Development of a widely applicable gradientless shape optimization based bone adaptation model for comparative parametric studies

Many gradientless optimization based methods have been developed to predict mechanically-driven strength adaptations of bone and to improve the failure resistance of inert mechanical components. However, because the gradientless optimization methods commonly used in these applications typically do not result in a unique solution, few are capable of providing quantitative comparisons of the effects of different boundary conditions on the resulting shape and strength changes of the objects studied. Driven by relative measures of the current local stress state, global stress state, and variation of the local stress state over the design region, a condition-independent, system-independent shape/strength adaptation model was developed that can be applicable to a system with a large number of design variables. Using a local extrema independent quantitative measure of the progression of the design region to a more uniform stress state, a consistent comparison point was defined that can be used regardless of the system studied, the boundary conditions applied, or the initial amount of stress variation. The implementation of the developed model demonstrated its effectiveness in the repeatable prediction of shape and strength changes over multiple orders of magnitude differences in boundary values with no changes to the modeling parameters or stopping criteria. The developed gradientless optimization based shape adaptation technique can be a useful tool in the comparison of the effects of various loading conditions on the strength changes in bones and in the creation of exercise regimens to strengthen fracture prone regions.