L'objectif de la présente thèse et de développer un cadre d'étude et de simulation apte à prédire les propriétés effectives de diffusion dans les matériaux cimentaires saturés. Le principe suivi, fondé sur les approches multi-échelles séquencées, permettra de modéliser chaque échelle d'intérêt, depuis le gel des C-S-H, jusqu'au matériau béton, et ainsi via des simulations de prédire les coefficients de diffusion effectifs.Le cadre d'étude est donc fondé sur les points clés suivant :- Des morphologies de type "matrice - inclusion" sont générées via des excursions de champs aléatoires corrélés tri-dimensionnels. Cette approche, combinée avec quelques opérations morphologiques, permet la génération de morphologies inclusionnaires 3D suivant des distributions de tailles imposées. Il est ensuite possible de faire évoluer ces morphologies, depuis un état initial, en fonction d'un modèle prescrit (par exemple en termes de fraction volumiques), via le seuil de l'excursion.- Les cibles morphologiques de chaque échelle considérées tentent de refléter les résultats expérimentaux et modèles les plus communément admis. En supplément, à l'échelle de la pâte de ciment, un modèle "simple" d'hydratation est développé afin de prédire l'évolution de celle-ci dans le temps en termes de fractions volumiques. Le choix a été fait d'utiliser pour fondement un modèle simple (Jennings & Tennis), incorporant des paramètres essentiels, tels que la composition minéralogique du ciment ou le rapport e/c. Des modifications mineures ont été apporté au modèle, afin de prendre en compte de récents résultats expérimentaux, concernant principalement la fin de l'hydratation ainsi que sa cinétique.- Le cadre d'homogénéisation a été construit pour être utilisable à toutes les échelles considérées, et il permet ainsi de prédire les propriétés effectives de diffusion avec des considération énergétiques d'équivalence entre échelles. De façon analogue à la théorie de Hill pour l'élasticité, le cadre d'étude assure une séparation d'échelle cohérente vis-à-vis des propriétés effectives de diffusion.- Enfin, d'un point de vue numérique, les simulations utilisent les méthodes E-FEM, couplées à l'utilisation de maillages non-adaptés sur lesquels les morphologies sont "projetées". De cette façon, les discontinuités géométriques (discontinuité de propriétés matériaux) sont sont assurés par les élément finis enrichis, et ne requièrent pas d'éléments joint, ou de "moyennage" de propriétés.Les résultats de chaque échelle sont utilisés comme paramètres d'entrés pour les échelles suivantes. Depuis l'échelle des hydrates (C-S-H), jusqu'à l'échelle du béton, les coefficients de diffusion effectifs sont ainsi estimés. / The aim of the present Ph.D. is to develop a methodology and a simulation framework able to predict as accurately as possible effective properties regarding diffusion in saturated cement based materials. A sequenced multiscale framework is developed to perform numerical homogenization on diffusive properties, and thus predict effective properties. The general outline is to model every scale in concrete-like materials, from the C-S-H gel, to the concrete scale, and with the help of a proper framework, be able to predict effective properties. The methodology relies on the following key points for every considered scale :- Inclusion-matrix like morphologies are generated through level set methods applied to multi-dimensional correlated random fields. This approach, together with few morphological operations allows to generate 3D morphologies with given particle size distributions (PSD), or pore size distributions. Then, it is also possible, from the initial state, to make those morphologies evolve according to any descriptive model (e.g. in terms of volume fraction), via the level set.- The morphological description of each scale is chosen according to the most acknowledged experimentations and models. In addition, at the cement paste scale, a hydration model was developed to predict the evolution of the cement paste through time, in terms of volume fractions. The choice was made to keep a simple model (Jennings & Tennis), with few but essential input parameters (mineral cement composition, w/c ratio, PSD). It has only been modified to include recent experimental results, such as the maximal hydration degree, or the hydration rates.- The upscaling framework was built to suit every considered scale, and allows to assess effective properties based on energy conservation principles. Similar to Hill's theory for elasticity, the framework is build to ensure to proper scale separation regarding effective diffusion coefficients.- Lastely, the numerical context is based on E-FEM techniques, which allows to use unstructured meshes, on which the morphologies are projected. This way, any material discontinuity in dealt within the FE, and thus does not require averaging properties, or joint elements. Results from every scale will be used as inputs at the higher scales, and effective diffusion coefficients are thus estimated.

Understanding how fluctuations continuously propagate across spatial scales is fundamental for our understanding of inanimate matter. This is exemplified by self-similar fluctuations in critical phenomena and the propagation of energy fluctuations described by the Kolmogorov-Law in turbulence. Our understanding is based on powerful theoretical frameworks that integrate fluctuations on intermediary scales, as in renormalisation group or coupled mode theory. In striking contrast to typical inanimate systems, living matter is typically organised into a hierarchy of processes on a discrete set of spatial scales: from biochemical processes embedded in dynamic subcellular compartments to cells giving rise to tissues. Therefore, the understanding of living matter requires novel theories that predict the interplay of fluctuations on multiple scales of biological organisation and the ensuing emergent degrees of freedom. In this thesis, we derive a general theory of the multi-scale propagation of fluctuations in non-equilibrium systems and show that such processes underlie the regulation of cellular behaviour. Specifically, we draw on paradigmatic systems comprising stochastic many-particle systems undergoing dynamic compartmentalisation. We first derive a theory for emergent degrees of freedom in open systems, where the total mass is not conserved. We show that the compartment dynamics give rise to the localisation of probability densities in phase space resembling quasi-particle behaviour. This emergent quasi-particle exhibits fundamentally different response kinetics and steady states compared to systems lacking compartment dynamics. In order to investigate a potential biological function of such quasi-particle dynamics, we then apply this theory to the regulation of cell death. We derive a model describing the subcellular processes that regulate cell death and show that the quasi-particle dynamics gives rise to a kinetic low-pass filter which suppresses the response of the cell to fast fluituations in cellular stress signals. We test our predictions experimentally by quantifying cell death in cell cultures subject to stress stimuli varying in strength and duration. In closed systems, where the total mass is conserved, the effect of dynamic compartmentalisation depends on details of the kinetics on the scale of the stochastic many-particle dynamics. Using a second quantisation approach, we derive a commutator relation between the kinetic operators and the change in total entropy. Drawing on this, we show that the compartment dynamics alters the total entropy if the kinetics of the stochastic many-particle dynamics violate detailed balance. We apply this mechanism to the activation of cellular immune responses to RNA-virus infections. We show that dynamic compartmentalisation in closed systems gives rise to giant density fluctuations. This facilitates the emergence of gelation under conditions that violate theoretical gelation criteria in the absence of compartment dynamics. We show that such multi-scale gelation of protein complexes on the membranes of dynamic mitochondria governs the innate immune response. Taken together, we provide a general theory describing the multi-scale propagation of fluctuations in biological systems. Our work pioneers the development of a statistical physics of such systems and highlights emergent degrees of freedom spanning different scales of biological organisation. By demonstrating that cells manipulate how fluctuations propagate across these scales, our work motivates a rethinking of how the behaviour of cells is regulated.

Au cours des dernières décennies, on observe dans les stocks d’eaux-de-vie une minimisation des défauts mais également une raréfaction des eaux-de-vie d’exception. Le vieillissement sous bois est une étape discriminante quant à la qualité finale du produit. L’étude a pour but de mettre en relation les différentes échelles de description disponibles tant d’un point de vue expérimental que numérique pour ensuite disposer d’une boîte à outils, qualifiant un chai, qui s’enrichira au cours du temps. La clé d’entrée est le climat dans le chai. Une analyse des caractéristiques physiques du bois utilisé et de sa modification lors de la fabrication des barriques permet de mieux appréhender les échanges d’oxygène à travers les différentes zones de la barrique pendant la phase de vieillissement. Un laboratoire est mis en place afin de suivre les conditions climatiques et les propriétés thermo physiques et chimiques des barriques. Les acquis expérimentaux permettront alors de valider les outils de simulations qui seront développés en parallèle. Les outils de simulations, en particulier à l’échelle du chai, seront ensuite confrontés aux données expérimentales issues de l’instrumentation d’un chai réel. La pertinence des effets liés au comportement climatique à l’intérieur des chais sur la qualité de l’eau de vie sera évaluée grâce à l’expertise du comité de dégustation. / Because of the various steps of the process, cognacs reveal highly distinctive organoleptic properties. Nevertheless, over the past decades, the tasting committee has noticed a slight trend towards standardisation of eaux-de-vie. The reasons for this evolution are most certainly multifactorial. The Maison Hennessy wants to understand the transformations occurring during the process of elaboration of Cognac, and particularly during the aging process which is a critical stage regarding the final quality of the product. In particular, the development of construction techniques and the size of the cellars is likely to influence the quality of the “eaux-de-vie”. In this study we built a toolbox modelling a Cognac cellar and its evolution over time. The model was developed to link multiple variables both computational and based on experimental data. On the experimental side, a laboratory was built in order to control the climatic conditions and the characteristics of the barrels. The experiments highlighted that the physico-chemical behaviour is linked to the temperature and the dimensions of casks. These lab-scale observations were further validated in an industrial scale pilot setting. The qualitative validation of the climatic conditions inside the cellar on the quality of the eaux-de-vie is performed by the testing committee. On the computational side, modelling was conducted first to estimate the mass transfers at the stave scale and then to simulate the heat transfers at the barrel or cellar scales. The convective effects appeared highly influential on the thermal dynamic of the liquid and the air in the building. The experimental data enabled the validation of the modelling tools at different scales.

This thesis addresses the problem of damage at elevated temperature with a view to analysing transverse cracking during the continuous casting of microalloyed steels. Based on the results of a previous project undertaken at the University of Liège to simulate the continuous casting process at the macroscopic level, the present research aims at studying the damage growth using a finite element mesoscopic approach that models the grains structure of the material. The developments are done at the mesoscopic scale using information from both the microscopic and macroscopic levels. In order to determine the constitutive laws governing the damage process at the mesoscopic scale, the physical mechanisms leading to the apparition of cracks during steel continuous casting are first investigated. It is acknowledged that in the studied temperature range (800 to 1200 °C), the austenitic grain boundary is a favourable place for cracks to initiate and propagate. The mechanisms of voids nucleation, growth and coalescence are established, the cavities evolving under diffusion and creep deformations. Having identified the damage mechanisms occurring under continuous casting conditions, a numerical approach for the modelling of these phenomena at the grain scale is proposed. The mesoscopic model, which is implemented in the Lagrangian finite element code LAGAMINE developed at the University of Liège, is built on the basis of a 2D mesoscopic cell representative of the material. The finite element discretization comprises solid elements inside the grains and interface elements on the grains boundaries. An elastic-viscous-plastic law of Norton-Hoff type, which represents the thermo-mechanical behaviour of the material, is associated to the solid elements for the modelling of the grains; and a damage law accounting for cavitation and sliding is linked to the interface elements for the modelling of the damage growth at the grains boundaries. The transfer between the macroscopic and mesoscopic scales is realised by imposing the stress, strain and temperature fields, collected during the parent macroscopic simulation, as boundary conditions on the mesosopic cell. Macroscopic experiments, analytical computations and finite element simulations, as well as literature review and microscopic analyses, are used to define the parameters of the material laws. The experimental results and the identification methodology leading to the definition of the set of parameters specific to the studied steel are described. Finally, the influence of oscillation marks and process defects on cracks formation during the industrial process of continuous casting is analysed. The results are compared with in-situ observations and cracking risk indicators computed by the macroscopic model.

Ce travail porte sur l’étude de la dégradation des convertisseurs électrochimiques haute température à oxydes solides. Une approche couplant des tests électrochimiques, des caractérisations post-mortem avancées et une modélisation multi-échelle a été mise en place afin d’établir les liens entre les performances, la microstructure des électrodes et leur dégradation. Dans ce but, des essais de durabilité de plus de mille heures ont été menés dans différentes conditions opératoires. La microstructure des électrodes a été reconstruite par nano-holotomographie des rayons X pour la cellule de référence avant et après vieillissement. Une attention particulière a été apportée à la mesure de la résolution spatiale et à la fiabilisation du protocole expérimental. Grâce aux volumes 3D, les propriétés microstructurales de l’électrode H2 en Ni-YSZ ont été quantifiées pour les cellules à l’état initial et vieillies. Un modèle physique d’agglomération des particules de Nickel a ensuite été ajusté sur les analyses tridimensionnelles et intégré dans une structure de modélisation multi-échelle développée au laboratoire. Il a auparavant été nécessaire de compléter l’outil numérique avec un module spécifique dédié aux matériaux composant l’électrode à oxygène fait avec un conducteur mixte ionique-électronique. Une fois le modèle validé sur des courbes de polarisation expérimentales, il a été utilisé pour quantifier la contribution de l’agglomération du Nickel sur les pertes de performances mesurées expérimentalement en mode pile à combustible et électrolyse. / This work aims at a better understanding of the high temperature Solid Oxide Cells degradation. An approach based on electrochemical tests, advanced post-test characterizations and multi-scale models has been used to investigate the links between the performances, the electrodes microstructure and their degradation. In that goal, long-term durability tests have been performed over thousand hours in different operating conditions. Electrode microstructures have been reconstructed by X-ray nano-holotomography for the pristine and the aged cells. It is worth noting that a special attention has been paid to improve both the process reliability for the tomographic experiments as well as the spatial resolution of the 3D reconstructed images. Thanks to the valuable 3D volumes, the Ni-YSZ microstructural properties of the H2 electrode have been quantified for the fresh and the aged samples. Then, a physically-based model for Nickel particle agglomeration has been adjusted on the microstructural parameters obtained by the 3D analysis and implemented in an in-house multi-scale modelling framework. Beforehand, it has been necessary to enrich the available numerical tool with a specific module dedicated to the oxygen electrode made in Mixed Ionic Electronic Conducting materials. Once validated on polarisation curves, the completed model has been used to quantify the contribution of Nickel agglomeration on the experimental degradation rates recorded in fuel cell and electrolysis modes.

Dans ce travail de thèse, une modélisation multi-échelle est mise en place à partir du concept d’homogénéisation périodique pour étudier le comportement cyclique et dépendant du temps des composites tissés à matrice thermoplastique. Avec l’approche proposée, le comportement macroscopique du composite est déterminé à partir d’une simulation éléments finis effectuée sur une cellule unitaire représentative de la microstructure périodique, où les lois de comportement des constituants sont directement intégrées, à savoir: la matrice et les torons. La réponse locale de la matrice est décrite par une loi de comportement phénoménologique multi-mécanismes intégrant viscoélasticité, viscoplasticité et endommagement ductile. Pour les torons, une loi de comportement hybride micromécanique-phénoménologique est considérée. Cette dernière prend en compte l’endommagement anisotrope et l’anélasticité induite par la présence d’un réseau diffus de microfissures à travers une description micromécanique d’un volume élémentaire représentatif contenant des microfissures. Les capacités du modèle multi-échelles sont validées en comparant les prédictions numériques aux essais expérimentaux. Les capacités du modèle sont également illustrées à travers plusieurs exemples où le composite subit des déformations dépendantes du temps lors de chargements monotones, de chargements à amplitude constante ou cyclique et encore lors de chargement multiaxiaux non proportionnels. En outre, le modèle multi-échelle est aussi utilisé pour analyser l’influence des mécanismes de déformation locaux sur la réponse macroscopique du composite. / In this thesis, a multi-scale model established from the concept of periodic homogenization is utilized to study the cyclic and time-dependent response of thermoplastic-based woven composites. With the proposed approach, the macroscopic behaviour of the composite is determined from a finite element simulation of the representative unit cell of the periodic microstructure, where the local constitutive behaviours of the components are directly integrated, namely: the matrix and the yarns. The local response of the thermoplastic matrix is described by a phenomenological multi-mechanisms constitutive model accounting for viscoelasticity, viscoplasticity and ductile damage. For the yarns, a hybrid micromechanical-phenomenological constitutive model is considered. The latter accounts for anisotropic damage and anelasticity induced by the presence of a diffuse micro-crack network through the micromechanical description of a micro-cracked representative volume element. The capabilities of the multi-scale model are validated by comparing the numerical prediction with experimental data. The capabilities of the model are also illustrated through several examples where the composite undergoes time-dependent deformations under monotonic loading, constant or cyclic stress levels and non-proportional multi-axial loading. Furthermore, the multi-scale model is also employed to analyse the influence of the local deformation processes on the macroscopic response of the composite.

Hydraulic fracturing is a multi-physics multi-scale problem related to natural processes such as the formation of dikes. It also has wide engineering applications such as extraction of unconventional resources, enhanced geothermal energy and carbon capture and storage. Current simulators are highly simplified because of the assumption of homogeneous reservoir. Unconventional reservoirs are heterogeneous owing to the presence of natural fracture network. Because of high computational effort, three-dimensional multi-scale simulations are uncommon, in particular, modelling material as a heterogeneous medium. Lattice Element Method (LEM) is therefore proposed for multi-scale simulation of heterogeneous material. In LEM, material is discretised into cells and their interactions are modelled by lattices, hence a three-dimensional model is simplified to a network of one-dimensional lattice. Normal, shear and rotational springs are used to define the constitutive laws of a lattice. LEM enables desktop computers for simulation of a lattice model that consists of millions of lattices. From simulations, normal springs govern the macroscopic bulk deformation while shear springs govern the macroscopic distortion. There is fluctuation of stresses even under uniform loading which is one of the characteristics of a lattice model. The magnitude increases with the stiffness ratio of shear spring to normal spring. Fracturing process can be modelled by LEM by introducing a microscopic tensile strength and a microscopic shear strength to the lattice properties. The strength parameters can be related to fracture toughness with the length scales of cells. From simulations, the relationships between model parameters and macroscopic parameters that are measurable in experiments are identified. From the simulations of uni-axial tension tests, both the spring stiffness ratio and the applied heterogeneity govern the fracturing process. The heterogeneity increases the ductility at the expense of the reduction on the macroscopic strengths. Different stages of fracturing are identified which are characterised by the model heterogeneity. Heterogeneous models go through the stages of the spatially distributed microscrack formation, the growth of multiple fracture clusters to the dominant fracture propagation. For homogeneous models, one of the microcracks rapidly propagates and becomes a dominant fracture with the absence of intermediate stages. From the uni-axial compression test simulations, the peak compressive stress is reached at the onset of the microscopic shear crack formation. Ductility is governed by the stiffness reduction ratio of a lattice in closed fractured stage to its unfractured stage. A novel Dual Lattice Model (DLM) is proposed for hydraulic fracture simulation by coupling a solid lattice model with a fluid lattice model. From DLM simulations of hydraulic fracturing of the classical penny shape crack problem under hydrostatic condition, the heterogeneities from both the fracture asperity and the applied heterogeneity increase the apparent fracture toughness. A semi-analytical solution is derived to consider the effect of fluid viscosity in the elastic deformation regime. Two asymptotes are identified that gives steep pressure gradients near the injection point and near the fracture tip which are also identified in the DLM simulations. Simulations also show three evolving regimes on energy dissipation/transfer mechanisms: the viscosity dominant, the elastic deformation dominant and the mixture of elastic deformation and toughness.

Le travail réalisé durant cette thèse a eu pour objectif de développer un modèle théorique spécifiquement dédié au contexte du développement tumoral tel qu'il peut être observé sous une fenêtre dorsale implantée sur une souris. Le modèle développé est un modèle hybride multi-physique et multi-échelle qui couple deux modules principaux. Le premier module modélise la croissance tumorale par un automate cellulaire qui permet de différencier l'état de chaque cellule en fonction de son histoire (cycle cellulaire), et de son environnement (espace disponible pour proliférer, présence d'oxygène). Le second module modélise le réseau vasculaire et le flux sanguin et rend compte de l'angiogenèse (apparition de nouveaux vaisseaux) et de l'adaptation du diamètre des vaisseaux, en fonction de l'évolution des contraintes hémodynamiques, nettement visible sous la fenêtre dorsale. L'ensemble des processus diffusifs (diffusion de l'oxygène et des facteurs de croissance vasculaire) sont décrits par des équations aux dérivées partielles, couplées à des automates cellulaires qui permettent de localiser à chaque instant pour chaque équation les termes sources (production) et les termes puits (consommation) pour chaque entité diffusive. Les simulations numériques réalisées montrent dans quelle mesure il est possible de rendre compte des observations expérimentales sur le plan qualitatif, qui nécessite la neutralisation des biais numériques ; et sur le plan quantitatif, pour reproduire la cinétique de croissance tumorale et l'évolution de la densité vasculaire. Le modèle numérique de l'évolution tumorale sous fenêtre dorsale est ensuite utilisé pour tester les effets de deux types de molécules : cytotoxiques et anti-vasculaires. Les simulations numériques de ces deux types de traitement explorent différents protocoles, définis par le mode d'action de la molécule, la dose administrée et la fréquence d'administration. Les résultats montrent comment il est alors possible de définir un protocole optimum pour une tumeur donnée en direction d'une individualisation de la thérapie. Ce modèle intégré a permis de poser de façon satisfaisante les bases d'un clone numérique du modèle expérimental d'évolution tumorale sous fenêtre dorsale même si certains aspects nécessitent encore quelques améliorations. La validation des aspects thérapeutiques restera encore à accomplir avant de pouvoir envisager à terme le remplacement (au moins partiel) de l'animal par l'ordinateur. / The work realised during this thesis had for objective to develop a theoretical model dedicated to the context of tumour development as observed on a dorsal skinfold chamber on a mouse. The model developed is hybrid, multi-physic and multi-scale, and associate two main modules. The first module model tumour growth with a cellular automaton which permit to differentiate the state of each cell regarding its history (cell cycle), its environment (available space to proliferate, oxygen availability). The second module model vascular network and blood flow, and accounts for angiogenesis (apparition of new vessels) and diameter adaptation of vessels, regarding hemodynamical constraints evolution which is distinctly visible on dorsal chamber. The diffusive processes (oxygen diffusion and vascular growth factors) are described by partiel differential equations, coupled with cellular automata which permit to localize at each time for each equation the source terms (production) and the well terms (consumption) for each diffusive entity. The numerical simulations realised show in which regard it is possible to accounts for the experimental observations on the qualitative basis, which require numerical bias neutralisation; and on the quantitative basis, to reproduce tumour growth kinetic and evolution of vascular density. The numerical model of tumour evolution on dorsal chamber is then used to test the effects of two types of molecules: cytotoxic and anti-vascular. Numerical simulation of these two types of treatment explore different protocols, defined by the action mode of the molecule, the dose administrated, and the administration frequency. Results show how it is possible to define an optimum protocol for a given tumour in direction of therapy individualisation. This integrated model has permitted to put in place in a satisfactory way the bases of a numerical clone of the experimental model of tumour growth on dorsal chamber, even if several aspects still necessitate some improvements. The validation of these theoretical aspects has yet to be accomplished before considering in term the replacement (at least partiallly) of animals by computers.

Le fonctionnement à haute température de certains composants des centrales nucléaires, provoque une dégradation de leurs propriétés à rupture. Cette dégradation provient essentiellement de l'activation de phénomènes thermodynamiques qui entraînent la ségrégation d'éléments aux joints des grains. L'objectif de ce travail est de proposer une modélisation multi-échelle permettant de relier la cinétique de cette ségrégation à l'évolution des propriétés à rupture du matériau. / The use of some PWR components at a relatively high temperature generates a drop of their fracture properties. This embrittlement is generally attributed to the segregation of some impurities at grains boundaries. This work aims at correlating the kinetics of this segregation to the embrittlement kinetics through a multi-scale approach, combining thermodynamical and micro-mechanical analysis.

Prédire, modéliser et analyser le métabolisme de xénobiotiques, substances étrangères à un organisme, à l'aide de méthodes informatiques est un challenge majeur mobilisant la communauté scientifique depuis de nombreuses années. Cette thèse vise à implémenter des méthodes informatiques multi-échelles pour prédire et analyser le métabolisme des xénobiotiques. Un premier axe de cette étude portait sur la construction et l'annotation automatique de novo de graphes métaboliques combinant fortes sensibilités et précisions. Ces graphes fournissent ainsi la prédiction du métabolisme de xénobiotiques chez l'homme, ainsi que la génotoxicité des molécules et atomes qui le composent. Puis, le travail s'est orienté sur l'implémentation d'un modèle mathématique dynamique modélisant des effets de compétition enzymatique à travers le développement d'une méthodologie permettant l'exploitation de données biologiques restreintes tout en limitant les biais inhérents. / Predicting, modelling and analysing the metabolism of xenobiotics, substances foreign to an organism, using computer methods, has been a major challenge for the scientific community for many years. This thesis aims to implement multiscale computing methods for predicting and analyzing the metabolism of xenobiotics. A first focus of this study was on the construction and automatic de novo annotation of metabolic graphs combining high sensitivity and precision. These graphs thus provide the prediction of the metabolism of xenobiotics in humans, as well as the genotoxicity of the molecules and atoms that make up xenobiotics. Then, the work focused on the implementation of a dynamic mathematical model modelling enzymatic competition effects through the development of a methodology allowing the exploitation of limited biological data while limiting inherent biases.