Zavatsky and O’Connor (1995) studied simulated isometric quadriceps action in seven cadaver specimens with the flexing effect of a force applied to the tibia parallel to the tibial plateau just balanced by extending forces applied to a wire sewn to the quadriceps tendon to give equilibrium at different flexion angles. They measured the tendon and resisting forces and the anteroposterior translation of the medial and lateral compartments of the tibia relative to the femur.
Anteroposterior translation proved to be dependent on flexion angle. When the resisting force was applied 30 cm below the tibial plateau, the tibia moved forwards relative to the femur at extension, 30° and 60° flexion but backwards at 90° and 120° (Fig. 3.24). With the resisting force at 20 cm below the plateau, motion in the same directions were observed at extension, 30°, 90°and 120° but no anteroposterior translation was observed at 60°. For both placements of the resisting force, the anterior translation was largest at 30°.
These results are consistent with measurements made in vivo by Jurist and Otis (1985) and by Howell (1990).
The results of the experiments were explained by the modelling work of Zavatsky and O’Connor (1993) and Huss et al. (2000) who used the sagittal plane knee model of Figures 3.14 and 3.15 to demonstrate that the forward pull of the patellar tendon between extension and about 65° exceeds the backwards push of the resisting force so that the tibia moves forward relative to the femur because the ACL is strained. At higher flexion angles as the patellar tendon rotates backwards about the tibial tubercle (Fig. 3.14), the backwards push of the restraining force dominates the more vertical patellar tendon force and the tibia moves backwards because the PCL is strained.
Figure 3.24 Displacement of the tibia relative to the femur during isometric quadriceps contractions plotted against the value of the resisting force at extension, 30°, 60°, 90° and 120° with the resisting force placed 30 cm distal to the tibial plateau. Mean values from 7 cadaver specimens. Statistical analysis performed at the largest values of the resisting force. (Reproduced with permission from Zavatsky AB, O’Connor JJ. Anteroposterior tibial translation during simulated isometric quadriceps contractions. The Knee. 1995;2:85-91.)
The modelling work reveals the values of quantities which are difficult or impossible to measure, in this case the values of the forces transmitted by the cruciate ligaments.
Figure 3.25 ACL forces at 0°, 20° and 40° and PCL forces (dashed lines) at 80° and 100° plotted against quadriceps force for (a) compressible and (b) incompressible cartilage when the resisting force is placed 20 cm distal to the tibial plateau. No cruciate ligament forces are required at 60°. (Reproduced with permission from Huss R A, Holstein H, O’Connor JJ. A mathematical model of forces in the knee under isometric quadriceps contractions. Clin Biomech 2000; 15: 112-22.)
Figure 3.25 shows the calculated values of the ACL and PCL forces (a) taking account of the extensibility of the cruciate ligaments (Fig. 3.20) and also the indentibility of the cartilage layers. When the articular surfaces were taken to be incompressible (Fig. 3.25(b)) as in Zavatsky and O’Connor (1993), the calculated values of the cruciate ligaments are larger than those from the compressible cartilage model. In both cases, the ACL is loaded up to about 60° and the PCL at higher flexion angles.
Although the calculated ACL force was largest at extension (Fig. 3.25), the calculated anterior displacement of the model tibia was largest at 20° to 30° flexion (Fig. 3.26). At extension, all ACL fibres are just tight in the unloaded state and can be recruited immediately to bear load whereas, in the flexed joint, most fibres are initially slack and have to be recruited progressively. As a result, the ACL of the flexed joint is less resistant to elongation and a smaller ACL force can produce a larger ACL extension. The calculated anteroposterior translation (Fig. 3.26) agrees well with the measurements of Zavatsky and O’Connor (1995) (Fig. 3.24).
Figure 3.26 Anterior (positive) and posterior (negative) tibial displacement induced by increasing quadriceps force against a resistance placed 20 mm distal to the tibial plateau, assuming extensible ligaments and (a) compressible articular surfaces (b) assuming rigid articular surfaces. (Reproduced with permission from Huss R A, Holstein H, O’Connor JJ. A mathematical model of forces in the knee under isometric quadriceps contractions. Clin Biomech 2000; 15: 112-22.)
An important lesson learnt from the mathematical models was that, as the quadriceps force was increased to 2500 N, the cruciate ligament forces (and extensions) did not increase in proportion but appeared to approach relatively small asymptotic values. Earlier studies with an inextensible ligament model predicted much higher cruciate ligament forces in association with quadriceps action. Collins and O’Connor (1991) predicted large ACL forces during level walking and O’Connor et al. (1990) predicted large PCL forces in flexion during deep squats. Indeed, it was this outcome which prompted the development of knee models with extensible ligaments (Fig. 3.20). The extensible-ligament knee model shows how even large muscle forces can be transmitted across the knee without involving large ACL forces. However, a study of deep squats in a group of young volunteers, taking account of ligament extensibility, found that, while peak ACL focus remained quite small, peak PCL forces reached values nearly three times body weight (Toutoungi et al,. 2000). The ACL is protected from large forces by its own elasticity. This might help to explain the high failure rates of relatively inextensible artificial ligaments.
Movement of the contact points under load
Walker et al. (1988) studied the movements of the contact points in cadaver knees in an apparatus similar to that used by Wilson et al. (2000) and by Feikes (1999) but with the specimen loaded by a weight hung from an intramedullary rod in the femoral shaft and resisted by tension in a wire sewn to the quadriceps tendon. Using the same methods of analysis of the measurements as Feikes (Fig. 3.7 above), they found that during the first 45° of flexion the contact points moved backwards on the tibia by 13 mm (SD 3) medially and 14 mm (SD 3) laterally, with no movement on further flexion. The patterns of movement differed in the two experiments which themselves differed only by the presence or absence of load and tissue deformation. Kurosawa et al. (1985) used the same apparatus to study femoral condyle movements. During flexion to 75°, the mean movement of the centres of the medial femoral condyles was forwards 4.5 mm (SD 2.1), and then backwards 2.3 mm (SD 2.8) during flexion to 120°. The centres of the lateral condyles moved steadily backwards by a mean of 17.0 mm (SD 5.5), during flexion. The differential movements of the medial and lateral centres implied external rotation of the femur of 20.2° (SD 6).
Discussion
Even modest loads can perturb the knee from its unique path of passive motion. This occurs because the ligaments can stretch and the articular surfaces can indent under load. In activity, the ligaments serve to provide a balance between the components parallel to the tibial plateau of the muscle tendon forces and the external loads. Each activity involves its own pattern of movement and muscle force and, therefore, its own pattern of ligament forces. The detailed movements of the bones upon each other are, therefore, activity-dependent. A truly ligament compatible prosthesis should allow the soft tissues to respond in a physiological way to each different activity. The prosthesis should not resist the movements demanded by the soft tissues. It is unlikely that one could devise a prosthesis with surface shapes which alone would guide all the many possible patterns of movement of the surfaces even during the activities of daily living.
