Finite element analysis of femoral component sagittal alignment in mobile-bearing total knee arthroplasty

Abstract

BACKGROUND:

Recently, there has been an increasing interest in mobile-bearing total knee arthroplasty (TKA). However, changes in biomechanics for femoral component alignment in mobile-bearing TKA have not been explored in depth.

OBJECTIVE:

This study aims to evaluate the biomechanical effect of sagittal alignment of the femoral component in mobile-bearing TKA.

METHODS:

We developed femoral sagittal alignment models with −3°, 0°, 3°, 5°, and 7° flexion. We also examine the kinematics of the tibiofemoral (TF) joint, contact point on the TF joint, contact stress on the patellofemoral (PF) joint, collateral ligament force, and quadriceps force using a validated computational model under a deep-knee-bend condition.

RESULTS:

Posterior kinematics of the TF joint increases as the femoral component flexes. The contact stress on the PF joint, collateral ligament force, and the quadriceps force decreases as the femoral component flexes.

CONCLUSIONS:

Our results show that a slight, approximately 0°∼3°, flexion of the implantation could be an effective substitute technique. However, excessive flexion should be avoided because of the potential loosening of the TF joint.

Keywords

Total knee arthroplasty mobile-bearing misalignment finite element analysis

1. Introduction

Mobile-bearing total knee arthroplasty (TKA) was developed in the 1970s as an alternative to fixed-bearing TKA to provide low contact stress and high conformity between the metallic component and the polyethylene (PE) insert [1–3]. Mobile-bearing TKA features full or partial conformity of the superior surface of the insert with femoral condylar geometry, while the inferior surface of the insert is flat to enable rotation or sliding on the tibial baseplate with minimal friction [4]. Conformity with mobility in mobile-bearing TKA allows both minimal contact stress and minimal constraint, which cannot be achieved in fixed-bearing TKA [4]. Moreover, the shear forces on the bone-implanted components are minimized because there is a lower risk of loosening of the tibial component and a higher resistance generated by the ligaments [5]. The associated potential risk of wear on superior and inferior surfaces has been plagued by controversies in recent retrieval studies [6,7]. Early positive results have been observed in the design of numerous mobile-bearing prostheses [6,8]. The number of prosthetic designs differs in terms of the degree of constraint between the bearing and the femoral components and the degree of constraint of the bearing on the tibial baseplate [5]. Several statistical clinical studies have shown that the postoperative range of motion is related to the preoperative range of motion and that a preoperative flexion may be a critical factor in causing postoperative flexion [9,10].

Misalignments of the tibial or femoral components have been known to cause chronic pain, potentially developing into arthrofibrosis. In the femoral component, a misalignment may even lead to patellar instability, ligamentous instability, and disturbed functional joint kinematics [11–13]. This has not yet been confirmed experimentally [14–16]. To avoid notching, the femoral component is anteriorly implanted in an extended position of a component. In a distal femoral cut in the flexion position, the femoral component can be located posteriorly to avoid an anterior gap between the bone and prosthesis. [17] In a previous study, it was stated that each 2° increase in the sagittal flexion of the femoral component resulted in a 1 mm reduction in the flexion gap [18]. However, no study has been conducted to evaluate the femoral sagittal misalignment of a mobile-bearing TKA.

This study aims to investigate the biomechanical effect of femoral component sagittal misalignment in mobile-bearing TKA. We developed models with sagittal alignments of −3°, 0°, 3°, 5°, and 7°. TF kinematics, TF contact point, patellofemoral (PF) contact stress, quadriceps force, and collateral ligament force were investigated under a deep-knee-bend condition. We hypothesized the biomechanical effect will be positive under slight flexion.

2. Materials and methods

The study was approved by the institutional review board of Yonsei Sarang Hospital on 17 September 2018 (approval number 18-DR-03, protocol number 3D MRI ver. 1.0).

2.1. Computational knee joint model

In this study, we used the previously developed and validated finite element (FE) model [19–22]. It used medical imaging data of a 36-year-old male to develop a three-dimensional (3D) non-linear FE model for a normal knee joint. The subject’s medical history showed no musculoskeletal disorders or related diseases due to misalignment of the lower extremities, which indicated a healthy knee joint. The model in this study contains bony structures of the knee joint with soft tissues in the tibiofemoral joint and patellofemoral. This model was developed using computed tomography (CT) and magnetic resonance imaging (MRI) (Fig. 1). CT was performed with a 0.1 mm thickness slice using a 64-channel CT scanner (Somatom Sensation 64, Siemens Healthcare, Erlangen, Germany). An MRI was performed by a 3 Tesla magnetic resonance system (Discovery MR750w^®, GE Healthcare, Milwaukee, WI, USA) using a GEM Flex-Medium coil. The MRI scans were obtained with a slice thickness of 0.4 mm in the sagittal plane. The reconstructed models of CT and MRI were combined in an appropriate alignment using commercial software (Rapidform version 2006; 3D Systems Korea Inc., Seoul, South Korea). The bones were assumed to be rigid because its stiffness is higher than that of the soft tissue and their effect was negligible in this study [23]. We modeled the major ligaments with tension-only spring elements and non-linear [24,25]. The insertion positions of the ligament were determined from the anatomy seen in the MRI of the subjects and based on previous studies. (Fig. 1) [26–28].

Fig. 1.

Methodology for ligament insertion points using magnetic resonance imaging when developing an intact knee joint 3D model.

To develop models for the changes in femoral sagittal alignment, two skilled surgeons (the second and sixth authors) performed a TKA surgical simulation. The simulation was conducted using Unigraphics NX (Version 7.0, Siemens PLM Software, Torrance, CA, USA). Low contact stress (LCS) computer-assisted design models of a mobile-bearing TKA acquired from Johnson & Johnson (DePuy Orthopaedics, Inc., Warsaw, IN, USA) were virtually implanted into the bone geometry. For TKA models, large femoral component sizes and tibial baseplate sizes of 4 were adopted based on the dimensions of the femur and tibial. When aligning the components in the coronal plane in the neutral position, the femoral component was set perpendicular to the mechanical axis that connects the center of the knee to the center of the femoral head. The tibial component was placed vertically on the mechanical axis connecting the center of the knee to the center of the ankle joint. The rotational alignment of the femoral component was arranged in line with the femoral epicondylar and that of the tibial component in line with the tibial anteroposterior axes. To develop the sagittal alignment models of the femoral component, the femoral component was placed at −3°, 0°, 3°, 5°, and 7° flexion in the plane parallel to the anterior cortex of the distal femur in the different simulated implantations (Fig. 2). The distal femoral cutting thickness was equal to the thickness of the distal condyle of the component.

Fig. 2.

Developed five mobile-bearing TKA models with (a) −3°, (b) 0°, (c) 3°, (d) 5°, and (e) 7° of femoral component flexion in sagittal alignments.

In the TKA simulation, contact conditions were applied between the femoral component and the PE insert, between the femoral component and the patellar button, and between the tibial component and the PE insert. The coefficient of friction between the PE material and the metal was set to 0.04 for maintaining consistency with previous studies [29]. The femoral component, the tibial component, PE insert, and the bone cement were composed of a cobalt-chromium alloy (CoCr), titanium alloy (Ti6Al4V), ultra-high molecular weight polyethylene (UHMWPE), and poly (methyl methacrylate) (PMMA), respectively [29–31]. The material properties for each TKA component are described in Table 1. We considered that the cement penetration depth into the bone is 3 mm. It was calculated based on a different cementing test at the surfaces of the femoral and tibial resection that were, respectively, in contact with the femoral and tibial components [32]. The interfaces between the bone and the prosthesis were rigidly fixed by the cement used in this study [31]. Convergence was defined as a relative change of more than 5% between two adjacent meshes with an average edge length of 1.2 mm [33]. The 15,302 elements were used to construct the TKA model.

Table 1

Material properies for the FE model

	Young’s modulus (MPa)	Poisson’s ratio
CoCr alloy	220,000	0.30
UHMWPE	685	0.47
Ti6AI4V alloy	110,000	0.30
PMMA	1,940	0.4

2.2. Loading and boundary conditions

The changes in the femoral sagittal alignment model topologies provided six degrees of freedom to the TF and PF joints. The FE study included two loading conditions that corresponded with the loads used in the experiments that investigated the validation and the predictions of the TKA model under deep-knee-bend loading conditions. It was used the intact model validated in a previous study [19–22], and the validation of the TKA model was performed using a comparison with the model in a previous study [34]. The mobile-bearing TKA model was verified under the first loading condition that applies a 133 N anterior force and an 89 N posterior to 30° and 75° flexions to measure the total anterior-posterior (AP) displacement [34]. The second loading conditions corresponded to a deep-knee-bend loading that was applied to assess the influences of the changes in femoral sagittal alignment. A computational analysis was performed with an AP force applied to the femur with respect to the compressive load applied to the hip with femoral internal-external rotation constrained, medial-lateral translation free, and flexion determined by a combination of vertical hip and quadriceps load, leading to a 6 degree of freedom TF joint [35,36]. A proportional integral-derivative controller was integrated into the computational model to control the quadriceps in a similar way to a previous experiment [37]. A control system was utilized to compute the instantaneous quadriceps displacement that was required to match the target flexion profile and was the same as that used in the experiment. Varus-valgus and internal-external torque were applied to the tibia, and all other degrees of tibial freedom were restrained [35,36].

The FE model was analyzed using Abaqus FEA (formerly ABAQUS) software, Version 6.11 (Dassault Systèmes Simulia Corp., Johnston, RI, USA). PF contact stress, the kinematics of the TF joint, quadriceps muscle forces and, force in the collateral ligaments were calculated under the deep-knee-bend loading conditions. The AP TF joint translation was computed based on Grood and Suntay’s definition of the joint coordinate system [38].

3. Results

3.1. Validation of mobile-bearing TKA model

In the FE model used for the TKA, the AP translations in the TF joint were 8.7 mm at 30° and 7.3 mm at 75° flexions (Fig. 3), which was in agreement with a previous study that used experiments within one standard deviation under identical loading conditions applied to the prosthesis [34].

Fig. 3.

Comparison of AP translations in TF joints at 30° and 75° flexions between our computational model and previous experiments conducted for the validation of the mobile-bearing TKA model.

3.2. Comparison of kinematic and contact point on TF joint and contact stress on PF joint

Figure 4 shows that the kinematics of the TF joint changed as the femoral component flexed under deep-knee-bend activity. Posterior translation on the TF joint also increased with the increase in femoral component flexion (Fig. 4). FE models for mobile-bearing TKA showed posterior femoral rollback of their lateral condyle, while the medial condyle remained in a similar contact position during a deep-knee-bend condition (Fig. 5). However, the posterior position of the contact point was observed when the femoral component sagittal flexion increased in any angle of flexion during deep-knee-bend activity (Fig. 5). Contact stress on the PF joint decreased as the femoral component flexed during deep-knee-bend activity (Fig. 6). The 7° flexion model showed that contact stress on the PF joint decreased by 9.4% as compared to the −3° model (Fig. 6).

Fig. 4.

Comparison of kinematic on TF joint with −3°, 0°, 3°, 5° and 7° of femoral component flexion models in deep-knee-bend loading condition.

Fig. 5.

Contact point changes on TF joint with (a) −3°, (b) 3°, and (c) 7° of femoral component flexion models at 0°, 30°, 60°, 90°, and 120° flexions.

Fig. 6.

Comparison of contact stress on PF joint with −3°, 0°, 3°, 5°, and 7° of femoral component flexion models in deep-knee-bend loading condition.

3.3. Comparison of collateral ligament force and quadriceps force

Figure 7 shows the change in collateral ligament force as the femoral component flexes during deep-knee-bend activity. Both medial and lateral collateral forces of the ligaments decreased as the femoral component flexed. A similar trend was found in the quadriceps force (Fig. 8). It required the largest lumped quadriceps forces during deep flexion as the femoral component flexed. The flexion 7° model showed that the quadriceps force decreased by 10.4% compared to the −3° model.

Fig. 7.

Comparison of (a) medial and (b) lateral collateral ligament force with −3°, 0°, 3°, 5°, and 7° of femoral component flexion models in deep-knee-bend loading condition.

Fig. 8.

Comparison of quadriceps force with −3°, 0°, 3°, 5°, and 7° of femoral component flexion models in deep-knee-bend loading condition.

4. Discussion

A main finding of this study was that an advantageous biomechanics effect occurred as the femoral component flexed. However, excessive flexion should be avoided because of the risk of progressive loosening of the TF joint.

The postoperative range of motion is affected by many factors. In previous studies, the effects of alignment and the relative position of the prosthesis are reported on the postoperative range of motion [39,40]. The plastic bone models that were used did not represent the variability that is typically present among subjects. However, this problem can be overcome by using a computational study. Computational simulation with a single subject has advantages that are to determine the effects of the femoral component’s sagittal alignment position within the same subject and eliminate unnecessary variables, such as the height, weight, ligament properties, bony geometry, and component size of the subject [41,42].

In this study, we have evaluated the important variables that may determine the biomechanical effect in mobile-bearing TKA. The mobile-bearing TKA model was validated using kinematics and experimental data [34]. Therefore, the TKA model of this study is considered reasonable. Our results showed that posterior translation on the TF joint increased as the femoral component flexed. Posterior TF translation is important in TKA because it can provide greater flexion before TF impingement occurs [43]. The femoral component is implanted more posteriorly and more proximally, together with a more anterior tibial insert located with a femoral component flexion. In other words, late TF impingement could occur as the TF joint posterior translation increased in femoral component flexion, and the range of motion may increase.

The TF joint contact point supported this result. In-vivo weight-bearing fluoroscopy had been used to assess TF kinematics after TKA in several studies. A previous study using a 3D inverse perspective technique evaluated the lateral condylar motion of TKAs in the case of a deep-knee-bend. The results of that study showed that the lateral condyles began slightly anterior to the midline of the tibial sagittal plane in extension and exhibited a posterior femoral rollback with flexion similar to normal knees [44]. The researchers reported an average posterior femoral rollback of 7.7 mm, with the highest amount being 12.3 mm [44]. Another study evaluated mobile-bearing TKA with the same fluoroscopic technique and analysis and found that the implant showed minimal rollback from 0° to 60° flexion followed by mild anterior translation with increased knee flexion [45]. It has been shown that all TKAs at a full extension start posterior to the sagittal midline.

The present study showed a contact position of a computational model of mobile-bearing TKA that occurs near the midline tibia in extension. It is similar to the trend shown in a fluoroscopic study using the same TKA as that used in this study [46]. Our computational model’s anterior slide of the femoral component occurred at either 30° or 60° knee flexion during deep-knee-bend activity. Our model exhibited more posterior femoral rollback of the lateral condyle, which leads to accomplishing normal axial rotation patterns. The LCS implant has high conformity with 30° flexion, which shows a relatively neutral positioning in extension. The femoral geometry changes of the posterior condylar with a reduced radius of curvature leads to a tendency toward anterior transformation in deeper flexion. Similar to the posterior cruciate ligament retaining TKA that experiences anterior translation as flexion increases, this movement may cause a diminished range of motion and extensor mechanism deficiency [46]. However, a previous study showed a range of motion of 162° for Japanese subjects who implanted this TKA. The midline positioning for mobile-bearing TKA may be considered optimal for the interface loading and articular wear [47]. Posterior TF translation is essential in TKA because it provides a higher degree of flexion before the incidence of TF impingement [41,48]. Our study showed increased posterior TF translation as the femoral component flexed. It provides a potential for a higher degree of flexion.

Our results showed that contact stress and the quadriceps force on the PF joint decreased as the femoral component flexed because a more posterior TF contact point at full flexion improves the quadriceps moment arm, which is related to the improvement of the International Knee Society Function scores of TKA [49,50]. Previous studies found more posterior TF contact points in-vivo and reduced quadriceps forces ex-vivo [51,52]. Such a trend can also be found in mobile-bearing TKAs indicating that posteriorly-positioned TF contact points deliver a better functionality [53]. Our results also showed that an increased femoral component flexion can reduce the PF contact stress and the quadriceps force required for the deep-knee-bend activity to some extent. Because osteoarthritis and TKA patients suffer from quadriceps weakness, an extension femoral component that increases the required quadriceps force could cause the patients more difficulty in kneeling, squatting, or rising from a chair [54].

The study shows interesting results for the collateral ligament. The collateral ligament force decreased as the femoral component flexed. Large amounts of sagittal femoral component extension may be harmful to the collateral ligament. Sagittal alignment errors of the femoral component cause imbalanced soft tissues that lead to a limited range of motion and instability. However, this study showed that a more femoral component flexion loosens the TF joint in flexion. Interestingly, an increase in femoral component flexion produces remarkable effects in extension. This can be described by the translation of the femoral component flexion to all points of the tibial plateau distally, which loosens the TF joint throughout the knee flexion-extension range. In clinical practice, if the extension gap has already been successfully balanced, any further increase in the femoral component flexion alters the level of the TF joint line, which increases the laxity of the knee and reduces the force of the collateral ligament in both flexion and extension [55]. It is not observed for collateral ligament force because excessive collateral ligament force may cause ligament rupture and decreased collateral ligament force may lead to TF joint loosening.

As mentioned previously, proper femoral component alignment is closely related to higher clinical scores, high stability, and low release rate [11–13,56,57]. A previous study focused only on varus-valgus and internal-external rotation in the femoral component. However, our results showed that femoral component sagittal alignment, flexion-extension, may affect biomechanics. In a recent study, Antony et al. showed that the femoral component angle demonstrated a positive correlation with maximum flexion angle and range of motion [58]. Another study showed that in patients with TKA, slight flexion implantation could be an effective substitutional technique for preventing excessive component overhang, especially in the trochlea and anterior region of the distal condyle [59]. Kim et al. studied the relationship between the postoperative sagittal alignment of the femoral component and implant survival [60]. They stated that a femoral sagittal alignment of 0°–3° improved the survival rate of the knee prosthesis [60]. Another advantage is the reduction of risk in femoral notching with the anterior bone cut as the femoral component is flexed [61,62].

For clinical relevance, the optimal femoral component sagittal angle helps surgeons cut the distal femur on the sagittal alignment properly. In this study, it was observed that excessive femoral component flexion led to an instability of the TF joint. Based on previous results and of this study, we recommended slight flexion, approximately 0°∼3°, in the femoral component, while avoiding extension of the femoral component.

There are several limitations to this study. First, only one mobile-bearing prosthesis was used for the simulation; hence, our result cannot represent all mobile-bearing TKA. Subsequently, this simulation was performed using a variable and virtual model. The material properties of the soft tissues were based on relevant cadaveric studies. These are common methods using a computational model. Moreover, because a standard computer simulation model was employed, it did not need to calculate the standard deviations and process the data statistics. Finally, as the results correspond to the computational output, the clinical outcomes could not be represented, and patient satisfaction could not be considered. However, the main factor of this study is to evaluate the biomechanical effect of components using computational analysis.

5. Conclusions

Based on the results, the sagittal positioning of the femoral component is an important factor that affects knee joint biomechanics. Therefore, surgeons should be aware that any error in distal femoral resection might lead to a negative effect on knee joint biomechanics. We recommend slight flexion in sagittal alignment and avoiding extension of the femoral component.

Footnotes

Conflict of interest

None to report.

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