The effect of three-dimensional shape optimization on the probabilistic response of a cemented femoral hip prosthesis

Abstract 

Probabilistic analyses allow the effect of uncertainty in system parameters on predicted model performance measures to be determined. Furthermore, using performance functions to describe a failure event, the probability of failure can be quantified. The effect of three-dimensional prosthesis shape optimization on the probabilistic response and failure probability of a cemented hip prosthesis system is investigated. Random variables include joint and muscle loading, cortical and cancellous bone and PMMA bone cement elastic properties, and strength parameters describing failure of the bone cement and the prosthesis–bone cement interface. Several performance functions describing the bone cement and prosthesis–cement interface are used to compute the probability of failure. When evaluated deterministically, most performance functions indicated a safe design, with the exception of interface tensile failure. However, when evaluated probabilistically, finite probabilities of failure were computed, some significant. The most likely mode of failure before shape optimization was prosthesis–bone cement interface tensile failure with a predicted probability of failure of 97.9%. Deterministic prosthesis shape optimization reduced the probability of failure for all performance functions and reduced prosthesis–bone cement interface tensile failure by 31.7%. Probability sensitivity factors indicate that the uncertainty in the joint loading, cement strength, and implant–cement interface strength have the greatest effect on the computed probability of failure. Implant shape optimization results in a more robust implant design that is less sensitive to uncertainties in joint loading, which cannot be easily controlled, and more sensitive to cement and interface properties, which are easier to modify.

Keywords: Probabilistic analysis, Cemented hip prosthesis, Design optimization, Reliability, Finite element analysis, Uncertainty analysis, Random variables, Robust design