Robust optimization of total joint replacements incorporating environmental variables

Direct search techniques for the optimal design of biomechanical devices ar e computationally intensive, requiring many iterations before converging to a global solution. This, along with the incorporation of environmental var iables such as multiple loading conditions and bone properties, makes direc t search techniques infeasible. In this study, we introduced new methods th at are based on the statistical design and analysis of computer experiments to account efficiently for environmental variables. Using data collected a ta relatively small set of training sites, the method employs a computatio nally inexpensive predictor of the structural response that is statisticall y motivated. By using this predictor in place of the simulator (e.g., finit e element model), a sufficient number of iterations can be performed to fac ilitate the optimization of the complex system. The applicability of these methods was demonstrated through the design of a femoral component for tota l hip arthroplasty incorporating variations in joint force orientation and cancellous bone properties. Beams on elastic foundation (BOEF) finite eleme nt models were developed to simulate the structural response. These simple models were chosen for their short computation time. This allowed us to rep resent the actual structural response surface by an exhaustive enumeration of the design and environmental variable space, and provided a means by whi ch to validate the statistical predictor. We were able to predict the struc tural response and the optimal design accurately using only 16 runs of the computer code. The general trends predicted by the BOEF models were in agre ement with previous three-dimensional finite element computer simulations, and experimental and clinical results, which demonstrated that the importan t features of intramedullary fixation systems were captures. These results indicate that the statistically based optimization methods are appropriate for optimization studies using computationally demanding models.