## 4 Discussion and Conclusions  
Quadriceps impairment reportedly induces occasional inability to fully activate the quadriceps following TKA due to voluntary quadriceps contraction disability [11; 12; 13; 14; 15; 16; 17; 18], resulting in hyperextension and posterior dislocation of the tibia [3; 6; 7; 8; 14; 17]. Although rehabilitation exercises are generally prescribed to enhance the activation of the quadriceps following TKA [17; 31; 32; 33; 34; 35], the fundamental clinical problems have not been resolved. Therefore, greater clarity is needed concerning the biomechanical mechanisms that cause hyperextension and posterior dislocation of the tibia due to quadriceps impairment. To our knowledge, previous studies have provided limited confirmation of alterations in the flexion-extension moment, despite alterations in all knee-joint reaction forces and moments [11; 12; 13; 14; 15; 16; 17; 18]. Overall, there is a need to confirm the characteristics of alterations in all knee-joint reaction forces and moments because impairment in VM, a component of the quadriceps, affects the muscle force vector. Accordingly, if alterations in all knee-joint reaction forces and moments appear repeatedly, they affect the surrounding ligaments and tendons that balance knee-joint motion, resulting in knee-joint instability (i.e., hypertension and posterior dislocation of the tibia in knee joints that have undergone TKA). Therefore, the current study investigated the characteristics of alterations in all knee-joint reaction forces and moments due to VM impairment and identified tendencies for changes in the vector directions of specific joint reaction forces and moments. The results indicate that changes in the vector directions of specific joint reaction forces and moments due to VM impairment may serve as undesirable kinematic mechanisms in the knee joint, which can induce posterior dislocation of the tibia. Our findings may offer mechanistic insights concerning posterior dislocation of the tibia from quadriceps impairment following TKA. It is important to control the quadriceps contraction forces when identifying the mechanisms of potential joint instability and malfunction due to VM impairment in knee joints that have undergone TKA. In this study, hamstring measurements were not considered because the quadriceps produces a comparatively greater contraction force [36]. Therefore, we presumed that a specific focus on the quadriceps was more appropriate. The normal quadriceps contraction forces were established on the basis of the contraction ratio loaded on each component of the quadriceps, in accordance with the observation by [PERSON] et al. that the muscle cross-sectional area is generally proportional to the muscle contraction force [28]. However, the quadriceps contraction forces in the VM impairment  
Figure 4: Knee–joint reaction forces and moments in knee joints that underwent total knee arthroplasty (TKA) with/without VM impairment during knee-joint flexion: (**a**) anterior–posterior reaction force (Fx); (**b**) varus–valgus moment (Tx); (**c**) medial–lateral reaction force (Fy); (**d**) flexion–extension moment (Ty); (**e**) proximal–distal reaction force (Fz); (**f**) internal–external moment (Tz). condition were established with the assumption that no contraction force acted on the VM, because no quadriceps contraction ratio has been reported for the VM impairment condition. Although it is difficult to determine whether the VM completely contracts in the VM impairment condition, VM contraction is presumed to function incorrectly because VM impairment is reportedly caused by a voluntary contraction disorder related to neuromuscular inhibition [21; 23; 34]. Furthermore, muscle force adjustment can complement the function of VM by strengthening muscles around the knee joint during the onset of VM impairment. The muscle force adjustment may exhibit greater alterations in the direction of muscle force, and thus it is likely to substantially influence the knee-joint reaction forces and moments.