**4. Discussion**

In post-total-hip-arthroplasty patients, the weight bearing on the lower limb during the STS motion is asymmetric because it is biased toward the healthy lower limb. In poststroke patients, the center of foot pressure during the STS movement is asymmetric because it is biased toward the nonparalyzed side. Thus, previous studies have shown that muscle torque and joint angle changes exerted in the gait and during the STS movement are asymmetric due to disability or muscle weakness in one lower limb [7,19,20]. It was assumed that the rehabilitation patient group in this study would also have asymmetric lower limb joint angle changes during the STS motion due to disability and muscle weakness.

In patients with post-stroke syndrome, the muscle synergy of the R–L lower limbs is reportedly related to the asymmetry of the lower limb joint angle changes during the STS motion [21]. It is already known that the muscle synergy in such patients is altered compared with normal muscle synergy [22,23], and it was inferred that the patients in this study also had altered motor synergy of the unilateral lower limb due to disability and muscle weakness, resulting in asymmetric R–L lower limb movement during the STS motion. Therefore, we hypothesized that it is important to bring the synergy of the impaired lower limb of the patient closer to the normal state for the patient to recover the STS ability [21] and that improving the R–L lower limb coordination during the STS movement means that the muscle or motor synergy of the impaired lower limb used to perform the STS movement is closer to the synergy expressed by the healthy lower limb. We hypothesized that this would be the case. For this reason, we thought that a method for evaluating the coordination of R–L lower limbs during the STS movement was necessary and sought a method for evaluating this coordination from the perspective of both EAs and the R–L vector line in this study.

The R–L differences in shank and thigh EAs were also observed in the healthy participants. The reason for the observed differences in EAs in the healthy participants, despite the absence of a functional impairment, is presumably the habitual use of the dominant leg. Although there is no difference in muscle strength between the dominant and nondominant leg [24,25], the dominant leg has priority in postural control [26]. In addition, placing one leg posteriorly at the start of the STS movement can reduce the external tension moment of the hip joint [27], which may have caused the difference in EAs in the healthy group. In the rehabilitation patients, both EA values and temporal–spatial differences were observed. These temporal–spatial differences were visually complex and difficult to analyze. Therefore, we performed an analysis using R–L vector lines.

The PLG is a geometric method used to identify the cooperative structure of lower limb movement patterns in the gait [15,16]. However, the PLG represents the coordinated motion of one lower limb and it cannot represent the coordinated movement of the R–L lower limbs. Therefore, in this paper, we proposed a method that presents information on the changes in the EA of the R–L thighs and tibia as a single line (the R–L vector line). This method suggests that the closer the drawn R–L vector line is to the symmetry reference line, the more parallel it is to the target reference line, and the higher is the degree of synchronization of the EA and the change per time point between the R–L segments. In other words, the symmetry of the movement pattern can be evaluated as high. The STS movement has a muscle coordination structure that is reportedly similar to that of walking [28,29], and the movements of the R–L lower limbs during the STS motion are considered to be the result of coordination. Therefore, we hypothesized that the symmetry of the coordinated movements of the R–L lower limbs during the STS motion could be evaluated by the R–L vector line. The *ME* of the R–L vector line analysis results provides information that can be used to identify which motion (left or right) is dominant based on the sign of the value (positive or negative) and its magnitude. In a previous study analyzing the STS motion of patients with femoral neck fractures, it was reported that the angular displacement of the knee joint and the hip joint is greater in the nonaffected lower limb, where the peak joint moment values are greater [30]. Therefore, by observing the *ME*, the lower limb that is the primary source of force used to perform the STS motion can be estimated, helping to interpret the visually complex information on elevation displacement. Previous studies have reported asymmetry in the STS motion in patients after a lower limb fracture or a stroke [4,5,7,19,20]. According to the R–L vector line and the sign of the *ME* value, two trends were observed in the rehabilitated patient group. The first is patients with increased use of one lower limb during STS movements (Figure 7, P-1 and P-3), where the R–L vector line was also drawn on the side indicated by the sign of the *ME* value. The second was a patient with alternating and irregular increases in R–L lower limb use (Figure 7, P-2 and P-4). In this case, it was difficult to determine whether the predominantly used lower limb was the right or left one only by observing the R–L vector line, but the direction of the predominantly used lower limb could be determined from the sign of the *ME* value. On the other hand, compared with the rehabilitation patients, the R–L vector line of the healthy participants passed near the symmetric reference line. In other words, the R–L lower limbs

of the healthy participants showed the possibility of coordinated temporal and spatial movement. Chun et al. reported that a robotic rehabilitation intervention for stroke patients improves the muscle synergy asymmetry between the affected and nonaffected lower limbs [31]. In the study by Chun et al., the symmetry between R–L lower extremities was assessed by the correlation coefficient of muscle synergy, but it only provides information on the similarity of muscle synergy changes between R–L lower extremities, not explicit symmetry. Another weakness of R–L symmetry evaluation using only muscle synergy is that the number of synergies must be the same in the R–L lower limb as a condition for comparison, and the results of muscle synergy analysis vary depending on the number and types of muscles being investigated [32].

The R–L vector line proposed in this study will clearly demonstrate the symmetry of STS R–L lower limb movements when the R–L vector line, which plots STS movements, approaches the symmetry reference line through rehabilitation of the patient. In addition, since the EAs of the thigh and lower leg are used, the problem of differences in the measurement target affecting the analysis results can be avoided. This makes the determination of the effectiveness of the rehabilitation of R–L symmetry reliable and easy to perform.

The *MSE*, which excludes the positive and negative signs of the *ME* and calculates the magnitude of the error between the symmetric reference line and the R–L vector line as a numerical value, is the mean error value obtained by dividing this value by the measurement time of each participant. Previous studies have reported that hemiplegia and pain reorganize the cooperative structure of muscles differently from the healthy side [14,33,34]. The R–L asymmetry of the lower limb movement pattern during the STS motion in the rehabilitation patient group could be quantified by *MSE* values. In the present study, the number of participants in both groups was small (four in each) and there was no significant difference in the statistical test for the *MSE*. Therefore, we can only mention the possibility that the *MSE* is an indicator that can determine asymmetry. If the sample size is too small, the power of the test is estimated to be small [35]. In a previous study on the comparison of peak muscle synergy values, 21 participants, 12 with mild stroke sequelae and 7 with severe stroke sequelae, were compared [21]. A study examining the accuracy of the perception of the asymmetry of lower limb weight bearing during standing movements compared 19 stroke survivors and 15 healthy participants [36]. In contrast to these previous studies, our study had a short duration, which did not allow us to have a large number of participants, particularly rehabilitation patients. By increasing the duration of the study and obtaining the cooperation of several medical institutions, we could increase the number of rehabilitation patients. If we could increase the number of participants, it would be possible to study more clearly the magnitude of the *MSE* error between healthy participants and rehabilitation patients and to calculate a cutoff value. If we could calculate a cutoff value for the *MSE*, we would have an R–L vector line that would make it easier to visually determine the effectiveness of rehabilitation and treatment, aiding the staff working in clinical settings.

A limitation of this study is the large age difference between healthy participants and rehabilitation patients. The typical rehabilitation patient admitted to a medical facility is an elderly person. To determine the effectiveness of rehabilitation, it is desirable to compare the STS performance of patients and healthy participants of a similar age. However, since it cannot be said that elderly patients who are considered healthy do not experience musculoskeletal or cardiovascular diseases, close attention must be paid to the definition of STS performance as a normal model. In addition, because this study evaluated R–L lower extremity coordination during the STS motion based on EAs, the theory was limited to a kinematic perspective. If we could compare the muscle synergies of the same participants during the STS motion, errors between the neurological assessment and the kinematic assessment obtained from the results of this study could be identified.

#### **5. Conclusions**

In this study, we proposed a method for evaluating the improvement in the R–L synergy of the impaired lower limb during the STS movement, i.e., the measurement of the EA and the measurement of the R–L vector line, which is a secondary type of information obtained from the EA. The information obtained from the EAs of multiple body segments of the R–L lower limbs is complex, with many variables, making it difficult to evaluate coordination. In contrast, the R–L vector line can be represented by a single line in two-dimensional coordinates, and the *ME* and the *MSE* facilitate comparison with a symmetrical reference line by a numerical representation. This means that the R–L vector line utilizes the kinematic synergy of the R–L lower limbs and can visually represent the difference in the kinematic coordination of the R–L lower limbs. The conventional assessment of R–L differences using muscle synergy consisting of multiple muscles can be depicted with fewer variables.

Because of the small number of participants in this study and the fact that the *MSE* did not yield useful conclusions from the statistical tests, we were unable to quantitatively determine the presence or absence of R–L differences using the *MSE* cutoff values. In the future, we hope to calculate the cutoff value of the *MSE* by increasing the number of participants and establish this method as a symmetry evaluation method. Furthermore, we would like to apply this method to the PLG, which can be expressed in two degrees of freedom, to verify whether this method can be applied not only to STS but also to the symmetry evaluation of the gait cycle of the R–L lower limbs in the gait.

**Author Contributions:** K.N., conceptualization and writing of the original draft; N.S., discussion of the original draft, review, and editing. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was partially funded by Kwansei Gakuin University.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

