The Appendix to this book describes a three-dimensional mathematical model of passive knee flexion which is predictive of the coupling of axial rotation, ab/adduction and three components of translation of one bone relative to each other (Fig. 3.13). Indeed, the solid lines in the five graphs of Figure 3.3 were calculated from the model and fit the experimental values quite well, giving confidence in the relevance of the model and the assumptions on which it is based.
Figure 3.13. Parallel spatial mechanism model of the knee at extension, 60° and 120° flexion. The surfaces of the femoral condyles remain in continuous contact with the tibial plateaux while the isometric fibres of the ACL (red), PCL (green) and MCL (blue) rotate about their insertions on the tibia.
The formulation of the model assumes that passive motion of the knee is constrained by isometric ligament fibres in the ACL, the PCL and the MCL and by continuous contact between the articular surfaces of the medial and the lateral compartments (Feikes, 1999; Wilson, 1995; Wilson et al., 1998; Feikes et al., 2003). The mathematical formulation was based on the assumptions that, during passive motion, the ligament fibres do not stretch or shorten and that the articular surfaces in each compartment do not separate or interpenetrate. These five constraints to motion reduce the possible six degrees of freedom of the tibia relative to the femur to unity, a single degree of freedom system, and explain the coupling of five components of movement at the joint to flexion angle observed experimentally (Figs. 3.2, 3.3 and 3.4)). The model is a theory of the screw-home mechanism. Figure 3.13 and the animation of the model (see website www.oxfordpartialknee.com, Animation 1) show the external rotation of the femur on a fixed tibia during flexion, internal rotation during extension. The five constraints can be satisfied during passive motion because the articular surfaces, while remaining continuously in contact, are free to roll and slide on each other and the three ligament fibres, while remaining isometric, can rotate about their points of origin and insertion on the bones. These movements can occur without tissue deformation, without stretching of ligament fibres or indentation of articular surfaces, suggesting that, during passive motion, the human knee has one degree of unresisted freedom.
The model reinforces the conclusions from Figure 3.6 above that intact articular surfaces and intact ligaments are necessary to achieve the ordered passive movement of the human knee. It suggests that the practice in current total knee replacement of sacrificing the cruciate ligaments and releasing the deep fibres of the MCL is unlikely to restore ordered movement. It seems improbable that additions or projections to the articular surfaces of a prosthesis (which resist interpenetration but not separation) can replace the ligamentous constraints which resist separation but not interpenetration.
