<p dir="ltr">The dissolution profile is one of the most important critical quality attributes (CQAs) for pharmaceutical solid oral dosage forms, as failure to meet the dissolution specification can impact bioavailability. Dissolution tests are essential to assess lot-to-lot product quality and guide the development of new formulations. Therefore, predictive dissolution reduced-order models (ROM) are crucial for the successful implementation of any real-time release testing (RTRT) strategy. Mechanistic and semi-mechanistic ROMs of tablet dissolution for realizing quality by control (QbC) and RTRT frameworks in continuous manufacturing are still scarce or nonexistent. Moreover, realizing the underlying coupled mechanics of wetting, swelling, disintegration, and dissolution is still an open question. This dissertation contributes to developing a mechanistic ROM of pharmaceutical tablet dissolution for the design, optimization, and control of manufacturing processes. We follow several steps towards the progression of the mechanistic model development. First, we develop a semi-mechanistic ROM to capture the relationship between critical process parameters (CPPs), critical material attributes (CMAs), and dissolution profiles. We demonstrate the versatility and the capability of the semi-mechanistic ROM to estimate changes in dissolution due to process disturbances in tablet porosity, lubrication conditions, and moisture content in the powder blend. Next, to understand the underlying coupled mechanism of wetting, swelling, disintegration, and dissolution, we use dynamic micro-computed tomography (micro-CT) with a high temporal resolution to visualize water penetration through the porous network of immediate-release tablets. We couple liquid penetration due to capillary pressure described by the Lucas-Washburn theory with the first-order swelling kinetics of the excipients to provide a physical interpretation of the experimental observations. From the mechanistic understanding of the water penetration kinetics using the micro-CT tests, we propose a two-stage mechanistic ROM, which is comprised of (i) a mechanistic dissolution model of the active pharmaceutical ingredient (API) that solves a population balance model (PBM) for a given API crystal size distribution and dissolution rate coefficient, and (ii) a tablet wetting function that estimates the rate at which the API is exposed to the buffer solution. These two sub-models are coupled by means of convolution in time to capture the start time of the API dissolution process as water uptake, swelling, and disintegration take place. Finally, we demonstrate the versatility and the capability of the mechanistic API dissolution model and the two-stage tablet dissolution ROM to represent the dissolution profile of different pharmaceutical formulations and its connection with CMAs, CPPs, and other CQAs, namely initial API crystal size distribution, porosity, composition, and dimensions of the tablet. In all of the cases considered in this work, the estimations of the model are in good agreement with experimental data. </p>

Cette thèse de doctorat porte sur le calcul par la méthode des éléments finis du comportement dynamique de réservoirs élastiques précontraints contenant un liquide interne à surface libre. Nous considérons que la pression hydrostatique exercée par le fluide interne incompressible sur les parois flexibles du réservoir est à l’origine de grands déplacements, conduisant ainsi à un état d’équilibre non-linéaire géométrique. Le changement de raideur lié à cet état précontraint induit un décalage des fréquences de résonances du problème de vibrations linéaires couplées.L’objectif principal du travail est donc d’estimer, par des approches numériques précises et efficaces, l’influence des non-linéarités géométriques sur le comportement hydroélastique du système réservoir/liquide interne autour de différentes configurations d’équilibre. La méthodologie développée s’effectue en deux étapes. La première consiste à calculer l’état statique non-linéaire par une approche éléments finis lagrangienne totale. L’action du fluide sur la structure est ici modélisée par des forces suiveuses hydrostatiques. La deuxième étape porte sur le calcul des vibrations couplées linéarisées. Un modèle d’ordre réduit original est notamment proposé pour limiter les coûts de calcul associés à l’estimation de l’effet de masse ajoutée. Enfin, divers exemples sont proposés et comparés à des résultats de la littérature (issus de simulations numériques ou d’essais expérimentaux) pour montrer l’efficacité et la validité des différentes approches numériques développées dans ce travail. / This doctoral thesis focuses on the calculation by the finite element method of the dynamic behavior of prestressed elastic tanks containing an internal liquid with a free surface. We consider that the hydrostatic pressure exerted by the incompressible internal fluid on the flexible walls of the tank causes large displacements, thus leading to a geometric non-linear equilibrium state. The change of stiffness related to this prestressed state induces a shift in the resonance frequencies of the coupled linear vibration problem. The main objective of the work is therefore to estimate, through precise and efficient numerical approaches, the influence of geometric nonlinearities on the hydroelastic behavior of the reservoir/internal liquid system around different equilibrium configurations. The methodology developed is carried out in two stages. The first one consists in calculating the non-linear static state by a total Lagrangian finite element approach.The action of the fluid on the structure is modelled here by hydrostatic following forces. The second step is the calculation of linearized coupled vibrations. In particular, an original reduced order model is proposed to limit the calculation costs associated with the estimation of the added mass effect. Finally, various examples are proposed and compared with results from the literature (from numerical simulations or experimental tests) to show the effectiveness and validity of the different numerical approaches developed in this work.

Cette thèse concerne le développement, l'extension et l'application d'une formulation stochastique des équations de la mécanique des fluides introduite par Mémin (2014). La vitesse petite échelle, non-résolue, est modélisée au moyen d'un champ aléatoire décorrélé en temps. Cela modifie l'expression de la dérivée particulaire et donc les équations de la mécanique des fluides. Les modèles qui en découlent sont dénommés modèles sous incertitude de position. La thèse s'articulent autour de l'étude successive de modèles réduits, de versions stochastiques du transport et de l'advection à temps long d'un champ de traceur par une vitesse mal résolue. La POD est une méthode de réduction de dimension, pour EDP, rendue possible par l'utilisation d'observations. L'EDP régissant l'évolution de la vitesse du fluide est remplacée par un nombre fini d'EDOs couplées. Grâce à la modélisation sous incertitude de position et à de nouveaux estimateurs statistiques, nous avons dérivé et simulé des versions réduites, déterministe et aléatoire, de l'équation de Navier-Stokes. Après avoir obtenu des versions aléatoires de plusieurs modèles océaniques, nous avons montré numériquement que ces modèles permettaient de mieux prendre en compte les petites échelles des écoulements, tout en donnant accès à des estimés de bonne qualité des erreurs du modèle. Ils permettent par ailleurs de mieux rendre compte des évènements extrêmes, des bifurcations ainsi que des phénomènes physiques réalistes absents de certains modèles déterministes équivalents. Nous avons expliqué, démontré et quantifié mathématiquement l'apparition de petites échelles de traceur, lors de l'advection par une vitesse mal résolu. Cette quantification permet de fixer proprement des paramètres de la méthode d'advection Lagrangienne, de mieux le comprendre le phénomène de mélange et d'aider au paramétrage des simulations grande échelle en mécanique des fluides. / This thesis develops, analyzes and demonstrates several valuable applications of randomized fluid dynamics models referred to as under location uncertainty. The velocity is decomposed between large-scale components and random time-uncorrelated small-scale components. This assumption leads to a modification of the material derivative and hence of every fluid dynamics models. Through the thesis, the mixing induced by deterministic low-resolution flows is also investigated. We first applied that decomposition to reduced order models (ROM). The fluid velocity is expressed on a finite-dimensional basis and its evolution law is projected onto each of these modes. We derive two types of ROMs of Navier-Stokes equations. A deterministic LES-like model is able to stabilize ROMs and to better analyze the influence of the residual velocity on the resolved component. The random one additionally maintains the variability of stable modes and quantifies the model errors. We derive random versions of several geophysical models. We numerically study the transport under location uncertainty through a simplified one. A single realization of our model better retrieves the small-scale tracer structures than a deterministic simulation. Furthermore, a small ensemble of simulations accurately predicts and describes the extreme events, the bifurcations as well as the amplitude and the position of the ensemble errors. Another of our derived simplified model quantifies the frontolysis and the frontogenesis in the upper ocean. This thesis also studied the mixing of tracers generated by smooth fluid flows, after a finite time. We propose a simple model to describe the stretching as well as the spatial and spectral structures of advected tracers. With a toy flow but also with satellite images, we apply our model to locally and globally describe the mixing, specify the advection time and the filter width of the Lagrangian advection method, as well as the turbulent diffusivity in numerical simulations.

<h4>A generalized physics-based modeling framework is presented to analyze: (a) the effects of temperature on identified degradation mechanisms, (b) interfacial debonding processes, including deterministic and stochastic mechanisms, and (c) establishing model performance benchmarks of electrochemical porous electrode theory models, as a necessary stepping stone to perform valid battery degradation analyses and designs. Specifically, the effects of temperature were incorporated into a physics-based, reduced-order model and extended for a LiCoO₂ -graphite 18650 cell. Three dimensionless driving forces were identified, controlling the temperature-dependent reversible charge capacity. The identified temperature-dependent irreversible mechanisms include homogeneous SEI, at moderate to high temperatures, and the chemomechanical degradation of the cathode at low temperatures. Also, debonding of a statistically representative electrochemically active particle from the surrounding binder-electrolyte matrix in a porous electrode was modeled analytically, for the first time. The proposed framework enables to determine the space of C-Rates and electrode particle radii that suppresses or enhances debonding and is graphically summarized into performance–microstructure maps where four debonding mechanisms were identified, and condensed into power-law relations with respect to the particle radius. Finally, in order to incorporate existing or emerging degradation models into porous electrode theory (PET) implementations, a set of benchmarks were proposed to establish a common basis to assess their physical reaches, limitations, and accuracy. Three open source models: dualfoil, MPET, and LIONSIMBA were compared, exhibiting significant qualitative differences, despite showing the same macroscopic voltage response, leading the user to different conclusions regarding the battery performance and possible degradation mechanisms of the analyzed system.</h4>