Collaborative Research: Methodology for Computer Experiments with Special Application to Biomedical Mechanics

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Motivated by problems of biomechanical engineering, this collaborative research project develops and implements statistical tools for the design and analysis of computer experiments that have particular application to prosthesis design. These tools are used to create ace tabular cups designs that are resistant to pelvic osteolysis in a 3D model finite-element model for bone adaptation in the pelvis. A second specific biomechanical task is to validate/calibrate the computer codes for polyethylene wear in knee components from mechanical knee simulator studies. More generally, this work provides a suite of implemented tools that allow cost-effective and rapid engineering development of a wide range of product applications. It helps merge the statistical and engineering design communities by forcing the former to address fully articulated design problems and the latter to anchor the solution of these problems in rigorous stochastic and statistical methodology. The methodology may also prove useful in the analysis of other large computer models such as the climate, exposure, and pollution models used in environmental science. On the statistical front, exploratory designs are developed for computer experiments that allow better estimation of extreme outcomes, important for assessing the frequency of dangerous high stress-strain situations in a given patient population when a given prosthesis-design is used. This objective can be thought of as a robustness assessment tool for the given prosthesis design. Second, sequential designs are devised for constrained optimization problems, which are important in prosthesis design where multiple, competing outcomes occur frequently. On the analysis front, predictors are developed that give more accurate assessment of optima of predicted surfaces; these are used to produce faster (in the sense of requiring fewer evaluation of time-demanding computer code) solutions of constrained optimization problems. Finally, prediction methodology is developed for computer codes that use both qualitative and quantitative inputs. This project develops and implement statistical tools for the design and analysis of computer experiments that have particular application to prosthesis design. Computer experiments are cost-effective in rapid engineering development of a wide range of product applications. The project develops both statistical and mathematical tools that are useful outside of the current application of prosthesis design.