Simple anisotropic model of Bone Adaptation - SAMBA

Abstract

Bone presents the ability to adapt itself to the evolving mechanical environment. A simple anisotropic model for bone adaptation allowing reproducing the evolution of the elastic properties and the reorientation of the anisotropy frame is proposed is this work. The elastic properties are related to the value of the bone apparent density. The evolution law of the density is described via two functions reflecting the activities of the osteoclast and osteoblast cells. The anisotropy of the elastic properties of the bone is assumed evolving continuously between those of trabecular and compact tissues. The existence of a target material frame is assumed to describe its reorientation. The rate of rotation or spin of the material frame is supposed to be proportional to the target orientation angle and to the activity of the osteoclasts and osteoblasts. The mechanical stimulus governing the evolution of the apparent density is defined as the ratio between the current strain energy density and its critical value corresponding to the initiation of bone damage. The simulations showed that this simple model can reproduce some essential phenomena observed during bone adaptation process.