Introduction

The anterior cruciate ligament (ACL) is integral in antero-posterior (AP) and rotational stability and the function of the knee. ACL deficiency (ACL-d) leads to knee instability. Many methods for assessing anterior knee instability have been developed and applied such as KT-1000 and stress radiography, however, it is challenging to quantify rotational instability. In addition, it is still unknown how much AP and rotational instability can be detected in high-demand daily activities, although quantification is partly possible in specific low-demand conditions.

The effects of ACL-d on kinematics and kinetics of the knee have been reported by various methods such as cadaveric study,¹ fluoroscopy,^2,3 and motion capture systems.^4,5 In terms of ACL-d knee kinematics, the lateral femoral condyle is positioned posteriorly, and the screw-home movement seems to be impaired during squatting motions using fluoroscopy and a two-dimension (2D), three-dimension (3D) registration technique.² Concerning kinetics, a significant increase in contact stress was observed in the posterocentral aspect of the medial tibial plateau during gait in a cadaveric study using a sensor device.⁶ Other cadaveric study showed that the in-situ force in the medial collateral ligament (MCL) in ACL-d knees reached approximately two times larger than that in an intact knee.⁷ However, kinematics and kinematics with slightly loose or tight ACL have not been investigated.

During ACL reconstruction surgery, the initial tension applied to the graft is one of the most important factors. In a static cadaver study with various ACL tensions during reconstruction, it was demonstrated that increasing the initial graft tension increased the tibiofemoral compressive forces, caused tibial external rotation, and caused posterior translation of the tibia when compared to the ACL intact knee.⁸ There are a limited number of reports about the influence on kinematics and kinetics by excessive or loose graft tension during various daily activities in motion.⁹

An important analysis tool is the use of computer simulations that include a musculoskeletal model to analyze knee kinematics and kinetics in detail in various loading conditions including high-demand activities.¹⁰ The purposes of this study were to analyze the kinematics and kinetics of normal knee models with loose and tight ACL tension in various activities, and to evaluate the effect of the tension of ACL on knee kinematics and kinetics. Our hypotheses were that AP and rotational instability were observed in ACL slack knees, especially in high-demand activities, and that excessive MCL tension and/or tibiofemoral force were applied in the abnormal ACL tension models.

Materials and methods

A musculoskeletal computer simulation was used to evaluate the effects of ACL tension on kinematics, force of MCL, and contact force. This model provides a dynamic simulation of the knee (LifeMOD/KneeSIM 2010; LifeModeler Inc., San Clemente, CA, USA) including the tibiofemoral contact, ACL, posterior cruciate ligament (PCL), MCL, lateral collateral ligament (LCL), elements of the knee capsule, quadriceps muscle and tendon, patellar tendon, and hamstring muscles (Fig. 1). Study participants provided informed consent, and the study design was approved by the appropriate ethics review boards.

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Fig. 1 The normal knee model with introduction of bone data including the articular surface of the femur, tibia, and patella. Orange line: ligament, red line: hamstrings, red bundle: patellar tendon and quadriceps tendon.

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The origins of the insertion points and the stiffness of the ACL, PCL, MCL, and LCL were determined from the relevant anatomical studies.^11–13 The ACL, MCL, and PCL comprised two bundles in this simulation model. All ligament bundles were modeled as nonlinear springs, with their material properties obtained from a published report.¹⁴ The stiffness coefficients of the ACL (AM bundle), ACL (PL bundle), PCL (AL bundle), PCL (PM bundle), MCL-anterior, MCL-posterior, and LCL were determined as 102, 102, 102, 102, 63, 63, and 59 N/mm, respectively.^13,15,16 The initial strain of each ligament was determined based on the results of previous cadaver studies.^16–18 The medial and lateral meniscus were not included, and deformation of articular cartilage was not considered. in this simulation model due to complex mechanical properties.

Squatting in a weight-bearing deep knee bend (DKB), gait, and stair descent activities were simulated using a musculoskeletal computer simulation. In the testing conditions, vertical forces applied at the hip were programmed to be constant during squatting and in wave patterns during gait and stair descent so that forces up to approximately 4000 N were loaded on the knee joint.¹⁹ The range of motion was 0° extension to 130° flexion, 0° extension to 60° flexion, and 0° extension to 90° flexion in DKB, gait, and stair descent activities, respectively. In DKB and stair descent activities, extension phase was included in each cycle. In the gait activity, the cycle started from heel strike, and stance and swing phases were included. The hip joint was modeled as a revolute joint parallel to the flexion axis of the knee and was allowed to slide vertically but constrained in the mediolateral and anteroposterior directions. The ankle joint was modeled as a combination of several joints that allowed free translation in the medial-lateral direction and free rotation in the flexion, axial, and varus-valgus directions. A closed-loop controller monitored knee flexion and compared it with the prescribed input. In the simulation program, relative positions of the femur and tibia were calculated, and then the AP positions of the medial and lateral condyles relative to the tibia were identified. The AP positions of the medial and lateral condyles were defined as each flexion facet center (FFC). Axial rotation was defined as the line between both FFCs. Anterior direction in the AP position and external rotation of the femur were denoted as positive in the kinematic analysis.

For the validation of the musculoskeletal computer simulation, a kinematic comparison was performed between in-vivo and simulated kinematics of the normal knee. The volunteer was asked to perform a weight-bearing DKB activity under fluoroscopic surveillance. Continuous sagittal radiological images were obtained using a flat-panel detector. Using a previously reported 2D-3D registration technique, the AP positions were determined from a single-perspective fluoroscopic image. The root-mean-square (RMS) errors for the 2D-3D registration technique were within 0.6 mm for in-plane translation, 0.7 mm for out-of-plane translation, and 0.6° for rotation.²⁰ A kinematic comparison between the musculoskeletal computer simulation and the fluoroscopic images was performed. The mean differences between in-vivo and simulated kinematics in the AP position and axial rotation were 1.7 mm for the AP position and 2.5° for rotation, respectively.

Based on the validated intact knee model, two ACL slack models and two ACL tight models were constructed. By changing the length setting for both bundles of the ACL, 2-mm and 4-mm slack models were made by elongating the ACL length by 2-mm and 4-mm, respectively. In addition, 2-mm and 4-mm tight models were made by shortening the ACL length by 2 mm and 4 mm, respectively. The knee kinematics, femorotibial contact forces, and tension of the MCL were computed for five different ACL length models during DKB, gait, and stair descent activities.

Results

The kinematic differences of the AP position were obvious at the lateral side for all activities (Fig. 2). The lateral FFC was positioned more posteriorly relative to the slack of the ACL, especially during the stair descent activity; the lateral FFC in the 2-mm and 4-mm slack models were positioned 5.7 mm and 14.4 mm posteriorly, respectively, at the maximum in comparison with the normal model. Conversely, the femur tended to move anteriorly relative to the tightness of the ACL, but the effects of the tightness were smaller than that of the slackness.

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Fig. 2 The anteroposterior positions of medial and lateral femoral facet center during the whole cycle of DKB, gait, and stair descent activities. Positive value: anterior translation of the femur.

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A more externally rotated angular position of the femur was exhibited with a looser ACL tension for all activities (Fig. 3). The difference between the normal and 4-mm slack models was at a maximum during the stair descent activity where the rotation of the femur reached up to 15.8° and 27.3° in the normal and 4-mm slack models, respectively.

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Fig. 3 The rotation of the femur during the whole cycle of DKB, gait, and stair descent activities. Positive value: external rotation of the femur.

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The average femorotibial contact force at the lateral compartment in a whole cycle tended to increase relative to the tightness of the ACL for all activities (Fig. 4). The contact forces at the lateral compartment in the 4-mm tight model showed a 16%, 4%, and 4% increase during gait, DKB, and stair descent activities, respectively, in comparison with the normal knee. The mean contact force at the medial condyle was variable between models.

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Fig. 4 The average femorotibial contact forces at the lateral and femoral compartment in a whole cycle of DKB, gait, and stair descent activities.

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The peak and average tension of the MCL had few differences noted between the normal and ACL slack models during gait and DKB activities (Fig. 5). During the stair descent activity, the peak and average tension of the MCL increased 9% and 47%, respectively, in the 4-mm slack model compared with the normal model.

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Fig. 5 The peak and average tension of medial collateral ligament in a whole cycle of DKB, gait, and stair descent activities.

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Discussion

AP and rotational instability was observed in ACL slack knees, which was particularly remarkable during stair descent movement and, in contrast, the effect of tightness was smaller. The femorotibial contact force tended to decrease relative to the slack of the ACL during all movements examined. Conversely, the tibiofemoral contact force of the lateral compartment increased relative to an increase in tension of the ACL during all activities. During stair descent activity, tension of the MCL increased relative to the slackness of the ACL. Abnormal kinematics and kinetics were detected in both slack and tight ACL models during high-demand activities. As the clinical relevance, the slackness of the ACL can induce residual instability and unfavorable clinical outcomes after surgery, whereas the tightness of the ACL can cause high tibiofemoral contact force and subsequent cartilage damage.

There are many studies showing the instability of ACL-d knees.^2,21,22 The tibial motion increased in several passive laxity tests including AP translation as well as varus-valgus and internal-external rotation after sectioning of the ACL in a cadaveric study.²¹ A study using fluoroscopy and a 2D-3D registration technique reported that no difference was observed in tibial rotation between the ACL-d knees and intact knees during squatting, whereas the tibiofemoral lateral contact points of the ACL-d knees were more posterior than that of the contralateral intact knees at low flexion angles.²² Another study using fluoroscopy and a 2D-3D registration technique reported that the lateral femoral condyle translated posteriorly around nearly full extension and that the screw-home movement appeared to be impaired during squatting motions in ACL-d knees.² However, a previous cadaver study and 2D-3D registration technique cannot represent high-demand activities such as stair descent because of the unavailability of the motion data. In the current study using computer simulation, AP and rotational instability was observed in an ACL slack knee during high-demand activities, and this demonstrates that computer simulation could be a valuable tool to detect kinematic and kinetic differences.

In the current study, differences between the normal knee model and slack ACL model were seen in all of the kinematics, tension of the MCL, and tibiofemoral contact force during stair descent activity. Differences in AP translation and axial rotation were greater during stair descent activity than during gait and DKB activities. Gao et al. stated that more kinematic differences were detected during stair descent than during stair ascent activities using a 3D optical motion capture system.²³ These differences could be related to the fact that stair descent is a more demanding activity than stair ascent and level walking.

The MCL is a second stabilizer for the AP direction in ACL-d knees.^24,25 In the current study, slack of the ACL had few effects on tension of the MCL during gait and DKB. During stair descent activity, tension of the MCL increased relative to the slack of the ACL. In a cadaveric study, increased valgus rotation of the tibia was observed during a simulated active extension maneuver after sectioning of the ACL.²¹ Other cadaveric studies reported that the in-situ force in the MCL in an ACL-d knee reached approximately two times as large as in the intact knee,⁷ and a more varus and internally rotated tibial position was reported in ACL-d knees during stair descent.²³ These results suggest that load on the MCL increases relative to the ACL deficiency especially in high-demand activity such as stair descent.

The computer simulation in our study showed that the tight ACL models increased the tibiofemoral contact force of the lateral compartment during all activities we tested. The initial tension applied to the graft at ACL reconstruction surgery is considered to be one of the most important factors for successful clinical results. A former study with a finite element model showed that a less slack ACL with a 4% larger initial strain resulted in a smaller tibial internal rotation at 90° of flexion.²⁶ Brady et al. reported that increasing the initial graft tension increased the tibiofemoral compressive forces and caused a tendency for the tibia to externally rotate and translate posteriorly compared to the ACL intact knee.⁸ The excessive tension of the ACL may cause joint stiffness and abnormal knee kinematics such as a decrease in tibial internal rotation and femoral rollback. These unfavorable changes may lead to meniscus damage, articular cartilage degeneration, and osteoarthritis.

There are several limitations in this study. First, we used a model without the meniscus in the computer simulation, which is a critical flaw of this study, because meniscus has significant effect on knee biomechanics such as kinematics, contact pressure, and knee stability. AP translation, rotation, the MCL force, and the contact forces were not actually represented in the current findings of the real knee because of the complex mechanical properties of the medial and lateral meniscus. Second, in the current study we analyzed the effect of slack and tightness of the ACL on kinematics and kinetics with only one normal knee model. There are individual differences in the geometry of the bones, and these individual differences of bone geometry could influence the knee kinematics and kinetics. Third, this model simplified the properties of the soft tissues (e.g., ligament and muscles), and muscle activity was not simulated, because muscle activity can also affect the stability of knee joint. In addition, the simulation model cannot reproduce all daily activities, however, it is difficult to reproduce the exact in-vivo mechanical conditions with any of the methods including mechanical tests and cadaver studies. Finally, we simulated tension change by length change of ACL, which would be different from the true ligament tension.

Conclusions

Using computer simulation, AP and rotational instability and excessive MCL tension were observed in the ACL slack knees especially during stair descent movement, whereas the tibiofemoral contact force of the lateral compartment increased in the tight ACL knees.