From the point of view of prosthesis design, it is important to understand how the articular surfaces of the natural joint move on each other.
It is obvious that, during flexion, the points of contact on the femur move from the inferior surfaces of the femoral condyles to their posterior surfaces. However, the positions of the contact points on the tibial plateau are less obvious because of the presence of the menisci. Radiographic studies of the natural joint are not ideal because cartilage is radiolucent, and MRI is unreliable because the fine detail of the contacting surfaces can be trapped within one line of pixels on the VDU monitor, and can appear as straight line segments (Monk et al. 2014). Also, MRI scanning during continuous movement is not possible. Load deforms the cartilage surfaces and the menisci, and creates areas, not points, of contact. These technical problems may account for some of the variability in descriptions of the contact regime.
After completion of the passive movement experiments (Wilson et al. 2000), the positions of a number of reference points (defined by small nails or plastic plugs) on the external surface of each bone were recorded with the joint in full extension and the posterior capsule tight (Feikes, 1999). The specimens were then disarticulated and the electromagnetic digitiser was used to record the relative positions of over 4000 points on each of the bones, with particular attention to the articular surfaces and the areas of attachment of the ligaments and to the aforesaid reference points. It was then possible to reconstruct mathematically the relative movements of each of the digitised points during the passive movement experiments, using an algorithm developed by Veldpaus et al. (1988).
Feikes (1999) fitted surfaces mathematically through the data points from the articular surfaces of each of the posterior femoral condyles and tibial plateaux of each specimen, with a mean error of <0.5 mm (see the images of the articular surfaces in Fig. 3.13 below). She could then determine the relative movements of these surfaces during passive flexion/extension through successive steps of 5°.
Because of inevitable experimental or reconstruction error, the surface images at various positions of flexion usually appeared either to separate (Fig. 3.7(b)), or interpenetrate (Fig. 3.7(c)).
Figure 3.7 Proximity method used to determine the position of the Point of Closest Approach of the articular surfaces, simplified in this example as a spherical femoral condyle and a flat tibial plateau. Whether the surfaces appeared to separate (b) or interpenetrate (c) due to experimental and/or reconstruction error, the position of the point of closest approach was taken to be defined by the position of the perpendicular to the flat surface through the centre of the sphere. (Reproduced from the DPhil thesis of JD Feikes, 1999.)
Feikes calculated the movement during flexion of a line through each of the surfaces joining their centres of curvature, defining the points of closest approach, and took that to be the movement of the contact point on each surface.
Table 3.1 gives the values of the contact point movement on the tibial plateaux from full extension to 100° flexion in the twelve intact specimens. Where Max movement exceeds Net movement at 100°, the maximum movement occurred at a flexion angle less than 100° and the contact point then moved forward with further flexion. A prosthesis designer probably should take account of the maximum rather than the net movement.
All specimens exhibited backwards movement of the contact point on the lateral tibial plateau during flexion, consistent with rolling of the femoral condyle on the tibia. One of the specimens (M) exhibited forward movement of the contact point on the medial plateau but all the others exhibited backwards rolling movement, with an overall average of 7.9 mm for the twelve specimens (SD 7.0 mm). The large variation on the medial side is reflected in the correspondingly larger standard deviation from the mean, compared with that on the lateral side.
Table 3.1 Estimated posterior movement of the tibial contact points with flexion. Negative values indicate anterior movement. Net movement corresponds to that recorded from full extension to 100° flexion while maximum (Max) movement is the maximum occurring within the range.
|
|
Medial |
Lateral |
||
Specimen |
Side |
Net (mm) |
Max (mm) |
Net (mm) |
Max (mm) |
J |
L |
11.4 |
13.1 |
9.2 |
9.2 |
D |
R |
6.3 |
6.3 |
13.1 |
13.1 |
L |
L |
0.7 |
0.7 |
16.5 |
16.5 |
M |
R |
-4.5 |
-7.3 |
9.0 |
9.0 |
X |
R |
7.4 |
7.4 |
18.0 |
18.0 |
I |
R |
3.3 |
3.5 |
24.6 |
24.6 |
E |
R |
1.9 |
1.9 |
22.3 |
22.3 |
G |
L |
19.6 |
19.8 |
12.9 |
14.5 |
F |
L |
9.1 |
9.8 |
10.2 |
10.2 |
B |
L |
18.0 |
18.1 |
15.2 |
15.2 |
A |
L |
8.8 |
10.5 |
11.6 |
11.6 |
H |
R |
12.4 |
12.4 |
13.5 |
13.5 |
Mean |
|
7.9 |
8.0 |
14.7 |
14.8 |
SD |
|
7.0 |
7.8 |
5.0 |
4.9 |
Table 3.1 does not tell the whole story. Goodfellow and O’Connor (1978) introduced the concept of slip ratio, being the ratio of the distance the contact point moved on the tibial plateau divided by the distance it moved on the femoral condyle. For pure rolling without slip (as with a car wheel on the ground), the contact point would move the same distance on both surfaces and the slip ratio would equal unity. For pure sliding on the tibia, the contact point would remain stationary on the tibia while moving on the femur and the slip ratio would be zero. By this definition, it should perhaps have been better called the ‘roll ratio’.
For each of the specimens, Feikes (1999) calculated the slip ratio for 5° degree flexion steps from extension to 100° (Fig. 3.8). The slip ratio in the lateral compartments averaged about 0.5 while, for the medial compartments, it averaged about 0.3. In neither compartment was the mean value zero at any flexion angle so that rolling took place continuously and at a reasonably constant rate over the flexion range, but less so in the medial compartment. In each compartment, the femur rolls backwards while sliding forwards on the tibia during flexion, vice versa during extension, as described by Goodfellow and O’Connor (1978) and O’Connor et al. (1989). The differences in the rolling movements in the two compartments reflects the coupled effect of internal tibial rotation with passive flexion, reducing but not eliminating medial rolling, relatively increasing lateral rolling.
Figure 3.8. Average slip ratio plotted against flexion angle for the medial and lateral compartments of twelve cadaver specimens, plus one standard deviation.
Figure 3.9. A smaller circle moving on a larger concave (a) and larger convex (b) circle. As contact moves from A to B, the centre of the smaller circle moves from C to D.
The digitising of the tibial plateau confirmed the widely held belief that the medial tibial plateau is concave and the lateral plateau is convex, particularly in sagittal sections (Kapandji, 1970). Figure 3.9(a) shows that when contact between a small circle (the medial femoral condyle) and a larger fixed concave circle (the medial tibial plateau) moves from A to B, the centre of the small circle moves from C to D. The ratio of these distances is about 0.68 for radii typical of the posterior surface of the medial femoral condyle (22.5 mm) and the medial tibial plateau (about 70 mm). Even without the contribution of axial rotation, the centre of the medial femoral condyle would be expected to move 5.4 mm, 32% less than the contact point (mean 7.9 mm Table 3.1). When contact between a small circle and a larger convex circle (the lateral tibial plateau) moves from A to B (Fig. 3.9(b)), the centre of the small circle moves from C to D. Thus, the centre of the lateral condyle would be expected to move about 27% more than the contact point, about 18.7 mm.
Iwaki et al. (2000) analysed sagittal plane MRI images of (nominally) unloaded cadaver knees. The centre of a circle fitted to the image of the posterior lateral condyle moved backwards by 19 mm on a straight line fitted to the (convex) lateral plateau, almost identical to our result 18.7 mm just quoted. Two intersecting circles were fitted to the image of the medial condyle, and two intersecting straight lines to the (concave) medial plateau. They claimed that the centre of the anterior medial circle remained stationary on the anterior ‘extension’ facet of the tibia during flexion from –5° to +5°; the centre of the posterior medial circle then moved backwards ± 1.5 mm on the posterior ‘flexion facet’ during flexion from 5° to 120°.
However, Iwaki et al. [(2000), caption to Fig. 6] described a discontinuity of 8 mm in the position of the medial condylar centre between 5° and 30° flexion as contact moved from the anterior facet to the posterior facet of the tibial plateau (see Fig. 2.4). They interpreted this as evidence that the posterior movement of the condyle was due to its rocking, not rolling, on the tibia. This apparent discontinuity could have arisen from their use of two straight lines to represent the articular surface of the medial tibial plateau, with a discontinuity of slope at their point of intersection.
Figure 3.10. A continuous circle rolling on two intersecting straight lines, at the instant that contact transfers from A to B.
If Figure 3.10 represents a circular femoral condyle flexing clockwise on the discontinuous tibial plateau at the instant of contact transfer, it must be concluded that the cartilage on the surface of the tibia between points A and B never comes into contact with the condyle, an intuitively unsatisfactory conclusion.
We conclude that the rocking motion apparent in the Iwaki et al. (2000) paper is an artefact created by their method of fitting discontinuous lines to the MRI images of the articular surfaces.