A study of the effect of non-linearities in the equation of bone remodeling.

In this paper, we introduced a high-order non-linear equation of bone remodeling to combine with FEM by introducing two non-linearities, i.e. the remodeling coefficient B(t) and the order of non-linear remodeling equation. The influence of each non-linearity was tested based on its mechanical and physiological implications discussed. We use two finite element models to investigate the influences of non-linearities in this equation: a plate subjected to a ramp load, and a 2D model of the cross-section of a vertebra. By importing the idea of topology optimization in engineering, their external shapes and internal density distributions were simulated from unfixed configurations. To a certain extent, the high-order non-linear equation of bone remodeling we suggested here can control the remodeling processes of bones in different stages of growth or at different anatomic sites more effectively, and make it more consistent with physiological reality, i.e. express the remodeling characteristic that bone's best morphology is adapted to its mechanical environment. Furthermore, it is likely to describe the process of bone growth and evolution.