Mobility
The rolling and sliding movements of the femur on the tibia are more clearly seen in the simpler two-dimensional four-bar linkage model of Figure A3 (see Animation 2) (O’Connor et al., 1989; Zavatsky & O’Connor, 1992a; Gill & O’Connor, 1996a; Lu & O’Connor, 1996). The figure shows the femur flexing on a fixed tibia with lines representing the extensor and flexor muscles. The distal surface of the femur has separate curves representing (1) the sulcus of the trochlea, anteriorly, in contact with the patella, and (2) the distal and posterior facets of the condyle in contact with the tibia. The model tibial articular surface is flat, a two-dimensional compromise between the slightly concave medial and slightly convex lateral plateaus of the human knee (see Fig. 12.1). Lines representing the isometric fibres of the two cruciates, rotating about their insertions on the tibia, and lines joining their attachments on the two bones form a crossed four-bar linkage (Hall, 1961). The two-dimensional model separates the kinematics of the joint in the sagittal plane from the effects of coupled axial rotation.
Figure A3 Two-dimensional four-bar linkage model of the knee in which isometric fibres in the ACL (dashed) and PCL (dashed white) guide the rolling and sliding movements of the femur on the tibia during passive flexion–extension. The point of contact C between the articular surfaces of the bones lies on the perpendicular to the tibial plateau through the intersection of the ligament fibres. Muscle tendons are shown as single lines. The rectangular model of the patella is held between the quadriceps and patellar tendons (dashed green). The hamstrings tendon and the gastrocnemius tendon are shown by pink and blue dashed lines, respectively.
The flexion axis of the joint passes through the point of intersection of the isometric ligament fibres (the ‘instant centre’ of the linkage) and moves backwards relative to the tibia during flexion, and forwards during extension. The point of contact between the femoral condyle and the flat tibial surface of the model always lies on the perpendicular to the tibial plateau through the flexion axis and therefore also moves backwards on the tibia during flexion and forwards during extension (as indicated by the vertical lines marked C in Fig. A3). The femur rolls as well as slides on the tibia; it rolls backwards (while sliding forwards) during flexion, and rolls forwards (while sliding backwards) during extension. The calculated value of the slip ratio (movement of the contact point on the tibia divided by its movement on the femur) varies between 0.2 and 0.4, similar to the range of values estimated by Feikes (1999) for the intact cadaver knee (Fig. 3.8). The model contact point moves backwards 11 mm over 120° flexion, similar to the mean value of the average movement of the contact point in human knees estimated by Feikes (1999), Table 3.1.
Therefore the model describes the average behaviour of the two compartments without axial rotation. The isometric ligament fibres keep the articular surfaces continuously in contact, and the articular surfaces keep the ligament fibres just tight. Unresisted passive flexion and extension can occur without tissue deformation because the isometric fibres rotate about their insertions on the bones without stretching, and the articular surfaces roll and slide on each other without indentation.
The directions of the model ligaments, the lengths of the lever arms of the flexor and extensor muscles, and their variation with flexion angle agree well with measurements on cadaver human knee specimens made by Hertzog and Read (Lu & O’Connor, 1996, Herzog & Read, 1993).
Figure A4 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 60º, the attachment point b of the PCL lies under the fibres and is not visible. See Animation 3.)
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