Finite Element Analysis of the Biomechanical Effects of 3 Posterolateral Corner Reconstruction Techniques for the Knee Joint

Finite Element Analysis of the Biomechanical Effects of 3 Posterolateral Corner Reconstruction Techniques for the Knee Joint Kyoung-Tak Kang, Ph.D., Yong-Gon Koh, M.D., Juhyun Son, M.S., Sung-Jae Kim, M.D., Ph.D., Sungryul Choi, M.D., Moonki Jung, Ph.D., and Sung-Hwan Kim, M.D., Ph.D.

Purpose: To compare the forces exerted on the cruciate ligaments and the contact stresses on the tibiofemoral (TF) and patellofemoral (PF) joints with respect to 3 different tibial- and fibular-based posterolateral corner (PLC) reconstructions under dynamic loading conditions. Methods: A subject-specific finite element knee model was developed by using 3-dimensional anatomic data from motion captures in gait and squat activities, including in vivo knee joint kinematics and muscle forces for the single subject. Cruciate ligament forces and contact stresses on the TF and PF joints under 3 PLC reconstruction techniques (tibial-based, TBR; modified fibular-based, mFBR; conventional fibular-based, cFBR) and PLC-deficient models were compared with those of the intact model in gait and squat loading conditions. Results: The cruciate ligament forces in the 3 surgical models differed from those in the intact model. The greatest differences in ligament forces from the intact model were found in the cFBR model, whereas there were no remarkable differences between the TBR and mFBR models in both gait and squat loading conditions. Contact stresses on the lateral TF and PF joints of the 3 surgical models were greater than those of the intact model under the squat loading condition. Conclusions: The biomechanical effects achieved using the anatomic reconstruction technique were found to be improved compared with those using nonanatomic reconstruction techniques. However, the ligament forces and contact stresses under normal conditions could not be restored through any of the 3 techniques. Clinical Relevance: Anatomic TBR and FBR for grade III PLC injuries could restore better biomechanics in the knee joint compared with nonanatomic reconstruction. However, discrepancy with the normal condition requires further modification of surgical techniques.

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njury to the posterolateral corner (PLC) structures of the knee causes severe disability and is increasingly being diagnosed as our understanding of this injury is

From the Department of Mechanical Engineering, Yonsei University (K-T.K., J.S.); Joint Reconstruction Center, Department of Orthopaedic Surgery, Yonsei Sarang Hospital (Y-G.K., S-J.K.); Department of Orthopedic Surgery, Arthroscopy and Joint Research Institute, Yonsei University College of Medicine, Gangnam Severance Hospital (S.C., S-H.K.), Seoul, Republic of Korea; and AnyBody Technology A/S (M.J.), Aalborg, Denmark. K-T.K. and Y-G.K. contributed equally to this work and should be considered co-first authors. The authors report that they have no conflicts of interest in the authorship and publication of this article. Received June 21, 2016; accepted February 10, 2017. Address correspondence to Sung-Hwan Kim, M.D., Ph.D., Department of Orthopedic Surgery, Arthroscopy and Joint Research Institute, Yonsei University College of Medicine, Gangnam Severance Hospital, 211 Eonju-ro, Gangnam-gu, Seoul 06273, Republic of Korea. E-mail: orthohwanbm@ gmail.com Ó 2017 by the Arthroscopy Association of North America 0749-8063/16558/$36.00 http://dx.doi.org/10.1016/j.arthro.2017.02.011

developing.1 The PLC comprises the lateral collateral ligament (LCL), popliteus tendon (PT), and popliteofibular ligament (PFL) in addition to the posterolateral knee capsule, proximal tibia-fibula joint, biceps femoris, and other posterolateral structures. In particular, the LCL, PT, and PFL are well-known, primary biomechanical components of the PLC.2 These structures prevent abnormal posterior translation, varus rotation, and coupled external rotation of the tibia. In addition to prevention, the PLC structures have a protective effect against forces exerted on the cruciate ligaments.3-5 The anterior cruciate ligament (ACL) and posterior cruciate ligament (PCL) reconstructions that do not address posterolateral rotatory instability have been shown to worsen in long-term follow-up, which can predispose patients to subsequent failures of the reconstructed ligament.6 Recent in vitro studies have reported that untreated grade III injuries to PLC structures led to increased forces on the reconstructed ACL or PCL in the knee joints.7 Thus far, there are several

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operative treatment methods for posterolateral instability that have not been standardized, with several reconstruction techniques reporting varying results.8-12 The ultimate goal of anatomic PLC reconstruction is to restore the 3 important structures. However, it has been argued that this technique is more demanding and may overconstrain the knee joint.13,14 There are several techniques that address varus and posterolateral rotatory instability in which 2 of these principal structures are addressed, which have been described as anatomic tibial-based reconstruction (TBR), anatomic fibularbased reconstruction (modified fibular sling, mFBR), and nonanatomic fibular-based reconstruction (conventional fibular sling, cFBR) (Fig 1).10,15,16 To properly understand the mechanism underlying reconstruction, several biomechanical studies have been conducted using cadaveric testing.1,14,15,17,18 In vitro experimental measurements provide useful knowledge; however, these studies are limited by the unrealistic replication of muscle and joint loading experienced in daily activity.19,20 It is impractical to use experimental measurements to directly evaluate ligament stress and contact stress on the knee joint in PLC reconstruction surgical techniques; however, these limitations can be overcome with computational models. Similarly, dynamic multibody rigid models are limited to the evaluation of stress distribution in the knee joint. In contrast, deformable body finite element (FE) models enable the evaluation of the ligament forces and contact stresses on the tibiofemoral (TF) and patellofemoral (PF) joints, which is important for understanding the factors that may affect structural joint deterioration.19,21 The available data on muscle forces in FE models are not subject-specific, but they have been referred to in previous studies.20,22 Studies using a validated FE model that includes all major ligaments and soft tissues for comparing subject-specific muscle forces have been seldom reported previously. The purpose of this study was to compare the forces exerted on the cruciate ligaments and the contact stresses on the TF and PF joints with respect to 3 different tibialand fibular-based PLC reconstructions under dynamic loading conditions. We hypothesized that anatomic PLC reconstruction has closer to normal knee mechanics.

Methods Gait and Squat Experiment The subject-specific FE and musculoskeletal (MSK) models were developed on the basis of subject-specific data from motion capture using electromyography (EMG) sensors. The hospital’s institutional review board approved this study for data capture from a model subject. A young healthy male volunteer who had neutral lower limb alignment without any anatomic abnormality, previous operation, and arthritis

was enrolled for this study (36 years, 178 cm, 75 kg). The subject performed 4 trials of activities with gait and squatting, and the ground reaction forces were then measured using a force plate (Fig 2). In addition, marker locations were traced using a 3-dimensional (3D) motion-capture system (Vicon, Oxford, United Kingdom), with EMG signals recorded by an EMG sensor (Delsys, Boston, MA) in the following muscles: the gluteus maximus, rectus femoris, vastus lateralis, biceps femoris, semimembranosus, gastrocnemius medialis, tibialis anterior, and soleus medialis. Initial data from the EMG signals were transformed into muscle activation data using root mean square analysis. To predict the muscle activation, an EMG-to-activation model was developed to represent the underlying muscle activation dynamics. The EMG-to-muscle activation data transformation procedure has been reported previously.23 MSK Model for Muscle Force Prediction A 3D MSK model of the subject-specific knee joint was developed using the AnyBody Modeling System (version 6.0.6; AnyBody Technology, Aalborg, Denmark). To simplify the development process of a completely subject-specific model, the MSK model of the lower extremity was extracted from the AnyBody Managed Model Repository (version 1.6.4; AnyBody Technology) and modified for this study.24 The 3D reconstruction and development procedures for the subject-specific model have been reported previously.25 The ligament insertion points were referenced to the anatomy from the subject’s magnetic resonance imaging sets and descriptions found in the literature.26-28 Two experienced orthopaedic surgeons (S-J.K. and S-H.K.) determined each location of the ligaments independently. In addition, the MSK model was validated by using passive flexion computed tomographic image and kinematics in our previous study.29 On the basis of the subject’s 3D femoral, tibial, fibular, and patellar models, the scales of bone in AnyBody were adjusted using nonlinear radial basis functions and a law of scaling. The remaining parts were adjusted according to the scale using an optimization scheme that minimized the differences between model markers and identified marker positions. In this study, the knee joint was considered to have 12 degrees of freedom (DOF) (TF, 6 DOF; and PF, 6 DOF). The hip and ankle joints were considered to provide 2 and 3 DOF, respectively. The ligament attachment sites were obtained from the subject’s magnetic resonance imaging scans. The attachment points in the AnyBody model were modified using the subject-specific attachment sites. As shown in Figure 3, 21 ligament bundles were modeled: the anterior cruciate ligament (anteromedial bundle of the ACL, aACL; posterolateral bundle of the

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Fig 1. Schematic of 3 surgical techniques on a right knee model: (A) fibular-based (conventional fibular sling) reconstruction (cFBR), (B) fibular-based (modified fibular sling) reconstruction (mFBR), and (C) tibial based reconstruction (TBR).

ACL, pACL), posterior cruciate ligament (anterolateral bundle of the PCL, aPCL; posteromedial bundle of the PCL, pPCL), anterolateral structures, lateral collateral ligament (LCL), PFL, medial collateral ligament

(anterior, central, and posterior portions), deep medial collateral ligament (anterior, aCM; posterior, pCM), medial and lateral posterior capsule, oblique popliteal ligament, medial PF ligament (superior, middle, and

Fig 2. Schematic of a subject-specific musculoskeletal model during (A) gait and (B) squat conditions.

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Fig 3. Schematic of a subjectspecific musculoskeletal right lower extremity model during gait and squat conditions: (A) with contact conditions and 21 ligament bundles; aACL and pACL; aPCL and pPCL; anterolateral structures; LCL; popliteofibular ligament (PFL); medial collateral ligament (anterior, aMCL; central, cMCL; and posterior, pMCL); deep medial collateral ligament (aCM and pCM); medial and lateral posterior capsules (mCAP and lCAP, respectively); oblique popliteal ligament; medial patellofemoral ligament (superior, sMPFL; medial, mMPFL; and inferior, iMPFL); and lateral patellofemoral ligament (superior, sLPFL; medial, mLPFL; and inferior, iLPFL), (B) with the popliteus muscle modification, and (C) with the 13 muscles incorporated into the lower extremity model. (aACL, anteromedial bundle of the ACL; ACL, anterior cruciate ligament; aCM, anterior portion of the deep medial collateral ligament; aPCL, anterolateral bundle of the PCL; LCL, lateral collateral ligament; pACL, posterolateral bundle of the ACL; PCL, posterior cruciate ligament; pCM, posterior portion of the deep medial collateral ligament; pPCL, posteromedial bundle of the PCL.)

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inferior), and lateral PF ligament (superior, middle, and inferior). Most of the stiffness and reference strain values were obtained from the literature, but some were modified.30-32 The menisci were modeled using linear springs to simulate their equivalent resistance.33 A wrapping surface was applied to the 21 ligament bundles and patella tendon to wrap around the bony structure using a cylinder and ellipsoid for preventing ligament penetration into the bone. The number of cylindrical and ellipsoidal wrapping surfaces varied from 1 to 3 depending on the geometry of curvature. Figure 3 shows 3 rigiderigid stereolithography-based contacts defined in the TF and PF joints. Three deformable contact models were defined between the femoral and tibial components and between the femoral component and patellar button.32 The PT in PLC structures from AnyBody was modified to minimize the effects of inaccuracy (Fig 3) to represent a more realistic anatomy.33,34 FE Model The knee-joint FE models included bony structures (tibia, patella, and femur), the TF and PF joints, and soft tissues, such as articular cartilage, 16 major ligaments, menisci, meniscal horn attachments, and 12 muscles (Fig 4). This FE model of the knee joint was established and validated in a previous study.25,35 The bony structures were modeled as rigid bodies.36 The cartilage was modeled as isotropic, and the menisci were modeled as transversely isotropic with linearly elastic material properties.37 These parameters were estimated by applying a time-independent and simple compressive load to the knee joint.38 All major ligaments were modeled using nonlinear and tension-only spring elements. The points for all ligament attachments and anatomic geometry were identical in both the MSK and FE models. A contact between the combinations of femoral cartilage, meniscus, and tibial cartilage was modeled for both the medial and lateral sides. A frictionless contact between the articular structures was defined according to a literature-based pressureeoverclosure relationship.30 Convergence was noted if the relative change between 2 adjacent meshes was <5%. The mean element size was 0.8 mm for the cartilage and menisci. Simulation of PLC Reconstruction and PLCDeficient Models In the TBR technique, we positioned the LCL and PT femoral insertions on the lateral femoral condyle on the basis of our surgical technique, which was slightly anterosuperior to the lateral epicondyle.10,17,39,40 The cFBR technique previously described consists of a single femoral tunnel placed posterior to the lateral epicondyle and an anteroposterior (AP) fibular

Fig 4. Developed finite element model for a right lower extremity.

tunnel.9,15 For the mFBR technique, as with the AP tunnel, the oblique tunnel was oriented parallel to the joint line. The oblique tunnel ran from the anteromedial to the posterolateral locations on the fibula. The double femoral tunnel reconstructions were performed using oblique fibular tunnels. The 2 femoral tunnels were placed at the anatomic landmarks that corresponded to the femoral attachments of the LCL and popliteus.41 Two experienced surgeons selected the LCL, PFL, and PT femoral insertion points under careful consideration to compare these 3 reconstruction techniques. For each PLC reconstruction, 6-mm tunnels were made on the basis of the insertions of the PLC structure on the TBR and FBRs. All reconstructions were performed using a graft tendon tensioned to 30 N, as previously described.14,15 Surgical graft fixation was simulated at a 30 flexion angle for the PLC reconstruction techniques.14,15,39,40 At a 30 flexion angle with 30 N tension, the graft’s initial tension (or reference length) was evaluated and then applied to the FE model as an initial value to perform the simulation under gait and squat loading conditions. A PLC-deficient model in which PT, PFL, and LCL were all eliminated was also developed. Inverse Dynamic Simulation With Muscle Force Calculation and Loading Conditions Applied to the FE Model Before performing inverse dynamic analyses, the kinematics of each trial were calculated on the basis of motion-capture data; kinematic optimization was used for this purpose. The objective of optimization was to

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Fig 5. The comparison between measurement and prediction for muscle activation using subject-specific musculoskeletal model in the (A) normal gait and (B) squat loading conditions.

minimize the difference between the AnyBody model marker trajectories and the motion-capture marker trajectories. After kinematic optimization was completed, inverse dynamic analysis was performed. The muscle recruitment criterion used in this study was a cubic polynomial. Muscle activation and ligament force were calculated using inverse dynamic analysis, and muscle activations were compared with the EMG signals. The FE model was developed using ABAQUS (version 6.11; Dassault Systèmes Simulia, Providence, RI) as a dynamic simulation, with only force and moment equilibrium considered at each time point. The inputs to the model were the active muscle forces obtained from the whole-body MSK model under gait and squat

loading conditions. In addition, each muscle force was used in the FE model as input data in the MSK and 3 reconstruction and PLC-deficient models. The forces exerted on the cruciate ligament were separately evaluated according to each bundle (aACL, pACL, aPCL, and pPCL). Contact stresses on the medial and lateral tibial articular and patellar cartilages were evaluated. For the articular cartilage, mean contact stresses were calculated under gait and squat loading cycles. The greatest differences for ligament forces and contact stresses in PLC-deficient, TBR, mFBR, and cFBR models compared with those in the intact model were determined as percentages, and the peak contact stress distributions on the tibial and patellar cartilages were also evaluated.

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Fig 6. Forces on the ACL and PCL with respect to the 3 reconstruction techniques and PLC-deficient models during the gait cycle loading condition. (aACL, anteromedial bundle of the ACL; ACL, anterior cruciate ligament; aPCL, anterolateral bundle of the PCL; cFBR, conventional fibular-based reconstruction; mFBR, modified fibular-based reconstruction; pACL, posterolateral bundle of the ACL; PCL, posterior cruciate ligament; PLC, posterolateral corner; pPCL, posteromedial bundle of the PCL; TBR, tibial-based reconstruction.)

Results Comparison of Experimental Muscle Activation With That From Computational Simulations The greatest muscle activities obtained from the computational model were consistent with the transformed EMG measurements under the gait and squat loading conditions (Fig 5). However, they did not show an identical trend because of the increase in prediction error for the tibialis anterior muscle. Cruciate Ligament Force Under Gait Loading Conditions The forces exerted on the ACL and PCL increased in deficient PLC compared with the intact model under gait loading conditions. However, different trends were observed for the ACL and PCL subjected to the 3 different surgical techniques compared with those in the intact model under gait loading conditions. The ligament forces on the aACL increased by 18%, 19%, and 29%, in the deficient PLC, TBR, and mFBR, respectively, and decreased by 31% in the cFBR compared with those in the intact model under gait

loading conditions. The forces exerted on the pACL increased by 20%, 8%, 11%, and 19% in the deficient PLC, TBR, mFBR, and cFBR, respectively, compared with those in the intact model under gait loading conditions. The ligament forces on the aPCL increased by 12% and 4% in the deficient PLC and cFBR and decreased by 18% and 20% in TBR and mFBR, respectively, compared with those in the intact model under gait loading conditions. The forces exerted on the pPCL increased by 24%, 14%, 16%, and 22% in the deficient PLC, TBR, mFBR, and cFBR, respectively, compared with those in the intact model under gait loading conditions (Fig 6). Cruciate Ligament Force Under Squat Loading Conditions The forces exerted on ACL and PCL all increased in the deficient PLC compared with the intact model under squat loading conditions. In addition, similar trends under the gait loading conditions were observed in the aACL and aPCL for the 3 surgical techniques. The ligament forces on the aACL increased by 42%, 9%, and 11% in the deficient PLC, TBR, and mFBR,

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Fig 7. Forces on the ACL and PCL with respect to the 3 reconstruction techniques and PLC-deficient models during the squat loading condition. (aACL, anteromedial bundle of the ACL; ACL, anterior cruciate ligament; aPCL, anterolateral bundle of the PCL; cFBR, conventional fibular-based reconstruction; mFBR, modified fibular-based reconstruction; pACL, posterolateral bundle of the ACL; PCL, posterior cruciate ligament; PLC, posterolateral corner; pPCL, posteromedial bundle of the PCL; TBR, tibial-based reconstruction.)

respectively, and decreased by 13% in the cFBR compared with those in the intact model under squat loading conditions. The forces exerted on the pACL increased by 30%, 4%, 6%, and 9% in the deficient PLC, TBR, mFBR, and cFBR, respectively, compared with those in the intact model under squat loading conditions. The ligament forces on the aPCL increased by 60% and 24% in the deficient PLC and cFBR and decreased by 9% and 11% in TBR and mFBR, respectively, compared with those in the intact model under squat loading conditions. The forces exerted on the pPCL increased by 84%, 24%, 26%, and 42% in the deficient PLC, TBR, mFBR, and cFBR, respectively, compared with those in the intact model under squat loading conditions (Fig 7).

decreased by 9% in cFBR compared with those of the normal condition model. The contact stress on the patellar cartilage was almost identical to that of the intact model under gait loading conditions (Fig 8A). Contact stress distributions changed in the tibial cartilage. The stresses were concentrated both on the lateral and medial tibial cartilages in the deficient PLC. There was wider contact stress distribution on the lateral tibial cartilage in cFBR than in TBR and mFBR. However, on the opposite side, the load was transferred to be concentrated on the medial tibial cartilage. There were no differences in the contact distribution on the patellar cartilage in all PLC reconstruction and PLC-deficient models compared with those in the intact model (Fig 8B).

Contact Stresses on the Articular and Patellar Cartilages Under Gait and Squat Loading Conditions The mean contact stress on the medial tibial articular cartilage was almost identical to that of the intact model under both gait and squat loading conditions. The mean contact stress increased by 18%, 8%, and 11% on the lateral tibial articular cartilage in the deficient PLC, mFBR, and TBR, respectively, but

Contact Stresses on the Articular and Patellar Cartilages Under Squat Loading Conditions In the squat loading condition, the mean contact stress increased by 33%,13%, 19%, and 24% on the lateral articular cartilage in the deficient PLC, TBR, mFBR, and cFBR, respectively, compared with those in the intact model. The mean contact stress increased by 46%, 21%, 23%, and 42% on the patellar cartilage in the deficient PLC, mFBR, TBR, and cFBR, respectively,

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Fig 8. (A) Contact stresses and (B) contact stress distributions on the tibial and patellar cartilages with respect to the 3 reconstruction techniques and PLC-deficient models during the gait cycle loading condition. (cFBR, conventional fibular-based reconstruction; mFBR, modified fibular-based reconstruction; PF, patellofemoral; PLC, posterolateral corner; TBR, tibial-based reconstruction; TF, tibiofemoral.)

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Fig 9. (A) Contact stresses and (B) contact stress distributions on the tibial and patellar cartilages with respect to the 3 reconstruction techniques and PLC-deficient models during the squat loading condition. (cFBR, conventional fibular-based reconstruction; mFBR, modified fibular-based reconstruction; PF, patellofemoral; PLC, posterolateral corner; TBR, tibial-based reconstruction; TF, tibiofemoral.)

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compared with those in the intact model under squat loading conditions (Fig 9A). For the contact stress distribution under the squat loading condition, the contact stresses on the tibial articular and patellar cartilages under the 3 surgical techniques and PLC-deficient models were remarkably different from those of the intact model. Regardless of a similar distribution range, a higher stress concentration was observed. The greatest contact stresses on the lateral tibial and patella cartilages were shown in the PLC-deficient model, and those trends were not restored in all the 3 reconstruction technique models (Fig 9B).

Discussion Our results showed that anatomic reconstruction restored the condition and mechanics closer to a normal knee joint compared with nonanatomic reconstruction. Although it could not perfectly conserve the mechanics of a normal knee joint, it led to remarkably similar outcomes in TBR and mFBR. In most previous studies, in vitro experiments were evaluated using cadavers under quasi-static loading conditions.1,14,15,17,18 Biomechanical studies using cadavers are usually conducted in the elderly; thus, if forces are repeatedly applied under loads for mechanical testing, not only loosening between the specimen and device but also some attenuation of the tissue itself may occur.42 A computational knee joint model eliminates some of the disadvantages of in vitro studies, such as limitations due to cadaveric specimens under quasi-static loading conditions. Computational models with validation could be considered to be an effective methodology in parametric analyses and population-based clinical studies.20 In orthopaedic research, a representative-validated FE model has been developed, and surgical simulation, injury mechanism evaluation, or implant assessment has been performed.20,22,25,43 In most previous studies related to FE analysis, muscle force was disregarded or simply represented by modification; otherwise, muscle force extracted from other subjects was used.20,22,43-45 Akbarshahi et al.19 primarily used an FE model to study the muscle force generated by a subject. They developed the MSK model with simplification in 3 DOF, without considering soft tissues such as menisci and ligaments in the FE model.19 In addition, computational studies involving the popliteus muscle seldom have been reported. However, we have introduced and validated a 12-DOF (TF, 6 DOF; and PF, 6 DOF) MSK model of the knee suitable for force-dependent kinematic simulation under gait and squat loading conditions, followed by validation using EMG sensors and muscle-force activation. Furthermore, to perform more realistic simulations, PLC reconstruction simulations were performed in all

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MSK models to apply the appropriate muscle force corresponding to the subject’s FE model that was used for validation. For the treatment of chronic PLC injuries, various techniques have been reported.12 Conventional techniques for restoration of PLC, such as posterolateral advancement of the arcuate complex46 or a biceps rerouting technique,47 has evolved with the development of anatomic techniques in accordance with further understanding of the anatomic and biomechanical knowledge. Current PLC reconstruction techniques could be classified as FBR in which LCL and PFL are re-created and TBR in which LCL and PT are e-created. In this study, we analyzed the following 3 techniques: singleefemoral tunnel FBR (conventional fibular sling), double femoral tunnel with oblique fibular tunnel FBR (modified fibular sling), and TBR. TBR techniques have a theoretical advantage in that PT is a crucial element in the posterolateral stability of the knee.42,48 The TBR technique adopted in the current study was introduced by Kim et al.,10,49,50 which addressed the LCL and PT with a graft limb overlying the anterior tibiofibular joint. They proposed the possibility of concomitant injury at the proximal tibiofibular joint in the setting of a PLC injury of the knee. Recently, Jabara et al.51 showed a 9% incidence of proximal tibiofibular joint instability in the setting of multiligament-injured knees. Historically, singleefemoral tunnel FBR, known as a fibular sling technique,7 has been the most commonly used method to reconstruct the PLC.16 Recently, there has been an emphasis on restoring native anatomy of the knee with an oblique fibular tunnel and 2 femoral tunnels in the FBR technique.52-55 Anatomic FBR restoration should provide better knee kinematics and could lead to improvement in patients’ functions.15 These were similar to the findings of the present study. The amounts of increase in ligament forces and contact stresses on the TF and PF joints in mFBR were less than those in cFBR. We found that the ACL was as important as the PCL for ligament force increases under gait loading conditions. In addition, there were similar trends in the ligament forces on the ACL and PCL under both gait and squat loading conditions. The ligament forces in cFBR decreased on the aACL, and those in TBR and mFBR decreased on the aPCL compared with those under native conditions. An interesting finding in this study was that the pattern of changes in the ligament forces in cFBR was remarkably different from those in the TBR and mFBR techniques. Moreover, the amounts of increase in ligament force in TBR and mFBR were less than that in cFBR. This finding suggests that these 2 anatomic reconstruction techniques had biomechanical effects more similar to those under the native knee condition. In addition, this trend was shown in a previous study using cadaveric experiments.17

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There was no significant variation in contact stress on the medial articular cartilage under both gait and squat loading conditions. However, the contact stresses on the lateral articular cartilage changed under the gait and squat loading conditions. Particularly for the patellar cartilage, the contact stress remarkably increased postoperatively under the squat loading conditions. Furthermore, the PLC-deficient model showed increased contact stresses on the lateral and patellar cartilages and higher stress concentration. However, in the surgical model without increases in contact stress, the contact stress distribution was somewhat different from that in the intact model. In other words, the findings suggest that none of the surgical techniques preserved the characteristics observed under the native conditions. LaPrade et al. reported that anatomic reconstruction is fundamental for improving the clinical results of PLC reconstruction. They developed an anatomic reconstruction technique for static stabilizers of the PLC; however, the PFL appeared to act as a TF joint stabilizer rather than passing from the femur to the fibula.56 Furthermore, Markolf et al.14 recently found that a TBR technique with the grafts tensioned to 30 N at a 30 flexion angle resulted in overconstraint of the varus rotation in the knee joint compared with that of an intact LCL. Similar trends have been shown in other previous studies. Nau et al. also reported that both surgical techniques for anatomic PLC reconstruction showed good results in static laxity tests. The anatomic reconstruction of all structures, including the popliteus tendon, resulted in an abnormal internal tibial rotation during dynamic testing.18 In addition, Yoon et al.13 showed that PT reconstruction had no effect on the stability and clinical results in anatomic PLC reconstruction. Therefore, no biomechanical evidence was found to support the conservation of more complex reconstruction methods. Although none of the surgical techniques restored native knee conditions, our results supported that anatomic reconstruction, such as mFBR and TBR, provided reasonably satisfactory postoperative results. Similar results have also been found in previous studies.57,58 In our study, there were no differences in either TF or PF joint biomechanics among the intact knee and 3 surgical techniques at 0 and 60 knee flexion under gait loading conditions. Our data suggested that the effect of 3 different surgical techniques can be clearly differentiated by evaluating the forces exerted on the cruciate ligaments and the contact stresses on the TF and PF joints. Limitations This study had some limitations. First, the computational model was developed using data from a young male subject. The use of subjects of various ages would

improve the validity of the results because the validity is also dependent on the geometry of the knee joint. Most significantly, the time and computational cost associated with subject-specific FE model generation were not efficient. In addition, although our initial FE model was well validated, it does not represent the environment in vivo considering anatomic variations and age-related changes in ligament and cartilage, so the number of subjects should be expanded in future research. Second, the ligaments were modified into only 2 or 3 bundles. Third, to improve wrapping around the bony structures, wrap objects were included. However, these surfaces were modified into simple geometric representations. Fourth, the articular cartilage was considered to be an elastic material, and the effects of anisotropy and viscoelasticity were not considered. Fifth, there was a difference between the predicted tibialis anterior muscle force and the EMG measurement. Muscles were divided into multiple branches in the AnyBody MSK model, and the EMG signal was more related to the activity in part of a large muscle group closest to the electrode. This may contribute to the large differences in some muscle activations.24 Finally, the reconstruction model was developed at only 1 flexion angle, and the graft was applied at only 1 tension, which could have been influenced by variations in different flexion angles and tension; this possibility should be studied in future research. However, the study results provide quantitative standards for surgeons that would not be possible to obtain by evaluating clinical studies.

Conclusions The biomechanical effects achieved using the anatomic reconstruction technique were found to be improved compared with those using nonanatomic reconstruction techniques. However, the ligament forces and contact stresses under normal conditions could not be restored through any of the 3 techniques.

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