Study of damage and remodelling models for bone tissueResolution with numerical methods

Abstract

The mechanical properties of vertebrate bone are complex, and they can be studied at two different scales: macroscopic and microscopic. The macroscopic properties are modelled phenomenologically while the microscopic dynamics are determined by cell populations. This thesis comprises a series of researches where we study mathematical models related to damage and remodelling in bone tissue. We explore both the biomechanical aspects of damage and remodelling from the macroscopic point of view and the microscopic models for cell populations. In the macroscopic part, we develop a novel model that couples damage and bone remodelling effects. Bone remodelling is crucial in order to maintain the integrity of the skeleton through our lives, since it is necessary to repair the damage that appears on our day-to-day activities. However, their coupling had not yet been deeply studied. In this thesis, the first thing we study is the damage model proposed by Frémond and Nedjar in 1996 so as to show its capabilities of modelling bone damage. Then, we present its coupling with the well-known ...