ABSTRACT
Alteration of physiological stress within bone induces unbalance of bone cell activity. Two types of functional adaptation may then occur simultaneously: internal adaptation (relative density and/or anisotropy variation with a fixed geometry) and external adaptation (periosteal and endosteal apposition or resorption changing the geometry). In this study, a 3D model of bone external adaptation was developed. The mechanical stimulus controlling the change of bone shape was based on an invariant scalar function, based on the stress tensor, the orientation unit vector (anisotropy) and the external normal unit vector. The evolution law was based on a sigmoid-type function including an equilibrium zone. The time integration was performed by a forward Euler scheme. The model was first applied on 2D bone samples. A trabecular bone unit was simplified by a 2D square with a central hole. This unit was used to build a piece a trabecular bone and applied to study the adaptation of the internal surface of trabecular bone. From the pores geometry, two internal variables were defined: the relative density and the anisotropy direction. After several loading alterations, it was observed that the adaptation of relative density occurred more quickly than the adaptation of anisotropy. This adaptation model was also applied to evaluate the evolution of the external shape of a turkey ulna subjected to specific external load. The results were compared with experimental data with good correlation.
