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1.
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   

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.
Three orthogonal components of the tibiofemoral and patellofemoral forces were measured simultaneously for knees with intact cruciate ligaments (nine knees), following anterior cruciate ligament resection (six knees), and subsequent posterior cruciate ligament resection (six knees). The knees were loaded using an experimental protocol that modeled static double-leg squat. The mean compressive tibial force increased with flexion angle. The mean anteroposterior tibial shear force acted posteriorly on the tibia below 50 deg flexion and anteriorly above 55 deg. Mediolateral shear forces were low compared to the other force components and tended to be directed medially on both the patella and tibia. The mean value of the ratio of the resultant tibial force divided by the quadriceps force decreased with increasing flexion angle and was between 0.6 and 0.7 above 70 deg flexion. The mean value of the ratio of the resultant tibiofemoral contact force divided by the resultant patellofemoral contact force decreased with increasing flexion and was between 0.8 and 1.0 above 55 deg flexion. Cruciate ligament resection resulted in no significant changes in the patellar contact forces. Following resection of the anterior cruciate ligament, the tibial anteroposterior shear force was directed anteriorly over all flexion angles tested. Subsequent resection of the posterior cruciate ligament resulted in an approximately 10 percent increase in the quadriceps tendon and tibial compressive force.  相似文献   

4.
Lateral view radiographs of ten autopsy knees were used to determine the orientation of the patellar ligament, patella and quadriceps tendon relative to tibia and femur at different flexion-extension angles (0-120 degrees) of the knee. The results show a linear relationship between the angle of flexion and the movement of the patellar ligament relative to the tibia and of the movement of the patella relative to tibia and femur. There is a non-linear relationship between angle of flexion and the movement of the quadriceps tendon relative to the patellar ligament, patella and femur. The angular changes between patella and patellar ligament are negligible. The complicated movements of the distal part of the quadriceps femoris muscle may significantly influence biomechanical parameters such as the forces acting at the patella and tibial tuberosity.  相似文献   

5.
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   

6.
The influence of both insertion and strength/elasticity of each extensor in patellofemoral disorders was fully investigated through a two-dimensional mathematical model analysis in a horizontal plane, in combination with experimental design theory for analyzing mutually correlated influences. In the model, patellofemoral joint profiles projected on a horizontal plane have been expressed as spline functions. Each muscle of the quadriceps has been represented as a string pulled by the respective force; fascias and tendons have been represented by springs. Nonlinear equations have been constructed to represent the forces involved, and then solved by numerical iteration. An analysis of variance was performed on the data derived from a series of simulations, obtaining the following results. The strength of most extensors has been shown to have an influence on the increase in lateral contact force but not patellar translation. The tibial tubercle position has significant influence on both patellar translation and lateral contact force. The quadriceps' insertion on the femur has no influence on patellar translation. The insertion of each extensor on the patella has been shown to have a strong effect on patellar translation but not on contact force.  相似文献   

7.
The object of this study is to develop a three-dimensional mathematical model of the patello-femoral joint, which is modelled as two rigid bodies representing a moving patella and a fixed femur. Two-point contact was assumed between the femur and patella at the medial and lateral sides and in the analysis, the femoral and patellar articular surfaces were mathematically represented using Coons' bicubic surface patches. Model equations include six equilibrium equations and eleven constraints: six contact conditions, four geometric compatibility conditions, and the condition of a rigid patellar ligament; the model required the solution of a system of 17 nonlinear equations in 17 unknowns, its response describing the six-degress-of-freedom patellar motions and the forces acting on the patella. Patellar motions are described by six motion parameters representing the translations and rotations of the patella with respect to the femur. The forces acting on the patella include the medial and lateral component of patello-femoral contact and the patellar ligament force, all of which were represented as ratios to the quadriceps tendon force. The model response also includes the locations of the medial and lateral contact points on the femur and the patella. A graphical display of its response was produced in order to visualize better the motion of the components of the extensor mechanism.Model calculations show good agreement with experimental results available from the literature. The patella was found to move distally and posteriorly on the femoral condyles as the knee was flexed from full extension. Results indicate that the relative orientation of the patellar ligament with respect to the patella remains unchanged during this motion. The model also predicts a patellar flexion which always lagged knee flexion.Our calculations show that as the angle of knee flexion increased, the lateral contact point moved distally on the femur without moving significantly either medially or laterally. The medial contact point also moved distally on the femur but moved medially from full extension to about 40° of knee flexion, then laterally as the knee flexion angle increased. The lateral contact point on the patella did not change significantly in the medial and lateral direction as the knee was flexed; however, this point moved proximally toward the basis of the patella with knee flexion. The medial contact point also moved proximally on the patella with knee flexion, and in a similar manner the medial contact point on the patella moved distally with flexion from full extension to about 40° of flexion. However, as the angle of flexion increased, the medial contact point did not move significantly in the medial-lateral direction.Model calculations also show that during the simulated knee extension exercise, the ratio of the force in the patellar ligament to the force in the quadriceps tendon remains almost unchanged for the first 30° of knee flexion, then decreases as the angle of knee flexion increases. Furthermore, model results show that the lateral component of the patello-femoral contact force is always greater than the medial component, both components increasing with knee flexion.  相似文献   

8.
A detailed 3D anatomical model of the patellofemoral joint was developed to study the tracking, force, contact and stability characteristics of the joint. The quadriceps was considered to include six components represented by 15 force vectors. The patellar tendon was modeled using four bundles of viscoelastic tensile elements. Each of the lateral and medial retinaculum was modeled by a three-bundle nonlinear spring. The femur and patella were considered as rigid bodies with their articular cartilage layers represented by an isotropic viscoelastic material. The geometrical and tracking data needed for model simulation, as well as validation of its results, were obtained from an in vivo experiment, involving MR imaging of a normal knee while performing isometric leg press against a constant 140 N force. The model was formulated within the framework of a rigid body spring model and solved using forth-order Runge-Kutta, for knee flexion angles between zero and 50 degrees. Results indicated a good agreement between the model predictions for patellar tracking and the experimental results with RMS deviations of about 2 mm for translations (less than 0.7 mm for patellar mediolateral shift), and 4 degrees for rotations (less than 3 degrees for patellar tilt). The contact pattern predicted by the model was also consistent with the results of the experiment and the literature. The joint contact force increased linearly with progressive knee flexion from 80 N to 210 N. The medial retinaculum experienced a peak force of 18 N at full extension that decreased with knee flexion and disappeared entirely at 20 degrees flexion. Analysis of the patellar time response to the quadriceps contraction suggested that the muscle activation most affected the patellar shift and tilt. These results are consistent with the recent observations in the literature concerning the significance of retinaculum and quadriceps in the patellar stability.  相似文献   

9.
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   

10.
Three-dimensional mathematical model analysis of the patellofemoral joint   总被引:1,自引:0,他引:1  
This paper is concerned with a mathematical model analysis of the patellofemoral joint in the human knee, taking into account the articular surface geometry and mechanical properties of the ligament. It was made by the application of a computer-aided design theory (previously studied) and it was possible to express the articular surface geometries in a mathematical formulation and hence elucidate the joint movement mechanics. This method was then applied to a three-dimensional geometrical model of the patellofemoral joint. For the modelling of tendofemoral contact at large angles of knee flexion, the geodestic line theory was adopted. Applying the Newton-Raphson method and the Runge-Kutta Gil method to the model, variables such as patellar attitudes, patellofemoral contact force and tensile force of the patellar ligament for various knee flexion angles were computed. Applying the Hertzian elastic theory, contact stress was also computed. These results showed good agreement with the previously reported experimental results. As an application for the model, some parameter analyses were performed in terms of the contact stress variations and compared with those of the normal knee. The simulation results indicated that both the Q-angle increase and decrease increased contact stress, the patella alta showed undulating variations of stress while the patella infera showed little change of stress, and the tibial tuberositas elevation showed 20-30% reduction of stress.  相似文献   

11.
The ability to climb a steep step or rise from a low chair after total knee replacement may be enhanced if the required force in the quadriceps muscle is reduced. This can potentially be achieved if the total knee produces a large lever arm measured from the femoral-tibial contact point to the patellar ligament. A reduced quadriceps force would also reduce the patello-femoral force and the femoral-tibial contact force. The contact point location is likely to be a function of the geometry of the femoral and tibial components in the sagittal plane, including the relative distal and posterior radii of the femoral profile, the location of the bottom-of-the-dish of the tibial surface, the radius of the tibial surface, and the presence or absence of the posterior cruciate ligament. A three-dimensional model of the knee was developed including the quadriceps and various ligaments. In the study, the motion was confined to flexion extension and displacement in the sagittal plane. The quadriceps was assumed to be the only muscle acting. A standard software package (Pro/Mechanica) was used for the analysis. For a femoral component with a smaller distal radius, there was 12% reduction in the quadriceps muscle force and up to 11% reduction in the patello-femoral force from about 100 up to 60 degrees flexion. However, apart from that, there were less than 10% differences in all the forces as a function of all of the design variables studied. This was attributed to the relatively small changes in the lever arm of the patella tendon, since the tendon moves in an anterior-posterior direction along with the femur. An additional factor explaining the results was the change in the anterior-posterior contact point as controlled by the forces in the patella tendon and in the soft tissues. The results imply that for a standard condylar replacement knee, the muscle and contact forces are not greatly affected by the geometrical design variables.  相似文献   

12.
Patellofemoral joint forces   总被引:1,自引:0,他引:1  
In this review of patellofemoral joint forces as they might apply to implant design, methodologies for estimating forces on the patella and estimates of the forces, as reported in the literature, are summarized. Two methodologies exist for studying joint loads; one that measures kinematics in-vivo and uses analysis to estimate the joint loads and another that measures ground reaction forces and uses analysis to estimate the joint loads. In both these analyses many assumptions are required with varying degrees of uncertainty; here, those assumptions are examined with data from the published literature. The topics covered include: relationships between quadriceps forces and patellofemoral forces or patella ligament forces, relationships between knee joint moments and quadriceps forces, knee joint moments in various gaits, relationships between patellofemoral forces and lateral subluxation forces, and relationships between patella forces and inferior-superior forces. In many cases, there is little data on patella forces during normal activities, in other cases, there are some discrepancies in reported patella forces, i.e. during squat.  相似文献   

13.
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   

14.
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   

15.
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   

16.
The knowledge of normal patellar tracking is essential for understanding the knee joint function and for diagnosis of patellar instabilities. This paper investigated the patellar tracking and patellofemoral joint contact locations during a stair ascending activity using a validated dual-fluoroscopic imaging system. The results showed that the patellar flexion angle decreased from 41.9° to 7.5° with knee extension during stair ascending. During first 80% of the activity, the patella shifted medially about 3.9mm and then slightly shifted laterally during the last 20% of the ascending activity. Anterior translation of 13mm of the patella was measured at the early 80% of the activity and the patella slightly moved posteriorly by about 2mm at the last 20% of the activity. The path of cartilage contact points was slightly lateral on the cartilage surfaces of patella and femur. On the patellar cartilage surface, the cartilage contact locations were about 2mm laterally from heel strike to 60% of the stair ascending activity and moved laterally and reached 5.3mm at full extension. However, the cartilage contact locations were relatively constant on the femoral cartilage surface (~5mm lateral). The patellar tracking pattern was consistent with the patellofemoral cartilage contact location pattern. These data could provide baseline knowledge for understanding of normal physiology of the patellofemoral joint and can be used as a reference for clinical evaluation of patellofemoral disorders.  相似文献   

17.
In vivo tracking of the human patella.   总被引:3,自引:0,他引:3  
The purpose of this study was to describe the dynamic, in vivo, three-dimensional tracking pattern of the patella for one normal male subject. Intracortical pins were inserted into the patella, tibia, and femur. The subject performed seated and squatting knee flexion/extension, and maximum voluntary quadriceps contractions. In addition, the vastus medialis oblique was subjected to maximal electrical stimulation. Motions of the markers attached to the intracortical pins were analyzed using an automated video system. Patellar and tibial motions were determined relative to a femoral reference system. While the tibia flexed 50 degrees from full extension (seated condition), the patella flexed 30.3 degrees, tilted laterally 10.3 degrees, and shifted laterally 8.6 mm. In general, these results show qualitative agreement with the data collected from cadaveric specimens [van Kampen and Huiskes, J. orthop. Res. 8, 372-382 (1990)]. The differences present may reflect different passive constraints to patellar motions, and different relative loading of the individual quadriceps components, in our study compared to the cadaveric study. Only small differences were found between patellar motions in the seated and squatting conditions. Differences in patellar displacements produced by (1) maximal electrical stimulation of the vastus medialis oblique, and (2) maximum voluntary quadriceps contraction, at 30 degrees knee flexion and full extension, may reflect the dominant influence of passive constraints, and the vastus lateralis, on normal patellar motions. Further in vivo study of patellar tracking seems warranted to evaluate surgical and conservative interventions for patellofemoral disorders.  相似文献   

18.
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   

19.
Patella alta is common in cerebral palsy, especially in patients with crouch gait. Correction of patella alta has been advocated in the treatment of crouch, however the appropriate degree of correction and the implications for knee extensor function remain unclear. Therefore, the goal of this study was to assess the impact of patellar position on quadriceps and patellar tendon forces during normal and crouch gait. To this end, a lower extremity musculoskeletal model with a novel 12 degree of freedom knee joint was used to simulate normal gait in a healthy child, as well as mild (23 deg min knee flexion in stance), moderate (41 deg), and severe (67 deg) crouch gait in three children with cerebral palsy. The simulations revealed that quadriceps and patellar tendon forces increase dramatically with crouch, and are modulated by patellar position. For example with a normal patellar tendon position, peak patellar tendon forces were 0.7 times body weight in normal walking, but reached 2.2, 3.2 and 5.4 times body weight in mild, moderate and severe crouch. Moderate patella alta acted to reduce quadriceps and patellar tendon loads in crouch gait, due to an enhancement of the patellar tendon moment arms with alta in a flexed knee. In contrast, patella baja reduced the patellar tendon moment arm in a flexed knee and thus induced an increase in the patellar tendon loads needed to walk in crouch. Functionally, these results suggest that patella baja could also compromise knee extensor function for other flexed knee activities such as chair rise and stair climbing. The findings are important to consider when using surgical approaches for correcting patella alta in children who exhibit crouch gait patterns.  相似文献   

20.
As knee flexion increases, so do tendofemoral and patellofemoral compression forces. Three cases of long-standing uncorrected flexion contractures of the knees are presented that resulted in marked erosion of the femoral trochlea, patella baja, and remodeled patellar articular surfaces likely reflecting increased angles of flexion. It is probable that the deep femoral grooves are the result of adaptation under high-level persistent contact loads from the quadriceps tendon. These examples expand our knowledge of bone remodeling and offer information of potential use in studying ancient skeletal samples.  相似文献   

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