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1.
One proposed mechanism of patellofemoral pain, increased stress in the joint, is dependent on forces generated by the quadriceps muscles. Describing causal relationships between muscle forces, tissue stresses, and pain is difficult due to the inability to directly measure these variables in vivo. The purpose of this study was to estimate quadriceps forces during walking and running in a group of male and female patients with patellofemoral pain (n=27, 16 female; 11 male) and compare these to pain-free controls (n=16, 8 female; 8 male). Subjects walked and ran at self-selected speeds in a gait laboratory. Lower limb kinematics and electromyography (EMG) data were input to an EMG-driven musculoskeletal model of the knee, which was scaled and calibrated to each individual to estimate forces in 10 muscles surrounding the joint. Compared to controls, the patellofemoral pain group had greater co-contraction of quadriceps and hamstrings (p=0.025) and greater normalized muscle forces during walking, even though the net knee moment was similar between groups. Muscle forces during running were similar between groups, but the net knee extension moment was less in the patellofemoral pain group compared to controls. Females displayed 30–50% greater normalized hamstring and gastrocnemius muscle forces during both walking and running compared to males (p<0.05). These results suggest that some patellofemoral pain patients might experience greater joint contact forces and joint stresses than pain-free subjects. The muscle force data are available as supplementary material.  相似文献   

2.
Influence of patella alta on knee extensor mechanics   总被引:2,自引:0,他引:2  
The purpose of this study was to compare the knee extensor mechanics in persons with and without patella alta. Thirteen subjects with patella alta and 14 subjects with normal patellar position participated in the study. Sagittal and axial MR images of the knee were acquired at 0°, 20°, 40°, and 60° of knee flexion. Measurements of actual moment arm, patellar ligament/quadriceps tendon force ratio, quadriceps effective moment arm, and joint reaction force/quadriceps force ratio were obtained. There were no differences between groups in terms of actual moment arm. However, subjects with patella alta had significantly larger patellar ligament/quadriceps tendon force ratios (1.04±0.02 vs. 0.92±0.02) and quadriceps effective moment arms (4.40±0.09 vs. 4.00±0.09 cm) when averaged across the range of knee flexion angles tested. There was no difference in the joint reaction force/quadriceps force ratio between groups. The observed differences in knee extensor mechanics suggest that individuals with patella alta have a more efficient knee extensor mechanism and would be expected to generate similar joint reaction forces per unit quadriceps force compared to subjects with normal patellar position. Therefore, persons with patella alta may experience less patellofemoral joint reaction force to overcome the same knee flexion moment in the range of 0°–60° of knee flexion.  相似文献   

3.
Although the relationship between contact area and pressure under physiological loading has been described in the feline patellofemoral joint, this interaction has only been examined under simplified loading conditions and/or considerably lower forces than those occurring during demanding activities in humans. We hypothesized that patellofemoral contact area increases non-linearly under an increasing joint reaction force to regulate patellofemoral pressure. Eight human cadaveric knees were ramp loaded with muscle forces representative of the stance phase of stair climbing at 30° knee flexion. Continuous pressure data were acquired with a pressure sensitive film that was positioned within the patellofemoral joint. While pressure was linearly dependent upon the resulting joint reaction force, contact area asymptotically approached a maximum value and reached 95% of this maximum at patellofemoral forces of 349–723 N (95% CI). Our findings indicate that the regulatory influence of increasing contact area to protect against high patellofemoral pressure is exhausted at relatively low loads.  相似文献   

4.
5.
In the commonly used SIMM software, which includes a complete musculoskeletal model of the lower limbs, the reaction forces at the knee are computed. These reaction forces represent the bone-on-bone contact forces and the soft tissue forces (e.g. ligaments) other than muscles acting at the joint. In the knee model integrated into this software, a patellotibial joint rather than a patellofemoral joint is defined, and a force acting along the direction of the patellar ligament is not included. Although this knee model results in valid kinematics and muscle moment arms, the reaction forces at the knee calculated do not represent physiologic knee joint reaction forces. Hence our objectives were to develop a method of calculating physiologic knee joint reaction forces using the knee model incorporated into the SIMM software and to demonstrate the differences in the forces returned by SIMM and the physiologic forces in an example. Our method converts the anatomically fictional patellotibial joint into a patellofemoral joint and computes the force in an inextensible patellar ligament. In our example, the rectus femoris was fully excited isometrically, with the knee and hip flexed to 90 degrees . The resulting SIMM tibiofemoral joint reaction force was primarily shear, because the quadriceps force was applied to the tibia via the fictional patellotibial joint. In contrast the physiologic tibiofemoral joint reaction force was primarily compression, because the quadriceps force was applied through the patellar ligament. This result illustrates that the physiologic knee joint reaction forces are profoundly different than the forces returned by SIMM. However physiologic knee joint reaction forces can be computed with postprocessing of SIMM results.  相似文献   

6.
Patellofemoral pain is a common knee disorder with a multi-factorial etiology related to abnormal patellar tracking. Our hypothesis was that the pattern of three-dimensional rotation and translation of the patella induced by selective activation of individual quadriceps components would differ between subjects with patellofemoral pain and healthy subjects. Nine female subjects with patellofemoral pain and seven healthy female subjects underwent electrical stimulation to selectively activate individual quadriceps components (vastus medialis obliquus, VMO; vastus medialis lateralis, VML; vastus lateralis, VL) with the knee at 0° and 20° flexion, while three-dimensional patellar tracking was recorded. Normalized direction of rotation and direction of translation characterized the relative amplitudes of each component of patellar movement. VMO activation in patellofemoral pain caused greater medial patellar rotation (distal patellar pole rotates medially in frontal plane) at both knee positions (p<0.01), and both VMO and VML activation caused increased anterior patellar translation (p<0.001) in patellofemoral pain compared to healthy subjects at 20° knee flexion. VL activation caused more lateral patellar translation (p<0.001) in patellofemoral pain compared to healthy subjects. In healthy subjects the 3-D mechanical action of the VMO is actively modulated with knee flexion angle while such modulation was not observed in PFP subjects. This could be due to anatomical differences in the VMO insertion on the patella and medial quadriceps weakness. Quantitative evaluation of the influence of individual quadriceps components on patellar tracking will aid understanding of the knee extensor mechanism and provide insight into the etiology of patellofemoral pain.  相似文献   

7.
EMG analysis has indicated that the vastus lateralis and vastus medialis contribute less to the quadriceps moment during knee extension than the physiological cross-sectional areas (PCSA's) of the muscles indicate. Both PCSA- and EMG-based quadriceps force distributions were utilized while computationally simulating knee extension. For both distributions, a 10 degrees increase in the Q-angle and a 50% decrease in the force applied by the vastus medialis were simulated, and the influence of these changes on the resultant force and moment applied by the quadriceps muscles and the patella tendon was quantified. For both quadriceps force distributions, increasing the Q-angle increased the lateral force and the moment acting to rotate the distal patella laterally. Due to the relatively large forces initially attributed to the vastus medialis and vastus lateralis for the PCSA-based quadriceps force distribution, decreasing the vastus medialis force created a large force imbalance between these two muscles. For the PCSA-based quadriceps force distribution, decreasing the vastus medialis force increased the lateral rotation moment and the moment acting to tilt the patella laterally. For the EMG-based quadriceps force distribution, decreasing the vastus medialis force produced relatively little change in the tilt and rotation moments. For both quadriceps force distributions, increasing the Q-angle increased the maximum and mean cartilage pressure during flexion, but decreasing the vastus medialis force only increased the cartilage pressures for the PCSA-based quadriceps distribution. The choice of the initial quadriceps distribution can influence the outcome of patellofemoral simulation when manipulating quadriceps muscle forces.  相似文献   

8.
A mathematical model of the patellofemoral joint   总被引:6,自引:2,他引:4  
A mathematical model of the patellofemoral joint taking into account movements and forces in the sagittal plane is described. The system parameters of the model are the locations of the attachments of the quadriceps muscle and the patellar ligament, the length of the patellar ligament, the dimensions of the patella and the geometry of the articulating surfaces. They were obtained from ten autopsy knees. The model enables calculation of the relative position of the patella, patellar ligament and quadriceps tendon, the location of the patellofemoral contact point and the magnitude of the patellofemoral compression force and the force in the patellar ligament as a function of the location of the tibial tuberosity at different flexion-extension angles of the knee. The model is validated by comparing model data with experimentally determined data.  相似文献   

9.
One possible cause of patellofemoral pain syndrome is excessive lateral force acting on the patella. Although several treatment methods focus on decreasing the lateral force acting on the patella, the relationship between the lateral force and the patellofemoral contact pressure distribution is unclear. A computational model has been developed to determine how loading variations alter the patellofemoral force and pressure distributions for individual knees. The model allows variation in the quadriceps and patella tendon forces, and calculates the predicted contact pressure distribution using the discrete element analysis technique. To characterize the accuracy of the model, four cadaver knees were flexed on a knee simulator with three initial Q-angles, while recording the force and pressure distributions with a pressure sensor. A model of each knee was created from CT data. Using the external force applied to the knee, the geometry of the knee, and the quadriceps origin as input, the pressure distribution was calculated during flexion. Similar trends were noted for the computational and experimental results. The percentage of the total force applied to the lateral cartilage increased with the Q-angle. The maximum contact pressure increased during flexion. The maximum lateral contact pressure increased with the Q-angle for three knees. For the other knee, increasing the Q-angle decreased the maximum lateral pressure. The maximum medial contact pressure decreased as the Q-angle increased. By characterizing the influence of patellofemoral loading on the force and pressure distributions, the computational model could be used to evaluate treatment methods prescribed for patellofemoral pain.  相似文献   

10.
In vivo patellofemoral forces in high flexion total knee arthroplasty   总被引:1,自引:0,他引:1  
This study compares the in vivo patellofemoral contact forces generated in high flexion fixed bearing posterior cruciate retaining Nexgen CR-Flex (PCR) and high flexion posterior stabilized Nexgen LPS-Flex (LPS) TKAs with that of normal knees from full knee extension to maximum weight bearing flexion. Ten patients with the PCR total knee arthroplasty (TKA), ten with the LPS TKA and seven patients having normal knees were fluoroscoped while performing a deep knee bend activity. In vivo femorotibial kinematics, obtained from 3D-to-2D registration technique, and patellar kinematics obtained by direct measurements from the fluoroscopic images were entered into a 3D inverse dynamics mathematical model to determine the in vivo contact forces at the knee. The variation in the patellofemoral and quadriceps forces with flexion were found to be similar across the three groups-increasing from full extension to 90 degrees of flexion, reaching a maximum between 90 degrees and 120 degrees of flexion and then decreasing until maximum flexion. At maximum knee flexion, these forces were found to be significantly lower in the normal knees than in the TKAs. The patellar ligament to quadriceps force ratio decreased with the increase in knee flexion while the patellofemoral to quadriceps force ratio increased. A strong correlation was found to exist between the patellofemoral forces, the femorotibial contact forces and the forces in the extensor mechanism. The PCR TKA in this study exhibited greater resemblance to the normal patients with respect to the patellofemoral forces than the LPS TKA though significant differences in the two implant types were not observed.  相似文献   

11.
The purpose of this study was to determine the influence of patellofemoral joint contact geometry on the modeling of three-dimensional patellofemoral joint forces. To achieve this goal, patellofemoral joint reaction forces (PFJRFs) that were measured from an in-vitro cadaveric set-up were compared to PFJRFs estimated from a computer model that did not consider patellofemoral joint contact geometry. Ten cadaver knees were used in this study. Each was mounted on a custom jig that was fixed to an Instron frame. Quadriceps muscle loads were accomplished using a pulley system and weights. The force in the patellar ligament was obtained using a buckle transducer. To quantify the magnitude and direction of the PFJRF, a six-axis load cell was incorporated into the femoral fixation system so that a rigid body assumption could be made. PFJRF data were obtained at 0 degrees , 20 degrees , 40 degrees and 60 degrees of knee flexion. Following in vitro testing, SIMM modeling software was used to develop computational models based on the three-dimensional coordinates (Microscribe digitizer) of individual muscle and patellar ligament force vectors obtained from the cadaver knees. The overall magnitude of the PFJRF estimated from the computer generated models closely matched the direct measurements from the in vitro set-up (Pearson's correlation coefficient, R(2)=0.91, p<0.001). Although the computational model accurately estimated the posteriorly directed forces acting on the joint, some discrepancies were noted in the forces acting in the superior and lateral directions. These differences however, were relatively small when expressed as a total of the overall PFJRF magnitude.  相似文献   

12.
A study was performed to evaluate a computational model used to characterize the influence of vastus medialis obliquus (VMO) function on the patellofemoral pressure distribution. Ten knees were tested in vitro at 40°, 60° and 80° of knee flexion with quadriceps loads applied to represent a normal VMO, and with the VMO force decreased by approximately 50% to represent a weak VMO. The tests were performed with the cartilage intact and with a full thickness cartilage lesion centered on the lateral facet of the patella. The experimental tests were replicated computationally by applying discrete element analysis to a model of each knee constructed from MRI images. Repeated measures statistical comparisons were used to compare computational to experimental data and identify significant (p<0.05) differences due to the lesion and the applied VMO force. Neither the lateral force percentage nor the maximum lateral pressure varied significantly between the computational and experimental data. Creating a lesion significantly increased the maximum lateral pressure for all comparisons, except for the experimental data at 40°. Both computationally and experimentally, decrease in the VMO force increased the lateral force percentage by approximately 10% for all cases, and each increase was statistically significant. The maximum lateral pressure increase was typically less than 10% but was still significant for the majority of comparisons focused on the VMO strength. The results indicate that computational modeling can be used to characterize how varying quadriceps loading influences the patellofemoral force and pressure distributions while varying the condition of cartilage.  相似文献   

13.

Introduction

Patellofemoral joint osteoarthritis (OA) is common and leads to pain and disability. However, current classification criteria do not distinguish between patellofemoral and tibiofemoral joint OA. The objective of this study was to provide empirical evidence of the clinical features of patellofemoral joint OA (PFJOA) and to explore the potential for making a confident clinical diagnosis in the community setting.

Methods

This was a population-based cross-sectional study of 745 adults aged ≥50 years with knee pain. Information on risk factors and clinical signs and symptoms was gathered by a self-complete questionnaire, and standardised clinical interview and examination. Three radiographic views of the knee were obtained (weight-bearing semi-flexed posteroanterior, supine skyline and lateral) and individuals were classified into four subsets (no radiographic OA, isolated PFJOA, isolated tibiofemoral joint OA, combined patellofemoral/tibiofemoral joint OA) according to two different cut-offs: ''any OA'' and ''moderate to severe OA''. A series of binary logistic and multinomial regression functions were performed to compare the clinical features of each subset and their ability in combination to discriminate PFJOA from other subsets.

Results

Distinctive clinical features of moderate to severe isolated PFJOA included a history of dramatic swelling, valgus deformity, markedly reduced quadriceps strength, and pain on patellofemoral joint compression. Mild isolated PFJOA was barely distinguished from no radiographic OA (AUC 0.71, 95% CI 0.66, 0.76) with only difficulty descending stairs and coarse crepitus marginally informative over age, sex and body mass index. Other cardinal signs of knee OA - the presence of effusion, bony enlargement, reduced flexion range of movement, mediolateral instability and varus deformity - were indicators of tibiofemoral joint OA.

Conclusions

Early isolated PFJOA is clinically manifest in symptoms and self-reported functional limitation but has fewer clear clinical signs. More advanced disease is indicated by a small number of simple-to-assess signs and the relative absence of classic signs of knee OA, which are predominantly manifestations of tibiofemoral joint OA. Confident diagnosis of even more advanced PFJOA may be limited in the community setting.  相似文献   

14.
The purpose of this study was to evaluate the effects of variations in quadriceps muscle forces on patellofemoral stress. We created subject-specific finite element models for 21 individuals with chronic patellofemoral pain and 16 pain-free control subjects. We extracted three-dimensional geometries from high resolution magnetic resonance images and registered the geometries to magnetic resonance images from an upright weight bearing squat with the knees flexed at 60°. We estimated quadriceps muscle forces corresponding to 60° knee flexion during a stair climb task from motion analysis and electromyography-driven musculoskeletal modelling. We applied the quadriceps muscle forces to our finite element models and evaluated patellofemoral cartilage stress. We quantified cartilage stress using an energy-based effective stress, a scalar quantity representing the local stress intensity in the tissue. We used probabilistic methods to evaluate the effects of variations in quadriceps muscle forces from five trials of the stair climb task for each subject. Patellofemoral effective stress was most sensitive to variations in forces in the two branches of the vastus medialis muscle. Femur cartilage effective stress was most sensitive to variations in vastus medialis forces in 29/37 (78%) subjects, and patella cartilage effective stress was most sensitive to variations in vastus medialis forces in 21/37 (57%) subjects. Femur cartilage effective stress was more sensitive to variations in vastus medialis longus forces in subjects classified as maltrackers compared to normal tracking subjects (p?=?0.006). This study provides new evidence of the importance of the vastus medialis muscle in the treatment of patellofemoral pain.  相似文献   

15.
The mechanical environment during stair climbing has been associated with patellofemoral pain, but the contribution of loading to this condition is not clearly understood. It was hypothesized that the loading conditions during stair climbing induce higher patellofemoral pressures, a more lateral force distribution on the trochlea and a more lateral shift and tilt of the patella compared to walking at early knee flexion. Optical markers for kinematic measurements were attached to eight cadaveric knees, which were loaded with muscle forces at instances of walking and stair climbing cycles at 12° and 30° knee flexion. Contact mechanics were determined using a pressure sensitive film. At 12° knee flexion, stair climbing loads resulted in higher peak pressure (p=0.012) than walking, more lateral force distribution (p=0.012) and more lateral tilt (p=0.012), whilst mean pressure (p=0.069) and contact area (p=0.123) were not significantly different. At 30° knee flexion, although stair climbing compared to walking loads resulted in significantly higher patellofemoral mean (p=0.012) and peak pressures (p=0.012), contact area (p=0.025), as well as tilt (p=0.017), the medial–lateral force distribution (p=0.674) was not significantly different. No significant differences were observed in patellar shift between walking and stair climbing at either 12° (p=0.093) or 30° (p=0.575) knee flexion. Stair climbing thus leads to more challenging patellofemoral contact mechanics and kinematics than level walking at early knee flexion. The increase in patellofemoral pressure, lateral force distribution and lateral tilt during stair climbing provides a possible biomechanical explanation for the patellofemoral pain frequently experienced during this activity.  相似文献   

16.
Quantifying the mechanical environment at the knee is crucial for developing successful rehabilitation and surgical protocols. Computational models have been developed to complement in vitro studies, but are typically created to represent healthy conditions, and may not be useful in modeling pathology and repair. Thus, the objective of this study was to create finite element (FE) models of the natural knee, including specimen-specific tibiofemoral (TF) and patellofemoral (PF) soft tissue structures, and to evaluate joint mechanics in intact and ACL-deficient conditions. Simulated gait in a whole joint knee simulator was performed on two cadaveric specimens in an intact state and subsequently repeated following ACL resection. Simulated gait was performed using motor-actuated quadriceps, and loads at the hip and ankle. Specimen-specific FE models of these experiments were developed in both intact and ACL-deficient states. Model simulations compared kinematics and loading of the experimental TF and PF joints, with average RMS differences [max] of 3.0° [8.2°] and 2.1° [8.4°] in rotations, and 1.7 [3.0] and 2.5 [5.1] mm in translations, for intact and ACL-deficient states, respectively. The timing of peak quadriceps force during stance and swing phase of gait was accurately replicated within 2° of knee flexion and with an average error of 16.7% across specimens and pathology. Ligament recruitment patterns were unique in each specimen; recruitment variability was likely influenced by variations in ligament attachment locations. ACL resections demonstrated contrasting joint mechanics in the two specimens with altered knee motion shown in one specimen (up to 5 mm anterior tibial translation) while increased TF joint loading was shown in the other (up to 400 N).  相似文献   

17.
A planar model of the knee joint to characterize the knee extensor mechanism   总被引:10,自引:4,他引:6  
A simple planar static model of the knee joint was developed to calculate effective moment arms for the quadriceps muscle. A pathway for the instantaneous center of rotation was chosen that gives realistic orientations of the femur relative to the tibia. Using the model, nonlinear force and moment equilibrium equations were solved at one degree increments for knee flexion angles from 0 (full extension) to 90 degrees, yielding patellar orientation, patellofemoral contact force and patellar ligament force and direction with respect to both the tibial insertion point and the tibiofemoral contact point. The computer-derived results from this two-dimensional model agree with results from more complex models developed previously from experimentally obtained data. Due to our model's simplicity, however, the operation of the patellar mechanism as a lever as well as a spacer is clearly illustrated. Specifically, the thickness of the patella was found to increase the effective moment arm significantly only at flexions below 35 degrees even though the actual moment arm exhibited an increase throughout the flexion range. Lengthening either the patella or the patellar ligament altered the force transmitted from the quadriceps to the patellar ligament, significantly increasing the effective moment arm at flexions greater than 25 degrees. We conclude that the levering action of the patella is an essential mechanism of knee joint operation at moderate to high flexion angles.  相似文献   

18.
From knee extension moments measured with a dynamometer, the quadriceps muscle force, the patellar ligament force and the reaction force in the patellofemoral joint at various knee angles (0-90 degrees) were estimated. The information needed to calculate the combined effect of both patellofemoral and tibiofemoral joint on the mechanical advantage of the muscle was obtained from lateral-view radiographs of autopsy knees. The results show that the smallest quadriceps force (2,000 N) is exerted at maximal extension, and the largest force (8,000 N) at about 75 degrees of flexion. The patellar ligament force reaches a maximum (5,000 N) at 60 degrees. The reaction force in the patellofemoral joint is the smallest (1,000 N) at extension and is of the same values as the muscle force in a range from 75 to 90 degrees. Especially at large flexion angles, the value of the estimated forces is considerably larger (by 100%) than reported in the literature. This difference is attributed to the influence of the patellofemoral joint on the mechanical advantage of the muscle, which has not been taken into account in other studies.  相似文献   

19.
IntroductionMusculoskeletal modeling allows insight into the interaction of muscle force and knee joint kinematics that cannot be measured in the laboratory. However, musculoskeletal models of the lower extremity commonly use simplified representations of the knee that may limit analyses of the interaction between muscle forces and joint kinematics. The goal of this research was to demonstrate how muscle forces alter knee kinematics and consequently muscle moment arms and joint torque in a musculoskeletal model of the lower limb that includes a deformable representation of the knee.MethodsTwo musculoskeletal models of the lower limb including specimen-specific articular geometries and ligament deformability at the knee were built in a finite element framework and calibrated to match mean isometric torque data collected from 12 healthy subjects. Muscle moment arms were compared between simulations of passive knee flexion and maximum isometric knee extension and flexion. In addition, isometric torque results were compared with predictions using simplified knee models in which the deformability of the knee was removed and the kinematics at the joint were prescribed for all degrees of freedom.ResultsPeak isometric torque estimated with a deformable knee representation occurred between 45° and 60° in extension, and 45° in flexion. The maximum isometric flexion torques generated by the models with deformable ligaments were 14.6% and 17.9% larger than those generated by the models with prescribed kinematics; by contrast, the maximum isometric extension torques generated by the models were similar. The change in hamstrings moment arms during isometric flexion was greater than that of the quadriceps during isometric extension (a mean RMS difference of 9.8 mm compared to 2.9 mm, respectively).DiscussionThe large changes in the moment arms of the hamstrings, when activated in a model with deformable ligaments, resulted in changes to flexion torque. When simulating human motion, the inclusion of a deformable joint in a multi-scale musculoskeletal finite element model of the lower limb may preserve the realistic interaction of muscle force with knee kinematics and torque.  相似文献   

20.
Patient selection for lateral retinacular release (LRR) and its efficacy are controversial. Iatrogenic medial subluxation can occur with inappropriate LRR. The aim of this study was to determine the reduction in patellofemoral stability with progressively more extensive LRR. The force required to displace the patella 10 mm medially and laterally in nine cadaveric knees was measured with and without loading of the quadriceps and iliotibial band. The knee was tested intact, then after progressive release beginning proximal to the patella (PR), the mid-level between the proximal and distal limit of the patella (MR) where the fibres are more transverse, then distally till Gerdy's tubercle (DR) and finally the joint capsule (CR). Both medial and lateral stability decreased with progressive releases, larger for the medial. The MR caused a significant reduction of lateral stability between 30° and 90° of knee flexion. There was an 8% reduction in medial stability at 0° flexion with a complete LRR (DR). A comparable reduction in medial stability in the loaded knee at 20° and 30° flexion was obtained with MR alone, with no further reduction after DR. A capsular release caused a further reduction in medial stability at 0° and 20° and this was marked in the unloaded knee. In extension, the main lateral restraint was the joint capsule. At 30° flexion, the transverse fibres were the main contributor to the lateral restraint.  相似文献   

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