Preservation of femoral and tibial coronal alignment to improve biomechanical effects of medial unicompartment knee arthroplasty: Computational study

Abstract

BACKGROUND:

Medial unicompartmental knee arthroplasty (UKA) could be concerned with wear of the cartilage or the wear in the polyethylene (PE) insert. Mechanical alignment determines the biomechanical effect in the long term. However, previous computational studies all found that femoral and tibial components alignment in the UKA were rare, and the results varied.

OBJECTIVE:

The purpose of this study was to evaluate the biomechanical effect of the femoral and tibial component coronal alignment in varus and valgus conditions through computational simulation.

METHODS:

A three-dimensional finite element model of the intact knee was constructed from medical image data of one healthy subject. A medial UKA model of neutral position and various coronal components was developed from the intact knee joint model. The tibial varus-femoral valgus and tibial valgus-femoral varus conditions were analyzed with parallel component angles of 3°, 6° and 9° by using validated finite element models. We considered the contact stresses in the PE inserts and articular cartilage and the force on collateral ligament under gait cycle condition.

RESULTS:

Compared to the contact stress in the neutral position model, the contact stress on the PE insert increased in both tibial varus-femoral valgus and tibial valgus-femoral varus models. These trends were also observed in the case of the articular cartilage in remain compartment. However, the contact stress on the PE insert and articular cartilage increased largely in the tibial valgus-femoral varus model than in the tibial varus-femoral valgus model. The forces on the medial and lateral collateral ligaments increased in the tibial valgus-femoral varus model, whereas in the tibial varus-femoral valgus model, the forces decreased compared to the forces in the neutral position. The force on the anterior lateral ligament and popliteofibular ligament increased in the tibial varus-femoral valgus model as compared to the neutral position.

CONCLUSIONS:

Our study suggests that neutral alignment or less than 3° tibial varus-femoral valgus alignment in the coronal plane can be recommended in medial UKA to reduce the postoperative complications and to enhance the life expectancy of implants.

Keywords

Unicompartmental knee arthroplasty coronal malalignment varus valgus finite element analysis

1. Introduction

Unicompartmental knee arthroplasty (UKA) is an alternate surgical treatment to total knee arthroplasty (TKA) for single-compartment knee osteoarthritis (OA), especially in the medial compartment [1]. Surgery for UKA is less invasive to the skin, enabling preservation of the cruciate ligaments and the contralateral tibiofemoral and patellofemoral compartments [2]. Although excellent results were reported for UKA, there still exist variabilities in failure rates [3].

The preservation of limb alignment and precise positioning of prosthesis are major factors that determine the success of UKA [4]. The aim of UKA is to preserve knee kinematics by restoring ligament tension to normal, enabling the knee alignment and leg to return to their predisease state [5]. In UKA, accurate ligament balance is restored by the correct positioning of prosthesis [4]. In addition, UKA is relatively small and it requires less bone resection and the surgical procedure that maintains the ligamentous stability and physiological behavior in knee joint [6]. However, the time period to implant failure is determined by the wear in the polyethylene (PE), and implant loosening is often considered to occur faster in UKA than in TKA [7]. One of the main causes for failure in TKA is the concentrated contact areas and the increased magnitude of contact pressure [8,9]. The concentrated contact areas in conjunction with high contact pressures lead to early failure of the PE insert [10]. From another biomechanical point of view, relative mechanical alignment is advised for medial UKA in the knee joint to avoid progressive OA of the cartilage [11,12]. The results of knee alignment on the long-term outcome of UKA were dealt with in some reports [12–14].

In addition, several complications such as medial or lateral collateral ligaments rupture, PE insert dislocation, dissociation of the prosthesis, degenerative changes in the cartilage, and fracture of the medial proximal tibia were reported in the case of UKA [3,12–16]. Failure could be caused by the aseptic loosening of the femoral or tibial component, dislocation or instability of the components, malalignment of the components, deep infection, periprosthetic fracture, abrasion of the PE insert, progression of arthritis based on the previous studies [17–19]. While post-operative alignment in the medial UKA for the varus osteoarthritic knee has been widely studied, only few studies have investigated the risk factors of post-operative malalignment [5,7,20].

Several factors that may lead to the wear of the PE and cartilage in UKA were evaluated in the literature; these factors include the hip-knee angle, slope of the tibial plateau, and horizontal malalignment [7,14,21,22]. In addition, the coronal angle in UKA is defined by the manner in which the components are surgically implanted, and therefore, this angle is highly variable [6]. This angle is per se independent on the mechanical axis. Iesaka et al. analyzed the effects of the inclination of the tibial component in the coronal plane on the contact pressure of the implant-bone surface and the stresses on the proximal tibia in UKA [23]. Zhu et al. analyzed the influence of the coronal alignment of the tibial component on knee biomechanics in mobile-bearing UKA and found a rational range of inclination angles [24]. However, there exist no published data on contact stress on the PE insert and the articular cartilage and the force on collateral ligaments after UKA for all consider femoral and tibial components the varus or valgus correction under gait cycle condition. It is not possible to apply experimental measurements directly to investigate the biomechanical effect on the femoral and tibial component malalignment. However, these limitations can be resolved using finite element (FE) analysis [25].

The aim of this study was to investigate the biomechanical effect on the tibial varus-femoral valgus and tibial valgus-femoral varus condition with parallel component angles of 3°, 6° and 9° under the gait cycle condition. This study investigated contact stress on the PE insert and articular cartilage in the remaining compartment and examined the force on collateral ligaments. The varus and valgus ranges in femoral and tibial components were 3°, 6° and 9°. We hypothesized that the minor tibial varus-femoral valgus alignment provides the optimal biomechanical effect in medial UKA.

2. Methods

2.1. Normal healthy knee model

The intact knee model was developed from computed tomography (CT) and magnetic resonance imaging (MRI) scans of the right knee joint of a 37-year-old healthy male volunteer (height 178 cm, weight 78 kg) [26,27]. Prior to the reconstruction, the medical records for the subject indicated neutral lower limb alignment without any of the following conditions: anatomical abnormality, previous operations, and arthritis.

The contours of the bony structures (including the femur, tibia, fibula, and patella) and the soft tissues (including the ligaments and menisci) were reconstructed from CT and MRI images, respectively. In previous studies, the computational knee joint model was developed and validated [25,28,29]. Medical imaging was performed by using a 64-channel CT scanner (Somatom Sensation 64; Siemens Healthcare, Erlangen, Germany) and a 3-T MRI system (Discovery MR750w; GE Healthcare, Milwaukee, WI, USA). The CT and MRI scans were performed with 0.1 mm and 0.4 mm slice thickness, respectively.

The distal of the reconstructed femur was 10.2 cm, and the proximal of the tibia was 7 cm in MRI. To match the positional coordinates of each model, we defined three anatomical reference points in the reconstructed CT and MRI models: the central point of the diaphysis of the femur, the midpoint of the trans-epicondylar axis and the intercondylar notch [28,30]. The image data were then imported into the image processing software Mimics 17.0 (Materialise Ltd., Leuven, Belgium) to extract the geometry and to develop three-dimensional (3D) models for all structures. The initial graphics exchange specification files exported from Mimics were entered into Unigraphics NX (version 7.0; Siemens PLM Software, Torrance, CA) to form solid models for each femur, tibia, fibula, patella and soft-tissue segment.

The cartilage and menisci were modeled as isotropic and transversely isotropic, respectively, with linear elastic material properties by using eight-node hexahedral elements (Fig. 1) [29,31,32]. All the major ligaments were defined as hyperelastic rubber-like materials that represent nonlinear stress-strain relations [33,34]. The interfaces between the cartilage and the bones were modeled as fully bonded. The contacts between the femoral cartilage and meniscus, the meniscus and tibial cartilage, and the femoral cartilage and tibial cartilage were modeled for both the medial and lateral sides, thereby resulting in six contact pairs [28]. Convergence was defined as a relative change of <5% between two adjacent meshes. The average element size of the simulated cartilage and menisci was 0.8 mm.

FE models with the varus/valgus conditions were composted of the femoral and tibial components for UKA. A fixed-bearing UKA (Zimmer, Inc., Warsaw, IN, USA) was virtually implanted in the medial compartment of the developed normal knee model. The bone models were imported and appropriately positioned, trimmed, and meshed with rigid elements by using surgical techniques [35].

Based on the dimension of the femur and tibia, devices of sizes 6 and 5 were selected for the femoral component and tibial component, respectively. The devices were then aligned with the mechanical axis and positioned at the medial edge of the tibia. The neutrally aligned tibial baseplate was defined as a square (0°) inclination in the coronal plane with a 5° posterior slope. A rotating axis was defined as a line parallel to the lateral edge of the tibial component that passes through the center of the femoral component peg. A neutral femoral component distal cut that is perpendicular to the mechanical axis of the femur and parallel to the tibial cut was reproduced. We produced 7 cut surfaces of the medial tibial plateau with different angles of the coronal plane (neutral position; 3°, 6° and 9° varus; 3°, 6° and 9° valgus; Fig. 2).

We chose the angles of the tibial inclination following a previous study, in which the tibial component obliquity in UKA was measured, and it was concluded that >3° varus tibial inclination relative to the tibiofemoral joint space can result in poor survival of UKA [36]. In addition, our varus and valgus models for the femoral component were developed parallel to the tibial component. We did not consider mismatch in the varus and valgus femoral and tibial components.

With respect to the implanted model, a 1 mm cement gap was simulated between the component and bone. The PE insert was modeled as elastoplastic materials, whereas the femoral and tibial components and bone cement were modeled as linear elastic isotropic materials [37–40]. The materials of the femoral component, PE insert, tibial component, and bone cement corresponded to cobalt chromium alloy (CoCr), ultra-high-molecular-weight-polyethylene (UHMWPE), titanium alloy (Ti6Al4V), and poly(methyl methacrylate) (PMMA), respectively. The material properties, in terms of Young’s modulus and Poisson’s ratio, were as follows: CoCr: E = 220 GPa and v = 0.3; UHMWPE: E = 685 MPa and v = 0.47; Ti6Al4V: E = 110 GPa and v = 0.3; and PMMA: E = 1,940 MPa and v = 0.4 [37–40]. For the UHMWPE, the yield strength, the ultimate tensile stress, and the plastic strain were 17 MPa, 33 MPa and 0.32, respectively [39]. The femoral component was in contact with the PE insert. The coefficient of friction between the PE and metal was set as 0.04 [39].

2.2. Loading and boundary conditions

The FE investigation included two types of loading conditions corresponding to the loads used in the experimental part of the study for UKA model validation and model predictions for gait cycle loading condition.

The intact model was validated in a previous study, and the UKA model was validated by comparing it with models in previous experimental studies [28,29,41]. The validation of the UKA model was performed for flexion angles of 0°, 30°, 60° and 90° by using passive flexion simulation. Additionally, anterior and posterior drawer loads of 130 N were applied separately to the tibia at the knee center in a manner similar to that adopted in a previous experimental study [41].

Gait cycle loading was applied as a second loading to compare the biomechanical effect of the varus/valgus malalignment of the femoral and tibial components. The contact stresses on the PE insert, articular cartilage, and force on the collateral ligaments were predicted using the model under gait-cycle loading conditions (ISO 14,243) [42]. Computational analysis was performed with force controls for both the tibiofemoral and patellofemoral joint motions with respect to the compressive load applied to the femoral component. A proportional-integral-derivative controller was incorporated into the computational model to allow for the control of the quadriceps in a manner similar to that in the experiment [43]. Furthermore, anterior-posterior (AP) load and internal-external (IE) rotation were applied to the PE insert, and varus-valgus rotation in the medial-lateral was controlled by the ankle joint followed by the force of the quadriceps attached to the patellar button [42–45]. The FE model was analyzed using ABAQUS software (version 6.11; Simulia, Providence, RI, USA). All the results are explained with tibial-based reference.

3. Results

3.1. Validation of the UKA model

The UKA model was validated using the anterior and posterior tibial translations in the anterior and posterior drawer tests at 134 N for 6.1 mm, 9.9 mm, 8.7 mm and 8.5 mm; and 5.8 mm, 4.3 mm, 3.8 mm and 4.9 mm; respectively, at 0°, 30°, 60° and 90° of knee flexion in the UKA model (Fig. 3). These findings of the simulation showed a good agreement with those of a previous experimental study within the ranges of values under the anterior and posterior drawer loadings [41].

3.2. Comparison of contact stress on the PE insert and articular cartilage under the varus and valgus malalignment conditions

Figure 4 shows the contact stress on the PE insert in the varus and valgus malalignment and neutral position models during the gait cycle condition. The contact stress on the PE insert in the varus and valgus malalignment models all increased as compared to the stress in the neutral position model.

The contact stress on the PE insert increased by 1.8%, 5.16% and 12.1% in the 3°, 6°, and 9° tibial varus-femoral valgus models, respectively, as compared to the stress in the neutral position model. The contact stress on the PE insert increased by 7.2%, 11.5% and 17.7% in the 3°, 6° and 9° tibial valgus-femoral varus models, respectively, as compared to the stress in the neutral position model. There were differences in the contact stress in the varus and valgus malalignment models only during the stance phase. However, the extent of increase in the contact stress in the tibial valgus-femoral varus model was greater than that in the tibial varus-femoral valgus model.

Figure 5 shows the contact stress on the articular cartilage in the neutral position and the varus/valgus malalignment and the neutral position models during the gait cycle condition. Such trends could also be seen in the case of the articular cartilage. The contact stress in the cartilage increased to a lesser extent than in the PE insert under the varus and valgus malalignment conditions. The contact stress in the cartilage increased by 1.5%, 3.2% and 9.3% in the 3°, 6° and 9° tibial varus-femoral valgus models, respectively, as compared to that in the neutral position model. The contact stress in the cartilage increased by 2.6%, 3.1% and 10.7% in the 3°, 6° and 9° tibial valgus-femoral varus models, respectively, as compared to that in the neutral position model.

3.3. Comparison of the collateral ligament forces under the varus and valgus femoral malalignment conditions

Figure 6 shows the ligament forces on the medial collateral ligament (MCL), lateral collateral ligament (LCL), popliteofibular ligament (PFL) and anterior lateral ligament (ALL) in the neutral position, and the varus and valgus malalignment condition models during the gait cycle condition.

The force on the MCL and LCL increased in the tibial valgus-femoral varus model and decreased in the tibial varus-femoral valgus model in comparison to the force in the neutral position model. The forces on the MCL and LCL increased by 91% and 72%, respectively, in the 9° tibial valgus-femoral varus model. On the other hand, they decreased by 80% and 58%, respectively, in the 9° tibial varus-femoral valgus as compared to the forces in the neutral position model. On the other hand, the forces on the PFL and ALL showed the opposite trend. The forces on the PFL and ALL increased in the tibial varus-femoral valgus model and decreased in tibial valgus-femoral varus model. The forces on the PFL and ALL increased by 23.0% and 20.3%, respectively, in the 9° tibial varus-femoral valgus and decreased by 16.5% and 30.3%, respectively, in the 9° tibial valgus-femoral varus model as compared to the forces in the neutral position model.

4. Discussion

The most important finding of this study was that compared to the neutral position, the varus and valgus malalignment conditions exhibited worse biomechanical effects as compared to the neutral position. However, the tibial varus-femoral valgus malalignment less than 3° did not differ remarkably from the neutral position.

As previously mentioned, UKA has many advantages than TKA. However, there have been various results from the studies that evaluated coronal alignment of component in UKA. Briefly, Collier et al. reported that the risk of failure was reduced when the tibial component was implanted as more valgus than the pre-operative coronal alignment of the tibial plateau [22]. Sawatari et al. reported that minor valgus inclination in the UKA tibial component may be preferable to the varus or square inclination in the coronal plane [46]. An excessive posterior slope of the tibial component should be avoided [46]. Innocenti et al. examined the biomechanical effects of different varus and valgus tibial alignments in the medial UKA [47]. They suggested that the neutral tibial alignment or a slight varus alignment (3°) in the coronal plane can effectively extend the life expectancy of a UKA and this alignment is also compatible with soft tissue strains [47]. Previously mentioned studies suggested that deviation greater than 5° of the tibial component orientation from the pre-operative angle leads to early UKA failure. However, it appears that the relative position of the UKA, which is independent from the general limb alignment, was not yet considered as a key factor [6,48]. In TKA, the coronal contact angle of the femur to the tibia is defined by the shape of the component because both the condyles are articulating. However, in UKA, this angle is defined by the manner in which the components are surgically implanted and is therefore potentially highly variable [6]. However, to the best of our knowledge, no study has considered the alignment of the femoral component; only the tibial component alignment has been examined as yet. Further, no study appears to have evaluated the biomechanical effect of the femoral and tibial components with coronal malalignment [22–24,37,46,47].

The aim of this study was to evaluate the contact stress on the PE insert and the cartilage and the force on the collateral ligaments for the femoral and tibial components in the coronal malalignment under dynamic loading conditions. We did not consider the mismatch between the femoral and tibial components. We only considered malalignment caused by the resection of the tibia, followed by that of the femur.

We investigated the contact stress on the PE insert and the cartilage. The contact parameters are known to be closely related to the wear of PE insert and degenerative OA in the cartilage of the knee joint [6,14]. We found that the contact stress on the PE insert increased in both varus and valgus malalignment. In addition, this trend was more clear in the case of the tibial valgus-femoral varus model. This trend could be explained by mainly the valgus deformity induced in medial UKA [49]. Therefore, contact stress on the PE insert increased in the femoral and tibial components under the tibial valgus-femoral varus condition. The interesting finding was that while the contact stress on the PE insert in the 3° varus and valgus models was not relatively high, those in the 9° varus and valgus models were remarkable. This trend could be caused by the geometry of the femoral and tibial components. If one of these components exhibited malalignment, the contact stress on the PE insert could increase because of edge loading. However, the effect of a slight angle could be reduced by the implant geometry in parallel varus and valgus malalignment.

The contact stress on the cartilage increased in both the varus and valgus models, and this increase was less than that in the case of PE insert. The implantation to the medial side inevitably affected the distribution of load transfer in the knee joint. Increased lateral load transfer was expected originally [50]. The femorotibial alignment is determined by the height of the contact point between the medial femoral condyle and the tibial component, which in turn depends on the resection level of the proximal tibia, ligament stability, preoperative deformity, implant thickness and the surgical technique for UKA [20,48]. In other words, although valgus existed under the parallel condition, the balanced compressive force could be switched to different contact points under the varus and valgus conditions, leading to an abnormal shear force. Furthermore, the contact stresses and patterns corresponding to the PE insert and articular cartilage showed good agreement with those obtained in a previous study [25,51].

An important finding was made with regard to the forces on the MCL and LCL in the varus and valgus malalignment models. The forces on the MCL and LCL increased in the tibial valgus-femoral varus model. In the knees with a stiffer MCL, the MCL provides greater resistance against valgus tilting. More loads will consequently be transferred through the medial compartment, even when the balancing seems optimal [49]. This may lead to clinical problems such as loosening of the tibial component and fractures of the medial tibial plateau or the underlying bone. Pain is a frequent revision reason in UKA. The valgus model may contribute to otherwise inexplicable pain owing to the higher force on the MCL and the assumed higher load transfer through the medial compartment [52]. Because of the difference in stiffness between the cartilages and because of CoCr-UHMWPE interaction, the loading on the knee joint was no longer balanced unlike in the initial unloaded state [47]. The coronal valgus malalignent induced by loading had two consequences: the percentage of load transferred in the lateral compartment increased, and the force on the MCL and LCL increased, while that on the ALL, PFL decreased, as confirmed by the computational simulation. In addition, the increased forces on the MCL and LCL under the valgus condition showed a good agreement with the results of Heyse et al. who found that overstuffing in UKA evidently led to considerable tension in the valgus knee joint and higher strains in the MCL [49].

Based on our results, tibial valgus-femoral varus malalignment >6° is not recommended in order to avoid extremely high forces on the MCL and LCL. In addition, tibial varus-femoral valgus malalignment >9° is not recommended to prevent increase in the contact stress on the PE insert even with reduced force on the collateral ligament. We recommend the neutral position UKA and less than 3° tibial varus-femoral valgus malalignment because they showed positive biomechanical effects [48].

It is important to emphasize the many strengths of the present study. First, in contrast to previous UKA studies, the FE model used in this study included the tibia, femur, and related soft tissues [23,37,46]. Second, in contrast to the previous biomechanical UKA model, the present study included the application of gait cycle loading instead of a simple vertical static loading condition [23,24,37,46,47]. Third, the current study validated the intact model and performed kinematic validation of the UKA FE model. Finally, the current study also considered the malalignment of the femoral component unlike in previous studies [23,24,37,46,47].

Nevertheless, several limitations of the study should be noted. First, the bony structures were assumed rigid. In reality, a bone is composed of cortical and cancellous tissues. However, the main purpose of the study did not involve evaluating the effects of different prostheses on bone. Additionally, this assumption exerted a minimal influence on the study because the stiffness of the bone exceeds that of the relevant soft tissues [28,31]. Second, the articular cartilage was considered as an elastic material, and the effects of anisotropy and viscoelasticity were not considered. Third, the results were obtained by single subject computational simulation, not clinical performance. However, the advantage of computational simulation using a single subject is that the effects of component alignment within the identical subject can be determined with the exception of variables such as weight, height, bony geometry, differences in ethnicities and sex, ligament properties, and component size [53]. Finally, we did not consider the mismatch malalignment condition in the femoral and tibial components; this subject will be investigated in a future study.

5. Conclusions

The data underline the importance of the coronal alignment in medial UKA. Our study suggests that neutral alignment of less than 3° tibial varus-femoral valgus alignment in the coronal plane can be recommended in medial UKA to reduce the postoperative complications and to enhance the life expectancy of implants.

Conflict of interest

None to report.

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