Time Simulation of Bone Adaptation

The structural adaptation of a three-dimensional finite element model ofthe proximal femur is considered. Presuming the bone possesses the optimalstructure under the given loads, the bone material distribution is foundby minimizing the strain energy averaged over ten load cases with avolume constraint.

Theoptimized design is used as a start-configuration for the remodelingsimulation.The parameter characterizing the equilibrium level where no remodeling occurs is estimated from the optimization parameters.The loads vary in magnitude, location and direction simulating timedependent loading. The remodeling algorithm is derived directly from theoptimization recurrence formula, and in a time increment the materialdistribution changes towards the optimal structure for the present load case.The speed of remodeling is taken from clinical data.Numerical examples of respectively increasing and reducing the jointforces are given.