The model (Fig. A1) explains the coupling of axial rotation to flexion and, more generally, how the joint achieves a range of unresisted passive mobility (Wilson et al., 1998). The model was formulated using the assumptions that the articular surfaces medially and laterally remain continuously in contact without interpenetration during passive flexion and that single fibres within each of the two cruciates and the MCL remain isometric. These five constraints to motion, when acting together, reduce the six possible degrees of freedom of the bones to one, so that axial rotation is coupled to flexion. The calculated coupling of axial rotation to flexion required to satisfy these assumptions agrees well with measurements described in Chapter 3 (Fig. A2).

###### Figure A1 Three-dimensional model of knee mobility at extension, 45º flexion, and 90º flexion. The brown shells are the surfaces of the model femoral condyles, the yellow shells are the surfaces of the tibial plateaux, and the red, green and blue lines are the isometric fibres of the ACL, PCL, and MCL, respectively.

Pictures of the model in extension and at 45° and 90° flexion (Fig. A1) show that during flexion the articular surfaces of the femur roll and slide on the surfaces of the tibia while the femur rotates externally on the tibia. The three isometric ligament fibres rotate about their insertions into the tibia. The sliding and rolling of the surfaces and the rotation of the ligament fibres are accomplished without tissue deformation and therefore without generating resistance to motion.

An animation of the model (Animation 1) can be found on the website accompanying this book, www.oxfordpartialknee.com, and demonstrates how the surfaces of the bones move on each other. The axial rotation of the surfaces of the femoral condyles can best be appreciated by watching the movements of their posterior edges.

The predictions of the model are sensitive to the choice of its parameters: (1) the shapes of the articular surfaces and (2) the positions of the points of origin and insertion of the isometric ligament fibres. If spherical femoral condyles and flat tibial surfaces are chosen, the result is greater anteroposterior movement of the contact points on the tibia in both compartments and larger values of coupled external femoral rotation. The model also demonstrates the important role of the MCL, and the absence of a role for the LCL, in guiding passive motion. If the model MCL is placed on the lateral rather than the medial side, obligatory internal rather than external rotation of the femur occurs during flexion, a result that is unlikely to be deduced except by modelling.