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Elaboration d'une modélisation mathématique du transfert multi-échelle des signaux mécaniques dans l'os cortical humain. Aspects théoriques et simulations numériques

Abstract : Understand bone remodelling needs the knowledge of mechanical information transfer: what information receives a cortical bony cell when the bone is solicited? The purpose of this study is the elaboration of a modeling and of mathematical tools allowing to estimate, from a mechanical loading applied on a human bone, various fields existing in collagen, hydroxyapatite and bony fluid.

Mathematical theories of homogenization and flow in porous media are used. Model is made by taking successively into account spatial organization of hydroxyapatite crystals, different mineralizations, a new behaviour's law, motion of fluid containing ions in each of architectural levels and homogenization of complex composite structures (lamellae, osteons, cortical bone).

On a mathematically point of view, asymptotic developments method in a new piezoelectric framework (with threshold) is used. One establishes all necessary relationships, a property of convergence and a local analysis is made. The return to microscopic level is made directly via a technique of localization or indirectly when the effect of threshold occurs. Developped computational methods have been packed in two softwares.

On a biomechanical point of view, it has been established that human cortical bone is a non piezoelectric orthotropic medium for which anisotropy is essentially involved by the nanoscopic architecture, that they are two types of flow in osteon and that flows in the osteons differ according to their architecture. A process being able to explain how cells know what architecture to give to the collagen tissue is thus pointed out.
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https://tel.archives-ouvertes.fr/tel-00011578
Contributor : Mihaela Racila <>
Submitted on : Saturday, February 18, 2006 - 7:45:40 PM
Last modification on : Thursday, January 28, 2021 - 10:26:02 AM
Long-term archiving on: : Monday, September 20, 2010 - 2:17:20 PM

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  • HAL Id : tel-00011578, version 2

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Mihaela Predoi Racila. Elaboration d'une modélisation mathématique du transfert multi-échelle des signaux mécaniques dans l'os cortical humain. Aspects théoriques et simulations numériques. Modélisation et simulation. Université de Franche-Comté, 2005. Français. ⟨tel-00011578v2⟩

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