Tibio-femoral movement in the living knee. A study of weight bearing and non-weight bearing knee kinematics using 'interventional' MRI

The aim of this study was to image tibio-femoral movement during flexion in the living knee. Ten loaded male Caucasian knees were initially studied using MRI, and the relative tibio-femoral motions, through the full flexion arc in neutral tibial rotation, were measured. On knee flexion from hyperextension to 120 degrees , the lateral femoral condyle moved posteriorly 22 mm. From 120 degrees to full squatting there was another 10 mm of posterior translation, with the lateral femoral condyle appearing almost to sublux posteriorly. The medial femoral condyle demonstrated minimal posterior translation until 120 degrees . Thereafter, it moved 9 mm posteriorly to lie on the superior surface of the medial meniscal posterior horn. Thus, during flexion of the knee to 120 degrees , the femur rotated externally through an angle of 20 degrees . However, on flexion beyond 120 degrees , both femoral condyles moved posteriorly to a similar degree. The second part of this study investigated the effect of gender, side, load and longitudinal rotation. The pattern of relative tibio-femoral movement during knee flexion appears to be independent of gender and side. Femoral external rotation (or tibial internal rotation) occurs with knee flexion under loaded and unloaded conditions, but the magnitude of rotation is greater and occurs earlier on weight bearing. With flexion plus tibial internal rotation, the pattern of movement follows that in neutral. With flexion in tibial external rotation, the lateral femoral condyle adopts a more anterior position relative to the tibia and, particularly in the non-weight bearing knee, much of the femoral external rotation that occurs with flexion is reversed.     

Three-dimensional knee model: constrained by isometric ligament bundles and experimentally obtained tibio-femoral contacts

The purpose of this study is to investigate the effect of anterior portion of anterior cruciate ligament, posterior cruciate ligament, anterior and deep portions of medial collateral ligament and the tibio-femoral articular contacts on passive knee motion. A well-accepted reference model for a normal tibio-femoral joint is reconstructed from the literature. The proposed three-dimensional dynamic tibio-femoral model includes the isometric fascicles, ligament bundles and irregularly shaped medial-lateral contact surfaces. With the approach we aim to analyze bone shape and ligament related abnormalities of knee kinematics. The rotations, translations and the contact forces during passive knee flexion were compared against a reference model and the results were found in close accordance. This study demonstrated that isometric ligament bundles play an important role in understanding the femur shape from contact points on tibia. Femoral condyles are not necessarily spherical. The surgical treatments should consider both ligament bundle lengths and contact surface geometries to achieve a problem free knee kinematics after a knee surgery.     

A spatial mechanism with higher pairs for modelling the human knee joint

By generalizing a previous model proposed in the literature, a new spatial kinematic model of the knee joint passive motion is presented. The model is based on an equivalent spatial parallel mechanism which relies upon the assumption that fibers within the anterior cruciate ligament (ACL), the medial collateral ligament (MCL) and the posterior cruciate ligament (PCL) can be considered as isometric during the knee flexion in passive motion (virtually unloaded motion). The articular surfaces of femoral and tibial condyles are modelled as 3-D surfaces of general shapes. In particular, the paper presents the closure equations of the new mechanism both for surfaces represented by means of scalar equations that have the Cartesian coordinates of the points of the surface as variables and for surfaces represented in parametric form. An example of simulation is presented in the case both femoral condyles are modelled as ellipsoidal surfaces and tibial condyles as spherical surfaces. The results of the simulation are compared to those of the previous models and to measurements. The comparison confirms the expectation that a better approximation of the tibiofemoral condyle surfaces leads to a more accurate model of the knee passive motion.     

Deformation of the distal femur: a contribution towards the pathogenesis of osteochondrosis dissecans in the knee joint.

Osteochondrosis dissecans (OD) is a process of subchondral bone necrosis occurring predominantly in young individuals at specific sites. The aetiology of this disease remains controversial with mechanical processes due to trauma and/or ischaemic factors being proposed. This study aims at explaining the aetiology of OD in the knee joint as a result of the particular deformation of the condyles. A finite element analysis of the distal third of the femur was performed. A three-dimensional model was developed based on computed tomography scans of a normal femur, consisting of cortical bone, cancellous bone and articular cartilage. This model was subjected to physiological loads at 0, 30, 60 and 90 degrees of knee flexion. A complex deformation was found within each condyle as well as between the two condyles. Both medial and lateral condyles are deformed in the medio-lateral direction and at the same time compressed between the patella and the tibia in the antero-posterior direction. This effect is highest at 60 degrees of knee flexion. In both planes, the medial condyle is distorted more than the lateral one. Strain concentration in the subchondral bone facing the patella varies with flexion, especially for angles exceeding 60 degrees. The deformation of the femur in the predominant locus of OD in the medial condyle exceeds that of the lateral condyle considerably. The analysis shows that repeated vigorous exercise including extreme knee flexion may produce rapidly changing strains which in turn could ultimately be responsible for local subchondral bone collapse.     

In vivo tibiofemoral contact analysis using 3D MRI-based knee models

This paper quantified the motion of the tibiofemoral contact points during in vivo weight bearing flexion using MRI- based 3D knee models and two orthogonal fluoroscopic images. The contact points on the medial and lateral tibial plateau were calculated by finding the centroid of the intersection of the tibial and femoral cartilage layers and by using the bony geometry alone. Our results indicate that the medial femoral condyle remains in the central portion of the tibial plateau and the lateral condyle translates posteriorly with increasing flexion. Using the bony contact model increased the total translation of the medial and lateral condyles by 250 and 55%, respectively, compared to the cartilage contact model. These results suggest that using the bony geometry alone may not accurately represent the articular surfaces of the knee. Articular cartilage geometry may have to be used to accurately quantify tibiofemoral contact.     

A finite element model of the human knee joint for the study of tibio-femoral contact

As a step towards developing a finite element model of the knee that can be used to study how the variables associated with a meniscal replacement affect tibio-femoral contact, the goals of this study were 1) to develop a geometrically accurate three-dimensional solid model of the knee joint with special attention given to the menisci and articular cartilage, 2) to determine to what extent bony deformations affect contact behavior, and 3) to determine whether constraining rotations other than flexion/extension affects the contact behavior of the joint during compressive loading. The model included both the cortical and trabecular bone of the femur and tibia, articular cartilage of the femoral condyles and tibial plateau, both the medial and lateral menisci with their horn attachments, the transverse ligament, the anterior cruciate ligament, and the medial collateral ligament. The solid models for the menisci and articular cartilage were created from surface scans provided by a noncontacting, laser-based, three-dimensional coordinate digitizing system with an root mean squared error (RMSE) of less than 8 microns. Solid models of both the tibia and femur were created from CT images, except for the most proximal surface of the tibia and most distal surface of the femur which were created with the three-dimensional coordinate digitizing system. The constitutive relation of the menisci treated the tissue as transversely isotropic and linearly elastic. Under the application of an 800 N compressive load at 0 degrees of flexion, six contact variables in each compartment (ie., medial and lateral) were computed including maximum pressure, mean pressure, contact area, total contact force, and coordinates of the center of pressure. Convergence of the finite element solution was studied using three mesh sizes ranging from an average element size of 5 mm by 5 mm to 1 mm by 1 mm. The solution was considered converged for an average element size of 2 mm by 2 mm. Using this mesh size, finite element solutions for rigid versus deformable bones indicated that none of the contact variables changed by more than 2% when the femur and tibia were treated as rigid. However, differences in contact variables as large as 19% occurred when rotations other than flexion/extension were constrained. The largest difference was in the maximum pressure. Among the principal conclusions of the study are that accurate finite element solutions of tibio-femoral contact behavior can be obtained by treating the bones as rigid. However, unrealistic constraints on rotations other than flexion/extension can result in relatively large errors in contact variables.     

The load-bearing area in the knee joint

Measurements were made of the location and size of the contact areas in cadaver knee joints, for a load of 150 Kgf applied for 5 sec down the long axis of the tibia. Results were obtained from a total of 4 knees, considering flexion angles from 0 to 120°. The methods used were to measure directly from castings of the joint cavity; and to calculate from measurements of radii of curvature and joint deflection. Average contact areas for lateral and medial condyles were 1·4 and 1·8 cm² respectively. Areas for the medial condyle were greater than for the lateral condyle and also the areas diminished as flexion angle increased. The implications of the results to contact stresses, joint lubrication and ‘condylar replacement’ knee prosthesis design were discussed.     

3-D anatomically based dynamic modeling of the human knee to include tibio-femoral and patello-femoral joints

An anatomical dynamic model consisting of three body segments, femur, tibia and patella, has been developed in order to determine the three-dimensional dynamic response of the human knee. Deformable contact was allowed at all articular surfaces, which were mathematically represented using Coons' bicubic surface patches. Nonlinear elastic springs were used to model all ligamentous structures. Two joint coordinate systems were employed to describe the six-degrees-of-freedom tibio-femoral (TF) and patello-femoral (PF) joint motions using twelve kinematic parameters. Two versions of the model were developed to account for wrapping and nonwrapping of the quadriceps tendon around the femur. Model equations consist of twelve nonlinear second-order ordinary differential equations coupled with nonlinear algebraic constraint equations resulting in a Differential-Algebraic Equations (DAE) system that was solved using the Differential/Algebraic System Solver (DASSL) developed at Lawrence Livermore National Laboratory. Model calculations were performed to simulate the knee extension exercise by applying non-linear forcing functions to the quadriceps tendon. Under the conditions tested, both "screw home mechanism" and patellar flexion lagging were predicted. Throughout the entire range of motion, the medial component of the TF contact force was found to be larger than the lateral one while the lateral component of the PF contact force was found to be larger than the medial one. The anterior and posterior fibers of both anterior and posterior cruciate ligaments, ACL and PCL, respectively, had opposite force patterns: the posterior fibers were most taut at full extension while the anterior fibers were most taut near 90 degrees of flexion. The ACL was found to carry a larger total force than the PCL at full extension, while the PCL carried a larger total force than the ACL in the range of 75 degrees to 90 degrees of flexion.     

A new in vivo technique for determination of 3D kinematics and contact areas of the patello-femoral and tibio-femoral joint

Patello-femoral disorders are often caused by changes of patello-femoral and/or tibio-femoral kinematics. However, until now there has been no quantitative in vivo technique, that is able to obtain 3D kinematics and contact areas of all knee compartments simultaneously on a non-invasive basis. The aim of this study was therefore to develop and apply a technique which allows for determination of 3D kinematics and contact areas of the patello-femoral and tibio-femoral joint during different knee flexion angles and under neuromuscular activation patterns. One knee of each of the 10 healthy volunteers was examined in an open MR system under flexing isometric muscle activity at 30 degrees and 90 degrees. Three-dimensional kinematics and contact areas of the patello-femoral and tibio-femoral joints were analyzed by 3D image postprocessing. The reproducibility of the imaging technique yielded a coefficient of variation of 4.6% for patello-femoral, 4.7% for femoro-tibial displacement and 8.6% for contact areas. During knee flexion (30-90 degrees ), patella tilt (opened to medial) decreased (8.8+/-3.4 degrees vs. 4.6+/-3.1 degrees, p<0.05), while lateral patellar shift increased significantly (1.6+/-2.3mm vs. 3.4+/-3.0mm, p<0.05). Furthermore, a significant posterior translation and external rotation of the femur relative to the tibia was observed. Patello-femoral contact areas increased significantly in size (134+/-60mm(2) vs. 205+/-96 mm(2)) during knee flexion. This technique shows a high reproducibility and provides physiologic in vivo data of 3D kinematics and contact areas of the patello-femoral and the tibio-femoral joint during knee flexion. This allows for advanced in vivo diagnostics, and may help to improve therapy of patello-femoral disorders in the future.     

How effective are added constraints in improving TKR kinematics?

Newer designs of total knee arthroplasty (TKA), through the use of added degrees of constraint, attempt to provide a "guided motion" to restore more normal and predictable kinematics. Two such design philosophies are the posterior stabilised (PS) using a cam-post and the medial pivot (MP) concepts. Knee kinematics of 12 patients with a PS TKA, 13 subjects with a MP TKA and 10 normal subjects were compared. For kinematic assessment, patients underwent fluoroscopic assessment of the knee during a step-up exercise and deep knee bend. Fluoroscopic images were corrected for distortion and assessed using 3D model fitting to determine relative 3D motion, and a 2D method to measure the patellar tendon angle (PTA) as function of knee flexion. For the PS design the cam-post mechanism engaged between 70 degrees and 100 degrees flexion. Between extension and 50 degrees there was forward motion of the contact points. Beyond 60 degrees both condyles rolled moved posteriorly. The majority of the external rotation of the femur occurred between 50 degrees and 80 degrees . The PTA was lower than normal in extension and higher than normal in flexion. The MP exhibited no anterior movement throughout the rage of motion. The medial condyle moved minimally. The lateral contact point moved posteriorly from extension to flexion. The femur rotated externally throughout the range of flexion analysed. The PTA was similar to normal from extension to mid flexion and then higher than normal beyond to high flexion. The PS design fails to fully restrain paradoxical anterior movement and although the cam engages, it does not contribute significantly to overall rollback. The MP knee does not show significant anterior movement, the medial pivot concept appears to achieve near normal kinematics from extension to 50 degrees of knee flexion. However, the results show that at high flexion this design does not achieve normal knee kinematics.     

Geometry and motion of the knee for implant and orthotic design

By analysing sections of distal femurs in the computer, and by making direct measurements, the posterior femoral condyles were shown to closely fit spherical surfaces. The center of the spheres were then used as reference points and used to define reference axes in a motion study. In flexing from 0 to 120 degrees the medial femoral condyle moved little, the lateral moved posteriorly by 17 mm, and there was an axial rotation of 20 degrees. The data were applied to implant and orthotic design and evaluation.     

Three-dimensional dynamical capabilities of the human masticatory muscles

Many habitual human jaw movements are non-symmetrical. Generally, it is observed that when the lower incisors move to one side the contralateral condyle moves forwards onto the articular eminence, whereas the ipsilateral condyle stays in the mandibular fossa, moving slightly to the ipsilateral side. These jaw movements are the result of contractions of active masticatory muscles and guided by the temporomandibular joints, their ligaments and passive elastic properties of the muscles. It is not known whether the movements are primarily dependent on passive guidance, active muscle control or both. Therefore, the objective of this study was to analyse the interplay between these factors during non-symmetrical jaw movements. A six-degrees-of-freedom dynamical biomechanical model of the human masticatory system was used. The movements were not restricted to a priori defined joint axes. Jaw movement simulations were performed by unilateral activity of the muscles. The ligaments or the passive elastic properties of the muscles could be removed during these simulations. Laterodeviations conform to naturally observed ones could be generated by unilateral muscle contractions. The movement of the lower incisors was hardly affected by the absence of passive elastic muscle properties or temporomandibular ligaments. The latter, however, influenced the movement of the condyles. The movements could be understood by analysing the combination of forces and torques with respect to the centre of gravity of the lower jaw. In addition, the loading of the condyles appeared to be an important determinant for the movement. This analysis emphasizes that the movements of the jaw are primarily dependent on the orientation of the contributing muscles with respect to this centre of gravity and not on the temporomandibular ligaments or passive elastic muscle properties.     

Articular contact at the tibiotalar joint in passive flexion

The knowledge of the contact areas at the tibiotalar articulating surfaces during passive flexion is fundamental for the understanding of ankle joint mobility. Traditional contact area reports are limited by the invasive measuring techniques used and by the complicated loading conditions applied. In the present study, passive flexion tests were performed on three anatomical preparations from lower leg amputation. Roentgen Stereophotogrammetric Analysis was used to accurately reconstruct the position of the tibia and the talus at a number of unconstrained flexion positions. A large number of points was collected on the surface of the tibial mortise and on the trochlea tali by a 3-D digitiser. Articular surfaces were modelled by thin plate splines approximating these points. Relative positions of these surfaces in all the flexion positions were obtained from corresponding bone position data. A distance threshold was chosen to define contact areas. A consistent pattern of contact was found on the articulating surfaces. The area moved anteriorly on both articular surfaces with dorsiflexion. The average position of the contact area centroid along the tibial mortise at maximum plantarflexion and at maximum dorsiflexion was respectively 58% posterior and 40% anterior of the entire antero-posterior length. For increasing dorsiflexion, the contact area moved from medial to lateral in all the specimens.     

In vivo kinematic evaluation and design considerations related to high flexion in total knee arthroplasty

In designing a posterior-stabilized total knee arthroplasty (TKA) it is preferable that when the cam engages the tibial spine the contact point of the cam move down the tibial spine. This provides greater stability in flexion by creating a greater jump distance and reduces the stress on the tibial spine. In order to eliminate edge loading of the femoral component on the posterior tibial articular surface, the posterior femoral condyles need to be extended. This provides an ideal femoral contact with the tibial articular surface during high flexion angles. To reduce extensor mechanism impingement in deep flexion, the anterior margin of the tibial articular component should be recessed. This provides clearance for the patella and patella tendon. An in vivo kinematic analysis that determined three dimensional motions of the femorotibial joint was performed during a deep knee bend using fluoroscopy for 20 subjects having a TKA designed for deep flexion. The average weight-bearing range-of-motion was 125 degrees . On average, TKA subjects experienced 4.9 degrees of normal axial rotation and all subjects experienced at least -4.4 mm of posterior femoral rollback. It is assumed that femorotibial kinematics can play a major role in patellofemoral kinematics. In this study, subjects implanted with a high-flexion TKA design experienced kinematic patterns that were similar to the normal knee. It can be hypothesized that forces acting on the patella were not substantially increased for TKA subjects compared with the normal subjects.     

Using relative velocity vectors to reveal axial rotation about the medial and lateral compartment of the knee

A new technique is presented that utilizes relative velocity vectors between articulating surfaces to characterize internal/external rotation of the tibio-femoral joint during dynamic loading. Precise tibio-femoral motion was determined by tracking the movement of implanted tantalum beads in high-speed biplane X-rays. Three-dimensional, subject-specific CT reconstructions of the femur and tibia, consisting of triangular mesh elements, were positioned in each analyzed frame. The minimum distance between subchondral bone surfaces was recorded for each mesh element comprising each bone surface, and the relative velocity between these opposing closest surface elements was determined in each frame. Internal/external rotation was visualized by superimposing tangential relative velocity vectors onto bone surfaces at each instant. Rotation about medial and lateral compartments was quantified by calculating the angle between these tangential relative vectors within each compartment. Results acquired from 68 test sessions involving 23 dogs indicated a consistent pattern of sequential rotation about the lateral condyle (approximately 60 ms after paw strike) followed by rotation about the medial condyle (approximately 100 ms after paw strike). These results imply that axial knee rotation follows a repeatable pattern within and among subjects. This pattern involves rotation about both the lateral and medial compartments. The technique described can be easily applied to study human knee internal/external rotation during a variety of activities. This information may be useful to define normal and pathologic conditions, to confirm post-surgical restoration of knee mechanics, and to design more realistic prosthetic devices. Furthermore, analysis of joint arthrokinematics, such as those described, may identify changes in joint mechanics associated with joint degeneration.     

Effect of superficial collagen patterns and fibrillation of femoral articular cartilage on knee joint mechanics-a 3D finite element analysis

Collagen fibrils of articular cartilage have specific depth-dependent orientations and the fibrils bend in the cartilage surface to exhibit split-lines. Fibrillation of superficial collagen takes place in osteoarthritis. We aimed to investigate the effect of superficial collagen fibril patterns and collagen fibrillation of cartilage on stresses and strains within a knee joint. A 3D finite element model of a knee joint with cartilage and menisci was constructed based on magnetic resonance imaging. The fibril-reinforced poroviscoelastic material properties with depth-dependent collagen orientations and split-line patterns were included in the model. The effects of joint loading on stresses and strains in cartilage with various split-line patterns and medial collagen fibrillation were simulated under axial impact loading of 1000 N. In the model, the collagen fibrils resisted strains along the split-line directions. This increased also stresses along the split-lines. On the contrary, contact and pore pressures were not affected by split-line patterns. Simulated medial osteoarthritis increased tissue strains in both medial and lateral femoral condyles, and contact and pore pressures in the lateral femoral condyle. This study highlights the importance of the collagen fibril organization, especially that indicated by split-line patterns, for the weight-bearing properties of articular cartilage. Osteoarthritic changes of cartilage in the medial femoral condyle created a possible failure point in the lateral femoral condyle. This study provides further evidence on the importance of the collagen fibril organization for the optimal function of articular cartilage.     

Partial medial meniscectomy and rotational differences at the knee during walking

Loss of meniscal function due to injury or partial meniscectomy is common and represents a significant risk factor for premature osteoarthritis. The menisci can influence the transverse plane movements (anterior–posterior (AP) translation and internal–external (IE) rotation) of the knee during walking. While walking is the most frequent activity of daily living, the kinematic differences at the knee during walking associated with the meniscal injury are not well understood. This study examined the influence of partial medial meniscectomy (PMM) on the kinematics and kinetics of the knee during the stance phase of gait by testing the differences in anterior–posterior translation, internal–external rotation, knee flexion range of movement, peak flexion/extension moments, and adduction moments between the PMM and healthy contralateral limbs. Ten patients (45±9 years old, height 1.75±0.06 m, weight 76.7±13.5 kg) who had undergone partial medial meniscectomy (33±100 months post-op) in one limb with a healthy contralateral limb were tested during normal walking. The contralateral limb was compared to a matched control group and no differences were found. The primary kinematic difference was a significantly greater external rotation (3.2°) of the tibia that existed through stance phase, with 8 of 10 subjects demonstrating the same pattern. The PMM subjects also exhibited significantly lower peak flexion and extension moments in their PMM limbs. The altered rotational position found likely results in changes of tibio-femoral contact during walking and could cause the type of degenerative changes found in the articular cartilage following meniscal injury.     

Combined finite-element and rigid-body analysis of human jaw joint dynamics

The jaw joint plays a crucial role in human mastication. It acts as a guidance for jaw movements and as a fulcrum for force generation. The joint is subjected to loading which causes tensions and deformations in its cartilaginous structures. These are assumed to be a major determinant for development, maintenance and also degeneration of the joint. To analyze the distribution of tensions and deformations in the cartilaginous structures of the jaw joint during jaw movement, a dynamical model of the human masticatory system has been constructed. Its movements are controlled by muscle activation. The articular cartilage layers and articular disc were included as finite-element (FE) models. As this combination of rigid-body and FE modeling had not been applied to musculoskeletal systems yet, its benefits and limitations were assessed by simulating both unloaded and loaded jaw movements. It was demonstrated that joint loads increase with muscle activation, irrespective of the external loads. With increasing joint load, the size of the stressed area of the articular surfaces was enlarged, whereas the peak stresses were much less affected. The results suggest that the articular disc enables distribution of local contact stresses over a much wider area of the very incongruent articular surfaces by transforming compressive principal stress into shear stress.     

Predicted and observed shapes of human mandibular condyles.

A mathematical model based on linear programming was used to study the directions of the joint forces used to maintain the human jaw in three-dimensional static equilibrium when producing bite forces of 100 N to a maximum of 1000 N down the long axis of a central incisor, first premolar, first molar and third molar. Seven different versions of the model were studied. The two simplest versions minimized the total muscle tension and the total joint load, respectively. Assuming that the joint force direction must be normal to some part of the articular surface of the condyle, neither version produced directions consistent with the observed shapes of human condyles. The other five versions minimized different combinations of muscle tensions and joint loads. Two of these versions produced joint force directions compatible with the shapes of condyles. Both minimized total muscle tension plus the (vertical) joint load on the back of the condyle. The results suggest that joint mechanoreceptors (probably non-directional) as well as muscle receptors contribute to the neuromuscular control of bite forces. Our results are consistent with some recent observations [Marshall and Tatton, Exp. Brain Res. 83, 137-150 (1990)] of the cat knee joint.     

Effect of knee joint flexion and femur rotation on retropatellar contact of the human knee joint]

The aim of the present study was to evaluate retropatellar contact characteristics at different angles of flexion of the knee joint. To this end, 6 cadaveric legs were examined using pressure sensitive film (Fuji Prescale type "super low") at angles of flexion of 45 degrees, 60 degrees, 90 degrees and 120 degrees both in neutral rotation and 10 degrees internal and external rotation of the femur in the same knee joints. A force of 140 N was applied to both the vastus medialis and lateralis, and a comparison made with a medially and a laterally dominating muscle force. The contact areas decreased with increasing angles of flexion. The medially dominating muscle traction increased the contact area. Comparison between internal and external rotation revealed a decrease in contact area on internal rotation. The pressure measurements were comparable in all loading situations. Comparison between neutral and medial traction revealed significant differences in contact area, pressure and force. The influence of femoral rotation showed no significant difference. A comparison of the different angles of flexion revealed only few significant differences. To prevent the development of retropatellar arthrosis, maximum contact areas are necessary. The study has shown an advantage for medially dominating muscle traction, and external rotation of the femur.