Variability of a Three-Dimensional Finite Element Model Constructed Using Magnetic Resonance Images of a Knee for Joint Contact Stress Analysis

Magnetic resonance (MR) imaging has been widely used to evaluate the thickness and volume of articular cartilage both in vivo and in vitro. While morphological information on the cartilage can be obtained using MR images, image processing for extracting geometric boundaries of the cartilage may introduce variations in the thickness of the cartilage. To evaluate the variability of using MR images to construct finite element (FE) knee cartilage models, five investigators independently digitized the same set of MR images of a human knee. The topology of cartilage thickness was determined using a minimal distance algorithm. Less than 8 percent variation in cartilage thickness was observed from the digitized data. The effect of changes in cartilage thickness on contact stress analysis was then investigated using five FE models of the knee. One FE model (average FE model) was constructed using the mean values of the digitized contours of the cartilage, and the other four were constructed by varying the thickness of the average FE model by $±5 percent$ and $±10 percent,$ respectively. The results demonstrated that under axial tibial compressive loading (up to 1400 N), variations of cartilage thickness caused by digitization of MR images may result in a difference of approximately 10 percent in peak contact stresses (surface pressure, von Mises stress, and hydrostatic pressure) in the cartilage. A reduction of cartilage thickness caused increases of contact stresses, while an increase of cartilage thickness reduced contact stresses. Furthermore, the effect of variation of material properties of the cartilage on contact stress analysis was investigated. The peak contact stress increased almost linearly with the Young’s modulus of the cartilage. The peak von Mises stress was dramatically reduced when the Poisson’s ratio was increased from 0.05 to 0.49 under an axial compressive load of 1400 N, while peak hydrostatic pressure was dramatically increased. Peak surface pressure was also increased with the Poisson’s ratio, but with a lower magnitude compared to von Mises stress and hydrostatic pressure. In conclusion, the imaging process may cause 10 percent variations in peak contact stress, and the predicted stress distribution is sensitive to the accuracy of the material properties of the cartilage model, especially to the variation of Poisson’s ratio.