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The authors have declared that no competing interests exist.

Conceived and designed the experiments: DJC. Performed the experiments: DJC DFLS. Analyzed the data: DJC DFLS AMJB. Wrote the paper: DJC DFLS AMJB.

Traditional descriptions of the knee suggest that the function of the patella is to facilitate knee extension by increasing the moment arm of the quadriceps muscles. Through modelling and evidence from the literature it is shown in this paper that the presence of the patella makes the ability of the quadriceps to rotate the thigh greater than their ability to rotate the tibia. Furthermore, this difference increases as the knee is flexed, thus demonstrating a pattern that is consistent with many human movements. This paper also shows that the anterior cruciate ligament plays a previously unheralded role in extending the shank and that translation at the tibiofemoral and patellofemoral joints is important in improving the capacity for thigh rotation when the knee is flexed. This study provides new insights as to how the structure of the knee is adapted to its purpose and illustrates how the functional anatomy of the knee contributes to its extension function.

The way in which the human knee joint extends has received considerable attention and is described primarily as a function of the extension of the tibiofemoral joint by the action of the quadriceps (mediated by the patella). However, this is a joint-based description of patellar function, based upon the assumption that the joint acts as a single degree of freedom hinge between the segments, and that the muscles rotate the segments about this hinge. However, this fundamental assumption does not hold true for the knee, where the bony anatomy provides little restraint and there is no obvious structure that could be considered to act as a hinge (the principal restraint is provided through tethering by a limited number of ligaments

The role of the patella has been of particular interest to biomechanists. Despite early discussion

Early commentators on the function of the patella assumed that it acted as a smooth pulley, such that the force in the quadriceps tendon (QT) was matched by that in the PT throughout the movement of the knee

Although these changes in geometry are known, the fundamental reasons for them have not been described, and the presence of the patella is normally justified by the effect it has on the moment arm of the QT about the tibiofemoral joint. It is the contention of this article, that this is a function of a joint-based analysis. In particular, this article will show that the presence of the patella allows the quadriceps muscle group to exert a different rotation effect on the tibial and femoral segments, an effect that cannot be captured underneath the typical assumptions of a joint-based analysis. The difference in the rotation of the tibial and femoral segments is important in properly understanding the function of the extensor apparatus of the knee.

In this study, a simple two dimensional sagittal plane model based upon existing data sets

The model consists of three rigid linked segments with zero mass representing the femur, tibia and patella. Flexion of the knee is simulated by rotating the femur about a stationary tibia. At each flexion angle the model is assumed to be in static force and moment equilibrium (i.e. each segment is in static force and moment equilibrium), and the only forces acting upon each segment are those that arise due to tension in the quadriceps. Therefore the resultant force acting on each segment is zero (note that because the resultant force acting upon each segment is zero, that the moment acting upon each segment is independent of the reference point from which it is calculated). The tendency of tension in the quadriceps to create rotation of the tibial and femoral segments is determined by calculating the external moment that must be applied to the COM of each segment to maintain its static moment equilibrium. As rectus femoris is both a biarticular muscle, and creates a joint reaction force at the hip, this model is restricted to an analysis of the vastus parts of the quadriceps – i.e. those that only cross the knee.

The geometry of the model (as depicted in

Given the known angles described above (

In this model, the patella is assumed to be in force and moment equilibrium at all knee flexion angles. Consequently, this produces a changing ratio of PT to QT forces (P/Q ratio) as the knee flexes, as has been described by previous authors. This ratio can be simply calculated from Equation 1, based upon the angles of incidence of the QT (

Next, all of the forces that act upon the tibial, femoral and patellar segments as a result of tension in the quadriceps are calculated, by assuming a nominal tension of 1 N in the QT. Firstly, the tension in the PT is calculated based upon the P/Q ratio, giving the PT force acting on the tibia. The tension in the cruciate ligaments can then be calculated by assuming that they are the sole restraints to anterior/posterior shear of the tibia and using the cruciate ligament angles calculated earlier (note that this assumption means that only one of the cruciate ligaments is recruited at any joint angle). The final force acting on the tibia is the tibiofemoral joint contact force (TFJ) which is equal and opposite to the sum of the PT and cruciate ligament forces, and in this model is assumed to be directed through the COM of the tibia. Next the three forces acting upon the patella are calculated, based upon the assumption that the contact force between patella and femur maintains force equilibrium at the patella, by equilibrating the QT and PT forces. Finally, four forces act upon the femur; the QT force and the patellofemoral joint contact force (PFJ) which are assumed to be equal and opposite to the analogous forces acting upon the patella, and the TFJ and cruciate ligament forces which are equal and opposite to those acting on the tibia. The forces acting upon all three segments are depicted on

Forces acting on the segments include the quadriceps tendon force (QT), patellofemoral joint contact force (PFJ), tibiofemoral joint contact force (TFJ), patellar tendon force (PT) and cruciate ligament forces (either anterior cruciate ligament (ACL) or posterior cruciate ligament (PCL) force – the ACL is depicted here). The insert shows the changing point of application of the PFJ and TFJ on the femoral segment with increasing knee flexion.

The forces acting upon the femur and tibia are assumed to create rotation about the COM of each segment, the position of which is taken from the data of Klein Horsman and colleagues

At this point, all of the force vectors acting on both femoral and tibial segments arising from 1 N of tension in the QT are known in conjunction with their effective point of application. Thus the moment created by each force for each 1 N of tension about the COM of the relevant segment can be calculated. It should be noted that as this calculation yields the moment per Newton of tension in the QT, the quantity calculated is simply a distance. For this reason, the results presented below describe the effective moment arm (in cm) of the rotation effect created by each structure that arises due to 1 N of quadriceps tension. That is, the actual moment exerted by a given structure, given a particular amount of quadriceps tension can be found by multiplying the effective moment arm of the structure by the amount of quadriceps tension. Equally, the net moment of all of the forces acting on each of the femoral and tibial segments that arises due to quadriceps tension would be calculated by multiplying the amount of quadriceps tension by the combined effective moment arm for the segment. In all of the figures presented below, a positive effective moment arm indicates a moment that would tend to extend the knee joint. Thus although the tibial and femoral segments rotate in opposite directions during knee extension in this paper both moments are presented as positive knee joint moments.

The results of this modelling study suggest that at low angles of knee flexion, extension of the tibia is a consequence of the ACL force, as the PT actually impresses a flexion moment on the segment (

The rotation effects of the individual forces acting upon the femoral segment are of a greater magnitude than those acting on the tibia (

The sum of the extension moments acting upon the tibial and femoral segments gives the effective moment that extends the tibiofemoral joint (

Traditional joint-based descriptions of the patella suggest that its function is to act as a “joint spacer”, increasing the moment arm of the PT about the tibiofemoral joint. This traditional analysis also suggests that the moment arm of the PT changes as the knee flexes, first increasing as the knee flexes (from full extension) until it peaks at between 30 and 60 degrees of knee flexion, before then decreasing again (see Tsaopoulos and colleagues

The results of this study suggest a very different picture of patellar function. In particular, the segment-based analysis presented here suggests that tension in the quadriceps creates a different rotation effect on the tibial and femoral segments. This finding is one that is precluded by a traditional joint-based analysis due to the common assumption that the rotation effect on the tibial segment is equal and opposite to that on the femoral segment. Equally, this study suggests that the overall tendency of quadriceps tension to create rotation of the knee joint remains fairly constant throughout knee flexion, again in contrast to the joint-based analysis. Thus, the results of a segment-based analysis suggest that the role of the patella is to keep the effective moment arm of quadriceps tension about the knee joint constant, but also changing the way in which extension is achieved. In particular, with increasing angles of knee flexion, the tendency for the mechanism to extend the tibial segment is reduced whilst the tendency for femoral extension is increased. This pattern is consistent with the kinematics of a number of common movement patterns that involve closed kinetic chain flexion and extension of the knee through a full range of motion (e.g. squatting or lunging). During these activities at deeper knee flexion angles the extension of the lower limb is primarily achieved by the rotation of the thigh about a relatively stationary shank. It is only at shallower knee flexion angles where there is appreciable rotation of the tibial segment.

A further advantage of the segment-based analysis is inherent in the increased detail of the approach. For instance, underneath a joint-based analysis some of the detail relating to the function of the joint is lost, as the forces and structures that create the rotation are not explicitly modelled. This study therefore is able to provide further insight into the way in which quadriceps tension creates extension of the lower limb.

In

A) when the knee angle is small the quadriceps actually exerts a flexion moment on the tibia and the extension moment is provided by the ACL; and B) with increased knee flexion angle, the patellar tendon can now produce an extension moment of the tibia, conversely recruitment of the PCL produces a flexion moment.

At deeper knee flexion angles the PT is orientated more posteriorly and able to independently produce an extension of the tibia. However, this study (

An understanding as to the rotation of the femoral segment (

The mechanical understanding of knee joint function reported in this study is based upon a simplified model of the knee. In common with previous similar studies of knee joint function

The traditional conception as to the role of the patella is that it acts as a “spacer” to increase the moment arm of the PT about the tibiofemoral joint. This study suggests that the reason for the unique structure of the extensor mechanism of the lower limb is to increase the tendency of quadriceps tension to create femoral rotation as the knee flexion angle increases with a concomitant reduction in tibial rotation. This is important to adjust to the demands of many human locomotor tasks. In addition, this paper demonstrates that recruitment of the ACL is important to extension of the tibia, and similarly that the translations at the tibiofemoral and patellofemoral joints play a pivotal role in producing a strong extension of the femur.

We thank J. E. Goodwin for critical discussions and for reading the manuscript.