Mathematical Model for Cartilage Tissue-Growth Using a Quadriphasic Mixture and Finite Element Analysis

The goal of this thesis is to build a clear model of biological tissues growth, especially cartilage. But because tissues are complicated, simplifications and assumptions have to be made. In experiments, engineered tissues are often using hydrogels, because of their ability to mimic the real system. However, strategies to date are suboptimal in part because designing degradable hydrogels is complicated by structural and temporal complexities of the gel and evolving tissue along multiple length scales. To address this problem, this study proposes a multi-scale mechanical model using a quadriphasic formulation (solid, fluid, unbound matrix molecules, enzymes) based on a single chondrocyte releasing extracellular matrix molecules and enzymes within a degrading hydrogel. This model describes the key players of the biological system within the hydrogel encompassing different length scales. Different mechanisms are included: temporal changes of bulk properties due to hydrogel degradation, and matrix molecules transport. Numerical results show the competition between the diffusion of the matrix molecules and the the diffusion of the enzymes degrading the scaffold

Fire regimes and variability in aboveground woody biomass in miombo woodland

This study combined a process-based ecosystem model with a fire regime model to understand the effect of changes in fire regime and climate pattern on woody plants of miombo woodland in African savanna. Miombo woodland covers wide areas in Africa and is subject to frequent anthropogenic fires. The model was developed based on observations of tree topkill rates in individual tree size classes for fire intensity and resprouting. Using current and near-future climate patterns, the model simulated the dynamics of miombo woodland for various fire return intervals and grass cover fractions, allowing fire intensity to be estimated. There was a significant relationship between aboveground woody biomass and long-term fire regimes. An abrupt increase in fire intensity and/or fire frequency applied as a model forcing led to reduced long-term average aboveground woody biomass and mean tree size. Fire intensity increased with increasing living grass biomass (which provides increased flammable fuel), thereby affecting the relationship between fire regime and tree size, creating a demographic bottleneck on the route to tree maturity. For the current fire regime in miombo woodland, with a fire return interval of about 1.6-3 years, the model-predicted fire intensity lower than 930-1700 kW m-1 is necessary to maintain today's aboveground woody biomass under current climate conditions. Future climate change was predicted to have a significant positive effect on woody plants in miombo woodland associated with elevated CO2 concentration and warming, allowing woody plants to survive more effectively against periodic fires

Modélisation de la croissance des peuplements réguliers de hêtre : dynamique des hiérarchies sociales et facteurs de production

Afin de permettre la simulation de la croissance de peuplements réguliers de hêtre soumis à divers traitements sylvicoles, un modèle indépendant des distances a été mis au point, à partir des données recueillies dans des essais comparatifs d'éclaircie observés sur de longues périodes. On a choisi de modéliser simultanément et de façon cohérente l'effet de la densité et des facteurs sociaux sur la croissance, aux deux niveaux de l'arbre et du peuplement. Le modèle repose sur une double représentation de la compétition interindividuelle. 1) Compétition verticale unilatérale entre classes sociales : le peuplement est subdivisé en deux sous-unités, l'étage principal de végétation et le sous-étage; l'étage principal inhibe totalement la croissance du sous-étage, lequel ne concurrence pas l'étage principal. 2) Compétition horizontale dans l'étage principal : la croissance d'un individu dépend de sa position sociale et de la densité partielle de l'étage principal. L'articulation entre les deux étages a lieu au voisinage d'une dimension-seuil, dont la valeur dépend de l'âge et de la densité du peuplement. Le choix d'une formulation mathématique simple permet l'étude explicite du comportement asymptotique des trajectoires individuelles : le modèle prédit une structuration continue des peuplements, des individus initialement dans l'étage dominant étant progressivement recouverts et relégués dans le sous-étage; ces régressions sociales se manifestent par l'apparition de distributions bimodales. Les prédictions sont testées favorablement pour des situations s'écartant fortement de celles qui ont servi à la construction du modèle. Toutefois, certains écarts constatés entre prédictions et observations laissent penser que la compétition pour la lumière ne suffit pas à rendre compte de la dynamique des différentes classes sociales : des différences de fonctionnement entre périodes de bonne alimentation en eau et périodes de stress hydrique suggèrent l'intervention d'une compétition souterraine. Ces résultats contribueront à la généralisation du modèle pour une large gamme de conditions écologiques et, éventuellement, pour d'autres espèces.Modelling the growth of even-aged beech stands: dynamics of hierarchical systems and yield factors. In order to buiid a growth simulator for even-aged stands of common beech (Fagus silvatica L) under various management regimes, a distance-independant individual-tree model was developed, on the basis of repeated measures in long-term thinning trials. The method aimed at representing, in a simultaneous and coherent way, the effect of density and social status on growth, at both tree- and stand-level. The model is based on two assumptions concerning inter-tree competition. 1) One-sided vertical competition between social classes: the stand is organized in two subsystems, the main vegetation storey and the understorey; the overstorey inhibits completely understorey growth, whereas understorey does not influence overstorey. 2) Horizontal competition in the overstorey: the growth of one tree depends on its social position and on the overstorey partial density. The two storeys are separated by a threshold dimension, the value of which depends on age and density of the stand. The rather simple mathematical formulation that was chosen allows an analytical study of the asymptotic behaviour of individual tree trajectories: the model predicts a continuous structuration of stands, as trees initially in the overstorey are progressively overtopped and drop back to the understorey; the consequence of such social regressions is the development of bimodal distributions. The predictions are favourably tested against actual observations, especially in the case of situations differing markedly from those used to build the model. But some discrepancies still subsist between predictions and observations and let us argue that competition for light is not sufficient to account for the differences in the dynamics of various social classes: dissimilar stand functioning between periods of favourable water conditions and periods of water stress indicate that competition also exists between root systems. These results will lead to a more general formulation of the model, for a large range of ecological conditions and, possibly, for other species

A model of even-aged beech stands productivity with process-based interpretations

In order to describe the productivity of pure even-aged stands of common beech, a system of three differential equations is proposed for dominant height, basal area and total volume growth. The model was derived and fitted to 317 observation periods in 29 long-term experimental plots ranging from northwest to northeast France. It involves parameters at the forest and stand levels. Site index is the asymptote of the height-age curve. Model structure is such that, for any given height, some differences in total volume yield exist between stands of different productivities. This result is in contradiction with Eichhorn's rule. However, in our model, no parameter other than site index is necessary to characterize stand productivity. The possibility to generalize the model to a larger range of ecological conditions is discussed by a process-based interpretation. The site dependence of the parameters can be understood by reference to carbon-balance models. A linear relationship between basal area and height-growth rates is investigated by a separate model of sapwood geometry and dynamics.Un modèle de productivité des hêtraies régulières avec des interprétations écophysiologiques. Afin de décrire la productivité de peuplements purs et réguliers de hêtre, on propose un système de trois équations différentielles pour la hauteur dominante, la surface terrière et le volume. Le modèle a été construit et ajusté à partir de 317 périodes d'observations dans 29 anciennes placettes expérimentales réparties entre le nord-ouest et le nord-est de la France. Il comprend des paramètres aux niveaux de la forêt et du peuplement. L'indice de fertilité est l'asymptote des courbes hauteur— âge. La structure du modèle est telle que, pour une hauteur dominante donnée, la production totale en volume diffère entre peuplements de fertilités différentes. Ce résultat est en contradiction avec la loi d'Eichhorn. Pourtant, dans notre modèle, seul l'indice de fertilité est nécessaire pour caractériser la production d'un peuplement. À partir d'une interprétation écophysiologique, on discute la possibilité de généraliser ce modèle à une large gamme de conditions écologiques. La dépendance des paramètres par rapport au milieu peut être justifiée par référence aux modèles de bilan de carbone. La relation linéaire entre croissances en hauteur et en surface terrière est explorée grâce à un modèle de la géométrie et de la dynamique de l'aubier

La conduite des peuplements forestiers

La gestion durable des forêts : contribution de la rechercheNational audienc