A Sagittal Plane Model of the Knee and Cruciate Ligaments With Application of a Sensitivity Analysis

Abstract

In this investigation the complex multi-bundle structure of the cruciate ligaments and their interaction with the tibiofemoral joint was modeled analytically by representing the different regions of the cruciates with ligament elements. A sensitivity analysis was then performed to describe the effect that variations of the model input parameters had on the model variables (outputs). The effect that the cruciate ligament bundles had in controlling joint kinematics was dependent on knee flexion angle, and the load applied to the tibiofemoral joint. For passive range of knee motion with the thigh in the horizontal plane (a common rehabilitation activity), all cruciate ligament bundles were strained with the joint positioned between 0 and 10 deg of knee flexion, between 10 and 50 deg only the anterior bundle of the posterior cruciate ligament A-PCL was strained, and from 50 to 90 deg both the anteromedial portion of the anterior cruciate ligament A-ACL and the A-PCL were strained. This finding indicates that a strain distribution about a transverse cross section of the cruciates exists, and demonstrates the importance of differentiating between the strained and unstrained (unloaded) states of these ligaments. The strain value of a cruciate ligament bundle was an indication of how the bundle controls joint kinematics, while the unstrained values describe how much the ligament bundle must deform before it becomes strained and a restraint to tibiofemoral joint motion. In response to anterior and posterior directed loads, applied parallel to the tibial plateau, the respective ACL and PCL load values were larger in magnitude. The sensitivity of the model outputs to the input parameters was highly dependent on knee flexion angle. The geometrical input parameters of the model (including the ligament insertion site locations and articular surface geometry) had the most pronounced effect on the model output quantities, while the stiffness and initial strain conditions of the ligament bundles had less of an effect on the model outputs. When loaded, the strain values of the ligament bundles were sensitive to the ligament insertion site position. The greatest sensitivity of the model outputs was the femoral insertion of the ACL; supporting clinical impressions and previous experimental findings. Changes in the anterior-posterior dimension of the femoral articular surface did not produce a substantial effect on the model outputs, while changes in the proximal-distal dimension created a large effect; similar results were found for the tibial surface dimensions. These findings indicate that rigid body contact between the articular surfaces may not be a realistic assumption particularly with application to the prediction of tibiofemoral compressive loading and the force/strain values of the cruciate ligament elements. This also has important implications for the design and clinical application of total knee replacements (that function as rigid bodies), particularly those that spare the PCL.