Design and analysis of robust total joint replacements: finite element model experiments with environmental variables.

Computer simulation of orthopaedic devices can be prohibitively time consuming, particularly when assessing multiple design and environmental factors. Chang et al. (1999) address these computational challenges using an efficient statistical predictor to optimize a flexible hip implant, defined by a midstem reduction, subjected to multiple environmental conditions. Here, we extend this methodology by: (1) explicitly considering constraint equations in the optimization formulation, (2) showing that the optimal design for one environmental distribution is robust to alternate distributions, and (3) illustrating a sensitivity analysis technique to determine influential design and environmental factors. A thin midstem diameter with a short stabilizing distal tip minimized the bone remodeling signal while maintaining satisfactory stability. Hip joint force orientation was more influential than the effect of the controllable design variables on bone remodeling and the cancellous bone elastic modulus had the most influence on relative motion, both results indicating the importance of including uncontrollable environmental factors. The optimal search indicated that only 16 to 22 computer simulations were necessary to predict the optimal design, a significant savings over traditional search techniques.

Robust optimization of total joint replacements incorporating environmental variables.

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