The main goal of total knee arthroplasty (TKA) is providing pain relief and restoring a neutral mechanical axis (Scott, 2007). The restoration of coronal alignment and optimal gap balancing have been long-held tenets for successful TKA (Longstaff et al., 2009; Lombardi et al., 2011), and accomplishing those features has led to good long-term survival rates in TKA patients (Fang et al., 2009; Ritter et al., 2011). However, it is difficult to obtain a complete rectangular gap or neutral alignment in TKA (Fang et al., 2009; Ritter et al., 2011; Kamenaga et al., 2018). Also, the good outcomes were obtained from a neutral alignment group (mechanical axis < ± 3°) compared with a coronal alignment outliers group (mechanical axis ≥ 3°) (Fang et al., 2009; Longstaff et al., 2009; Lombardi et al., 2011; Ritter et al., 2011). However, with this classification, it is unable to compare the biomechanical effects between 2° of varus/valgus alignment and neutral alignment groups. Therefore, the biomechanical effect of 2° varus/valgus alignments remains unclear.

Currently, most surgeons permit an unbalanced gap (≤ 2°) or perform additional varus/valgus (≤ 2°) bone cuts to obtain a balanced gap. Constitutional varus was proposed in the 2010s and showed that the under-correction of the varus alignment resulted in excellent clinical outcome scores (Vanlommel et al., 2013). Moreover, the kinematic alignment has been introduced to restore the joint line of pre-arthritic knees, even though the knee alignment can be out of the neutral alignment range (Howell et al., 2013). Also, robotic-assisted surgery increased the accuracy of targeting neutral mechanical alignment by reducing alignment errors within 1°–3° compared to surgery using conventional instruments (Bellemans et al., 2007; Song et al., 2013), enabling more precise targeting of specific alignment by subtle degrees.

Previous studies have focused on evaluating the effect of alignment outliers (Fang et al., 2009; Longstaff et al., 2009; Lombardi et al., 2011; Ritter et al., 2011; Lerner et al., 2015; Kang et al., 2017; Lee et al., 2018; Nishitani et al., 2019). Various studies using computational methods evaluated the contact stress and force at more than 3° of varus/valgus alignment. Lerner et al. (2015) constructed a dynamic simulation model and calculated knee contact forces up to 8° varus- and valgus-aligned TKA. A musculoskeletal knee simulator model was used to evaluate the knee contact force and kinematics of a 7° valgus alignment model while providing 4 mm of slack on the medial collateral ligament (MCL) during deep-knee bend cycles (Nishitani et al., 2019). Therefore, evaluating the biomechanical effects of moderate varus and valgus alignments of less than 3° is necessary.

Ligament balancing is critical for maintaining knee stability and achieving equal medial/lateral gaps, as well as extension/flexion gaps in TKA (Mitsuyasu et al., 2011). Blakeney et al. (2020) reported that coronal alignment correction caused ligament imbalance. From this clinical point of view, it is necessary to construct a model containing ligaments in the knee joint for a better understanding of the biomechanical effects of balance/imbalance or medial/lateral laxity in the coronal alignment in TKA. However, previous studies did not fully reflect ligament balancing in the simulation models. Many studies have made efforts to develop TKA musculoskeletal models to predict the in vivo contact force (Lerner et al., 2015; Marra et al., 2015; Jung et al., 2016; Smith et al., 2016). However, some of them did not include ligament models (Lerner et al., 2015; Jung et al., 2016). Only a limited number of studies introduced their models including ligament elements and evaluated the biomechanical effect of coronal alignment outliers (Thelen et al., 2014; Chen et al., 2015; Smith et al., 2016). Hence, it is worthwhile to investigate the effect of coronal alignment changes using a simulation model that includes a detailed ligament balancing process.

Therefore, the purposes of this study were 1) to develop a cruciate-retaining (CR) TKA musculoskeletal model, which enabled the adjustment of ligament length and implant alignment; 2) validate the model; and 3) evaluate the effects of varus/valgus alignment adjustment and unbalanced medial/lateral ligament laxity on contact force and ligament tension during gait.

The accuracy of the estimated contact forces compared to the in vivo data was equivalent to or higher than that in previous studies. The RMSEs of the TCF, MCF, and LCF were less than 0.28 BW during one gait trial. To the best of our knowledge, the TCF RMSE was lower in all previous studies, except for one (range, 0.26 BW—0.51 BW) (Marra et al., 2015). In particular, the RMSE of the MCF (0.19 BW) in our study demonstrated that the developed model well-predicted the quantitative contact force compared to previous studies (range, 0.21 BW—0.26 BW). Likewise, the RMSE of the LCF in the present study was 0.23 BW, while the RMSEs of the MCF in recent studies ranged from 0.22 BW to 0.42 BW (Jung et al., 2016; Marra et al., 2015; Smith et al., 2016; Thelen et al., 2014) (Table 2). In addition, our results showed that the magnitude of the contact force in the medial compartment accounted for 65.5% of the TCF, which agrees with the previous findings that 64.2 ± 6.0% of the TCF passes through the medial compartment during walking (Werner et al., 2005). We were able to develop an accurate model by benchmarking the features modeled in the two most accurate previous studies, which minimized errors in the marker location between the model and the experimental trial by using a reference trial (Marra et al., 2015) and releasing the constraint of the knee joint to a spherical joint during the kinematics calculation (Jung et al., 2016). Therefore, the computational TKA model developed and analyzed in this study seemed to sufficiently predict contact forces and assess the effect of ligament tension by varying the coronal alignment of the TKA during a gait cycle.

The main observation of this study was that 2° valgus alignment adjustment with balanced ligament (models B and C) or neutral alignment with 2° medial laxity (model D) decreased the contact force compared to the balanced neutral alignment. In contrast, 2° of varus alignment adjustment with balanced ligament (models E and F) or neutral alignment with 2° lateral laxity (model G) increased the contact force and ligament tension compared to the balanced neutral alignment. The TCF is simply a summation of the MCF and LCF. Since the MCF constitutes a larger proportion of the TCF than LCF (Werner et al., 2005), the reduction of MCF in models B, C, and D may have caused the reduction in TCF. In the same manner, the increase in MCF in models E, F, and G may have caused the increase in TCF. Similar tendencies of MCF and LCF values were observed in a previous study that evaluated the effects of varus/valgus outliers more than 2° (Chen et al., 2015). Also, the results of the finite element analysis study showed that the medial contact stress change was larger than the lateral contact stress change in the varus/valgus alignment (Suh et al., 2017). Increased contact forces in TKA may lead to severe wear and result in early revision (D’Lima et al., 2001; Srivastava et al., 2012). Therefore, 2° of valgus alignment adjustment with balanced ligament or neutral alignment with 2° medial laxity may be safer than neutral alignment, whereas varus alignment adjustment with balanced ligament or neutral alignment with 2° lateral laxity may not be beneficial in terms of implant survivorship.

It is interesting to note that neutral alignment with ligament adjustment in 2° valgus (model D) or varus (model G) alignment showed large reductions in MCL or LCL tension, respectively, while stabilized ligament tension was observed in the opposing side. Suh et al. (2017) reported that 3°–5° varus alignment led to excessive decreases in MCL force but no remarkable change in the ALL and LCL force. However, they did not describe whether the ligaments were balanced or not. The discrepancy between the results of our study and the previous study may be inferred from the presence or absence of novel laxity adjustment in the models. Not only the peak tensions of the MCL and LCL decreased in medial and lateral laxity but also the ligament activation (i.e., tightening) time decreased compared to that of neutral alignment. The MCL in the medial laxity model (model D) was activated in only 40.9% of the gait cycle, whereas in other neutral alignment models, the MCL was activated during the entire gait cycle. Likewise, the LCL in the lateral laxity model (model G) was activated in only 8.0% of the gait cycle, whereas in other neutral alignment models, the LCL was activated in 55.5–85.4% of the gait cycle. Since the medial (model D) and lateral (model G) laxity models give slack to the medial and lateral soft tissues, respectively, ligament tension on the lax side will be loaded later and unloaded earlier. In this regard, we verified that MCL and LCL slack were provided properly in the medial (model D) and lateral (model G) laxity models.

The results of this study showed that the contact force of the femoral varus alignment was 2.9% greater than that of the tibial varus alignment. The greater contact force in the femoral than the tibial varus alignment observed in our study may have resulted from increased MCL and PCL tension (Figure 6). Our findings agree with a previous simulation study that reported that the maximum contact force in a 5° femoral varus alignment was 6.2% greater than that in the tibial varus alignment (Chen et al., 2015). Lee et al. (2018) conducted a long-film study evaluating the failure mechanism of femoral/tibial malalignment and found that femoral varus alignment had an increased mechanical failure rate, consistent with our results. In contrast to the results that tibial varus/valgus alignment can be safer than femoral varus/valgus alignment, Innocenti et al. (2016) showed that 2°–6° femoral varus/valgus alignment resulted in lower stress than those of tibial malalignment, although the model they used included only MCL and LCL without other ligaments or soft tissues in the knee joint. A short-film study reported inferior outcomes in the tibial varus alignment compared to the femoral varus alignment (Ritter et al., 2011). Due to wide variations in the femoral shaft bowing in the coronal plane (Kim et al., 2015), the anatomical axis evaluated with short films may be insufficient compared to the evaluation of the mechanical axis in long-film studies. Altogether, our results comparing femoral and tibial varus alignments indicate that the femoral varus alignment should be avoided in case 2° of the varus alignment adjustment is necessary for a balanced ligament.

The kinematics results in this study showed that medial/lateral laxity did not affect joint instability. Our results showed that internal/external rotation decreased due to medial or lateral laxity during gait. These results agree with a previous cadaveric study that reported MCL release reduced the internal rotation of the tibia during flexion (Wada et al., 2017). Takagi et al. (2021) also reported that intraoperative medial and lateral laxity influenced the rotational kinematics during a deep knee bend activity. In contrast, valgus alignment showed to rotate more internally and varus alignment showed to rotate more externally than the neutral alignment model (Figure 8B). The alignment differences of the varus/valgus alignment were well reflected in the results of varus/valgus angle (Figure 8C). These findings agree with a previous study reported that valgus alignment of the tibiofemoral joint was shifted toward its alignment direction (Thelen et al., 2014). In addition, varus/valgus alignment models showed to translate inferiorly compared to the neutral alignment model. As varus and valgus models were medially and laterally overresected, respectively, this may have resulted in decreased knee joint space compared to the neutral alignment model. Consequently, there existed changes in kinematics influenced by coronal alignment change, whereas comparable kinematics of 2° medial/lateral laxity models were observed compared to the balanced neutral alignment model.

This study had some limitations that should be considered when interpreting the results. First, the model was validated by one participant performing a gait trial. Gait motion is the most frequently performed activity in daily living. Nevertheless, the knee flexion angle varies from 0° to 65°, and it is not appropriate to predict tibiofemoral contact force at high flexion beyond 65°. Second, the subject in this study received a TKA with a CR-type tibial insert. Different insert options, such as a posterior-stabilized (PS) type, may result in different biomechanical behaviors. A previous study reported that joint gaps differed between PS and CR-TKA (Matsumoto et al., 2009). Third, only the contact forces were analyzed at the articulating surface. For better understanding the phenomenon in the view of structural mechanics, it may be necessary to check pressure or stress distribution through structural analysis. Fourth, the varus/valgus alignment more than 2° was not considered in this study. Fifth, previous studies (Suh et al., 2017; Marra et al., 2018a; Marra et al., 2018b) and the current study performed validation of the musculoskeletal model prior to evaluating the alignment in TKA. However, the modified musculoskeletal models used to evaluate the effects on alignment were based on the motion of the subjects’ alignment but not on the motion of the varus/valgus alignment limb. Our model was based on a subject within average age, height, and body weight for TKA. Nevertheless, one has to be cautious when generalizing the results from this study to all TKAs. Sixth, the kinematics such as internal/external rotation of this model was not validated against in vivo kinematics; thus, it must be considered while interpreting the kinematic results of this study. In this study, we evaluated the effect of varus–valgus 2°, which was within the outliers, and included ligament laxity adjustment in the model to mimic more realistic situations.

In conclusion, the present study developed a musculoskeletal model to predict the contact force of CR-TKA during walking that enabled ligament laxity adjustment for coronal alignment changes, and the model was validated using in vivo contact forces. We found that 2° of valgus alignment adjustment with balanced ligament or neutral alignment with 2° medial laxity could be safe without increasing the contact force or ligament tension. However, 2° of varus alignment adjustment with balanced ligament or neutral alignment with 2° lateral laxity may be unfavorable due to biomechanical overloading of the joints and knee ligaments. In addition, excessive loading was observed in the medial and posterior ligaments in femoral varus alignment. Hence, surgeons should be cautious in making decisions involving tibial/femoral alignment with 2° of varus/valgus alignment.