Figure 3.15 Model knee with arrays of fibres representing the ACL and two bundles of the PCL, attached to the femur along ab and cab respectively. (At 60°, the attachment point b of the PCL lies under the fibres and is not visible.)
Figure 3.15 shows an elaboration of the model with each of the cruciate ligaments represented as arrays of fibres (Zavatsky & O’Connor, 1992a; Lu & O’Connor, 1996a) (see website, Animation 3).
The fibre mapping in both ligaments is based on the anatomical studies of Friederich et al. (1992) and Mommersteeg et al. (1995) (Fig. 3.11). For both ligaments, the fibres marked ay are the isometric fibres of Figure 3.14 and the rolling and sliding movements of the femur on the tibia are the same as in the simpler model. The ACL is modelled as an array of fibres almost parallel to and passing behind the isometric fibre in extension. The PCL is shown as two bundles of fibres, one passing in front of the isometric fibres in extension and the other lying behind. In extension, all fibres of the ACL and the posterior fibres of the PCL are assumed to be just tight and are shown straight. In extension, the anterior fibres of the PCL are assumed to be slack and are shown buckled (Fig 3.15(d)).
During flexion through 120°, the femoral attachment areas ab and cab rotate through 120° relative to the tibia and points of fibre origin on the femur either approach or move away from the tibia so that most fibres either slacken or tighten. The posterior fibres of the ACL slacken (and are shown buckled) during flexion to 80°. The ACL in the human knee passes from the lateral condyle on the femur to insert medially on the tibia. Zavatsky and O’Connor (1994) have shown how posterior fibres such as bx (Fig. 3.15), can pass under the anterior fibres and are then positioned anterior to the isometric fibre and to the flexion axis. Such fibres then begin to tighten again with further flexion. The same is true of the most posterior fibres of the PCL such as bz (Fig. 3.15). The anterior bundle of the PCL is slack in extension (and shown buckled) but tightens progressively as the joint flexes.
The drawings of the model cruciate ligaments in Figure 3.15 are remarkably similar to the sketches made by Friederich et al. (1992) (Fig. 3.12 above), Brantigan and Voshell (1941), and Girgis et al. (1975). The apparent shape changes of the model ligaments are similar to those shown by the same authors and to those derived from the RSA studies of van Dijk et al. (1979). The calculated patterns of model fibre slackening and tightening are similar to those reported for the ACL by Sidles et al. (1988), Sapega et al. (1990), and Wang and Walker (1973) and to those reported for the PCL by Covey et al. (1996).
It should be emphasised again that the fibre arrays of Figure 3.15 contain the isometric fibres shown in Figure 3.14. The drawings of the PCL look quite similar to the photographs in Nakagawa et al. (2004) although those photographs were used by those authors as part of their argument that, quoting Strasser (1917), “soon after the beginning of flexion the whole PCL is loose”. Our experimental and mathematical analyses support the large body of work which shows that not to be the case.
Lu and O’Connor (1996b) showed that the calculated values of the rotations of the model ligaments and muscle tendons about their tibial insertions agreed well with measurements on cadaver specimens by Hertzog and Read (1993).
Discussion
In unloaded knees, as far as possible free from the effects of intrinsic and extrinsic loads, passive movements are controlled solely by the shapes of the articular surfaces and the design of the ligaments. The pattern of these movements is constant and repeatable as long as the surfaces and the ligaments are all intact. Flexion and extension are coupled to obligatory rotation and require backward translation of the contact areas on the tibia in flexion (‘rollback’), with the medial contact area moving less than the lateral contact area. The ACL, the PCL and the MCL contain fibres which remain isometric during passive flexion/extension. All other fibres slacken and tighten as the joint flexes and extends so that ligaments can appear to be loose. All these slack fibres can be recruited to bear load in activity, as we shall shortly discuss, giving the joint its passive and dynamic laxity. The three-dimensional and two-dimensional models of the knee with its ligaments predict and explain behaviour similar to that observed experimentally in many laboratories.
