Ce travail de thèse porte sur la modélisation de la cinétique de stratification des phases liquides oxyde et métallique dans un bain de corium (système U-O-Zr-acier) du point de vue de la diffusion multi-composants et multiphasique. Cette démarche de recherche s’inscrit dans le cadre du développement d’une modélisation « fine » du comportement d’un bain de corium basée sur une approche CFD (« Computational Fluid Dynamics ») de la thermo-hydraulique. Elle vise à améliorer la compréhension des phénomènes mis en jeu et construire des lois de fermetures adéquates pour des modèles macroscopiques intégraux.Pour ce faire, la méthode du champ de phase couplée avec une fonctionnelle d’énergie utilisant la méthode CALPHAD se révèle être un outil pertinent.Dans une première partie, nous nous sommes intéressés au système binaire U-O. Nous avons développé un modèle à interface diffuse (basé sur une équation de Cahn-Hilliard) pour décrire la diffusion dans ce système. Nous avons procédé à la mise en place du couplage entre ce modèle et une base de données thermodynamiques CALPHAD, ainsi qu’au paramétrage d’un tel modèle avec en particulier une procédure d’élargissement de l’interface.Ensuite, dans le cadre d’une modélisation sur le système ternaire U-O-Zr nous avons proposé une généralisation du modèle à interface diffuse par le biais d’une hypothèse d’équilibre local des mécanismes d’oxydo-réduction. Nous avons porté une attention particulière à l’analyse de ce modèle par le biais de simulations numériques 1D en nous intéressant notamment à l’état stationnaire et aux profils de composition obtenus.Finalement, nous avons montré l’application de ce modèle au système U-O-Zr-Fe. Pour cela, nous avons considéré une configuration similaire aux essais expérimentaux à « petite échelle » relatifs à l’étude de la stratification d’un bain oxyde-métal. / This Ph.D. topic is focused on the modelling of stratification kinetics for an oxide-metal corium pool (U-O-Zr-steel system) in terms of multicomponent and multiphase diffusion. This work is part of a larger research effort for the development of a detailed corium pool modelling based on a CFD approach (“Computational Fluid Dynamics”) for thermal-hydraulics. The overall goal is to improve the understanding of the involved phenomena and obtain closure laws for integral macroscopic models.The phase-field method coupled with an energy functional using the CALPHAD method appears to be relevant for this purpose.In a first part, this works has been focused on the U-O binary system. We have developed a diffuse interface model (based on a Cahn-Hilliard equation) in order to describe the diffusion process in this system. This model has been coupled with a CALPHAD thermodynamic database and its parameterization has been developed with, in particular, an upscaling procedure related to the interface thickness.Then, within the framework of a modelling for the U-O-Zr ternary system, we have proposed a generalization of the diffuse interface model through an assumption of local equilibrium for redox mechanisms. A particular attention was paid to the model analysis by 1D numerical simulations with a special focus on the steady state composition profiles.Finally we have applied this model to the U-O-Zr-Fe system. For that purpose, we have considered a configuration close to small-scale experimental tests dedicated to the study of oxide-metal corium pool stratification.

No description available.

New advances in computational modeling and instrumentation in the past decade has enabled the use of electromagnetic radiation for non-invasive monitoring of the physio-logical state of biological tissues. The near infrared (NIR) light having the wavelength range of 600 nm -1000 nm has been the main contender in these emerging molecular imaging modalities. Assessment of accurate pathological condition of the tissue under investigation relies on the contrast in the molecular images, where the endogenous contrast may not be sufficient in these scenarios. The fluorescence (exogenous) contrast agents have been deployed to overcome these difficulties, where the preferential uptake by the tumor vasculature leads to high contrast,making this modality one of the biggest contenders in small-animal and soft-tissue molecular imaging modalities. In Fluorescence diffuse optical spectroscopy/imaging, this exogenous drug is excited by NIR laser light causing the emission of the fluorescence light. The emitted fluorescence light is typically dependent on the life time and concentration of the exogenous drug coupled with physiology associated with the tissue under investigation. As there is an excitation and emission of the light,the underlying physics of the problem is described by a coupled diffusion equations. These coupled diffusion equations are typically solved by advanced numerical methods, which tend to be computationally demanding. In this work, analytical solutions for these coupled partial differential equations (PDEs) for the regular geometries for both time-domain and frequency-domain cases were developed. Till now, the existing literature has not dealt with all regular geometries and derived analytical solutions were only for couple of geometries. Here a universally acceptable generic solution was developed based on Green’s function approach that is applicable to any regular geometry. Using this, the analytical solutions for the regular geometries that is encountered in diffuse fluorescence spectroscopy/imaging were obtained. These solutions can play an important role in determining the bulk fluorescence properties of the tissue, which could act as good initial guesses for the advanced image reconstruction techniques and/or can also facilitate the calibration of experimental fluorescence data by removing biases and source-detector variations. In the second part of this work, the developed analytical models for regular geometries were validated through comparison with the established numerical models that are traditionally used in the diffuse fluorescence spectroscopy/imaging. This comparison not only validated the developed analytical models, but also showed that analytical models are capable of providing bulk fluorescence properties with at least one order of magnitude less computational cost compared to the highly optimized traditional numerical models.

This thesis reports the work done towards design and fabrication of a versatile and low cost, frequency domain DOT (Diffuse Optical Tomography) Imager. A design which uses only a single fiber for the source and a single fiber bundle for the detector is reported. From near the source, to diametrically opposite to the source, the detected intensity of scattered light varies by three to four orders in magnitude, depending on the tissue/phantom absorption and scattering properties. The photo multiplier tube’s (PMT’s) gain is controlled to operate it in the linear range, thus increasing the dynamic range of detection. Increasing the dynamic range by multi channel data acquisition is also presented. Arresting the oscillations of a stepper using a negative torque braking method is also adopted in this application for increasing the speed of data acquisition. The finite element method (FEM) for obtaining photon density solution to the transport equation and the model based iterative image reconstruction (MPBIIR) algorithm are developed for verifying the experimental prototype. Simulation studies presented towards the end of this thesis work provide insight into the nature of measurements. The optical absorption reconstructed images from the simulation, verified the validity of implementation of the reconstruction method for further reconstructions from data gathered from the developed imager. A single iteration of MOBIIR to segment the region of interest (ROI) using an homogeneous measurement estimate is presented. Using the single iteration MOBIIR to obtain a relatively more accurate starting value for the optical absorption coefficient, and the reconstruction results for data obtained from tissue mimicking solid epoxy-resin phantom with a single in-homogeneity inclusion is also presented to demonstrate the imager prototype.

Computational imaging has been playing an important role in understanding and analysing the captured images. Both image segmentation and restoration has been in-tegral parts of computational imaging. The studies performed in this thesis has been focussed toward developing novel algorithms for image segmentation and restoration. Study related to usage of Morozov Discrepancy Principle in Di use Optical Imaging was also presented here to show that hyper parameter selection could be performed with ease. The Laplacian of Gaussian (LoG) and Canny operators use Gaussian smoothing be-fore applying the derivative operator for edge detection in real images. The LoG kernel was based on second derivative and is highly sensitive to noise when compared to the Canny edge detector. A new edge detection kernel, called as Helmholtz of Gaussian (HoG), which provides higher di suavity is developed in this thesis and it was shown that it is more robust to noise. The formulation of the developed HoG kernel is similar to LoG. It was also shown both theoretically and experimentally that LoG is a special case of HoG. This kernel when used as an edge detector exhibited superior performance compared to LoG, Canny and wavelet based edge detector for the standard test cases both in one- and two-dimensions. The linear inverse problem encountered in restoration of blurred noisy images is typically solved via Tikhonov minimization. The outcome (restored image) of such min-imitation is highly dependent on the choice of regularization parameter. In the absence of prior information about the noise levels in the blurred image, ending this regular-inaction/hyper parameter in an automated way becomes extremely challenging. The available methods like Generalized Cross Validation (GCV) may not yield optimal re-salts in all cases. A novel method that relies on minimal residual method for ending the regularization parameter automatically was proposed here and was systematically compared with the GCV method. It was shown that the proposed method performance was superior to the GCV method in providing high quality restored images in cases where the noise levels are high Di use optical tomography uses near infrared (NIR) light as the probing media to recover the distributions of tissue optical properties with an ability to provide functional information of the tissue under investigation. As NIR light propagation in the tissue is dominated by scattering, the image reconstruction problem (inverse problem) is non-linear and ill-posed, requiring usage of advanced computational methods to compensate this. An automated method for selection of regularization/hyper parameter that incorporates Morozov discrepancy principle(MDP) into the Tikhonov method was proposed and shown to be a promising method for the dynamic Di use Optical Tomography.

This thesis describes the development and applications of an extension of DWS which enables the recovery of ‘localized’ mechanical properties, in a specified region of a complex jelly-like object which is inhomogeneous, marked out by the focal volume of an ultrasound transducer, also called the region-of-interest (ROI). Introduction of the sinusoidal forcing creates a sinusoidal phase variation in the detected light in a DWS experiment which modulates the measured intensity autocorrelation, g2 (τ ). Decay in the modulation depth with τ is used to recover the visco-elastic spectrum of the material in the ROI. En route to this, growth of the mean-squared dis- placement (MSD) with time is extracted from the modulation depth decay, which was verified first by the usual DWS experimental data from an homogeneous object with properties matching those in the ROI of the inhomogeneous object and then those obtained by solving the generalized Langevin equation (GLE) modelling the dynamics of a typical scattering centre in the ROI. A region-specific visco-elastic spectral map was obtained by scanning the inhomogeneous object by the ultrasound focal volume. Further, the resonant modes of the vibrating ROI were measured by locating the peaks of the modulation depth variation in g2(τ ) with respect to the ultrasound frequency. These resonant modes were made use of to recover elasticity of the material of the object in the ROI. Using a similar strategy, it was also shown that flow in pipe can be detected and flow rate computed by ‘tagging’ the photons passing through the pipe with a focussed ultrasound beam. It is demonstrated, both through experiments and simulations that the ultrasound-assisted technique devel- oped is better suited to both detect and quantitatively assess flow in a background of Brownian dynamics than the usual DWS. In particular, the MSD of particles in the flow, which shows forth a super-diffusive dynamics with MSD growing following τ α with α < 2, is captured over larger intervals of τ than was possible using existing methods. On the theoretical front, the main contribution is the derivation of the GLE, with multiplicative noise modulating the interaction ‘spring constant’. The noise is derived as an average effect of the micropolar rotations suffered by the ‘bath’ particles on the ‘system’ particle modelled. It has been shown that the ‘local’ dynamics of the system particle is nontrivially influenced by the dynamics, both translation and rotation, of ‘nonlocal’ bath particles.

L'utilisation de systèmes électromécaniques microstructurés pour analyser et manipuler des solutions biologiques ou des cellules vivantes (bio-MEMS) a pris un essor considérable ces dernières années. Dans ce genre de dispositifs, l'utilisation de champs électriques est fréquente, que ce soit pour percer les membranes des cellules et effectuer une transfection de gènes par exemple (électroporation), pour les déplacer ((di )électrophorèse) ou agir sur le milieu dans lequel elles baignent (électro-hydrodynamique). La modélisation des phénomènes induits par ces champs électriques dans les solutions aqueuses est un problème multi-physique et multi-échelle. Au déplacement des électrons s'ajoute en effet la migration des ions présents dans la solution. Ceux-ci se concentrent en particulier aux abords des électrodes formant des couches minces dont les paramètres évoluent de façon encore mal connue en fonction notamment des conditions d'alimentation. La thèse se concentre sur les applications électro-hydrodynamiques dans lesquelles une solution saline est mise en mouvement par des forces électriques agissant sur ses ions, concentrés dans des couches de charges minces, au voisinage des électrodes. Sont d'abord présentés les résultats expérimentaux et des modèles simples du problème électromécanique dans le cas de structures 2D à électrodes coplanaires. Devant l’importance des écarts entre les résultats théoriques et expérimentaux, des modèles plus complets sont alors proposés et évalués. Malgré les améliorations fournies par ces modèles, des écarts importants subsistent entre théorie et expérimentation, et une étude totalement découplée des aspects électriques et mécaniques est alors réalisée sur une structure 1D. Cette étude permet de mieux cerner les dépendances de certains paramètres physiques vis-à-vis des conditions d’alimentation avec une comparaison systématique des résultats expérimentaux et des résultats de modèles circuits linéaires et non linéaires, au travers d’une approche fréquentielle par diagrammes de Bode et d’une approche temporelle par figures de Lissajous. Il a ainsi pu être mis en évidence l’importance pratique potentielle de certains phénomènes rarement pris en compte dans des modèles globaux : saturation des couches minces, permittivité non constante, effets de bords,… Des applications pratiques ont pu être dégagées et testées expérimentalement, dans le domaine des micro-mélangeurs. Outre ces développements, une brève étude est décrite, portant sur la modélisation des cellules et de leurs membranes extrêmement fines en regard des autres dimensions caractéristiques du système, dans la perspective par exemple d'applications en électroporation. Une autre étude est faite portant sur l’utilisation potentielle de méthodes numériques dites « sans maillage » pour ce type d’applications, l’accent étant mis sur la résolution du problème de Poisson dans des systèmes 2D. / Analysis and manipulation of biological solutions or cells in micro-electromechanical systems has considerably improved during last years. In such systems, it is common to use electric fields, in order e.g. to increase cells membrane porosity, which is known as electroporation, and thus allow for gene transfection. Electric fields can also generate the motion of cells in a solution by (di-)electrophoresis effects or induce the movement of the solution itself, through electro-hydrodynamic effects. Finding theoretical models for those phenomena requires a multi-physic and multi-scale approach. The ions present in the saline solution react mechanically to the electrical excitation of the system. They migrate to the regions close to the electrodes, in very thin layers whose parameters vary in non-obvious ways, depending namely on the power supply conditions. The text focuses on electro-hydrodynamic applications in which a flow is generated by electric forces acting on the ions present in the solution, mostly in thin charge layers near the electrodes. Experimental results and simple existing models are first presented for 2D coplanar electrodes systems. Regarding the important differences between models and experimentation, more complete models are then proposed and tested. In spite of the improvements of those new models, some important differences remain, so that a fully decoupled approach of electrical and mechanical aspects is needed, which is pursued on a 1D structure. This new study allows for a better understanding of the dependences of some physical parameters with regard to supply conditions, with a systematic comparison of experimental results and non-linear circuit models results. A frequency approach with Bode diagrams is used, as well as a time approach with Lissajous figures. It has been shown that some phenomena are of practical and fundamental importance, which are not always taken into account in more general and global models : saturation phenomena, non constant physical parameters, border effects,… Practical applications have been deduced and tested experimentally, in the case of micro-mixing. A brief study is also mentioned, concerning the modeling of cells with extremely thin membranes compared to the other characteristic dimensions of the system, in the perspective e.g. of electroporation applications. Another short study is performed about the potential use of « meshless » numerical methods for the solving of this kind of applications, focusing more specifically on the solving of a Poisson problem in 2D.

L’étude du cerveau humain est un domaine en plein essor et les techniques non-invasives de l’étudier sont très prometteuses. Afin de l’étudier de manière non-invasive, notre laboratoire utilise principalement l’imagerie par résonance magnétique fonctionnelle (IRMf) et l’imagerie optique diffuse (IOD) continue pour mesurer et localiser l’activité cérébrale induite par une tâche visuelle, cognitive ou motrice. Le signal de ces deux techniques repose, entre autres, sur les concentrations d’hémoglobine cérébrale à cause du couplage qui existe entre l’activité neuronale et le flux sanguin local dans le cerveau. Pour être en mesure de comparer les deux signaux (et éventuellement calibrer le signal d’IRMf par l’IOD), où chaque signal est relatif à son propre niveau de base physiologique inconnu, une nouvelle technique ayant la capacité de mesurer le niveau de base physiologique est nécessaire. Cette nouvelle technique est l’IOD résolue temporellement qui permet d’estimer les concentrations d’hémoglobine cérébrale. Ce nouveau système permet donc de quantifier le niveau de base physiologique en termes de concentrations d’hémoglobine cérébrale absolue. L’objectif général de ma maîtrise était de développer un tel système afin de l’utiliser dans une large étude portant sur la condition cardiovasculaire, le vieillissement, la neuroimagerie ainsi que les performances cognitives. Il a fallu tout d’abord construire le système, le caractériser puis valider les résultats avant de pouvoir l’utiliser sur les sujets de recherche. La validation s’est premièrement réalisée sur des fantômes homogènes ainsi qu’hétérogènes (deux couches) qui ont été développés. La validation des concentrations d’hémoglobine cérébrale a été réalisée via une tâche cognitive et appuyée par les tests sanguins des sujets de recherche. Finalement, on présente les résultats obtenus dans une large étude employant le système d’IOD résolue temporellement en se concentrant sur les différences reliées au vieillissement. / Our understanding of the functional organization of the human brain has been greatly influenced by the development of new medical imaging techniques. Pr. Hoge’s research has focused on the use of functional magnetic resonance imaging (fMRI) and continuous diffuse optical imaging (DOI) for non-invasive localization and quantification of brain activity associated with behavioral stimuli or tasks (e.g. cognitive, motor or visual). The respective signals of both techniques are based on cerebral haemoglobin concentrations because of the coupling that exists between neuronal activity and cerebral blood flow. Relating BOLD fMRI signals with those acquired using DOI has been complicated by the fact that fMRI yields fractional change values, while the majority of DOI methods have provided absolute changes from an unknown baseline. To address this, we adopted a newer technique known as time-resolved DOI, which allows absolute quantification of cerebral haemoglobin concentrations. Time-resolved DOI thus has the capacity to quantify the subject’s resting hemoglobin concentrations in absolute micromolar units. The main objective of my masters’ project was to implement and optimize a time-resolved DOI system for use in a large study exploring the links between cardiovascular fitness, aging, neuroimaging markers, and cognitive performance. In this thesis we describe the fabrication of the system, followed by its characterisation and validation using solid optical phantoms (homogeneous and heterogeneous) developed for this purpose. Haemoglobin concentrations obtained non-invasively with the system are validated against blood draws, while the sensitivity to variations in concentration are assessed during a cognitive task. Finally, we present the results of a large study in which the time-resolved DOI system was used to characterize age-related vascular changes in the brain.

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La forte croissance démographique (~3%.an-1) observée au cours des dernières décennies en Afrique subsaharienne a engendré la conversion de grandes étendues de savane arborée en cultures pluviales ou irriguées et la diminution de la durée des jachères. Afin de déterminer l'impact de tels changements d'usage du sol sur la recharge des nappes phréatiques, la zone non saturée a été investiguée pendant trois ans (2009-2011) pour deux régions du Niger (sud-ouest et sud-est) aux conditions climatiques et géomorphologiques différentes.Une approche expérimentale in-situ a tout d'abord permis de caractériser qualitativement les propriétés de la zone non saturée et les flux hydriques associés (profondeur 0-10 m) pour les principaux usages du sol : savane naturelle ; jachère ; culture pluviale de mil ; et culture irriguée de poivron. Des profils granulométriques et de résistivité électrique apparente ont été réalisés et des suivis temporels de la teneur en eau et du potentiel matriciel du sol ont été mis en place. A partir des résultats et de la synthèse des données ainsi recueillies, deux analyses détaillées ont été proposées.Afin de quantifier le différentiel de recharge diffuse entre une jachère à Guiera senegalensis et une culture pluviale de mil (Pennisetum sp.) au sud-ouest Niger, une modélisation à base physique via le code Hydrus-1D a été appliquée. Dans un premier temps, une inversion basée sur la méthode GLUE a permis d'établir les densités de probabilité pour les paramètres hydrodynamiques de la zone non saturée ; dans un second temps, des simulations pluriannuelles (2 × 100 ans) du drainage profond (0-10 m) lors d'une transition jachère-mil ont été réalisées. Il a ainsi été montré que l'expansion des surfaces cultivées en mil pourrait se traduire par une augmentation du drainage profond, de 20 à 25 mm.an-1 après un délai de 35 à 60 ans.Afin d'étudier les conséquences des mises en culture pluviales et irriguées sur le potentiel de salinisation des sols et des eaux souterraines au sud-est Niger, les concentrations en ions majeurs dissous dans l'eau des pores de la zone non saturée ont été mesurées, puis comparées à la composition géochimique des apports d'eau associés (pluie, eau d'irrigation). Il a été ainsi mis en évidence que la mise en culture pluviale a un effet négligeable sur la qualité des eaux interstitielles et souterraines tandis que l'irrigation est associée à un enrichissement de l'eau de la zone non saturée en solutés qui pourrait induire, à terme, une salinisation de la nappe par lessivage des sols devenus salins/sodiques. / In semiarid sub-Saharan Africa, the rapid population growth (~3%.yr-1) during the past few decades has resulted in land clearing and large-scale conversion from savannah and fallow to rainfed or irrigation crop fields. The traditional duration of fallow has been also shortened. In order to estimate the impact of these land use changes on groundwater recharge, the vadose zone was investigated during three years (2009-2011) for two regions located in Niger (south-west and south-east).A qualitative analysis was first carried out for identifying vadose zone properties and for characterizing the corresponding water fluxes (0-10 m depth) for the main land use types: natural savannah; fallow; rainfed millet crop; and irrigated sweet pepper crop. Grain size and electrical resistivity profiles were established and soil water content and matric potential were monitored. Based on the results of this analysis, two more detailed investigations were performed.In southwestern Niger, in order to estimate changes in diffuse recharge from a fallow with Guiera senegalensis to a rainfed millet crop (Pennisetum sp.), a physically-based modeling with Hydrus-1D code was completed. Probability density functions were first built for the soil hydraulic parameters based on the GLUE approach; then, deep drainage (0-10 m depth) was simulated for a 2 × 100 year time-period including a fallow-millet conversion. It was shown that the increase in millet crop areas could result in an increase in deep drainage from 20 to 25 mm.yr-1 after a delay of 35 to 60 years.In southeastern Niger, in order to assess the impact of rainfed and irrigated cropping development on soil and groundwater salinization, major ion concentrations in pore water of the vadose zone were measured and compared with the geochemical composition of water inputs (rainfall, irrigation). It was shown that rainfed cropping does not affect soil water and groundwater quality whereas irrigation results in an increase of solutes concentrations in soil pore water, which could lead to a groundwater salinization at mid-term through soil leaching.