14.1.1 Incongruency of the Articulating Bones

When examining the architecture of a “typical” joint, one is immediately aware that the surface shapes of the articulating bones do not match: the articulating surfaces are incongruent. In the knee joint ( Fig. 14.1 ) neither the surfaces of the femur and tibia nor those of the femur and patella match exactly. Far from it: in fact, the shapes of their articulating surfaces are grossly different. This characteristic incongruency is common to virtually all joints of the body: think only of the joints of the hand, or the skeleton of the foot, or the vertebral joints. The hip joint, with its matching spherical head and spherical acetabular dome, seems to be an exception—though the academic discussion as to whether the head and acetabulum in the hip match precisely, or whether they start out incongruent and only develop congruency under load is not yet settled.

Contact between rigid bodies with incongruent surface shapes can occur only at points or along lines. In the joints of the human body, these points develop into contact areas between the articulating bones through the deformation of cartilage and bone under load. Nevertheless, these contact areas are usually small, so the pressure on them is accordingly high. In some highly loaded joints—between femur and tibia, for instance, and between vertebral bodies—nature considered it advantageous to place soft tissue (menisci, intervertebral disks) between the articulating bones to increase the articulating (pressure-transmitting) area and thus limit the magnitude of the pressure.

14.1.2 Architecture of the Bones in the Vicinity of a Joint

The dimensions of all bones are greater near the joints than in the mid-section of the bones. Like all long bones and like the vertebral bodies, the femur and tibia exhibit the typical waisted shape. However, the larger surface area thus created at the ends of the bones is not utilized as a whole for force transmission; because of the incongruency of the articulating surfaces, and depending on the position of the articulating bones, usually only a fraction of this area is placed under pressure. In the femur and tibia, the cortical bone beneath the articulating cartilage is very thin. The cortical bone in the mid-section of both these bones may well exceed 1 cm in thickness. Close to the joint, both femur and tibia are filled with trabecular bone; in their mid-portion they are practically hollow. These observations are broadly valid for the other long bones, too. (The only reason why vertebral bodies are completely filled with trabecular bone is because of their small height.) The thin layer of cortical bone and the trabecular bone beneath the surface of the joint are more easily deformable than a thicker layer of cortical bone. The resulting deformation under load effectively damps short peak forces, while at the same time it momentarily increases the pressure-transmitting area, further reducing the pressure on the joint surface.

14.1.3 Force-Transmitting Area

It seems that nature has “designed” all joints to tolerate high localized pressure. At the same time, during joint motion the loaded area shifts and so alternating loading and unloading occur. It is assumed that the resulting variation in pressure is of importance both for maintaining the friction properties of the joint and for cartilage metabolism. Fig. 14.2 shows data on the contact area between the femur and the tibia measured with and without menisci. As stated above, even with intact menisci the contact area between femur and tibia never extends over the entire tibial plateau. The pressure-loaded area is seen to shift with the motion of the joint. As flexion increases, the contact area shifts from anterior to posterior. When menisci are missing, the contact area is reduced by a factor of 2 to 3. In the femoropatellar joint ( Fig. 14.3 ) the patella, despite the great thickness of its cartilage, never comes into complete contact with the femoral condyles. The shifting of the contact area between patella and femur with knee flexion is clearly visible.

14.1.4 Friction Properties of Joint Surfaces

The coefficients of static and kinetic friction between cartilage surfaces wetted by synovial fluid are very small. The coefficient of static friction between cartilage surfaces amounts (depending on test conditions) to between 0.001 and 0.005. 4, 5 In broad terms, therefore, we may regard the knee joint, and all other joints with cartilage surfaces, as friction-free. As high forces are transmitted through the joints, low friction is of extreme importance to their mechanical functioning. If friction in the joints was at any appreciable level, the joints would become virtually immobile and thus useless under high load, due to the high moment exerted by the friction force. In a moving joint shear forces act on the joint surfaces. If shear forces were to become too high, due to a large coefficient of friction, the cartilage could be damaged.

14.1.5 Guidance of the Joint Motion by Ligaments

The integrity of the joints, the guidance of their motion, and the restriction of the range of motion is brought about by ligaments. If the ligaments are torn or destroyed, the joints “fall apart” and their range of motion is no longer controlled. These observations are likewise valid for the cruciate and collateral ligaments of the knee as well as, for example, for the ligaments of the hand skeleton or the spinal ligaments. The guidance of motion by the shape of the articulating bones (as seen in the hip joint) or solely by muscles (as between the scapula and the thorax) are exceptions to the general rule.

14.2.1 Knee Joint Modeled as a Pure Hinge Joint

If the knee joint is modeled as a hinge joint with its axis of rotation oriented perpendicular to the sagittal plane, the location of the axis can be determined from measurements on specimens (see Chapter 6 ). With the tibia held in a fixed position, two small metallic markers (easily visible in a radiograph) are placed on the femur ( Fig. 14.4 ). Radiographs are taken with the joint in extension and in flexion. Under the assumptions of the model of a hinge, during the change from extension to flexion the marks move in concentric circles about the center of rotation. The radiographs do not show the trajectories of the movement, only its start and end points. The common center of the circles, the center of rotation, is given by the intersection of the perpendicular bisectors of the chords.

If, however, the joint is moved in small angular intervals, and if the procedure depicted in Fig. 14.4 is repeated for each of these intervals, it turns out that the location of the center of rotation determined in this way shifts by a few millimeters as a function of the joint angle. This observation is an indicator that the hinge model of the joint gives only an approximate description of the joint’s true motion. If one disregards this detail, the center of rotation of the knee joint is located in the posterior third of the femoral condyle and approximately 2.5 cm above the tibial plateau. This specification suffices for the determination of moment arms of muscles or external loads for the purposes of estimating the load on the femorotibial joint.

14.2.2 Motion of the Knee Seen as Guided by the Cruciate Ligaments

Menschik 6 described the motion of the knee guided by the cruciate ligaments by a surprisingly simple model. If we assume that the length of the cruciate ligaments remains unchanged in the course of the flexion–extension motion, the cruciates guide the motion of the femur relative to the tibia like a four-bar linkage. The four bars of this linkage are formed by the two cruciates and the lines connecting their points of insertion into the femur and tibia. Under the assumptions of this model, the instantaneous center of rotation is located at the point of intersection of the cruciates ( Fig. 14.5 ). The rationale for this is that, in the case of a finite motion of the tibia with respect to the femur, the center of rotation C₁ is constructed as the intersection of the perpendicular bisectors of the lines B₁−Bʹ₁ and A₁−Aʹ₁. In the case of a very small (infinitesimal) motion, the points of intersection X and X₁ of the cruciates coincide with the point C₁. If the joint is flexed, the location of the center of rotation constructed thus is shifted posteriorly and proximally ( Fig. 14.6 ). If the path of the collateral ligaments is viewed in addition ( Fig. 14.7 ), these ligaments are found to cross in a region close to the instantaneous center of rotation. Crossing the center of rotation ensures that the change in the length of the collateral ligaments during flexion or extension of the knee remains small.

Contrary to the assumptions of Menschik’s model,6 the diameters of the two femoral condyles are not equal, and some fiber bundles of the cruciate ligaments do actually change their length during flexion and extension. 8– 10 Fuss 9 showed that over the whole range of motion only a fraction of the fibers of the cruciate ligaments are continuously under tension. Due to the extended (rather than punctiform) area of insertion of the cruciates, a constant tensile stress on all fiber bundles is impossible for geometrical reasons alone. The fibers under tension guide the motion and limit the posteroanterior translation of the tibia relative to the femur. At the end points of motion, however, all fibers are under tension.

14.2.3 Interpretation of Knee Motion Based on the Shape of the Condyles

Freeman and Pinskerova 11 pointed out that the contour of the femoral condyles can be subdivided into three regions ( Fig. 14.8 ). In region 1, the region of contact in maximum extension (approximately −5° to 20°), the contour may be approximated by a circle with a midpoint Z₁ and a radius slightly greater than 30 mm. In region 2, representing normal, active motion from about 20° to 120° of flexion, the contour more or less circular with a midpoint at Z₂ and a radius slightly greater than 20 mm. In region 3, the region of maximum active and passive flexion (approximately 120° to 140°), the radius of the medial condyle is somewhat smaller than in region 2. Taken together, the three circular contours combine to form an approximately elliptical shape.

In the region of normal, active motion between 20° and 120° of flexion, the joint rotates about an axis through Z₂. In this region, rotation of the tibia about its longitudinal axis is also possible, but is not rigidly coupled with the flexion motion. In this region the medial condyle approximates a spherical joint, because in the frontal plane the curvature of the lateral condyle is smaller than the curvature of the medial condyle ( Fig. 14.9 ). The lateral condyle slides and rolls in the posterior and anterior directions, thus enabling the rotation of the tibia about its long axis. 12 Some studies, in specimens as well as in vivo, have demonstrated obligatory coupling between extension and external rotation in the region of maximum extension between 20° and −5° (see, for example, Moro-oka et al 13). This coupled motion is termed screw home motion. This external rotation, which is in the order of 15°, is hypothesized to be due to an asymmetry of the femoral condyles in region 1 or to the anterior cruciate ligament. Other studies were unable to confirm the existence of a screw home motion. Apparently considerable interindividual differences exist in respect of this motion, or it may be possible that measurement errors could simulate its existence. 14

14.2.4 Description of Knee Motion in Terms of a Helical Axis

Combining flexion and extension, external and internal rotation, and medial and lateral translation of the femur and tibia, the motion of the knee joint is motion in three-dimensional space. This motion can be described as rotation about and simultaneous translation along an axis oriented in space, termed a helical axis (see Chapter 7 ). Blankevoort et al 15 determined the location and orientation of the helical axis in knee joint specimens by measuring flexion motion carried out in small steps combined with a moment effecting internal or external rotation about the tibia. (The additional moment was used to obtain reproducible data for the helical axes. Without this moment, minor adjustment errors or uncontrollable forces exerted by the experimental setup would cause wide scatter of the results.) Metallic markers were placed on the femur and tibia of the specimens and the position of the markers was measured with high precision by stereoradiography. The location and orientation of the helical axis was computed from the relative motion of the tibial and femoral markers. Since the motion was performed in steps of approximately 4°, the axis determined in this way is referred to as a finite helical axis. This in contrast to the instantaneous helical axis which would have been obtained from the observation of infinitesimal steps of motion. After the motion had been observed, the specimens were dissected. After placement of additional markers, stereoradiography was then used again to map the articulating surfaces and the insertion areas of the cruciate ligaments and relate them to the three-dimensional coordinate systems fixed to the tibia and the femur.

For pure flexion and extension in the sagittal plane one would intuitively expect the orientation of the helical axis to be horizontal. For a pure internal or external rotation of the tibia one would expect it to be vertical. For a motion combining flexion and rotation we would thus expect the axis to be oriented obliquely. Fig. 14.10 shows as an example the helical axis in the coordinate system of the tibia. The measurements were performed in increments of approximately 4° from full extension to 95° flexion. In the example shown, a moment effecting internal rotation acted on the tibia. The authors observed that in almost all cases the helical axes they determined crossed the space between the insertion areas of the cruciate ligaments. In this respect their findings are qualitatively consistent with the Menschik model,6 which predicts a center of rotation at the intersection of the cruciate ligaments.

14.2.5 So-called Compromise Axis of the Knee Joint

Ideally the axis of rotation of an orthosis should coincide with the anatomical axis of rotation of the knee, because a rotation cannot occur simultaneously about two different axes. Commonly orthoses for the knee joint are equipped with pure hinge joints because of their simple construction and reliable functioning. Experience does also show that persons with a total knee replacement of the hinge joint type can walk without problems. We thus expect that having knee joint motion guided by an orthosis with a pure hinge joint should not result in major functional constraints. It might well be possible to devise joints for orthoses that are better adapted to the anatomical motion, but to do this properly would require determining the location and orientation of the axis of rotation of the anatomical joint in the individual patient. In practice this cannot be done, because when markers are placed externally, the movement of the soft tissues makes it impossible to measure the motion of the femur and tibia precisely. Measurement employing radiography is ruled out because of the radiation exposure.

From radiographs of specimens of the knee joint, Nietert 16 reconstructed the point where the rotational axis for plane flexion and extension intersected with the sagittal plane. He observed that the location of this point (the center of rotation) varied only within a very small area ( Fig. 14.11 ). A fixed axis running through the center of this region is called a compromise axis, as it disregards the details of the shifting of the true axis during the motion. We may assume that this axis coincides approximately with the axes resulting from Menschik’s6 or Freeman’s11 models discussed above. Nietert16 proposed adjusting the axis of an orthosis as shown in Fig. 14.12 . To do this, the external diameter D of the knee is measured and the location of the joint line is palpated. An orthosis fitted as shown here will not noticeably interfere with the physiological motion of the joint. Any unavoidable remaining divergences between the axes of the orthosis and the anatomical knee will result in tilting and translation of the orthosis relative to the thigh and lower leg, but experience shows that small amounts of tilting and translation are easily absorbed by the soft tissues.