Discrete element analysis for characterizing the patellofemoral pressure distribution: model evaluation

Abstract

The current study was performed to evaluate the accuracy of computational assessment of the influence of the orientation of the patellar tendon on the patellofemoral pressure distribution. Computational models were created to represent eight knees previously tested at 40 deg, 60 deg, and 80 deg of flexion to evaluate the influence of hamstrings loading on the patellofemoral pressure distribution. Hamstrings loading increased the lateral and posterior orientation of the patellar tendon, with the change for each test determined from experimentally measured variations in tibiofemoral alignment. The patellar tendon and the cartilage on the femur and patella were represented with springs. After loading the quadriceps, the total potential energy was minimized to determine the force within the patellar tendon. The forces applied by the quadriceps and patellar tendon produced patellar translation and rotation. The deformation of each cartilage spring was determined from overlap of the cartilage surfaces on the femur and patella and related to force using linear elastic theory. The patella was iteratively adjusted until the extension moment, tilt moment, compression, and lateral force acting on the patella were in equilibrium. For the maximum pressure applied to lateral cartilage and the ratio of the lateral compression to the total compression, paired t-tests were performed at each flexion angle to determine if the output varied significantly (p < 0.05) between the two loading conditions. For both the computational and experimental data, loading the hamstrings significantly increased the lateral force ratio and the maximum lateral pressure at multiple flexion angles. For the computational data, loading the hamstrings increased the average lateral force ratio and maximum lateral pressure by approximately 0.04 and 0.3 MPa, respectively, compared to experimental increases of 0.06 and 0.4 MPa, respectively. The computational modeling technique accurately characterized variations in the patellofemoral pressure distribution caused by altering the orientation of the patellar tendon.

Figures

Fig. 1

(A) Initially, the forces representing the vastus lateralis (VL), the combination of the vastus intermedius/vastus medialis longus/rectus femoris (VI), and vastus medialis obliquus (VMO) are applied to the patella. The reaction forces in the springs representing the patellar tendon are calculated. (B) The resultant force and moment from the quadriceps and patellar tendon are applied to the patella. (C) The patella (transparent) translates and rotates in response to the applied force and moment producing overlap between the cartilage on the patella and femur (dark). The reaction force and moment acting on the patella from the cartilage is quantified from the overlap of the cartilage surfaces.

Fig. 2

Contact pressure patterns from the DEA model and the in vitro experimental measurements superimposed over the patella for two knees at 60 deg of flexion. Pressure shifts laterally when loading the hamstrings increases the lateral and posterior orientation of the patellar tendon.

Fig. 3

The average (±standard deviation) lateral force ratio from the DEA models (no border) and the in vitro experimental data (border). Significant increases at a flexion angle due to increasing the lateral and posterior orientation of the patellar tendon by loading the hamstrings are marked with an asterisk (*).

Fig. 4

The average (±standard deviation) lateral distance from the center of force to the patellar ridge from the DEA models (no border) and the in vitro experimental data (border). Significant increases at a flexion angle due to increasing the lateral and posterior orientation of the patellar tendon by loading the hamstrings are marked with an asterisk (*).

Fig. 5

The average (±standard deviation) maximum lateral pressure from the DEA models (no border) and the in vitro experimental data (border). Significant increases at a flexion angle due to increasing the lateral and posterior orientation of the patellar tendon by loading the hamstrings are marked with an asterisk (*).

Fig. 6

The average (±standard deviation) maximum medial pressure from the DEA models (no border) and the in vitro experimental data (border). No significant differences were identified due to loading the hamstrings.

Fig. 7

The average (±standard deviation) contact area from the DEA models (no border) and the in vitro experimental data (border). No significant differences were identified due to loading the hamstrings.