Simulation of Bone Mechanical Adaptation Using Different Mathematical Models: A Comparative Numerical Study

Abstract

The adaptation of bones to mechanical loads or bone remodeling can be simulated using specific mathematical models in conjunction with the finite element method. There are several theories proposed within the literature for the prediction of the bone behavior under mechanical loads and all have been used successfully, within certain limits of prediction details, but no unanimous acceptance have been reported yet. Within this context, it is important to know the differences and similarities between the results which these theories can produce, in order to improve their interpretation. On the basics of the above observation, the paper presents the comparison between density distributions achieved using three different models of bone remodeling: the original strain energy density equation developed at the University of Nijmegen, the principle of cellular accommodation incorporated into the Nijmegen model and the variant developed at the University of Manchester obtained by adding the quadric term which eliminates the density accumulation at physiologically unrealistic high loads. It is shown, using a suggestive test problem, that the three models generate significantly different results.