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Multi scale mathematical modeling of coupled phenomena in porous media: application to the bone remodeling; case of healthy and pathological bone - RP7 |
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Main objective of the project
This work deals with the study of human bone behaviour considered as a living tissue able to adapt its architecture to various mechanical solicitations. Since bony pathologies (osteoporosis, fractures, malformations …) can often generate handicap, the development of tools intended to limit their harmful consequences is an important stake of public health. In tissular engineering, understanding of bony phenomena occurring during bone remodelling need a modelization taking into account all the physical aspects at each architectural scale. Indeed, this tissue is a multi-scale and mineralized composite medium. Its structural and multiphasic complexity induces a large difficulty in the understanding of the interactions between cell activity, microstructure, mineral contents and mechanical properties. The necessity of a better understanding is enlarged by the evolution of the actual society (related for example to ageing of the population) and we propose the elaboration of a mathematical model allowing a significant advance in the knowledge of mechanotransduction processes. Our aim is the study, in an exhaustive way, the physical mechanisms implied in the evolution of bone tissue, during natural bone remodeling or under the action of mechanical stresses or in contact with orthopaedic implants. These questions, essentials when treating osteoporotic patients or replacing in a durable way a defective articulation, remain largely open. The present project is in the continuity of previous activities which had as final aim the modeling and the numerical simulation of bone remodeling. But the actual studies don’t take into account the fact that bone is a living tissue which evolves in time and changes its structure according to the applied stresses. To supplement our mathematical modeling and the biomechanical evaluation, we must integrate this functionality of bone adaptation. Bone remodelling is the process by which the bone adapts its solidity to the loading undergone not only by structural modification, but also by change of its mechanical properties. The possibility for bony cell of perceiving the mechanical stimuli via the mechanotransduction process for bringing a biological answer is ensured by the motion of the interstitial fluid around the cell. The objective of this work consists in the development of a multi-scale model integrating the motion of bony fluid in the cortical structure and biochemical interactions at the cellular level. From a mathematical point of view this could conduct to an extremely complex and very interesting model.
General objectives
SiNuPrOs is a multi scale mathematical modeling of the human cortical bone which can be used in two ways : from the nanoscopic scale to the macroscopic one (knowing an architecture, one determines the physical properties at each scale) and from the macroscopic scale to the nanoscopic one (knowing a physiological mechanical solicitation at the macroscopic scale, one computes all the physical fields at each scale). In this project, we plan to develop our work according to 5 axes which are respectively: the developments and the addition of potentialities to the existing model, a mathematical study of the fluid - structure coupling, a mathematical study of the damage in bone, an investigation in the modeling of some pathological cases and finally a summary of the obtained results. We present here under these objectives: 1. Developing the numerical existing model by adding new modules 2. Mathematical study of the fluid-structure coupling 3. Dissemination of partial results 4. The mathematical study of the damage in bone 5. Modeling some pathological cases 6. Dissemination of the results
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