Probabilistic computational modeling of total knee replacement wear

Abstract

Polyethylene wear remains a clinically relevant issue affecting total knee replacement (TKR) performance, with considerable variability observed in both clinical retrieval and experimental wear studies. Recently, computational wear simulations have been shown to predict similar results to in vitro and retrieval studies. The objectives of this study were to develop a probabilistic wear prediction model capable of incorporating uncertainty in component alignment, constraint and environmental conditions, to compare computational predictions with experimental results from a knee wear simulator, and to identify the most significant parameters affecting predicted wear performance during simulated gait. The current study utilizes a previously verified wear model; the Archard's law-based wear formulation represents a composite measure, incorporating the effects and relative contributions of kinematics and contact pressure. Predicted wear was in reasonable agreement in trend and magnitude with experimental results. After 5 million cycles, the predicted ranges (1–99%) of variability in linear wear penetration and gravimetric wear were 0.13 mm and 25 mg, respectively, for the input variability levels evaluated. Using correlation-based sensitivity factors, the coefficient of friction, insert tilt and femoral flexion–extension alignment, and the wear coefficient were identified as the parameters most affecting predicted wear. Comparisons of stability, accuracy and efficiency for the Monte Carlo and advanced mean value (AMV) probabilistic methods are also described. The probabilistic wear prediction model provides a time and cost efficient framework to evaluate wear performance, including considerations of malalignment and variability, during the design phase of new implants.

Introduction

Functionality and survivorship of current total knee replacement (TKR) implants are influenced by joint kinematics, contact mechanics, and wear. Polyethylene wear and wear-related complications (e.g. osteolysis) continue to be a leading cause of revision surgery [1]. Retrieval studies are often used to evaluate wear clinically, with findings exhibiting significant variability both in the wear level on the implant as well as in overall TKR performance [2], [3].

Experimental knee wear simulators are often used to evaluate implant designs prior to clinical studies and to provide quantitative insight into the wear process and the effects of kinematic, geometric and material changes. Reported simulator wear results contain a significant amount of variability both in reported experimental wear volume and wear rates. Wear rate standard deviations of up to 14 mm³/million cycles [4] and up to 2.9 mg/million cycles [5] for aged conventional polyethylene have been reported in the literature. In tibial insert wear testing, Muratoglu et al. [6] reported wear rate standard deviations of up to 0.3, 1.4 and 0.5 mm³/million cycles for aged highly cross-linked, aged conventional and unaged conventional polyethylene, respectively.

The wear variability observed both in vivo and in simulator testing is likely caused by variability in the implant's kinematics and distribution of contact pressure, both of which are impacted by implant design, alignment, constraint and environmental conditions. Simulator testing has shown that wear is sensitive to kinematic level [4], [7], [8] and contact mechanics [9] and that a potentially significant level of kinematic variability is present [10]. As a precursor to simulator studies, computational wear prediction models may provide a useful tool to efficiently evaluate wear, often as part of the design process where experiments would be time consuming and cost prohibitive. Finite element-based wear predictions are based on a nodal formulation and adaptive remeshing [11], [12] and utilize the theory proposed by Archard [13]. While this type of adaptive finite element-based wear prediction has primarily been applied in hip implants [11], [12], [14], [15], recently, computational assessments of TKR components have shown good agreement with both simulator and clinical studies [3], [16], [17].

Explicit finite element models [18], [19] have previously evaluated the kinematics and contact mechanics during gait loading conditions present in the experimental Stanmore–Instron knee wear simulator. Probabilistic finite element analyses have quantified the effects of variability in component alignment, loading, and environmental conditions on the distribution of kinematics and contact pressure [20], [21]. However, the impact of the kinematic and pressure variability on potential wear has not been previously evaluated.

Accordingly, the objective of the current study was to develop a probabilistic model to evaluate the effects of variability in component alignment, constraint and environmental conditions on polyethylene wear during simulated gait. The computational framework provides an efficient prediction of wear results, and a viable platform for assessing the effects of parameters that would be difficult to implement experimentally. The probabilistic model predicted the variability in linear wear penetration and gravimetric wear, as well as kinematics and peak contact pressure. Model predictions were verified through comparison with kinematic and wear results from the simulator including comparisons of the efficiency and accuracy of two probabilistic methods. In addition, the sensitivity of the joint mechanics and wear performance was assessed in order to identify the critical input parameters.