Bone remodeling and structural optimization.

Bone remodeling has been viewed both as a process which adapts bone tissue to the mechanical environment at each point in the structure, and as a process which optimally adjusts the tissue distribution within bones to bear the loads placed on them. We have developed a connection between these two views of bone remodeling, in a restricted sense. We start with a remodeling rate equation based on strain energy density. We then define an indicator function which is a weighted sum of total strain energy and a measure of bone mass, and we show that finding bone density distributions in which the remodeling rate equation predicts no changes with time is the same as finding density distributions in which the indicator function is insensitive to small changes in density. The set point in the remodeling rate equation corresponds to a parameter in the indicator function which determines the relative importance of bone mass and strain energy in the optimization indicator function. We have not assessed whether the density distributions which make the density rate of change zero are actually local or global minima for the indicator function in this study, but a related study shows that there is a single unique minimum for the indicator function developed here, implying that a unique solution exists for the bone remodeling rate equations considered in this study.