A two-dimensional mathematical model of OUKA created by Imran (1999) explains the observed differences between passive and active flexion described in Chapter 3.
Figure A7 Model of the unicompartmental meniscal knee in situ with arrays of fibres from Fig A4 representing the ACL (green) and the PCL (white) with the extensor mechanism and hamstrings tendon of Figure A3. At each flexion angle, the position of the femur on the tibia was that which produced zero force in each cruciate ligament.
The sequence of images in Figure A7 represents passive motion in the absence of load. Those in Figure A8 model a drawer test, with the bones at a fixed flexion angle and moved anteroposteriorly relative to each other by an external force against the resistance of the ligaments.
The model of passive motion (Fig. A7) finds the position of the femur on the tibia which minimises ligament strain. The anteroposterior position of the femur on the tibia was adjusted mathematically, as in Figure A8(b), until both cruciate ligaments had just fully slackened, with zero force in each. This condition requires rollback of the femur on the tibia and consequently, posterior translation of the meniscal bearing during flexion (see website, Animation 7).
The patterns of fibre strain in Figure A7 are very similar to those in Figure A4 which were based on the assumed presence of the two isometric fibres of Figure A3 (see Fig 3.12). Therefore, the model in Figure A7 predicts rather than assumes the presence of isometric fibres. It is emphasised that the only inputs to the model were the geometry of the arrays of fibres in extension, the positions of the prosthetic components, the femoral trochlea, and the tibial tubercle relative to the ligament attachment areas, the length of the patellar tendon, and the shape of the model patella. The positions of the bones relative to each other were then calculated using the laws of geometry and mechanics. The model of passive mobility (Fig. A7) predicts passive bearing movements very similar to those observed fluoroscopically (see Fig. 3.16).
Figure A8 (a) Forward movement of the tibia from the neutral position (b) tightens the ACL and slackens the PCL. Backward movement (c) slackens the ACL and tightens the PCL (see Animation 8).
Figure A9 Model of active flexion–extension when the weight of the leg is balanced by tension in the patellar tendon. In extension (a), the tibia is pulled anteriorly relative to the femur, the ACL is stretched, and the PCL is slack. At 57º, all fibres of both ligaments are just slack. At 90º, the PCL has begun to tighten. The excursion of the meniscal bearing on the tibia is reduced compared with passive flexion (Fig. A7) (see Animation 9).
Model of the active extension exercise
Comparison of Figures A7 and A8 shows that the anteroposterior movements of the meniscal bearing on the tibia required to tighten slack ligaments are similar in magnitude to those which occur during passive movements. These two effects are superimposed in activity and can augment or cancel each other. Figure A9 shows a model of active extension with the femur horizontal and the weight of the leg balanced by tension forces in the patellar and quadriceps tendons. In extension, the patellar tendon pulls the tibia upwards, a movement resisted by tension in the ACL (and MCL). All fibres of the ACL are shown stretched tight. The stretch of the ligament allows the femur (and the bearing) to move backwards on the tibial plateau relative to their positions in the unloaded joint. As the knee bends and the leg falls, the forces in the ACL (and MCL) diminish. At 57° (Fig. A9(b)), only the most anterior fibre of the ACL is just tight and the bearing lies close to its corresponding position in the unloaded joint. With further flexion, the PCL begins to tighten and stretch and the ACL goes completely slack, allowing the femur to move forward relative to its position in the unloaded joint. Therefore the total excursion of the bearing on the tibia is much reduced compared with passive motion, because of the stretching of the ligaments. While this two-dimensional model does not account for axial rotation and does not therefore predict exactly the observed pattern of bearing movement during active extension–flexion (see Figs. 3.28 and 3.29), it demonstrates the effects of ligament strain and explains the differences between active and passive motion observed fluoroscopically.
In the unloaded state, the meniscal bearing moves to that position which minimises ligament strain, requiring rollback of the femur on the tibia. Under load, the bearing moves to the position required to balance ligament and muscle force components parallel to the tibial plateau. These criteria are different and the movements of the bearings are also different. This analysis validates the assertion we made in 1978 that ‘the components [of a knee prosthesis] should allow and should not resist the movements demanded by the soft tissues’ (Goodfellow & O’Connor, 1978). This criterion can also be satisfied by unconstrained two-component designs but at the expense of excessive wear. The fully congruent meniscal bearing meets the criteria of both minimum wear and minimum constraint.
