Two-dimensional quasi-static knee model for the estimation of ligament and quadriceps forces as a function of knee flexion

The knee joint is one of the most commonly injured joints in sport activities. A two-dimensional quasi-static knee model was developed to estimate the forces sustained by the ligaments and generated by the quadriceps as a function of knee flexion. The tibio-femoral and patello-femoral joints were defined mathematically and modeled as frictionless joints. The anterior and posterior cruciate ligaments and the collateral ligament were modeled as single fiber extensible units. The instantaneous center of rotation was used in the estimation of the rolling and sliding characteristics of the knee joint. External forces were used as input parameters to the model. The model was tested using kinematic and kinetic data obtained during squatting for three different conditions: normal, ACL-deficient and ACL-reconstructed. The results obtained with the model showed the expected increase in anterior-posterior motion of the femur relative to the tibia in the ACL-deficient knee. Laxity values were higher for the ACL-deficient knee and had return to normal following the ACL-reconstruction.