Coupled motions under compressive load in intact and ACL-deficient knees: a cadaveric study

Knowledge of the coupled motions, which develop under compressive loading of the knee, is useful to determine which degrees of freedom should be included in the study of tibiofemoral contact and also to understand the role of the anterior cruciate ligament (ACL) in coupled motions. The objectives of this study were to measure the coupled motions of the intact knee and ACL-deficient knee under compression and to compare the coupled motions of the ACL-deficient knee with those of the intact knee. Ten intact cadaveric knees were tested by applying a 1600 N compressive load and measuring coupled internal-external and varus-valgus rotations and anterior-posterior and medial-lateral translations at 0 deg, 15 deg, and 30 deg of flexion. Compressive loads were applied along the functional axis of axial rotation, which coincides approximately with the mechanical axis of the tibia. The ACL was excised and the knees were tested again. In the intact knee, the peak coupled motions were 3.8 deg internal rotation at 0 deg flexion changing to -4.9 deg external rotation at 30 deg of flexion, 1.4 deg of varus rotation at 0 deg flexion changing to -1.9 deg valgus rotation at 30 deg of flexion, 1.4 mm of medial translation at 0 deg flexion increasing to 2.3 mm at 30 deg of flexion, and 5.3 mm of anterior translation at 0 deg flexion increasing to 10.2 mm at 30 deg of flexion. All changes in the peak coupled motions from 0 deg to 30 deg flexion were statistically significant (p<0.05). In ACL-deficient knees, there was a strong trend (marginally not significant, p=0.07) toward greater anterior translation (12.7 mm) than that in intact knees (8.0 mm), whereas coupled motions in the other degrees of freedom were comparable. Because the coupled motions in all four degrees of freedom in the intact knee and ACL-deficient knee are sufficiently large to substantially affect the tibiofemoral contact area, all degrees of freedom should be included when either developing mathematical models or designing mechanical testing equipment for study of tibiofemoral contact. The increase in coupled anterior translation in ACL-deficient knees indicates the important role played by the ACL in constraining anterior translation during compressive loading.     

In vitro forces in the normal and cruciate-deficient knee during simulated squatting motion

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.     

Optimal replacement of the cruciate ligaments from the functional-anatomical point of view

By means of a combined technique of dissection and radiography, the function of cruciate ligament fibers was analyzed for motions in the sagittal plane, and different functional fiber bundles were reconstructed in cadaver knees. In order to grant permanent stability, crucial replacement must be concentrated on the reconstruction of the constantly taut 'guiding bundle' of each cruciate ligament. The femoral attachment point of each guiding bundle was found to be in a constant position within the femoral attachment of the respective cruciate ligament. The femoral attachment areas of different functional fibers are also defined geometrically, and the consequences of improper guiding bundle replacement are discussed.     

Kinematic motion of the anterior cruciate ligament deficient knee during functionally high and low demanding tasks

The purpose of this study was to determine whether mechanical adaptations were present in patients with anterior cruciate ligament (ACL)-deficient knees during high-demand activities. Twenty-two subjects with unilateral ACL deficiency (11 males and 11 females, 19.6 months after injury) performed five different activities at a comfortable speed (level walking, ascending and descending steps, jogging, jogging to a 90-degree side cutting toward the opposite direction of the tested side). Three-dimensional knee kinematics for the ACL-deficient knees and uninjured contralateral knees were evaluated using the Point Cluster Technique. There was no significant difference in knee flexion angle, but an offset toward the knee in less valgus and more external tibial rotation was observed in the ACL-deficient knee. The tendency was more obvious in high demand motions, and a significant difference was clearly observed in the side cutting motions. These motion patterns, with the knee in less valgus and more external tibial rotation, are proposed to be an adaptive movement to avoid pivot shift dynamically, and reveal evidence in support of a dynamic adaptive motion occurring in ACL-deficient knees.     

Can altered neuromuscular coordination restore soft tissue loading patterns in anterior cruciate ligament and menisci deficient knees during walking?

Injuries to the anterior cruciate ligament (ACL) and menisci commonly lead to early onset osteoarthritis. Treatments that can restore normative cartilage loading patterns may mitigate the risk of osteoarthritis, though it is unclear whether such a goal is achievable through conservative rehabilitation. We used musculoskeletal simulation to predict cartilage and ligament loading patterns during walking in intact, ACL deficient, menisci deficient, and ACL-menisci deficient knees. Stochastic simulations with varying coordination strategies were then used to test whether neuromuscular control could be modulated to restore normative knee mechanics in the pathologic conditions. During early stance, a 3 mm increase in anterior tibial translation was predicted in the ACL deficient knee. Mean cartilage contact pressure increased by 18% and 24% on the medial and lateral plateaus, respectively, in the menisci deficient knee. Variations in neuromuscular coordination were insufficient to restore normative cartilage contact patterns in either the ACL or menisci deficient knees. Elevated cartilage contact pressures in the pathologic knees were observed in regions where cartilage wear patterns have previously been reported. These results suggest that altered cartilage tissue loading during gait may contribute to region-specific degeneration patterns, and that varying neuromuscular coordination in isolation is unlikely to restore normative knee mechanics.     

Loss of ACL function leads to alterations in tibial plateau common dynamic contact stress profiles

It has been suggested that the repetitive nature of altered joint tissue loading which occurs after anterior cruciate ligament (ACL) rupture can contribute to the development of osteoarthritis (OA). However, changes in dynamic knee joint contact stresses after ACL rupture have not been quantified for activities of daily living. Our objective was to characterize changes in dynamic contact stress profiles that occur across the tibial plateau immediately after ACL transection. By subjecting sensor-augmented cadaveric knees to simulated gait, and analyzing the resulting contact stress profiles using a normalized cross-correlation algorithm, we tested the hypothesis that common changes in dynamic contact stress profiles exist after ACL injury. Three common profiles were identified in intact knees, occurring on the: (I) posterior lateral plateau, (II) posterior medial plateau, and (III) central region of the medial plateau. In ACL-transected knees, the magnitude and shape of the common dynamic stress profiles did not change, but their locations on the tibial plateau and the number of knees identified for each profile changed. Furthermore, in the ACL transected knees, a unique common contact stress profile was identified in the posterior region of the lateral plateau near the tibial spine. This framework can be used to understand the regional and temporal changes in joint mechanics after injury.     

A mathematical model of the patellofemoral joint

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.     

关节镜下多种移植物联合重建膝关节前、后交叉韧带

目的：评估关节镜下膝关节前交叉韧带（ACL）与后交叉韧带（PCL）同时重建的技术和临床效果。方法：自2003年6月～2009年10月,27例病人（28膝）经MRJ检查及关节镜检查证实ACL和PCL均断裂,其中9膝伴内侧副韧带损伤（MCL）,8膝伴后外侧角损伤（PLC）,5膝伴内侧半月板破裂,4膝伴外侧半月板损伤。27例患者于伤后3～10周在关节镜下行膝关节前、后交叉韧带联合重建。结果：本组术后早期均未发生严重并发症。术后随访12-88个月,平均（42．67±3．34）个月,Lysholm膝关节功能评分为78-93分,平均（86．67±5．21）分。国际膝关节文件编制委员会（mDC）综合评定由术前显著异常（D级）28膝,改进为随访时正常（A级）9膝、接近正常（B级）16膝、异常（C级）3膝。结论：关节镜下膝关节前交叉韧带（ACL）与后交叉韧带（PCL）同时重建创伤小、手术操作精细,术后膝关节功能恢复满意。     

关节镜下多种移植物联合重建膝关节前、后交叉韧带

目的:评估关节镜下膝关节前交叉韧带(ACL)与后交叉韧带(PCL)同时重建的技术和临床效果。方法:自2003年6月～2009年10月,27例病人(28膝)经MRI检查及关节镜检查证实ACL和PCL均断裂,其中9膝伴内侧副韧带损伤(MCL),8膝伴后外侧角损伤(PLC),5膝伴内侧半月板破裂,4膝伴外侧半月板损伤。27例患者于伤后3～10周在关节镜下行膝关节前、后交叉韧带联合重建。结果:本组术后早期均未发生严重并发症。术后随访12～88个月,平均(42.67±3.34)个月,Lysholm膝关节功能评分为78～93分,平均(86.67±5.21)分。国际膝关节文件编制委员会(IKDC)综合评定由术前显著异常(D级)28膝,改进为随访时正常(A级)9膝、接近正常(B级)16膝、异常(C级)3膝。结论:关节镜下膝关节前交叉韧带(ACL)与后交叉韧带(PCL)同时重建创伤小、手术操作精细,术后膝关节功能恢复满意。     

The influence of patellofemoral joint contact geometry on the modeling of three dimensional patellofemoral joint forces

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.     

In vivo patellofemoral forces in high flexion total knee arthroplasty

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.     

Pure passive hyperextension of the human cadaver knee generates simultaneous bicruciate ligament rupture

Knee hyperextension has been described as a mechanism of isolated anterior cruciate ligament (ACL) tears, but clinical and experimental studies have produced contradictory results for the ligament injuries and the injury sequence caused by the hyperextension loading mechanism. The hypothesis of this study was that bicruciate ligament injuries would occur as a result of knee hyperextension by producing high tibio-femoral (TF) compressive forces that would cause anterior translation of the tibia to rupture the ACL, while joint extension would simultaneously induce rupture of the posterior cruciate ligament (PCL). Six human knees were loaded in hyperextension until gross injury, while bending moments and motions were recorded. Pressure sensitive film documented the magnitude and location of TF compressive forces. The peak bending moment at failure was 108?N?m±46?N?m at a total extension angle of 33.6?deg±11?deg. All joints failed by simultaneous ACL and PCL damages at the time of a sudden drop in the bending moment. High compressive forces were measured in the anterior compartments of the knee and likely produced the anterior tibial subluxation, which contributed to excessive tension in the ACL. The injury to the PCL at the same time may have been due to excessive extension of the joint. These data, and the comparisons with previous experimental studies, may help explain the mechanisms of knee ligament injury during hyperextension. Knowledge of forces and constraints that occur clinically could then help diagnose primary and secondary joint injuries following hyperextension of the human knee.     

Effect of ACL deficiency on MCL strains and joint kinematics

The knee joint is partially stabilized by the interaction of multiple ligament structures. This study tested the interdependent functions of the anterior cruciate ligament (ACL) and the medial collateral ligament (MCL) by evaluating the effects of ACL deficiency on local MCL strain while simultaneously measuring joint kinematics under specific loading scenarios. A structural testing machine applied anterior translation and valgus rotation (limits 100 N and 10 N m, respectively) to the tibia of ten human cadaveric knees with the ACL intact or severed. A three-dimensional motion analysis system measured joint kinematics and MCL tissue strain in 18 regions of the superficial MCL. ACL deficiency significantly increased MCL strains by 1.8% (p<0.05) during anterior translation, bringing ligament fibers to strain levels characteristic of microtrauma. In contrast, ACL transection had no effect on MCL strains during valgus rotation (increase of only 0.1%). Therefore, isolated valgus rotation in the ACL-deficient knee was nondetrimental to the MCL. The ACL was also found to promote internal tibial rotation during anterior translation, which in turn decreased strains near the femoral insertion of the MCL. These data advance the basic structure-function understanding of the MCL, and may benefit the treatment of ACL injuries by improving the knowledge of ACL function and clarifying motions that are potentially harmful to secondary stabilizers.     

The influence of ligament modelling strategies on the predictive capability of finite element models of the human knee joint

In finite element (FE) models knee ligaments can represented either by a group of one-dimensional springs, or by three-dimensional continuum elements based on segmentations. Continuum models closer approximate the anatomy, and facilitate ligament wrapping, while spring models are computationally less expensive. The mechanical properties of ligaments can be based on literature, or adjusted specifically for the subject. In the current study we investigated the effect of ligament modelling strategy on the predictive capability of FE models of the human knee joint. The effect of literature-based versus specimen-specific optimized material parameters was evaluated. Experiments were performed on three human cadaver knees, which were modelled in FE models with ligaments represented either using springs, or using continuum representations. In spring representation collateral ligaments were each modelled with three and cruciate ligaments with two single-element bundles. Stiffness parameters and pre-strains were optimized based on laxity tests for both approaches. Validation experiments were conducted to evaluate the outcomes of the FE models.Models (both spring and continuum) with subject-specific properties improved the predicted kinematics and contact outcome parameters. Models incorporating literature-based parameters, and particularly the spring models (with the representations implemented in this study), led to relatively high errors in kinematics and contact pressures. Using a continuum modelling approach resulted in more accurate contact outcome variables than the spring representation with two (cruciate ligaments) and three (collateral ligaments) single-element-bundle representations. However, when the prediction of joint kinematics is of main interest, spring ligament models provide a faster option with acceptable outcome.     

A role for calcitonin gene-related peptide in rabbit knee joint ligament healing

Knee joint ligament healing has been shown to be improved when the torn ligament ends remain in contact, however, the rationale for these effects is unknown. The sensory neuropeptide calcitonin gene related peptide (CGRP) has potent trophic and vasodilatatory properties and as such is thought to be advantageous in wound repair. In ascertaining a role for CGRP in rabbit medial collateral ligament healing, the present study examined changes in CGRP-like immunoreactivity (CGRP-LI) and CGRP-mediated vasomotor responses in gap injured (non-contact), Z-plasty apposed (contact), and sham operated control medial collateral ligaments. At 6 weeks post-trauma, CGRP-LI decreased in the healing zone of gap injured and Z-plasty apposed medial collateral ligaments compared with controls, and non-contact ligament nerve fibres exhibited an abnormal morphology. Topical administration of CGRP (10(-13) to 10(-9) mol) caused a dose-dependent increase in ligament perfusion in each experimental group of knees. The CGRP-mediated vasodilatation associated with gap injured ligaments was not significantly different from controls (P = 0.06), whereas apposed medial collateral ligaments showed an augmented response to the peptide (P < 0.0005). These findings indicate that the beneficial effects of ligament interposition post-trauma may be related to an enhanced responsiveness to CGRP in conjunction with a more typical re-innervation profile. Conversely, the aberrant characteristics of CGRP-LI nerves occurring in gap injured tissue is suggestive of impaired CGRP release which may explain the poor functional recovery associated with these ligaments.     

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.     

Carpal bone kinematics and ligament lengthening studied for the full range of joint movement

Present data on carpal kinematics and carpal ligament behaviour are limited to flexion and deviation movements of the hand. These motions do not represent all the wrist-joint motions which are important for the activities of daily living. The goal of this project was to obtain insight into carpal kinematics and carpal ligament behaviour during motions of the hand covering the full range of motion of the wrist joint.

The carpals and the ligaments of four wrist-joint specimens were provided with radiopaque markers. These joints were subjected to Röntgenstereophotogrammetric experimentation in a large number of hand positions to determine carpal positions and ligament lengths. The movements of the carpal bones were described by means of finite helical axes (FHA).

It was found that the movements of the carpals in the distal row closely resemble those of the hand. Conversely, the motions of the carpals of the proximal row appeared not to be directly proportional to the hand motions and exhibited clear out-of-plane movements. Furthermore, it could be shown that movements of the hand into the ulnodorsal quadrant of the full range of hand motion corresponds to larger helical rotations and translations for most of the carpals than when the hand was moved into any other quadrant. The maximal ligament length changes determined did not exceed the length changes reported for pure flexion and pure deviation movements of the hand.     

Prediction of total knee motion using a three-dimensional computer-graphics model

Twenty-three knees were sectioned, digitized, and standardized to determine the 'average' three-dimensional bony geometry and ligamentous attachments. Data on normal knee motion were obtained from a cadaveric study. An algorithm was written to simulate three-dimensional patella motion. Verification of the knee model was achieved by determining femoro-tibial and patello-femoral contact locations, as well as ligament length patterns, and comparing the results with published data. The criterion for maximum predicted knee motion with a prosthesis in place was the length of the posterior cruciate ligament. Three total knee replacement surfaces were mathematically generated: flat, laxity and conforming. A greater flexion angle was obtained with a flat tibial surface than for the laxity or conforming. Posterior tibial component displacement increased the range of motion, but only slightly. For all tibial surfaces, increased range of motion was achieved with a 10 degrees posterior tilt of the tibial tray. Anterior femoral component displacement increased motion due to reduction in posterior cruciate tension during flexion. The results are applicable to the design and surgical technique of total knee replacement.     

Comparison of kinematics in the healthy and ACL injured knee using MRI

Magnetic Resonance Imaging (MRI) was used to examine the characteristics of abnormal motion in the injured knee by mapping tibiofemoral contact. Eleven healthy subjects and 20 subjects with a unilateral ACL injury performed a leg-press against resistance. MRI scans of both knees at 15 degrees intervals from 0 degrees to 90 degrees of flexion were used to record the tibiofemoral contact pattern. The tibiofemoral contact pattern of the injured knees was more posterior on the tibial plateau than the healthy knees, particularly in the lateral compartment. The tibiofemoral contact pattern of the loaded knees did not differ from the unloaded knees. The difference in the tibiofemoral contact pattern in the ACL injured knee was associated with more severe knee symptoms, irrespective of the passive anterior laxity of the knee.     

Can markers injected into a single-loop anterior cruciate ligament graft define the axes of the tibial and femoral tunnels? A cadaveric study using roentgen stereophotogrammetric analysis

Lengthening of a soft-tissue anterior cruciate ligament (ACL) graft construct over time, which leads to an increase in anterior laxity following ACL reconstruction, can result from relative motions between the graft and fixation devices and between the fixation devices and bone. To determine these relative motions using Roentgen stereophotogrammetry (RSA), it is first necessary to identify the axes of the tibial and femoral tunnels. The purpose of this in vitro study was to determine the error in using markers injected into the portions of a soft-tissue tendon graft enclosed within the tibial and femoral tunnels to define the axes of these tunnels. Markers were injected into the tibia, femur, and graft in six cadaveric legs the knees of which were reconstructed with single-loop tibialis grafts. The axes of the tunnels were defined by marker pairs that were injected into the bones on lines parallel to the walls of the tibial and femoral tunnels (i.e., standard). By using marker pairs injected into the portions of the graft enclosed within the tibial and femoral tunnels and the marker pairs aligned with the tunnel axes, the directions of vectors were determined by using RSA, while a 150 N anterior force was transmitted at the knee. The average and standard deviations of the angle between the two vectors were 5.5+/-3.3 deg. This angle translates into an average error and standard deviation of the error in lengthening quantities (i.e., relative motions along the tunnel axes) at the sites of fixation of (0.6+/-0.8)%. Identifying the axes of the tunnels by using marker pairs in the graft rather than marker pairs in the walls of the tunnels will shorten the surgical procedure by eliminating the specialized tools and time required to insert marker pairs in the tunnel walls and will simplify the data analysis in in vivo studies.