Formulation of a Mathematical Model for Mechanical Bone Remodeling Process

Abstract

This paper is concerned with the formulation of a mathematical model to describe mechanical bone remodeling process. Firstly, mechanical stimulus is defined as a function of the rate-of-deformation power per unit mass. Physiological signal transmission processes of remodeling from the mechanical stimulus to change of bone density are described by n+1 sequential evolution equations with n+1 macroscopic internal state variables. The evolution equations are established on the basis of the experimental results in a literature. The value of the internal variable in the last step specifies the balance level of bone density, which is the target of the current bone density. The comparison of the predicted results with the corresponding experimental ones shows that this model can quantitatively describe a time-dependent process of bone remodeling.