Functional adaptation of bone as an optimal control problem

The functional adaptation of bone is a process of bone tissue remodeling induced by variable in time mechanical demands that the skeleton has to satisfy. It is a very complex but highly organized process composed of events at micro-level (molecular and cellular) but having effects in macro-scale (variation of bone internal structure and external shape). Mathematical models of this phenomenon proposed in the literature represent formulas postulated on the basis of the results of medical observations or laboratory investigations and describe locally the evolution of a material in space and time. In the present paper a use is made of the hypothesis of optimal response of bone, proposed earlier by the author, what enables derivation (instead of postulation) the remodeling rules from a very general and global assumption. It turns out that such a formulation has many similarities to engineering optimal control problems. The link between the postulated local adaptation rules and those derived from the global assumption is also discussed.