The Effect of the Geometry of the Tibia on Prediction of the Cruciate Ligament Forces: A Theoretical Analysis

Abstract

This paper attempts to highlight the importance of the tibial geometry in the prediction of forces along the cruciate ligaments. A two-dimensional model of the knee which comprises the femur, the tibia and the cruciates was used. The model was subjected to an external antero-posterior force and an external axial compressive force. The analysis showed that, with aflat tibial plateau the tension arising along either cruciate as a result of the application of an external antero-posterior force is determined solely by the inclination of the ligament to the direction of that force; it is independent of the magnitude of the external axial compressive force. A curved tibial plateau modifies the tension along either cruciate, and in the absence of an axial compressive load on the joint small changes in the geometry of the tibial surface cause slight changes (increase/decrease) in the tension. However, these changes can become considerable when a large axial compressive load is applied on the joint. A concave tibial plateau, where the tangent to the surfaces at the point of contact is inclined to the direction of the same external antero-posterior force by 7.8°, can reduce the tension along either cruciate to zero, if a sufficiently large axial compressive load is applied on the joint. It was shown that the convexity of the lateral tibial plateau can provide an important protective function for the posterior cruciate ligament (PCL) at extreme positions of flexion. The analysis showed that the PCL should experience a larger force than that experienced by the anterior cruciate ligament (ACL) and hence explain why the former should be the stronger of the two. Finally, a hypothesis is proposed suggesting that bone remodelling may occur in the tibiae of the older people, causing them to become more concave with age and as a consequence provides greater protection to the cruciates in the aged, in order to compensate for decreasing strength in the older person.