Comparison of two methods for probabilistic finite element analysis of total knee replacement

Probabilistic Finite Element (FE) models have recently been developed to assess the impact of experimental variability present in knee wear simulator on predicted Total Knee Replacement (TKR) mechanics by determining the performance envelope of joint kinematics and contact mechanics. The gold standard for this type of analysis is currently the Monte Carlo method, however, this requires a larger number of trials and is therefore computationally expensive. Alternatively, probabilistic methods exist, such as response surface methods that can offer considerable savings in computational cost. The aim of the current study was to compare the performance envelopes obtained for three metrics (Anterior-Posterior (AP) translation, Internal-External (IE) rotation and peak Contact Pressure (CP)) for a FE model of TKR mechanics using two different probabilistic methods: the Monte Carlo technique and the Response Surface Method (RSM), implemented with PamCrash FE solver and PamOpt optimization/probabilistic software. The influence of implant alignment was considered, based on a study from the literature. The results of a 1000 trial Monte Carlo analysis were compared to predictions from 25, 50 and 100 trial response surface calculations. Overall, the Response Surface Method (RSM) was capable of predicting similar results to the Monte Carlo method, but with a substantially reduced computational cost (RSM-50 4 hours as compared to 4 days with the Monte Carlo method

Probabilistic finite element predictions of the human lower limb model in total knee replacement

The purpose of this paper is to explore both an extended and a reduced set of input parameters of the Finite Element (FE) model of the human lower limb with a Total Knee Replacement (TKR) implant. The most influential parameters in determining the size and the shape of the performance envelopes of eight kinematics and peak contact pressure output variables of the tibio-femoral joint and the patello-femoral joint are sought. The lower limb FE model, which includes bones, TKR implant, soft tissues and applied forces of realistic size, is used in the context of the stair ascent simulation. Two probabilistic methods are used together with the FE model to generate the performance envelopes and to explore the sensitivities of the input parameters of the FE model: the Monte Carlo simulation and the Response Surface Method (RSM). A total of four probabilistic FE analyses assess how the uncertainties in an extended set of 77 input variables and a reduced set of 22 input variables obtained from the RSM/sensitivity analyses affect the performance envelopes. It is shown that the FE model with the reduced set of variables is able to replicate the full FE model. The differences between the Monte Carlo envelopes of performance obtained with the FE model with the full set of variables and the FE model with the reduced set of variables were on average over all output measures under 1.67 mm for translations, 1.75° for rotations and under 2 MPa for peak contact pressures. The differences between the RSM and the Monte Carlo envelopes of performances obtained with the reduced set of input variables were, on average, over all output measures under 0.75 mm for translations, 1.26° for rotations and 2.39 MPa for peak contact pressures. While saving computational time with the reduced set of variables, the findings are especially of high importance to the orthopedic surgeons who would like to know the most important parameters that can influence the performance of the TKR for a given human activity

Model Selection with PLANN-CR-ARD

This paper presents a new compensation mechanism to be used with a Partial Logistic Artificial Neural Network for Competing Risks with Automatic Relevance Determination (PLANN-CR-ARD) and tested comprehensibly on a real breast cancer dataset with excellent convergence properties and numerical stability for the non-linear model. The Model Selection is implemented for the PLANN-CR-ARD model, benefiting from a scaling of the prior error term which together with the data error term forms the total error function that is optimized. The PLANN-CR-ARD proves to be an excellent prognostic tool that can be used in regression analysis tasks such as the survival analysis of cancer datasets

A multi-platform comparison of efficient probabilistic methods in the prediction of total knee replacement mechanics

Explicit finite element (FE) and multi-body dynamics (MBD) models have been developed to evaluate total knee replacement (TKR) mechanics as a complement to experimental methods. In conjunction with these models, probabilistic methods have been implemented to predict performance bounds and identify important parameters, subject to uncertainty in component alignment and experimental conditions. Probabilistic methods, such as advanced mean value (AMV) and response surface method (RSM), provide an efficient alternative to the gold standard Monte Carlo simulation technique (MCST). The objective of the current study was to benchmark models from three platforms (two FE and one MBD) using various probabilistic methods by predicting the influence of alignment variability and experimental parameters on TKR mechanics in simulated gait. Predicted kinematics envelopes were on average about 2.6 mm for tibial anterior-posterior translation, 2.9° for tibial internal-external rotation and 1.9 MPa for tibial peak contact pressure for the various platforms and methods. Based on this good agreement with the MCST, the efficient probabilistic techniques may prove useful in the fast evaluation of new implant designs, including considerations of uncertainty, e.g. misalignment

Partial logistic artificial neural network for competing risks regularized with automatic relevance determination

Time-to-event analysis is important in a wide range of applications from clinical prognosis to risk modeling for credit scoring and insurance. In risk modeling, it is sometimes required to make a simultaneous assessment of the hazard arising from two or more mutually exclusive factors. This paper applies to an existing neural network model for competing risks (PLANNCR), a Bayesian regularization with the standard approximation of the evidence to implement automatic relevance determination (PLANNCR-ARD). The theoretical framework for the model is described and its application is illustrated with reference to local and distal recurrence of breast cancer, using the data set of Veronesi et al (1995)