L'objectif de cette thèse est de proposer des modèles mathématiques permettant de décrire l'instabilité dynamique d'une population de microtubules (MTs) et l'effet de médicaments sur cette instabilité. L'instabilité dynamique des MTs joue un rôle extrêmement important dans les processus de la mitose et de la migration cellulaire et donc dans la progression tumorale. L'instabilité dynamique est un processus complexe qui implique différents états de la tubuline (polymérisée ou non-polymérisée, tubuline-GTP ou tubuline-GDP qui correspondent à deux états énergétiques différents des dimères) et qui résulte de processus chimiques (polymérisation, dépolymérisation, hydrolyse, recyclage, nucléation) liant ces différents états de la tubuline. Décrire cette complexité par le biais de modèles mathématiques permet alors de tester des hypothèses biologiques quant à l'impact de chacun de ces processus et l'action de molécules anti-MTs. De récents travaux suggèrent que le "vieillissement" des MTs impacte leur dynamique. Nous avons testé dans ce travail l'hypothèse que ce "vieillissement" accélère l'hydrolyse du GTP au sein de la tubuline. Nous avons construit de nouveaux modèles couplant deux équations de transport multi-D avec deux équations différentielles ordinaires impliquant des termes intégraux. Nous avons calibrer notre nouveau modèle à partir des données expérimentales; tester l'hypothèse biologique sur le mécanisme du processus de vieillissement; analyser la sensibilité du modèle par rapport aux paramètres décrivant les processus; tester différentes hypothèses quant l'effet des médicaments anti-MTs. / The aim of this thesis is to design new mathematical models that are able to appropriately describe dynamic instability of a population of microtubules (MTs) and effect of drugs on MT dynamics. MT dynamic instability play an important role in the processes of mitosis and cell migration and, thus, in cancer progression. Dynamic instability is a complex process that involves different states of tubulin (polymerized or non-polymerized, GTP-tubulin or GDPtubulin that correspond to two different energetic states of tubulin dimers) that resulted from chemical processes (polymerization, depolymerization, hydrolysis, recycling, nucleation) linking these different states of tubulin. Description of this complexity by mathematical models enables one to test biological hypotheses concerning the impact of each process and action of drugs on microtubule dynamics. Recent observations show that MT dynamics depends on aging of MT. One of the aims of the work is to test the hypothesis that MT aging results from the acceleration of the GTP hydrolysis. We construct for that new models that couple two multidimensional transport equations with two ordinary differential equations involving integral terms. We have calibrated our models on the basis of experimental data; tested biological hypothesis on mechanism of aging process; performed a sensitivity analysis of the model with respect to parameters describing chemical processes; and tested hypotheses concerning actions of drugs.

Inconel 718 (IN 718) is widely used in applications, such as aircraft and power turbine components. Recently, fiber laser welding has become an attractive joining technique in industry for fabrication and repair of service-damaged components. However, a major limitation in the laser welding of IN 718 is that liquation cracking occurs. In the present work, autogenous fiber laser welding of IN 718 was used to study the effects of welding parameters and different pre-weld heat treatments on liquation cracking. Contrary to previous studies, a dual effect of heat input on cracking is observed. A rarely reported effect of heat input is attributed to process instability. Liquation cracking increases with pre-weld heat treatment temperatures that increase grain size and/or, possibly, intregranular boron segregation. The study shows that pre-weld heat treatment at 950oC can be used for repair welding of IN 718 without significant loss in cracking resistance.

Inconel 718 (IN 718) is widely used in applications, such as aircraft and power turbine components. Recently, fiber laser welding has become an attractive joining technique in industry for fabrication and repair of service-damaged components. However, a major limitation in the laser welding of IN 718 is that liquation cracking occurs. In the present work, autogenous fiber laser welding of IN 718 was used to study the effects of welding parameters and different pre-weld heat treatments on liquation cracking. Contrary to previous studies, a dual effect of heat input on cracking is observed. A rarely reported effect of heat input is attributed to process instability. Liquation cracking increases with pre-weld heat treatment temperatures that increase grain size and/or, possibly, intregranular boron segregation. The study shows that pre-weld heat treatment at 950oC can be used for repair welding of IN 718 without significant loss in cracking resistance.