the D(f) for the blood vessels were significantly higher (P <.05) in the specimens of the group 2 (1.969 +/- 0.169) than the group 1 (1.556 +/- 0.246). Conclusion The presence of more blood vessels in the group 2 is another indication that 3 mm is a preferable distance for contiguous implants than the 2 mm distance. To cite this article:Traini T, Novaes AB, Piattelli A, Papalexiou V, Muglia VA. The relationship between interimplant distances and vascularization of the interimplant bone.Clin. Oral Impl. Res. 21, 2010; 822-829.doi: 10.1111/j.1600-0501.2010.01926.x.

Avaliação da caracterização de lesões em mamografia com recurso a sistemas CAD (Diagnóstico Assistido por Computador)

Mestrado em Radiações Aplicadas às Tecnologias da Saúde. Área de especialização: Imagem Digital com Radiação X.

Avaliação da caracterização de lesões em mamografia com recurso a sistemas CAD (Computer-Aided Diagnosis)

Os sistemas Computer-Aided Diagnosis (CAD) auxiliam a deteção e diferenciação de lesões benignas e malignas, aumentando a performance no diagnóstico do cancro da mama. As lesões da mama estão fortemente correlacionadas com a forma do contorno: lesões benignas apresentam contornos regulares, enquanto as lesões malignas tendem a apresentar contornos irregulares. Desta forma, a utilização de medidas quantitativas, como a dimensão fractal (DF), pode ajudar na caracterização dos contornos regulares ou irregulares de uma lesão. O principal objetivo deste estudo é verificar se a utilização concomitante de 2 (ou mais) medidas de DF – uma tradicionalmente utilizada, a qual foi designada por “DF de contorno”; outra proposta por nós, designada por “DF de área” – e ainda 3 medidas obtidas a partir destas, por operações de dilatação/erosão e por normalização de uma das medidas anteriores, melhoram a capacidade de caracterização de acordo com a escala BIRADS (Breast Imaging Reporting and Data System) e o tipo de lesão. As medidas de DF (DF contorno e DF área) foram calculadas através da aplicação do método box-counting, diretamente em imagens de lesões segmentadas e após a aplicação de um algoritmo de dilatação/erosão. A última medida baseia-se na diferença normalizada entre as duas medidas DF de área antes e após a aplicação do algoritmo de dilatação/erosão. Os resultados demonstram que a medida DF de contorno é uma ferramenta útil na diferenciação de lesões, de acordo com a escala BIRADS e o tipo de lesão; no entanto, em algumas situações, ocorrem alguns erros. O uso combinado desta medida com as quatro medidas propostas pode melhorar a classificação das lesões.

Analysis of the respiratory dynamics during normal breathing by means of pseudo phase plots and pressure-volume loops

This paper reports on the analysis of tidal breathing patterns measured during noninvasive forced oscillation lung function tests in six individual groups. The three adult groups were healthy, with prediagnosed chronic obstructive pulmonary disease, and with prediagnosed kyphoscoliosis, respectively. The three children groups were healthy, with prediagnosed asthma, and with prediagnosed cystic fibrosis, respectively. The analysis is applied to the pressure–volume curves and the pseudophaseplane loop by means of the box-counting method, which gives a measure of the area within each loop. The objective was to verify if there exists a link between the area of the loops, power-law patterns, and alterations in the respiratory structure with disease. We obtained statistically significant variations between the data sets corresponding to the six groups of patients, showing also the existence of power-law patterns. Our findings support the idea that the respiratory system changes with disease in terms of airway geometry and tissue parameters, leading, in turn, to variations in the fractal dimension of the respiratory tree and its dynamics.

Analysis of the Respiratory Dynamics During Normal Breathing by Means of Pseudophase Plots and Pressure–Volume Loops

This paper reports on the analysis of tidal breathing patterns measured during noninvasive forced oscillation lung function tests in six individual groups. The three adult groups were healthy, with prediagnosed chronic obstructive pulmonary disease, and with prediagnosed kyphoscoliosis, respectively. The three children groups were healthy, with prediagnosed asthma, and with prediagnosed cystic fibrosis, respectively. The analysis is applied to the pressure-volume curves and the pseudophase-plane loop by means of the box-counting method, which gives a measure of the area within each loop. The objective was to verify if there exists a link between the area of the loops, power-law patterns, and alterations in the respiratory structure with disease. We obtained statistically significant variations between the data sets corresponding to the six groups of patients, showing also the existence of power-law patterns. Our findings support the idea that the respiratory system changes with disease in terms of airway geometry and tissue parameters, leading, in turn, to variations in the fractal dimension of the respiratory tree and its dynamics.

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.

Multifractal portrayal of the Swiss population

Fractal geometry is a fundamental approach for describing the complex irregularities of the spatial structure of point patterns. The present research characterizes the spatial structure of the Swiss population distribution in the three Swiss geographical regions (Alps, Plateau and Jura) and at the entire country level. These analyses were carried out using fractal and multifractal measures for point patterns, which enabled the estimation of the spatial degree of clustering of a distribution at different scales. The Swiss population dataset is presented on a grid of points and thus it can be modelled as a "point process" where each point is characterized by its spatial location (geometrical support) and a number of inhabitants (measured variable). The fractal characterization was performed by means of the box-counting dimension and the multifractal analysis was conducted through the Renyi's generalized dimensions and the multifractal spectrum. Results showed that the four population patterns are all multifractals and present different clustering behaviours. Applying multifractal and fractal methods at different geographical regions and at different scales allowed us to quantify and describe the dissimilarities between the four structures and their underlying processes. This paper is the first Swiss geodemographic study applying multifractal methods using high resolution data.

Analysis of space-time environmental data in complex regions

This thesis develops a comprehensive and a flexible statistical framework for the analysis and detection of space, time and space-time clusters of environmental point data. The developed clustering methods were applied in both simulated datasets and real-world environmental phenomena; however, only the cases of forest fires in Canton of Ticino (Switzerland) and in Portugal are expounded in this document. Normally, environmental phenomena can be modelled as stochastic point processes where each event, e.g. the forest fire ignition point, is characterised by its spatial location and occurrence in time. Additionally, information such as burned area, ignition causes, landuse, topographic, climatic and meteorological features, etc., can also be used to characterise the studied phenomenon. Thereby, the space-time pattern characterisa- tion represents a powerful tool to understand the distribution and behaviour of the events and their correlation with underlying processes, for instance, socio-economic, environmental and meteorological factors. Consequently, we propose a methodology based on the adaptation and application of statistical and fractal point process measures for both global (e.g. the Morisita Index, the Box-counting fractal method, the multifractal formalism and the Ripley's K-function) and local (e.g. Scan Statistics) analysis. Many measures describing the space-time distribution of environmental phenomena have been proposed in a wide variety of disciplines; nevertheless, most of these measures are of global character and do not consider complex spatial constraints, high variability and multivariate nature of the events. Therefore, we proposed an statistical framework that takes into account the complexities of the geographical space, where phenomena take place, by introducing the Validity Domain concept and carrying out clustering analyses in data with different constrained geographical spaces, hence, assessing the relative degree of clustering of the real distribution. Moreover, exclusively to the forest fire case, this research proposes two new methodologies to defining and mapping both the Wildland-Urban Interface (WUI) described as the interaction zone between burnable vegetation and anthropogenic infrastructures, and the prediction of fire ignition susceptibility. In this regard, the main objective of this Thesis was to carry out a basic statistical/- geospatial research with a strong application part to analyse and to describe complex phenomena as well as to overcome unsolved methodological problems in the characterisation of space-time patterns, in particular, the forest fire occurrences. Thus, this Thesis provides a response to the increasing demand for both environmental monitoring and management tools for the assessment of natural and anthropogenic hazards and risks, sustainable development, retrospective success analysis, etc. The major contributions of this work were presented at national and international conferences and published in 5 scientific journals. National and international collaborations were also established and successfully accomplished. -- Cette thèse développe une méthodologie statistique complète et flexible pour l'analyse et la détection des structures spatiales, temporelles et spatio-temporelles de données environnementales représentées comme de semis de points. Les méthodes ici développées ont été appliquées aux jeux de données simulées autant qu'A des phénomènes environnementaux réels; nonobstant, seulement le cas des feux forestiers dans le Canton du Tessin (la Suisse) et celui de Portugal sont expliqués dans ce document. Normalement, les phénomènes environnementaux peuvent être modélisés comme des processus ponctuels stochastiques ou chaque événement, par ex. les point d'ignition des feux forestiers, est déterminé par son emplacement spatial et son occurrence dans le temps. De plus, des informations tels que la surface bru^lée, les causes d'ignition, l'utilisation du sol, les caractéristiques topographiques, climatiques et météorologiques, etc., peuvent aussi être utilisées pour caractériser le phénomène étudié. Par conséquent, la définition de la structure spatio-temporelle représente un outil puissant pour compren- dre la distribution du phénomène et sa corrélation avec des processus sous-jacents tels que les facteurs socio-économiques, environnementaux et météorologiques. De ce fait, nous proposons une méthodologie basée sur l'adaptation et l'application de mesures statistiques et fractales des processus ponctuels d'analyse global (par ex. l'indice de Morisita, la dimension fractale par comptage de boîtes, le formalisme multifractal et la fonction K de Ripley) et local (par ex. la statistique de scan). Des nombreuses mesures décrivant les structures spatio-temporelles de phénomènes environnementaux peuvent être trouvées dans la littérature. Néanmoins, la plupart de ces mesures sont de caractère global et ne considèrent pas de contraintes spatiales com- plexes, ainsi que la haute variabilité et la nature multivariée des événements. A cet effet, la méthodologie ici proposée prend en compte les complexités de l'espace géographique ou le phénomène a lieu, à travers de l'introduction du concept de Domaine de Validité et l'application des mesures d'analyse spatiale dans des données en présentant différentes contraintes géographiques. Cela permet l'évaluation du degré relatif d'agrégation spatiale/temporelle des structures du phénomène observé. En plus, exclusif au cas de feux forestiers, cette recherche propose aussi deux nouvelles méthodologies pour la définition et la cartographie des zones périurbaines, décrites comme des espaces anthropogéniques à proximité de la végétation sauvage ou de la forêt, et de la prédiction de la susceptibilité à l'ignition de feu. A cet égard, l'objectif principal de cette Thèse a été d'effectuer une recherche statistique/géospatiale avec une forte application dans des cas réels, pour analyser et décrire des phénomènes environnementaux complexes aussi bien que surmonter des problèmes méthodologiques non résolus relatifs à la caractérisation des structures spatio-temporelles, particulièrement, celles des occurrences de feux forestières. Ainsi, cette Thèse fournit une réponse à la demande croissante de la gestion et du monitoring environnemental pour le déploiement d'outils d'évaluation des risques et des dangers naturels et anthro- pogéniques. Les majeures contributions de ce travail ont été présentées aux conférences nationales et internationales, et ont été aussi publiées dans 5 revues internationales avec comité de lecture. Des collaborations nationales et internationales ont été aussi établies et accomplies avec succès.

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.

Construction of fractal interpolation surfaces on rectangular grids

We present a general method of generating continuous fractal interpolation surfaces by iterated function systems on an arbitrary data set over rectangular grids and estimate their Box-counting dimension.

Construction of recurrent fractal interpolation surfaces(RFISs) on rectangular grids

A recurrent iterated function system (RIFS) is a genaralization of an IFS and provides nonself-affine fractal sets which are closer to natural objects. In general, it's attractor is not a continuous surface in R3. A recurrent fractal interpolation surface (RFIS) is an attractor of RIFS which is a graph of bivariate continuous interpolation function. We introduce a general method of generating recurrent interpolation surface which are at- tractors of RIFSs about any data set on a grid.

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.