Optimality conditions for finite element simulation of adaptive bone remodeling (Q1210639)

We re-state the conditions necessary for stability of a particular bone remodeling rate equation derived in a related study, and we investigate whether the rate equation used can produce an optimal structure. Within the context of a finite element discretization, we show that this rate equation does not produce a structure optimized with respect to density. By making a simple modification to the stable remodeling rate equation, we show that the remodeling stimulus used can produce an optimal structure if the state variable manipulated is density taken to a power. We conclude that if bone is a stable, self-optimizing structure, there are specific requirements for the point-by-point rate of change of bone density in response to mechanical stress. The implications of these requirements for simulation of adaptive bone remodeling are discussed.