Multi scale mathematical modeling of coupled phenomena in porous media: application to the bone remodeling; case of healthy and pathological bone - RP7  

Introduction

The proposed problem in the framework of this project is with application in the biomechanical field. It deals with the study and modeling of human bone remodeling that becomes a more and more accurate problem with the ageing of population. Such a process is extremely complex because many phenomena are coupled and it is difficult to experimentally study the simultaneous effects of coupled parameters.

This project proposes primarily the construction of a mathematical modeling of three phenomena: the flow of the bony fluid in the human cortical bone at cellular scale, the mineral apposition and the damage of the bone. In the same time, it must be plausible and realistic on physical and biological points of view. The long term aim is to understand and numerically simulate the mechanisms of the bony remodeling in the healthy case but also in the pathological cases.

Bone remodeling is realized through two phases: a destruction phase during which specific cells destroy an area where the high mineralization degree induces too high stresses and a building phase extremely complex which can be divided in two steps. In the first step, cellular activity allows the elaboration of a collagenic tissue and in a second step, other cells support the elaboration and the aggregation of crystals. A better knowing of this second step is absolutely essential on a clinical point of view because it characterizes the quality of new bone: this quality has a major influence on the behavior of a new implant or on the bone itself during ageing.

These problems are well known and many studies have been pursued on this thematic. Some bone remodeling laws have already been published but there are quite ineffective because they are too global. A research team at the University of Franche-Comte (France) has developed since many years a new approach based on multiscale analysis. This project is in the continuity of these investigations and will be made in part in a close cooperation with this team.