chapter 2: Biomechanics of the Patellofemoral Joint

Statics

Statics is a useful engineering tool to describe forces acting on a body in equilibrium. Using mathematical calculations to analyze the forces applied to the knee joint in various positions of flexion, one can calculate minimum compressive loads that cross the patellofemoral joint for a given degree of flexion. This exercise has been carried out by numerous authors (4, 7, 12‑20), with considerable divergence of quantitative values. This is not surprising because any determination of net patellofemoral contact force will depend on many factors, including body weight, quadriceps force, angle of flexion, rotation, and individual anatomic variations.

Calculation of Patellofemoral Compression

The patellofemoral joint reaction (PFJR) force is equal and opposite to the resultant of the quadriceps tension (M1) and patellar tendon tension (M2) acting perpendicular to the articular surfaces (Fig. 2.1). The PFJR force increases with increasing flexion on two accounts: first, as the angle between the patellar tendon and the quadriceps becomes more acute, and the resultant vector increases; second, as knee flexion increases, the effective lever arms of the femur and the tibia increase, requiring greater quadriceps power to resist the flexion moment of body weight (Fig. 2.2). Some authors have used the entire length of the femur in carrying out their calculations. Bandi (4) has pointed out, however, that during normal activities requiring knee flexion under load, hip flexion is also present, thus bringing the center of gravity forward and shortening the femoral lever arm. This difference in calculation alone results in nearly halving calculated PFJR force (Fig. 2.3).

Earlier authors, including those of the original edition of this book, made the incorrect assumption that quadriceps force (M1) equaled patellar tendon force (M2), viewing the patellofemoral joint as a frictionless pulley. This has now been shown to be incorrect, and the ratio M1/M2 does not equal 1 throughout most of the range of motion. Maquet (21) pointed out the complex relationship between M1 and M2 through the static force analysis of line drawings of the lateral view of the knee in several angles of flexion. The essential findings of his original work have been experimentally confirmed by several authors (18‑20, 22, 23). The most comprehensive analysis was published recently by Ahmed et al (20). Potentially, the extensor mechanism could be viewed as a frictionless pulley or as frictionless contact. The frictionless contact concept best fits the experimental data. The ratio of M1/M2 is shown in Figure 2.4. Huberti et al (19) and Ahmed et al (20), using a direct method of measuring M1, but a buckle transducer for M2, obtained quantitatively different but qualitatively similar results to those of Buff et al (18). From a knowledge of M1 and M2, body weight, angle of knee flexion, extensor lever arm, flexor lever arm, and angle of quadriceps tendon (qt)/patellar tendon (pt), the PFJR can be calculated according to the formula:

PFJR =

Although the ratio of M1/M2 increases steadily with increasing knee flexion under normal weight‑bearing, both patellar tendon force (M2) and PFJR increase with increasing flexion (Fig. 2.4).

Although mathematical manipulations are necessary to arrive at quantitative figures for a given situation, analyzing certain qualitative factors will facilitate an understanding of patellofemoral mechanics. For the same degree of knee flexion, the center of gravity may be shifted forward, having the effect of reducing the flexion moment arm. An example of this is the movement in rising from a chair. Certain sports, notably skiing, may shift the center of gravity backward, increasing this moment arm considerably and increasing the PFJR force. Bandi (4) calculated PFJR according to degree of knee flexion, but more recent studies (18, 19) permit more accurate determination of PFJR force.

One should not be fooled, however, into thinking that in vitro models used in many biomechanical studies give more than a superficial view of the mechanical factors affecting the patellofemoral joint. Most models do not take into account retinacular tensions or the effect of acceleration and deceleration. They do, however, give some appreciation of the several‑fold multiplication of body weight across the articulation and potential concentration of these loads on patellar cartilage when the knee is in certain positions.

Reilly and Martens (17) calculated the highest PFJR force for level walking to be 0.5 times body weight. In contrast, with stair climbing and descending, PFJR force reached 3.3 times body weight. Hungerford and Barry (24) showed that extending the knee against the weight of a 9‑kg boot attached to the foot produced a peak PFJR force at 36° of knee flexion. Huberti and Hayes (25) extrapolated contact forces of 4600 N (approximately 6.5 X body weight) on the patella, again emphasizing the magnitude of patellar contact pressures that can occur over very small surface areas.


        

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