The Impact of the Yeoh Model's Variability in Contact on Knee Joint Mechanics

Abstract

The aim of this study was to assess the impact of the variability of the Yeoh model when modeling the contact of bones through cartilage in the knee in compression and flexion-extension within a hybrid knee model. Firstly, a Sobol sequence of 64 samples and four variables representing the Yeoh parameters of the cartilage of the femur and tibia was generated. Based on these samples, 2 × 64 finite element contact models of the geometry of the sphere plane were generated and solved for healthy tissue affected by osteoarthritis. The resulting indentation curves were incorporated into a multibody knee joint model. The obtained results suggested that cartilage variability severely affected the knee in compression by up to 32%. However, the same variability also affected the flexion-extension motion, although to a lesser extent, with a relative change to the range of angular displacements of almost 7%. Osteoarthritic tissue was consistently more affected by this variability, suggesting that when modeling degenerated tissue, complex joint models are necessary.

Keywords: Sobol sequence; cartilage material properties; finite element; hybrid modeling; ligament; multibody; uncertainty.

Figure 1

A schematic overview of the present study [13].

Figure 2

The FE contact model with the cartilage parts: the Yeoh model’s variable parameters.

Figure 3

A schematic drawing of the hybrid model of the knee joint in the sagittal plane with parameters based on [13], except for the cartilage material parameters, which were based on [9]. The model is at around 55 degrees of flexion, which was the starting point for both flexion and extension.

Figure 4

The contact force versus the indentation in 64 variants and the mean of the FE model of the sphere–plane layered contact pair in the knee with the Yeoh model for cartilage, accounting for its variability in both healthy and OA-affected tissues.

Figure 5

The external moment M_ext as a function of the angle of the knee joint θ, with 0 deg corresponding to a fully extended knee for both the healthy and OA tissue groups, for all 32 variants of the hybrid model.

Figure 6

The external moment M_ext as a function of the angle of the knee joint θ, with 0 deg corresponding to a fully extended knee for the healthy and OA tissue groups, first variant only for clarity.

Figure 7

Forces generated by ligaments with respect to the knee joint angle θ under external moment loads of up to 3.5 Nm in both flexion and extension for the healthy and OA groups, only for the first variant of the hybrid model, for clarity. Healthy is drawn on top of OA, with an additional white line representing the last solution in the OA group, to showcase that OA covers most of the solution ranges.

Figure 8

Forces generated by the contact pairs with respect to the angle of the knee joint angle θ under external moment loads of up to 3.5 Nm in both flexion and extension for the healthy and OA groups, for one selected variant of the hybrid model only, for clarity. Healthy is drawn on top of OA.