A model of bone adaptation as an optimization process

The internal bone adaptation of the proximal femur is considered. A three-dimensional finite element model of the proximal femur is used. The bone remodeling in this work is numerically described by an evolutionary remodeling scheme with anisotropic material parameters and time-dependent loading. The memory of past loading is included in the model to account for the delay in the bone response from the load changes. The remodeling rate equation is derived from the structural optimization task of maximizing the stiffness in each time step. Additional information can be extracted from the optimization process; the remodeling equilibrium parameter where no apposition or resorption takes place, is defined as the element optimality conditions and the optimal design is used as an initial design for the onset of the remodeling simulation. Two examples of bone adaptation resulting from load changes are given, and the irreversible nature of the model is illustrated.