<p>Paper A: In this paper, the development and implementation of a contact algorithm based on C2-continuous surface representations is discussed. In 3D contact simulations involving models with arbitrarily curved surfaces (as in the case of vessel walls), the discretization of the contact surfaces by means of facet-based techniques could lead to numerical instabilities and finally loss of quadratic convergence. These instabilities arise mainly due to the sliding of contractor (slave) nodes over the boundaries of target (master) contact facets, where jumps of the normal vector are experienced. The paper addresses successfully this problem, by discretization of the target surfaces by means of C2-continuous parameterization schemes. Initially, the uniform cubic B-spline surfaces are introduced. Next, in an attempt for more accurate representations of the geometric models of the contact surfaces, a new parameterization based on the expression of cubic B-splines is developed. The two approaches are implemented into a finite element framework and more specifically, into the multipurpose finite element analysis program FEAP. The special merits of the developed algorithms and the advantages of the smooth surfaces over facet-based approaches are exhibited through a classical contact mechanics problem, considering incompressibility, finite deformations and large slidings. Next, a simulation of balloon angioplasty with stenting is presented, where the contact between both medical devices (balloon and stent) with the arterial wall is modeled. The arterial wall is modeled in this first approach, as hyperelastic, homogeneous, isotropic, while a cylindrically orthotropic model is developed to capture the nonlinear, anisotropic behavior of the balloon catheter under pressure. Two stents with the same geometry but different strut thickness, are studied. Both are considered elasto-plastic. The performed simulations point out the outcome of the balloon angioplasty and stenting in terms of luminal gain and mechanical strains. Finally, a comparison between the two stent configurations is presented.</p><p>Paper B: The second paper makes use of the contact tool developed in Paper A and focuses on the changes of the mechanical environment of the arterial wall due to stenting, as a function of a set of stent design parameters. In particular, Paper B presents a detailed geometric and material model of a postmortem human iliac artery, composed by distinct tissue components, each associated with specific mechanical properties. The constitutive formulation for the artery considers anisotropic, highly nonlinear mechanical characteristics under supraphysiological loadings. The material and structural parameters of the arterial model are obtained through uniaxial tensile tests on stripes extracted from the several arterial tissues that form the stenosis, axially and circumferentially oriented. Through cooperation with a well-established stent manufacturing company, an iliac stent was acquired. The dimensions of the stent are measured under a reflected-light microscope, while it is parameterized in such a way as to enable new designs to be simply generated through variations of its geometric parameters. The 3D balloon-stent-artery interaction is simulated by making use of the smooth contact surfaces with C2-continuity, as previously mentioned. Next, scalar quantities attempt to characterize the arterial wall changes after stenting, in form of contact forces induced by the stent struts, stresses within the individual components and luminal change. These numerically derived quantities allow the determination of the most appropriate stent configuration for an individual stenosis. Therefore, the proposed methodology has the potential to provide a scientific basis for optimizing treatment procedures, stent material and geometries on a patient-specific level.</p>

Cette thèse porte sur l'étude de la régression non paramétrique en présence de mesures répétées. D'abord, nous étendons aux estimateurs splines de lissage les vitesses de convergence présentées dans la littérature pour d'autres estimateurs usuels sous différentes hypothèses classiques de dépendance des données. Ensuite, dans le cadre de l'estimation de la moyenne d'un processus aléatoire à temps continu, nous généralisons les résultats existants sur la convergence en moyenne quadratique et nous établissons de nouveaux résultats de normalité asymptotique pour les distributions finies-dimensionnelles. Enfin, dans le cadre d'un échantillon fini et corrélé, nous comparons les performances d'estimateurs construits par moindres carrés ordinaires ou généralisés, nous proposons une méthode efficace de sélection du paramètre de lissage tenant compte de la structure de covariance des données, et à travers des simulations, nous mettons en évidence l'apport du lissage local par rapport au lissage global.

Dans les industries agro-alimentaires ainsi que dans d'autres secteurs d'activités, l'analyse sensorielle est la clé pour répondre aux attentes des consommateurs. Cette discipline est le plus souvent basée sur l'établissement de profils sensoriels à partir de notes attribuées par des juges entraînés selon une liste de descripteurs (variables sensorielles). Dans ce type d'étude, il importe d'étudier la performance des juges et d'en tenir compte dans l'établissement des profils sensoriels. Dans cette perspective, nous proposons une démarche qui permet de procurer des indicateurs de performance du jury et de chacun des juges et de tenir compte de cette performance pour une détermination d'un tableau moyen. Des tests d'hypothèses pour évaluer la significativité de la contribution des juges à la détermination du compromis sont également proposés.<br />Depuis une vingtaine d'années, les courbes temps-intensité (TI) qui permettent de décrire l'évolution d'une sensation au cours de l'expérience sont de plus en plus populaires parmi les praticiens de l'analyse sensorielle. La difficulté majeure pour l'analyse des courbes TI provient d'un effet juge important qui se traduit par la présence d'une signature propre à chaque juge. Nous proposons une approche fonctionnelle basée sur les fonctions B-splines qui permet de réduire l'effet juge en utilisant une procédure d'alignement de courbes.<br />D'autres données sensorielles au cours du temps existent telles que le suivi de la dégradation organoleptique de produits alimentaires. Pour les étudier, nous proposons la modélisation par des chaînes de Markov cachées, de manière à pouvoir ensuite visualiser graphiquement la suivi de la dégradation.

Reproduction de : Thèse de 3e cycle : mathématiques appliquées : Grenoble 1 : 1987. / Titre provenant de l'écran-titre.

Thèse doctorat : Informatique : Rennes 1 : 2008. / Titre provenant de la page du titre du document électronique. Bibliogr. p. 169-182.

Reproduction de : Thèse de doctorat : Informatique : Lille 1 : 2004. / N° d'ordre (Lille 1) : 3520. Résumé en français. Titre provenant de la page de titre du document numérisé. Bibliogr. p. 193-204. Index.

The current thesis is structured in four parts. Vector smoothing methods are used to study environmental data, in particular records of extreme precipitation, the models utilized belong to the vector generalized additive class. In the statistical analysis of observational studies the identification and adjustment for prognostic factors is an important component of the analysis; employing flexible statistical methods to identify and characterize the effect of potential prognostic factors in a clinical trial, namely "generalized additive models", presents an alternative to the traditional linear statistical model. The classes of models for which the methodology gives generalized additive extensions include grouped survival data from the Surveillance, Epidemiology, and End Results tumors of the brain and the central nervous system database; we are employing piecewise linear functions of the covariates to characterize the survival experienced by the population. Finally, both descriptive and analytical methods are utilized to study incidence rates and tumor sizes associated with the disease.

To simulate increasingly complex physical phenomena and systems, tightly integrated design-through-analysis (DTA) tools are essential. In this dissertation, the complementary strengths of isogeometric analysis and T-splines are coupled and enhanced to create a seamless DTA framework. In all cases, the technology de- veloped meets the demands of both design and analysis. In isogeometric analysis, the smooth geometric basis is used as the basis for analysis. It has been demonstrated that smoothness offers important computational advantages over standard finite elements. T-splines are a superior alternative to NURBS, the current geometry standard in computer-aided design systems. T-splines can be locally refined and can represent complicated designs as a single watertight geometry. These properties make T-splines an ideal discretization technology for isogeometric analysis and, on a higher level, a foundation upon which unified DTA technologies can be built. We characterize analysis-suitable T-splines and develop corresponding finite element technology, including the appropriate treatment of extraordinary points (i.e., unstructured meshing). Analysis-suitable T-splines form a practically useful subset of T-splines. They maintain the design flexibility of T-splines, including an efficient and highly localized refinement capability, while preserving the important analysis-suitable mathematical properties of the NURBS basis. We identify Bézier extraction as a unifying paradigm underlying all isogeometric element technology. Bézier extraction provides a finite element representation of NURBS or T-splines, and facilitates the incorporation of T-splines into existing finite element programs. Only the shape function subroutine needs to be modified. Additionally, Bézier extraction is automatic and can be applied to any T-spline regardless of topological complexity or polynomial degree. In particular, it represents an elegant treatment of T-junctions, referred to as "hanging nodes" in finite element analysis We then detail a highly localized analysis-suitable h-refinement algorithm. This algorithm introduces a minimal number of superfluous control points and preserves the properties of an analysis-suitable space. Importantly, our local refinement algorithm does not introduce a complex hierarchy of meshes. In other words, all local refinement is done on one control mesh on a single hierarchical “level” and all control points have similar influence on the shape of the surface. This feature is critical for its adoption and usefulness as a design tool. Finally, we explore the behavior of T-splines in finite element analysis. It is demonstrated that T-splines possess similar convergence properties to NURBS with far fewer degrees of freedom. We develop an adaptive isogeometric analysis framework which couples analysis-suitable T-splines, local refinement, and Bézier extraction and apply it to the modeling of damage and fracture processes. These examples demonstrate the feasibility of applying T-spline element technology to very large problems in two and three dimensions and parallel implementations. / text

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