## 4 Discussion and Conclusions
However, VM impairment in knee joints that have undergone TKA may weaken the posterior force applied to the femur through the patella and restrict both the posterior translation of the femur and internal rotation of the tibia by inducing the patellar tendon to pull the tibia in the direction of the external rotation, as shown in Figure 5. Finally, VM impairment may cause a paradoxical roll-back motion during knee-joint flexion, resulting in a greater risk of posterior dislocation of the tibia. Although there were no significant changes in the joint reaction forces and moments due to VM impairment for knee joints with/without TKA, there was a change from valgus and external to varus and internal due to VM impairment on the native knee joint. In this report, the change was observed in 50% of cases (six cases) due to VM impairment. In addition, we observed increases in the external moment and the anterior joint reaction force due to VM impairment on the knee joint that underwent TKA. Here, 80% of cases (nine cases) showed increases due to VM impairment. Therefore, posterior dislocation of the tibia may be induced if VM impairment occurs after TKA. This is consistent with clinical reports showing that posterior dislocations of the tibia have been reported in patients with VM impairment, particularly quadriceps impairment, following TKA in clinical practice [9; 19; 20]. Figure 5: Changes in quadriceps and patellar tendon vectors of the load (QIF: quadriceps force without VM impairment; QZF: quadriceps force with VM impairment; PT1F: patellar tendon force without VM impairment; PT2F: patellar tendon force with VM impairment) due to VM impairment: (**a**) increased external moment due to VM impairment on the frontal plane; (**b**) posterior dislocation of the tibia due to VM impairment on the sagittal plane. This study had some limitations. First, it was not possible to change quadriceps contraction during flexion of the knee. In general, the quadriceps contraction force changes during flexion. However, in this study, our technology was limited in its ability to simultaneously change each of the VM, VL, and RF/VI at the same rate. Therefore, we presume that by overcoming the technical limitation of simultaneously and continuously changing the same ratio or desired contractile forces in each muscle, we will obtain results more similar to clinical findings. Second, motion analysis of the knee joint could not be performed concurrently with measurements of joint reaction forces and moments. To obtain the joint reaction forces and moments in a six-axis load cell, we were required to restrain many degrees of freedom of the tibia, which limited measurement of the change in motion. In a future study, we plan to consider simultaneous motion analysis and measurement of the joint reaction forces and moments after finding a method that can be applied to the knee with six degrees of freedom. This will aid in reliable identification of the mechanisms of potential instability and malfunction due to VM impairment after TKA. In conclusion, we showed that VM impairment in the knee joint after TKA may be associated with posterior dislocation of the tibia by a paradoxical roll-back with increases in the anterior joint reaction force and the external moment during knee joint flexion. This increases our understanding of the mechanism of potential instability and malfunction due to VM impairment on the knee joint after TKA, and can be used to optimize clinical/rehabilitation training plans for improving the prognosis (stability and function) of the knee joint after TKA. Conceptualization, D.L. ; methodology, Y.L., H.-M.Y., J.J., D.-S.K. ; investigation, Y.L., H.-M.Y., J.J.; writing--original draft preparation, Y.L., H.-M.Y. ; writing--review and editing, J.K., H.-J.C., D.J., D.L. ; supervision, D.L. All authors have read and agreed to the published version of the manuscript. National Research Foundation of Korea and Korea Medical Device Development Fund. Not applicable.