The architecture of the ACL and PCL ligament arrays has been described by Friederich et al. (1992) and Mommersteeg et al. (1995) (see Figs. 3.11 & 3.12), and the model’s cruciate ligaments (Fig. A4) are based on those studies. The attachment areas are shown as straight lines, with a definite arrangement between the point of origin of an individual fibre and its point of insertion (fibre mapping). Tight fibres are shown as straight lines, and slack fibres are shown buckled.
The fibres of the model ACL are straight, almost parallel, just tight in extension, and attached to the femur along the line ab (Fig. A4(a)). The PCL is modelled as two bundles of fibres attached to the femur along the lines ca and ab, with the anterior bundle being slack and the posterior bundle just tight in extension (Fig. A4(d)). Five representative fibres are drawn in the ACL and in each bundle of the PCL, but the mathematics assumes a continuous distribution of fibres along each attachment line. The most anterior ACL fibre ay and the most anterior of the PCL posterior bundle ay are the isometric fibres of Figure A3, and the relative motion of the bones is the same in both figures.
During flexion of the joint to 120°, the femoral attachment areas of both ligaments rotate through the same 120° relative to the tibia, appearing to pivot about the insertions of the isometric fibres. As a result, the ligaments change their shapes. In both ligaments, fibres originating along the attachment line ab are more or less parallel in extension but are crossed on each other at 120°. Cross-over occurs when the attachment line ab lies along the isometric fibre ay. This occurs at about 70° flexion for the ACL and 60° flexion for the posterior fibres of the PCL (see Animation 3).
Fibres passing behind the intersection of the isometric fibres slacken during flexion and tighten during extension. Fibres passing in front of the intersection of the isometric fibres tighten during flexion and slacken during extension. Prior to cross-over, points of origin and insertion in the ACL and in the posterior bundle of the PCL approach each other during flexion, and fibres slacken. After cross-over, these points depart from each other and fibres tighten. The anterior fibres of the model PCL pass in front of the intersection of the isometric fibres and tighten during flexion as its femoral attachment area ac rotates away from the tibia. They are just tight and straight at 120°. Thus, most ligament fibres are slack in most positions of the unloaded joint. No fibres are stretched.
The changes in shape of the model ACL are very similar to those reported in the cadaver human knee using Röntgen stereometric analysis (van Dijk et al., 1979) and to the sketches of Friederich et al. (1992) (see Fig 3.12) and Girgis et al. (1975). The shape changes of the model PCL are similar to the sketches of Brantigan and Voschell (1941), and the patterns of fibre slackening and tightening predicted by the model are quantitatively similar to those measured in cadaver knees (Sidles et al., 1988; Sapega et al., 1990; Wang & Walker, 1973; Amis & Dawkins, 1991; Covey et al., 1992). These comparisons with experiment serve to validate the model and the assumptions on which it is based.
Animation 4 is of a knee model with arrays of fibres representing all four principal ligaments, including the two cruciates of Figure A4. Many observers agree that all fibres within the LCL become slack once flexion begins (Wang & Walker, 1973; Rovick et al., 1991; Robinson, 2002). This is because the fibres always lie behind the flexion axis of the joint.
The behaviour of the model MCL demonstrates one of the deficiencies of a two-dimensional model. The fibres of that ligament cover the intersection of the two isometric cruciate fibres so that the flexion axis of the joint passes through the ligament. As a result, the most anterior of the superficial fibres of the model MCL stretch during passive flexion. However, the two-dimensional model does not account for obligatory axial rotation. The associated forward movement of the femoral attachment area of the MCL relative to the tibia, as seen in the three-dimensional model in Figure A1 (and in Animation 1 on the website), slackens these stretched fibres and allows unresisted flexion. This feature of the two-dimensional model prompted the development of the three-dimensional model and the incorporation of an isometric MCL fibre in addition to the cruciates (see Chapter 3.)
Discussion
The rolling of the femur on the tibia during passive flexion–extension is required to minimise ligament strain in the unloaded knee and allow unresisted passive movement. Predictions of the mathematical models of passive motion compare well with measurements made on cadaver specimens in our own and other laboratories, validating the principal assumptions underlying the models, i.e. that the human knee behaves as a mechanism during passive motion, guided by the articular surfaces in contact and by isometric fibres within the cruciates and the MCL. Every implantation of an Oxford prosthesis which succeeds in matching the 110° flexion gap to the 20° flexion gap when the bone surfaces are distracted by gap gauges is evidence of ligament isometricity. The slack model LCL in the flexed knee is believed to explain the high rate of bearing dislocation in lateral OUKA (see Chapter 12).
These concepts have recently been challenged by Freeman (2001), without confronting the many experimental validations of the models but on the grounds that the PCL is (apparently) slack in flexion, an argument advanced by Strasser (1917) in a criticism of the first description of the four-bar linkage model given by Zuppinger (1904). All fibres of a ligament cannot be isometric unless they all originate on or pass through the flexion axis of the joint. Slackness of most fibres does not preclude the isometry of some. The isometric fibres within the PCL lie within the body of the ligament and are difficult to observe visually. Nonetheless, the shapes of the model ligament in extension and flexion shown in Figure A4 are very similar to those shown in Section 8 of Freeman’s booklet (2001), and are consequences of the isometricity of some fibres, not an argument against it. The changes of fibre length in the PCL predicted by the model are very similar to those described by Wang and Walker (1973) and by Covey et al. (1992). Freeman also shows how the PCL is readily deflected sideways by a transverse force. But even a very tight rope, like a bowstring, offers little resistance to transverse motion of a point in the middle of its span. A better demonstration of the function of the PCL is to show how its slack fibres are systematically recruited to resist backward movement of the tibia relative to the femur when the knee is appropriately loaded.
