Ligament-Bone Interaction in a Three-Dimensional Model of the Knee

In mathematical knee-joint models, the ligaments are usually represented by straight-line elements, connecting the insertions of the femur and tibia. Such a model may not be valid if a ligament is bent in its course over bony-surfaces, particularly not if the resulting redirection of the ligament force has a considerable effect on the laxity or motion characteristics of the knee-joint model. In the present study, a model for wrapping of a ligament around bone was incorporated in a three-dimensional mathematical model of the human knee. The bony edge was described by a curved line on which the contact point of the line element representing a ligament bundle was located. Frictionless contact between the ligament bundle and the bone was assumed. This model was applied to the medial collateral ligament (MCL) interacting with the bony edge of the tibia. It was found that, in comparison with the original model without bony interactions, the bony edge redirected the ligament force of the MCL in such a way that it counterbalanced valgus moments on the tibia more effectively. The effect of the bony interaction with the MCL on the internal-external rotation laxity, however, was negligible.