A planar model of the knee joint to characterize the knee extensor mechanism

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.     

The biomechanical function of the patellar tendon during in-vivo weight-bearing flexion

Few studies have investigated the function of the patellar tendon in-vivo. This study quantified the three-dimensional (3D) kinematics of the patellar tendon during weight-bearing flexion. Eleven subjects were imaged using magnetic resonance (MR). Sagittal plane images were outlined to create a 3D model of the patella, tibia, and femur and included the attachment sites of the patellar tendon. Each attachment site was divided into central, medial, and lateral thirds. Next, the subjects were imaged using fluoroscopy from two orthogonal directions while performing a single-leg lunge. The models and fluoroscopic images were used to reproduce the motion of the patella, tibia, and femur. The apparent elongation, sagittal plane angle, and coronal plane angle of each third of the patellar tendon were measured from the relative motion of the attachment sites. All three portions of the patellar tendon deformed similarly with flexion. The length of the patellar tendon significantly from full extension to 30 degrees . From 30 degrees -110 degrees , no significant change in the length of the patellar tendon was observed. The patellar tendon was oriented anteriorly at flexion angles less than 60 degrees and posteriorly thereafter. From full extension to 60 degrees , the medial orientation of the patellar tendon decreased significantly with flexion. These data may have important implications for anterior cruciate ligament reconstruction using patellar tendon autografts and for the design of rehabilitation regimens for patients of patellar tendon repair.     

The 3D patellar tendon moment arm: quantified in vivo during volitional activity

The patellar tendon moment arm is a critical quantity in that it defines the quadriceps ability to generate a moment on the tibia. Thus, the primary purpose of this study was to establish the first in vivo three-dimensional measures of the patellar tendon moment arm, measured non-invasively and in vivo during dynamic activity in a large normative population (n=34) using a dynamic MRI technique (fast-PC MRI). The magnitude of the moment arm was defined as the shortest distance between the finite helical axis and the patellar tendon line of action. Using these data, the hypothesis that the patellar tendon moment arm is independent of gender was tested. In general, the moment arm increased from 20 to 50 mm during knee extension. There were significant differences (P<0.05) in the moment arm between gender, but these differences were eliminated when the moment arm was scaled by the femoral epicondylar width. This study took a large step forward towards the ultimate goal of defining how pathology may alter joint dynamics through alteration in moment arms by establishing the first in vivo normative data base for the patellar tendon moment arm using non-invasive measures during volitional activity in a relatively large population (n=34). The fact that the scaled moment arm was independent of gender may lend insights into impairments that tend to be gender specific, such as patellar maltracking. The next steps will be to quantify the patellar tendon moment arm in populations with specific pathologies.     

The coupled motion of the femur and patella during in vivo weightbearing knee flexion

The movement of the knee joint consists of a coupled motion between the tibiofemoral and patellofemoral articulations. This study measured the six degrees-of-freedom kinematics of the tibia, femur, and patella using dual-orthogonal fluoroscopy and magnetic resonance imaging. Ten normal knees from ten living subjects were investigated during weightbearing flexion from full extension to maximum flexion. The femoral and the patellar motions were measured relative to the tibia. The femur externally rotated by 12.9 deg and the patella tilted laterally by 16.3 deg during the full range of knee flexion. Knee flexion was strongly correlated with patellar flexion (R(2)=0.91), posterior femoral translation was strongly correlated to the posterior patellar translation (R(2)=0.87), and internal-external rotation of the femur was correlated to patellar tilt (R(2)=0.73) and medial-lateral patellar translation (R(2)=0.63). These data quantitatively indicate a kinematic coupling between the tibia, femur, and patella, and provide base line information on normal knee joint kinematics throughout the full range of weightbearing flexion. The data also suggest that the kinematic coupling of tibia, femur, and patella should be considered when investigating patellar pathologies and when developing surgical techniques to treat knee joint diseases.     

The orientation of the distal part of the quadriceps femoris muscle as a function of the knee flexion-extension angle

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.     

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.     

In vivo assessment of the interaction of patellar tendon tibial shaft angle and anterior cruciate ligament elongation during flexion

A potential cause of non-contact anterior cruciate ligament (ACL) injury is landing on an extended knee. In line with this hypothesis, studies have shown that the ACL is elongated with decreasing knee flexion angle. Furthermore, at low flexion angles the patellar tendon is oriented to increase the anterior shear component of force acting on the tibia. This indicates that knee extension represents a position in which the ACL is taut, and thus may have an increased propensity for injury, particularly in the presence of excessive force acting via the patellar tendon. However, there is very little in vivo data to describe how patellar tendon orientation and ACL elongation interact during flexion. Therefore, this study measured the patellar tendon tibial shaft angle (indicative of the relative magnitude of the shear component of force acting via the patellar tendon) and ACL length in vivo as subjects performed a quasi-static lunge at varying knee flexion angles. Spearman rho rank correlations within each individual revealed that flexion angles were inversely correlated to both ACL length (rho = −0.94 ± 0.07, mean ± standard deviation, p < 0.05) and patellar tendon tibial shaft angle (rho = −0.99 ± 0.01, p < 0.05). These findings indicate that when the knee is extended, the ACL is both elongated and the patellar tendon tibial shaft angle is increased, resulting in a relative increase in anterior shear force on the tibia acting via the patellar tendon. Therefore, these data support the hypothesis that landing with the knee in extension is a high risk scenario for ACL injury.     

Orientation of tendons in vivo with active and passive knee muscles

Tendon orientations in knee models are often taken from cadaver studies. The aim of this study was to investigate the effect of muscle activation on tendon orientation in vivo. Magnetic resonance imaging (MRI) images of the knee were made during relaxation and isometric knee extensions and flexions with 0 degrees , 15 degrees and 30 degrees of knee joint flexion. For six tendons, the orientation angles in sagittal and frontal plane were calculated. In the sagittal plane, muscle activation pulled the patellar tendon to a more vertical orientation and the semitendinosus and sartorius tendons to a more posterior orientation. In the frontal plane, the semitendinosus had a less lateral orientation, the biceps femoris a more medial orientation and the patellar tendon less medial orientation in loaded compared to unloaded conditions. The knee joint angle also influenced the tendon orientations. In the sagittal plane, the patellar tendon had a more anterior orientation near full extension and the biceps femoris had an anterior orientation with 0 degrees and 15 degrees flexions and neutral with 30 degrees flexions. Within 0 degrees to 30 degrees of flexion, the biceps femoris cannot produce a posterior shear force and the anterior angle of the patellar tendon is always larger than the hamstring tendons. Therefore, co-contraction of the hamstring and quadriceps is unlikely to reduce anterior shear forces in knee angles up to 30 degrees . Finally, inter-individual variation in tendon angles was large. This suggests that the amount of shear force produced and the potential to counteract shear forces by co-contraction is subject-specific.     

A three-dimensional anatomical model of the human patello-femoral joint,for the determination of patello-femoral motions and contact characteristics

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.     

Influence of patella alta on knee extensor mechanics

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.     

In vivo tracking of the human patella using cine phase contrast magnetic resonance imaging

Improper patellar tracking is often considered to be the cause of patellar-femoral pain. Unfortunately, our knowledge of patellar-femoral-tibial (knee) joint kinematics is severely limited due to a lack of three-dimensional, noninvasive, in vivo measurement techniques. This study presents the first large-scale, dynamic, three-dimensional, noninvasive, in vivo study of nonimpaired knee joint kinematics during volitional leg extensions. Cine-phase contrast magnetic resonance imaging was used to measure the velocity profiles of the patella, femur, and tibia in 18 unimpaired knees during leg extensions, resisted by a 34 N weight. Bone displacements were calculated through integration and then converted into three-dimensional orientation angles. We found that the patella displaced laterally, superiorly, and anteriorly as the knee extended. Further, patellar flexion lagged knee flexion, patellar tilt was variable, and patellar rotation was fairly constant throughout extension.     

In vivo tracking of the human patella.

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.     

A Three-Dimensional Musculoskeletal Model of the Human Knee Joint. Part 2: Analysis of Ligament Function

A three-dimensional model of the knee is used to study ligament function during anterior-posterior (a-p) draw, axial rotation, and isometric contractions of the extensor and flexor muscles. The geometry of the model bones is based on cadaver data. The contacting surfaces of the femur and tibia are modeled as deformable; those of the femur and patella are assumed to be rigid. Twelve elastic elements are used to describe the geometry and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by thirteen musculotendinous units, each unit represented as a three-element muscle in series with tendon. The calculations show that the forces applied during a-p draw are substantially different from those applied by the muscles during activity. Principles of knee-ligament function based on the results of in vitro experiments may therefore be overstated. Knee-ligament forces during straight a-p draw are determined solely by the changing geometry of the ligaments relative to the bones: ACL force decreases with increasing flexion during anterior draw because the angle between the ACL and the tibial plateau decreases as knee flexion increases; PCL force increases with increasing flexion during posterior draw because the angle between the PCL and the tibial plateau increases. The pattern of ligament loading during activity is governed by the geometry of the muscles spanning the knee: the resultant force in the ACL during isometric knee extension is determined mainly by the changing orientation of the patellar tendon relative to the tibia in the sagittal plane; the resultant force in the PCL during isometric knee flexion is dominated by the angle at which the hamstrings meet the tibia in the sagittal plane.     

A Three-Dimensional Musculoskeletal Model of the Human Knee Joint. Part 2: Analysis of Ligament Function

A three-dimensional model of the knee is used to study ligament function during anterior-posterior (a-p) draw, axial rotation, and isometric contractions of the extensor and flexor muscles. The geometry of the model bones is based on cadaver data. The contacting surfaces of the femur and tibia are modeled as deformable; those of the femur and patella are assumed to be rigid. Twelve elastic elements are used to describe the geometry and mechanical properties of the cruciate ligaments, the collateral ligaments, and the posterior capsule. The model is actuated by thirteen musculotendinous units, each unit represented as a three-element muscle in series with tendon. The calculations show that the forces applied during a-p draw are substantially different from those applied by the muscles during activity. Principles of knee-ligament function based on the results of in vitro experiments may therefore be overstated. Knee-ligament forces during straight a-p draw are determined solely by the changing geometry of the ligaments relative to the bones: ACL force decreases with increasing flexion during anterior draw because the angle between the ACL and the tibial plateau decreases as knee flexion increases; PCL force increases with increasing flexion during posterior draw because the angle between the PCL and the tibial plateau increases. The pattern of ligament loading during activity is governed by the geometry of the muscles spanning the knee: the resultant force in the ACL during isometric knee extension is determined mainly by the changing orientation of the patellar tendon relative to the tibia in the sagittal plane; the resultant force in the PCL during isometric knee flexion is dominated by the angle at which the hamstrings meet the tibia in the sagittal plane.     

Influence of patellar position on the knee extensor mechanism in normal and crouched walking

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.     

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.     

A detailed and validated three dimensional dynamic model of the patellofemoral joint

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.     

Are hamstrings activated to counteract shear forces during isometric knee extension efforts in healthy subjects?

The hamstring muscles have the potential to counteract anterior shear forces at the knee joint by co-contracting during knee extension efforts. Such a muscle recruitment pattern might protect the anterior cruciate ligament (ACL) by reducing its strain. In this study we investigated to what extent co-activation of the knee flexors during extension efforts is compatible with the hypothesis that this co-activation serves to counteract anterior tibial shear forces during isometric knee extension efforts in healthy subjects. To this aim, it is investigated whether co-activation varies with the required knee extension moment, with the knee joint angle, and with the position of the external flexing force relative to the knee joint. With unaltered moment and muscle activation, distal positioning of the flexing force on the tibia causes higher resultant (muscular plus external) forward shear forces at the knee as compared to proximal positioning. In ten subjects, knee flexor and extensor EMG was measured during a quasi-isometric positioning task for a range (5-50 degrees) of knee flexion angles. It was found that the co-activation of the knee flexors increased with the extension moment, but this increase was less than proportional (p<0.001). The extension moment increased 2.7 to 3.4 times, whereas the activation of Biceps Femoris and Semitendinosus increased only a factor 1.3 to 2.0 (joint angle dependent). Furthermore, a strong increase in co-activation was seen near full extension of the knee joint. The position of the external extension load on the tibia did not affect the level of co-contraction. It is argued that these results do not suggest a recruitment pattern that is directed at reduction of anterior shear forces in the knee joint during sub-maximal isometric knee extension efforts in healthy subjects.     

In vivo determination of normal and anterior cruciate ligament-deficient knee kinematics

The objective of the current study was to use fluoroscopy to accurately determine the three-dimensional (3D), in vivo, weight-bearing kinematics of 10 normal and five anterior cruciate ligament deficient (ACLD) knees. Patient-specific bone models were derived from computed tomography (CT) data. 3D computer bone models of each subject's femur, tibia, and fibula were recreated from the CT 3D bone density data. Using a model-based 3D-to-2D imaging technique registered CT images were precisely fit onto fluoroscopic images, the full six degrees of freedom motion of the bones was measured from the images. The computer-generated 3D models of each subject's femur and tibia were precisely registered to the 2D digital fluoroscopic images using an optimization algorithm that automatically adjusts the pose of the model at various flexion/extension angles. Each subject performed a weight-bearing deep knee bend while under dynamic fluoroscopic surveillance. All 10 normal knees experienced posterior femoral translation of the lateral condyle and minimal change in position of the medial condyle with progressive knee flexion. The average amount of posterior femoral translation of the lateral condyle was 21.07 mm, whereas the average medial condyle translation was 1.94 mm, in the posterior direction. In contrast, all five ACLD knees experienced considerable change in the position of the medial condyle. The average amount of posterior femoral translation of the lateral condyle was 17.00 mm, while the medial condyle translation was 4.65 mm, in the posterior direction. In addition, the helical axis of motion was determined between maximum flexion and extension. A considerable difference was found between the center of rotation locations of the normal and ACLD subjects, with ACLD subjects exhibiting substantially higher variance in kinematic patterns.     

In vivo determination of the Achilles tendon moment arm in three-dimensions

Two-dimensional methods have been applied to determine the Achilles tendon moment arm in previous studies, although the talocrural joint rotates in three-dimension. The purpose of this study was to develop a method for determining the Achilles tendon moment arm in three-dimensions (3DMA). A series of sagittal ankle images were obtained at ankle positions of -20°, -10° (dorsiflexed position), 0° (neutral position), +10°, +20°, and +30° (plantarflexed position). The talocrural joint axis was determined as the finite helical axis of the ankle joint over 20° of displacement, and the 3DMA was determined as the shortest distance from the talocrural joint axis to the line of action of the Achilles tendon force. The corresponding 2DMA was determined with the center of rotation method using the images captured on the sagittal plane passing through the mid-point of the medio-lateral width of the tibia. The 3DMA ranged from 35 to 41 mm across various ankle positions and was, on average, 11 mm smaller than 2DMA. The difference between the two measures was attributable primarily to the deviations of the talocrural joint axis from the anatomical medio-lateral direction. The deviations on the coronal plane (21.4±20.7°) and on the transverse planes (14.8±22.6°) accounted for the errors of 1.3 mm and 3.0 mm, respectively. In addition, selecting either a medially or laterally misaligned sagittal-plane image for determining the 2DMA gave rise to error by 3.5 mm. The remaining difference was accounted for by the random measurement error.