COMPUTATIONAL METHOD BASED ON CONTINUUM DAMAGE MECHANICS TO DETERMINE THE DISTRIBUTION OF BONE DENSITY

Abstract

The internal bone remodeling is a repair mechanism, which aims to maintain bone strength, while keeping its mass and preventing fractures. This paper proposes a remodeling numerical algorithm based on the Continuum Damage Mechanics theory, and its basic idea is to simulate the porosity of the bone as damage. Is adopted the damage matrix as a mechanical stimulus to direct cellular responses in this process. This matrix is written as a function of the strain vector, remodeling matrix and damage scalar. The well-known "dead zone" - the region where the volume of voids within the tissue remains constant - is established in the domain of thermodynamics force matrix. The proposed mathematical formulation incorporates the possibility of bone resorption when the accumulated damage in the tissue, resulting from daily activities, is exceeded a critical value. Computer simulations using the Finite Element Method are made from a simplified two-dimensional model of the end of a long bone with cemented prosthesis, with reference to the human proximal femur. The results show the ability of the algorithm to obtain a tendency for the distribution of bone density, evidencing basic morphological characteristics of bone in regions of the epiphysis and diaphysis.