Mathematical Modeling Of Knee Joint Stress During Squatting Using Matlab

Abstract

The knee joint is crucial for movement, especially during squatting, which puts a lot of mechanical stress on it. In this study, we developed a mathematical model to explore how stress is distributed across the knee joint while squatting. Using MATLAB, we simulated the forces acting on the knee’s cartilage, ligaments, and tendons. Findings identified key areas where stress tends to concentrate, providing important insights for preventing injuries and improving rehabilitation strategies. Interestingly, the highest stress was found at the Tibiofemoral contact area, with a maximum flexion angle of 90°—in vitro, it reached 90.67 MPa, while our mathematical model showed 95.2 MPa. We derived the relevant equations in MATLAB and plotted the results to visualize the data.