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Modélisation mathématique et simulations numériques de la mé́canotransduction dans l'os cortical humain

Abstract : Bone remodeling is a highly complex process involving several interrelated phenomena. This thesis deals with one of these phenomena - the mechanotransduction, in particular with mathematical modeling and associated numerical simulations. In order to understand the nature of the information received by the cell before the reconstruction of the new osteon that is the best adapted to local mechanical stresses, several studies are developed from an existing model. Cortical bone is considered as a multiscale porous medium. Three architectural levels are proposed and a mathematical development based on the homogenization theory allows a numerical determination of the permeability tensor coefficients. An analysis based on viscoelastic laws is persued at nanoscopic level. For giving a plausible explanation of the mechanotransduction phenomenon independent of localization in bone, a study allowing the computation of all physical fields existing at a given level as consequence of macroscopic loading is presented. The only fluid aspect doesn't allow a good knowledge by the cell of its environment and therefore it cannot induce an adapted cellular activity. This study shows that the collagen fibers, by their piezoelectric nature, transform the mechanical stresses induced by the surrounding part in an electric potential that the cells can sense.
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Submitted on : Sunday, February 6, 2011 - 8:02:33 PM
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  • HAL Id : tel-00563580, version 1



Cristina Mirela Stroe. Modélisation mathématique et simulations numériques de la mé́canotransduction dans l'os cortical humain. Mathématiques [math]. Université de Franche-Comté, 2010. Français. ⟨tel-00563580⟩



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