A numerically validated probabilistic model of a simplified total hip replacement construct

Hip replacement constructs are paradigms of uncertain systems, and as such are suited to the application of probabilistic methods to assess their structural integrity. In order to gain confidence in a probabilistic model, it would be useful to verify the findings with experimental data; however, this is difficult to achieve in practice because of the exhaustive number of parameter combinations that need to be tested. As an alternative to experimental testing, benchmarking can be carried out provided a known analytical solution is available. To this end, a simplified 2D two-beam model of the femoral part of a total hip replacement construct was utilised to analyse uncertainties and variability in the construct as it is subjected to load. The use of a simplified model enabled geometric parameters to be investigated; these are commonly not considered in probabilistic models due to the increased complexity involved. Analytical and finite element representations of the model were developed and compared. The probabilistic study used the Monte Carlo simulation technique and the first-order reliability method to look at the inducible displacement of a hip implant, a phenomenon that has been linked to the most common cause of hip implant failure, aseptic loosening. Excellent correlation was observed between the analytical and probabilistic solutions, and it was shown that probabilistic approaches could efficiently predict the response of the simplified beam model while readily identifying the parameters most likely to compromise the structural integrity of the construct.