Bone remodeling has been viewed both as a process which adapts bone ti
ssue to the mechanical environment at each point in the structure, and
as a process which optimally adjusts the tissue distribution within b
ones 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 bon
e 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 densit
y. The set point in the remodeling rate equation corresponds to a para
meter in the indicator function which determines the relative importan
ce of bone mass and strain energy in the optimization indicator functi
on. We have not assessed whether the density distributions which make
the density rate of change zero are actually local or global minima fo
r 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.