Probabilistic analysis of an uncemented total hip replacement

Abstract 

This paper describes the application of probabilistic design methods to the analysis of the behaviour of an uncemented total hip replacement femoral component implanted in a proximal femur. Probabilistic methods allow variations in factors which control the behaviour of the implanted femur (the input parameters) to be taken into account in determining the performance of the construct. Monte Carlo sampling techniques were applied and the performance indicator was the maximum strain in the bone. The random input parameters were the joint load, the angle of the applied load and the material properties of the bone and the implant. Two Monte Carlo based simulations were applied, direct sampling and latin hypercube sampling. The results showed that the convergence of the mean value of the maximum strain improved gradually as a function of the number of simulations and it stabilised around a value of 0.008 after 6200 simulations. A similar trend was observed for the cumulative distribution function of the output. The strain output was most sensitive to the bone stiffness, followed very closely by the magnitude of the applied load. The application of latin hypercube sampling with 1000 simulations gave similar results to direct sampling with 10,000 simulations in a much reduced time. The results suggested that the number of simulations and the selection of parameters and models are important for the reliability of both the probability values and the sensitivity analyses.

Keywords: Biomechanics, Orthopedics, Finite element, Probability, Total hip replacement