Probabilistic Finite Element Prediction of the Active Lower Limb Model

Abstract

The scope of this paper is to explore the input parameters of a Finite Element (FE) model of an active lower limb that are most influential in determining the size and the shape of the performance envelope of the kinematics and peak contact pressure of the knee implant introduced during the Total Knee Replacement (TKR) surgery. The active lower limb FE model simulates the stair ascent and it provides a more complicated setup than the isolated TKR model which includes only the implant femoral component and the implant tibial insert. It includes bones, TKR implant, soft tissues and applied forces. The kinematics of the FE model is reported in the Grood and Suntay system, where all motion is relative to the femoral component of the TKR. Reported tibial component kinematics are tibial-femoral flexion angle, anterior-posterior displacement, and internal-external rotation, while the reported patella kinematics are patella-femoral flexion angle, medial-lateral shift and medial-lateral tilt. Tibial-femoral and patella-femoral contact pressures are also determined. Two probabilistic methods are used together with the FE model, which is termed probabilistic FE analysis, to generate performance envelopes for the reported output kinematics and peak contact pressures and to explore the input parameters: the Monte Carlo Simulation Technique (MCST) and the Response Surface Method (RSM). It is considered a large set of 77 input variables of the FE active lower limb model which have associated a Gaussian variability. Following a sensitivity analysis with the RSM, a reduced set of 22 input variables is derived, which represent the key parameters which influence the performance envelopes. It is shown that the envelopes of performance obtained with the probabilistic FE analysis using the RSM with the reduced set of 22 input variables are similar with the envelopes of performance obtained with the probabilistic FE analysis using the MCST with 800 points for the same degree of variability in the 22 input key parameters. The findings of this work are paramount to the orthopedic surgeons who may want to know the key parameters that can influence the performance of the TKR for a given human activity.