Model and Simulation of Bone Remodeling Considering Residual Stress

Abstract

In bone remodeling, some bone material is resorbed and new bone material is then synthesized. In this context, the new bone material may have its own natural state which is different from that of the old bone materials in its neighbors, and this nonuniform distribution of the natural state is suggested to cause the stress/strain that remains even when all external loads are removed. Our preliminary observations have also suggested the existence of residual stress/strain in the bone structure, and the model of bone remodeling is expected to take these into account. This chapter describes a mathematical model of the bone remodeling that considers residual stress from the statical indeterminacy of the bone structure. The basic idea is discussed by using a lumped parameter system and is then extended to distributed parameter systems of the conventional continuum. The idea is also combined with the lattice continuum, that is, a continuum consisting of the rigidly interconnected elastic members as the microstructure, and this is used as a mechanical model of cancellous bone with trabecular architecture. The fundamental characteristics of the model are examined through remodeling simulations of the diaphysis bone under axial load by using a cylindrical model. The proposed model for the conventional continuum and the lattice continuum is applied to remodeling simulations of leporine tibiofibula bone and bovine vertebral bone. The capability of the remodeling simulation is demonstrated by the morphology of the bone structure as well as residual stress in comparison with experimental observations.