53 resultados para dimensional analysis
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The choice of sample preparation protocol is a critical influential factor for isoelectric focusing which in turn affects the two-dimensional gel result in terms of quality and protein species distribution. The optimal protocol varies depending on the nature of the sample for analysis and the properties of the constituent protein species (hydrophobicity, tendency to form aggregates, copy number) intended for resolution. This review explains the standard sample buffer constituents and illustrates a series of protocols for processing diverse samples for two-dimensional gel electrophoresis, including hydrophobic membrane proteins. Current methods for concentrating lower abundance proteins, by removal of high abundance proteins, are also outlined. Finally, since protein staining is becoming increasingly incorporated into the sample preparation procedure, we describe the principles and applications of current (and future) pre-electrophoretic labelling methods.
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PURPOSE: To investigate the feasibility of high-resolution selective three-dimensional (3D) magnetic resonance coronary angiography (MRCA) in the evaluation of coronary artery stenoses. MATERIALS AND METHODS: In 12 patients with coronary artery stenoses, MRCA of the coronary artery groups, including the coronary segments with stenoses of 50% or greater based on conventional x-ray coronary angiography (CAG), was performed with double-oblique imaging planes by orienting the 3D slab along the major axis of each right coronary artery-left circumflex artery (RCA-LCX) group and each left main trunk-left anterior descending artery (LMT-LAD) group. Ten RCA-LCX and five LMT-LAD MR angiograms were obtained, and the results were compared with those of conventional x-ray angiography. RESULTS: Among 70 coronary artery segments expected to be covered, a total of 49 (70%) segments were fully demonstrated in diagnostic quality. The identification of segmental location of stenoses showed as high an accuracy as 96%. The retrospective analysis for stenosis of 50% or greater yielded the sensitivity, specificity, and accuracy of 80%, 85%, and 84%, respectively. CONCLUSION: Selective 3D MRCA has the potential for segment-by-segment evaluation of major portions of the right and left coronary arteries with high accuracy.
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In this study we have demonstrated the potential of two-dimensional electrophoresis (2DE)-based technologies as tools for characterization of the Leishmania proteome (the expressed protein complement of the genome). Standardized neutral range (pH 5-7) proteome maps of Leishmania (Viannia) guyanensis and Leishmania (Viannia) panamensis promastigotes were reproducibly generated by 2DE of soluble parasite extracts, which were prepared using lysis buffer containing urea and nonidet P-40 detergent. The Coomassie blue and silver nitrate staining systems both yielded good resolution and representation of protein spots, enabling the detection of approximately 800 and 1,500 distinct proteins, respectively. Several reference protein spots common to the proteomes of all parasite species/strains studied were isolated and identified by peptide mass spectrometry (LC-ES-MS/MS), and bioinformatics approaches as members of the heat shock protein family, ribosomal protein S12, kinetoplast membrane protein 11 and a hypothetical Leishmania-specific 13 kDa protein of unknown function. Immunoblotting of Leishmania protein maps using a monoclonal antibody resulted in the specific detection of the 81.4 kDa and 77.5 kDa subunits of paraflagellar rod proteins 1 and 2, respectively. Moreover, differences in protein expression profiles between distinct parasite clones were reproducibly detected through comparative proteome analyses of paired maps using image analysis software. These data illustrate the resolving power of 2DE-based proteome analysis. The production and basic characterization of good quality Leishmania proteome maps provides an essential first step towards comparative protein expression studies aimed at identifying the molecular determinants of parasite drug resistance and virulence, as well as discovering new drug and vaccine targets.
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Introduction: Ankle arthropathy is associated with a decreased motion of the ankle-hindfoot during ambulation. Ankle arthrodesis was shown to result in degeneration of the neighbour joints of the foot. Inversely, total ankle arthroplasty conceptually preserves the adjacent joints because of the residual mobility of the ankle but this has not been demonstrated yet in vivo. It has also been reported that degenerative ankle diseases, and even arthrodesis, do not result in alteration of the knee and hip joints. We present the preliminary results of a new approach of this problem based on ambulatory gait analysis. Patients and Methods: Motion analysis of the lower limbs was performed using a Physilog® (BioAGM, CH) system consisting of three-dimensional (3D) accelerometer and gyroscope, coupled to a magnetic system (Liberty©, Polhemus, USA). Both systems have been validated. Three groups of two patients were included into this pilot study and compared to healthy subjects (controls) during level walking: patients with ankle osteoarthritis (group 1), patients treated by ankle arthrodesis (group 2), patients treated by total ankle prosthesis (group 3). Results: Motion patterns of all analyzed joints over more than 20 gait cycles in each subject were highly repeatable. Motion amplitude of the ankle-hindfoot in control patients was similar to recently reported results. Ankle arthrodesis limited the motion of the ankle-hindfoot in the sagittal and horizontal planes. The prosthetic ankle allowed a more physiologic movement in the sagittal plane only. Ankle arthritis and its treatments did not influence the range of motion of the knee and hip joint during stance phase, excepted for a slight decrease of the hip flexion in groups 1 and 2. Conclusion: The reliability of the system was shown by the repeatability of the consecutive measurements. The results of this preliminary study were similar to those obtained through laboratory gait analysis. However, our system has the advantage to allow ambulatory analysis of 3D kinematics of the lower limbs outside of a gait laboratory and in real life conditions. To our knowledge this is a new concept in the analysis of ankle arthropathy and its treatments. Therefore, there is a potential to address specific questions like the difficult comparison of the benefits of ankle arthroplasty versus arthrodesis. The encouraging results of this pilot study offer the perspective to analyze the consequences of ankle arthropathy and its treatments on the biomechanics of the lower limbs ambulatory, in vivo and in daily life conditions.
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Résumé : Les jasmonates (JA), une famille d'hor1none végétale, jouent un rôle central dans la réponse à la blessure, et aux attaques d'insectes et de pathogènes. Les JA sont principalement dérivés d'un acide gras, l'acide linolénique. L'addition par une lipoxygénase d'une molécule d'oxygène à l'acide linolénique initie la synthèse de JA. Cependant les mécanismes régulant l'activation de la biosynthèse de JA ne sont pas encore connus. C'est pour cette raison que dans ce travail, nous avons caractérisé chez Arabidopsis thaliana (l'Arabette des Dames) un mutant fou2 dont l'activité lipoxygénase est plus élevée que celle d'une plante sauvage. Les niveaux de JA sont constitutivement plus élevés et l'activation de la synthèse de JA après blessure est fortement plus induite chez fou2 que chez le type sauvage. En outre, fou2 est plus résistant au pathogène Botrytis cinerea et à la chenille Spodoptera littoralis. Afin de comprendre quel mécanisme chez fou2 génére ce phénotype, nous avons cloné le gène responsable du phénotype de fou2. Le mutant fou2 porte une mutation dans le gène d'un canal à deux pores transportant probablement du potassium, du lumen de la vacuole végétale vers le compartiment cytosolique. L'analyse du protéome de fou2 a permis d'identifier une expression plus élevée de sept protéines régulées par les JA ou le stress. La découverte de l'implication d'un canal dans le phénotype de fou2 renforce l'hypothèse que les flux de cations pourraient être impliqués dans les étapes précoces de la synthèse des JA. Nous avons également étudié le protéome et la physiologie d'une feuille blessée, Pour évaluer les changements d'expression protéique en réponse à la blessure et contrôlés par les JA, nous avons quantifié l'expression de 5937 protéines chez une plante d'Arabidopsis sauvage et chez un mutant incapable de synthétiser des JA. Parmi ces 5937 protéines, nous avons identifié 99 protéines régulées par la blessure chez le type sauvage. Nous avons observé pour 65% des protéines dont l'expression protéique changeait après blessure une bonne corrélation entre la quantité de transcrits et de protéines. Plusieurs enzymes de la voie des chorismates impliquées dans la biosynthèse des acides aminés phénoliques étaient induites par les JA après blessure. Une quantification des acides aminés a montré que les niveaux d'acides aminés phénoliques augmentaient significativement après blessure. La blessure induisait aussi des changements dans l'expression de protéines impliquées dans la réponse au stress et particulièrement au stress oxydatif. Nous avons quantifié l'état réduit et oxydé du glutathion, un tripeptide qui, sous sa forme réduite, est l'antioxydant majeur des cellules. Nous avons trouvé une quantité significativement plus élevée de glutathion oxydé chez le type sauvage blessé que chez la plante aus blessée. Ce résultat suggère que la génération d'un stress oxydatif et la proportion relative de glutathions réduits et oxydés sont contrôlés par les JA après blessure. Abstract : Plants possess a family of potent fatty acid-derived wound-response and developmental regulators: the jasmonates. These compounds are derived from the tri?unsaturated fatty acid a-linolenic-acid (18:3). Addition of an oxygen molecule to 18:3 by 13-lipoxygenases (13-LOX) initiates JA biosynthesis. Actually components regulating the activation of JA biosynthesis are poorly defined. Therefore we characterized in Arabidopsis thaliana the fatty acid Qxygenation upregulated 2 (fou2) mutant, which was previously isolated in a screen for mutants with an enhanced 13-LOX activity. As a consequence of this increased 13-LOX activity, JA levels in fou2 are higher than in wild type (WT) and wounding strongly increased JA biosynthesis compared to WT. fou2 was more resistant to the fungus Botrytis cinerea and the generalist caterpillar Spodaptera littomlis, The fou2 mutant carries a missense mutation in the Two Pore Channel 1 gene (TPCJ), which encodes a vacuolar cation channel transporting probably K* into the cytosol. Patchclamp analysis of fou2 vacuolar membranes showed faster time-dependent conductivity and activation of the mutated channel at lower membrane potentials than wild-type. Proteomic analysis of fou2 leaves identified increased levels of seven biotic stress- and JA- inducible proteins. The discovery of the implication of a channel in the fou2 phenotype strenghtens the hypothesis that cation fluxes might be implicated in early steps of JA synthesis. We further concentrated on the proteome and leaf physiology in the region proximal to wounds in Arabidopsis using the WT and the aos JA-biosynthesis deficient mutant in order to find JA- induced proteins changes. We used two successive proteomic methods to assess protein changes in response to wounding Arabidopsis leaves, two dimensional electrophoresis (2DE) and linear trap quadrupole ion-trap mass spectrometry. In total 5937 proteins were quantified. We identified 99 wound-regulated proteins in the WT. Most these proteins were also wound-regulated at the transcript level showing a good correlation between transcript and protein abundance. We identified several wound-regulated enzymes involved in amino acid biosynthesis and confirmed this result by amino acid quantification. Proteins involved in stress reponses were upregulated, particularly in redox species regulation. We found a significantly higher quantity of oxidized glutathione in wounded WT relative to wounded aos leaves. This result suggests that levels of reduced glutathione are controlled by JA after wounding.
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Three-dimensional sequence stratigraphy is a potent exploration and development tool for the discovery of subtle stratigraphic traps. Reservoir morphology, heterogeneity and subtle stratigraphic trapping mechanisms can be better understood through systematic horizontal identification of sedimentary facies of systems tracts provided by three-dimensional attribute maps used as an important complement to the sequential analysis on the two-dimensional seismic lines and the well log data. On new prospects as well as on already-producing fields, the additional input of sequential analysis on three-dimensional data enables the identification, location and precise delimitation of new potentially productive zones. The first part of this paper presents four typical horizontal seismic facies assigned to the successive systems tracts of a third- or fourth-order sequence deposited in inner to outer neritic conditions on a elastic shelf. The construction of this synthetic representative sequence is based on the observed reproducibility of the horizontal seismic facies response to cyclic eustatic events on more than 35 sequences registered in the Gulf coast Plio-Pleistocene and Late Miocene, offshore Louisiana in the West Cameron region of the Gulf of Mexico. The second part shows how three-dimensional sequence stratigraphy can contribute in localizing and understanding sedimentary facies associated with productive zones. A case study in the early Middle Miocene Cibicides opima sands shows multiple stacked gas accumulations in the top slope fan, prograding wedge and basal transgressive systems tract of the third-order sequence between SB15.5 and SB 13.8 Ma.
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Background/Aims. Recently, peripheral blood mononuclear cell transcriptome analysis has identified genes that are upregulated in relapsing minimal-change nephrotic syndrome (MCNS). In order to investigate protein expression in peripheral blood mononuclear cells (PBMC) from relapsing MCNS patients, we performed proteomic comparisons of PBMC from patients with MCNS in relapse and controls. METHODS: PBMC from a total of 20 patients were analysed. PBMC were taken from five patients with relapsing MCNS, four in remission, five patients with other glomerular diseases and six controls. Two dimensional electrophoresis was performed and proteome patterns were compared. RESULTS: Automatic heuristic clustering analysis allowed us to pool correctly the gels from the MCNS patients in the relapse and in the control groups. Using hierarchical population matching, nine spots were found to be increased in PBMC from MCNS patients in relapse. Four spots were identified by mass spectrometry. Three of the four proteins identified (L-plastin, alpha-tropomyosin and annexin III) were cytoskeletal-associated proteins. Using western blot and immunochemistry, L-plastin and alpha-tropomyosin 3 concentrations were found to be enhanced in PBMC from MCNS patients in relapse. Conclusions. These data indicate that a specific proteomic profile characterizes PBMC from MCNS patients in relapse. Proteins involved in PBMC cytoskeletal rearrangement are increased in relapsing MCNS. We hypothesize that T-cell cytoskeletal rearrangement may play a role in the pathogenesis of MCNS by altering the expression of cell surface receptors and by modifying the interaction of these cells with glomerular cells.
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Biochemical systems are commonly modelled by systems of ordinary differential equations (ODEs). A particular class of such models called S-systems have recently gained popularity in biochemical system modelling. The parameters of an S-system are usually estimated from time-course profiles. However, finding these estimates is a difficult computational problem. Moreover, although several methods have been recently proposed to solve this problem for ideal profiles, relatively little progress has been reported for noisy profiles. We describe a special feature of a Newton-flow optimisation problem associated with S-system parameter estimation. This enables us to significantly reduce the search space, and also lends itself to parameter estimation for noisy data. We illustrate the applicability of our method by applying it to noisy time-course data synthetically produced from previously published 4- and 30-dimensional S-systems. In addition, we propose an extension of our method that allows the detection of network topologies for small S-systems. We introduce a new method for estimating S-system parameters from time-course profiles. We show that the performance of this method compares favorably with competing methods for ideal profiles, and that it also allows the determination of parameters for noisy profiles.
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We review methods to estimate the average crystal (grain) size and the crystal (grain) size distribution in solid rocks. Average grain sizes often provide the base for stress estimates or rheological calculations requiring the quantification of grain sizes in a rock's microstructure. The primary data for grain size data are either 1D (i.e. line intercept methods), 2D (area analysis) or 3D (e.g., computed tomography, serial sectioning). These data have been used for different data treatments over the years, whereas several studies assume a certain probability function (e.g., logarithm, square root) to calculate statistical parameters as the mean, median, mode or the skewness of a crystal size distribution. The finally calculated average grain sizes have to be compatible between the different grain size estimation approaches in order to be properly applied, for example, in paleo-piezometers or grain size sensitive flow laws. Such compatibility is tested for different data treatments using one- and two-dimensional measurements. We propose an empirical conversion matrix for different datasets. These conversion factors provide the option to make different datasets compatible with each other, although the primary calculations were obtained in different ways. In order to present an average grain size, we propose to use the area-weighted and volume-weighted mean in the case of unimodal grain size distributions, respectively, for 2D and 3D measurements. The shape of the crystal size distribution is important for studies of nucleation and growth of minerals. The shape of the crystal size distribution of garnet populations is compared between different 2D and 3D measurements, which are serial sectioning and computed tomography. The comparison of different direct measured 3D data; stereological data and direct presented 20 data show the problems of the quality of the smallest grain sizes and the overestimation of small grain sizes in stereological tools, depending on the type of CSD. (C) 2011 Published by Elsevier Ltd.
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Background: Panitumumab (pmab), a fully human monoclonal antibody against the epidermal growth factor receptor (EGFR), is indicated as monotherapy for treatment of metastatic colorectal cancer. This ongoing study is designed to assess the efficacy and safety of pmab in combination with radiotherapy (PRT) compared to chemoradiotherapy (CRT) as initial treatment of unresected, locally advanced SCCHN (ClinicalTrials.gov Identifier: NCT00547157). Methods: This is a phase 2, open-label, randomized, multicenter study. Eligible patients (pts) were randomized 2:3 to receive cisplatin 100 mg/m2 on days 1 and 22 of RT or pmab 9.0 mg/kg on days 1, 22, and 43. Accelerated RT (70 to 72 Gy − delivered over 6 to 6.5 weeks) was planned for all pts and was delivered either by intensity-modulated radiation therapy (IMRT) modality or by three-dimensional conformal (3D-CRT) modality. The primary endpoint is local-regional control (LRC) rate at 2 years. Key secondary endpoints include PFS, OS, and safety. An external, independent data monitoring committee conducts planned safety and efficacy reviews during the course of the trial. Results: Pooled data from this planned interim safety analysis includes the first 52 of the 150 planned pts; 44 (84.6%) are male; median (range) age is 57 (33−77) years; ECOG PS 0: 65%, PS 1: 35%; 20 (39%) pts received IMRT, and 32 (61%) pts received 3D-CRT. Fifty (96%) pts completed RT, and 50 pts received RT per protocol without a major deviation. The median (range) total RT dose administered was 72 (64−74) Gy. The most common grade _ 3 adverse events graded using the CTCAE version 3.0 are shown (Table). Conclusions: After the interim safety analysis, CONCERT-2 continues per protocol. Study enrollment is estimated to be completed by October 2009.
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An epidemic model is formulated by a reactionâeuro"diffusion system where the spatial pattern formation is driven by cross-diffusion. The reaction terms describe the local dynamics of susceptible and infected species, whereas the diffusion terms account for the spatial distribution dynamics. For both self-diffusion and cross-diffusion, nonlinear constitutive assumptions are suggested. To simulate the pattern formation two finite volume formulations are proposed, which employ a conservative and a non-conservative discretization, respectively. An efficient simulation is obtained by a fully adaptive multiresolution strategy. Numerical examples illustrate the impact of the cross-diffusion on the pattern formation.
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The research considers the problem of spatial data classification using machine learning algorithms: probabilistic neural networks (PNN) and support vector machines (SVM). As a benchmark model simple k-nearest neighbor algorithm is considered. PNN is a neural network reformulation of well known nonparametric principles of probability density modeling using kernel density estimator and Bayesian optimal or maximum a posteriori decision rules. PNN is well suited to problems where not only predictions but also quantification of accuracy and integration of prior information are necessary. An important property of PNN is that they can be easily used in decision support systems dealing with problems of automatic classification. Support vector machine is an implementation of the principles of statistical learning theory for the classification tasks. Recently they were successfully applied for different environmental topics: classification of soil types and hydro-geological units, optimization of monitoring networks, susceptibility mapping of natural hazards. In the present paper both simulated and real data case studies (low and high dimensional) are considered. The main attention is paid to the detection and learning of spatial patterns by the algorithms applied.
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We performed an analysis of a substudy of the randomized Tamoxifen Exemestane Adjuvant Multinational trial to determine the effects of exemestane (EXE) and tamoxifen (TAM) adjuvant treatment on bone mineral density (BMD) measured by dual-energy X-ray absorptiometry compared with the trabecular bone score, a novel grey-level texture measurement that correlates with 3-dimensional parameters of bone texture in postmenopausal women with hormone receptor-positive breast cancer for the first time. In total, 36 women were randomized to receive TAM (n = 17) or EXE (n = 19). Patients receiving TAM showed a mean increase of BMD in lumbar spine from baseline of 1.0%, 1.5%, and 1.9% and in trabecular bone score of 2.2%, 3.5%, and 3.3% at 6-, 12-, and 24-mo treatment, respectively. Conversely, patients receiving EXE showed a mean decrease from baseline in lumbar spine BMD of -2.3%, -3.6%, and -5.3% and in trabecular bone score of -0.9%, -1.7%, and -2.3% at 6-, 12-, and 24-mo treatment, respectively. Changes in trabecular bone score from baseline at spine were also significantly different between EXE and TAM: p = 0.05, 0.007, and 0.006 at 6, 12, and 24mo, respectively. TAM induced an increase in BMD and bone texture analysis, whereas EXE resulted in decreases. The results were independent from each other.
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Glial fibrillary acidic protein, GFAP, is a major intermediate filament protein of glial cells and major cytoskeletal structure in astrocytes. The entorhinal cortex has a key role in memory function and is one of the first brain areas to reveal hallmark structures of Alzheimer's disease and therefore provides an ideal tissue to investigate incipient neurodegenerative changes. Here we have analyzed age- and disease-related occurrence and composition of GFAP in the human entorhinal cortex by using one- and two-dimensional electrophoresis, Western blots and immunocytochemistry combined with confocal microscopy. A novel monoclonal antibody, GF-02, was characterized that mainly reacted with intact GFAP molecules and indicated that more acidic and soluble GFAP forms were also more susceptible to degradation. GFAP and vimentin increased with aging and in Alzheimer's disease (AD). Two-dimensional electrophoresis and Western blots revealed a complex GFAP pattern, both in aging and AD with different modification and degradation forms. Immunohistochemistry indicated that reactive astrocytes mainly accumulated in relation to neurofibrillary tangles and senile plaques in deeper entorhinal cortex layers. GFAP may be used as an additional but not exclusive diagnostic tool in the evaluation of neurodegenerative diseases because its levels change with age and respond to senile plaque and tangle formation.
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The proportion of population living in or around cites is more important than ever. Urban sprawl and car dependence have taken over the pedestrian-friendly compact city. Environmental problems like air pollution, land waste or noise, and health problems are the result of this still continuing process. The urban planners have to find solutions to these complex problems, and at the same time insure the economic performance of the city and its surroundings. At the same time, an increasing quantity of socio-economic and environmental data is acquired. In order to get a better understanding of the processes and phenomena taking place in the complex urban environment, these data should be analysed. Numerous methods for modelling and simulating such a system exist and are still under development and can be exploited by the urban geographers for improving our understanding of the urban metabolism. Modern and innovative visualisation techniques help in communicating the results of such models and simulations. This thesis covers several methods for analysis, modelling, simulation and visualisation of problems related to urban geography. The analysis of high dimensional socio-economic data using artificial neural network techniques, especially self-organising maps, is showed using two examples at different scales. The problem of spatiotemporal modelling and data representation is treated and some possible solutions are shown. The simulation of urban dynamics and more specifically the traffic due to commuting to work is illustrated using multi-agent micro-simulation techniques. A section on visualisation methods presents cartograms for transforming the geographic space into a feature space, and the distance circle map, a centre-based map representation particularly useful for urban agglomerations. Some issues on the importance of scale in urban analysis and clustering of urban phenomena are exposed. A new approach on how to define urban areas at different scales is developed, and the link with percolation theory established. Fractal statistics, especially the lacunarity measure, and scale laws are used for characterising urban clusters. In a last section, the population evolution is modelled using a model close to the well-established gravity model. The work covers quite a wide range of methods useful in urban geography. Methods should still be developed further and at the same time find their way into the daily work and decision process of urban planners. La part de personnes vivant dans une région urbaine est plus élevé que jamais et continue à croître. L'étalement urbain et la dépendance automobile ont supplanté la ville compacte adaptée aux piétons. La pollution de l'air, le gaspillage du sol, le bruit, et des problèmes de santé pour les habitants en sont la conséquence. Les urbanistes doivent trouver, ensemble avec toute la société, des solutions à ces problèmes complexes. En même temps, il faut assurer la performance économique de la ville et de sa région. Actuellement, une quantité grandissante de données socio-économiques et environnementales est récoltée. Pour mieux comprendre les processus et phénomènes du système complexe "ville", ces données doivent être traitées et analysées. Des nombreuses méthodes pour modéliser et simuler un tel système existent et sont continuellement en développement. Elles peuvent être exploitées par le géographe urbain pour améliorer sa connaissance du métabolisme urbain. Des techniques modernes et innovatrices de visualisation aident dans la communication des résultats de tels modèles et simulations. Cette thèse décrit plusieurs méthodes permettant d'analyser, de modéliser, de simuler et de visualiser des phénomènes urbains. L'analyse de données socio-économiques à très haute dimension à l'aide de réseaux de neurones artificiels, notamment des cartes auto-organisatrices, est montré à travers deux exemples aux échelles différentes. Le problème de modélisation spatio-temporelle et de représentation des données est discuté et quelques ébauches de solutions esquissées. La simulation de la dynamique urbaine, et plus spécifiquement du trafic automobile engendré par les pendulaires est illustrée à l'aide d'une simulation multi-agents. Une section sur les méthodes de visualisation montre des cartes en anamorphoses permettant de transformer l'espace géographique en espace fonctionnel. Un autre type de carte, les cartes circulaires, est présenté. Ce type de carte est particulièrement utile pour les agglomérations urbaines. Quelques questions liées à l'importance de l'échelle dans l'analyse urbaine sont également discutées. Une nouvelle approche pour définir des clusters urbains à des échelles différentes est développée, et le lien avec la théorie de la percolation est établi. Des statistiques fractales, notamment la lacunarité, sont utilisées pour caractériser ces clusters urbains. L'évolution de la population est modélisée à l'aide d'un modèle proche du modèle gravitaire bien connu. Le travail couvre une large panoplie de méthodes utiles en géographie urbaine. Toutefois, il est toujours nécessaire de développer plus loin ces méthodes et en même temps, elles doivent trouver leur chemin dans la vie quotidienne des urbanistes et planificateurs.