## 4 Discussion and Conclusions
However, it is difficult to estimate the required muscle adjustment and the necessary extent of compensatory contraction force. Thus, there is a limit to the application of the accurate quadriceps contraction ratio in the VM impairment condition. Removing only the load applied to the VM is presumably the worst situation for VM impairment that can be achieved in practice. Additionally, characteristics of the alterations of the knee-joint reaction forces and moments are presumed to be clearly visible when the worst situation is applied, and the biomechanical mechanism of TKA instability due to VM impairment can be clearly confirmed. [PERSON] et al. [37] and [PERSON] et al. [38] reported that anterior translation was enhanced up to low knee-joint flexion and reduced thereafter in the native knee joint, which is consistent with our findings. Enhancements of the anterior translation and reaction force within 0-20\({}^{\circ}\) of knee-joint flexion occur because the direction of the patellar tendon load transmitted from the quadriceps is gradually shifted from the anterior to the proximal direction during low knee-joint flexion [29; 39]. [PERSON] et al. [37] reported that the tibia was translated medially and rotated in the varus and internal directions as the knee joint flexed in the native knee joint, which is consistent with our findings. In particular, internal rotation occurs at 0-30\({}^{\circ}\) flexion by screw home rotation of the knee, which we have identified as internal moment. Additionally consistent with our findings, [PERSON] et al. [40], [PERSON] et al. [41], and [PERSON] et al. [42] showed that tendencies of the anterior, medial translation, and internal rotation directions were similar in knee joints that had undergone TKA and did not exhibit VM impairment when compared with those of the native knee joint. However, the current study confirmed that the valgus moment generally occurred in knee joints that had undergone TKA, in contrast to the findings of previous studies [38; 41; 43; 44]. [PERSON] et al. [38] and [PERSON] et al. [41] reported that a varus moment had occurred (as in previous studies [43; 44]), but [PERSON] et al. [42] confirmed that a valgus moment was present in knee joints that underwent TKA. These findings indicate that varus-valgus moments may vary according to TKA design and the surgeon's surgical methodology and technique. Accordingly, our experimental protocol and results are largely adequate and may be reliable for assessing the aim of the current study. In this study, we showed that knee joints with VM impairment generated a lateral reaction force and valgus/external moment that differed from those of the native knee joint within 10-20\({}^{\circ}\) knee-joint flexion. This result was likely caused by the lateral translation of the contraction force of the quadriceps due to VM impairment (Figure 5). Knee joints that underwent TKA showed that the joint reaction forces and moments tended to change from internal to external moments due to VM impairment. In particular, knees that had undergone TKA and exhibited VM impairment showed a sharp enhancement of the anterior joint reaction force within 40-90\({}^{\circ}\) knee-joint flexion, in contrast to knee joints that had not undergone TKA but exhibited VM impairment. These results might have been caused by alteration of the degree of resistance to the anterior reaction force due to anterior cruciate ligament removal in the TKA operation, as well as the restriction of roll-back motion during knee-joint flexion. Roll-back of the knee joint is reportedly induced by moving the contact point of the femur and tibia in the posterior direction by internal rotation of the tibia and posterior translation of the femur.