A Symmetry Evaluation Method, Using Elevation Angle, for Lower Limb Movement Patterns during Sitting-to-Standing

: In this paper, we propose a method that uses the femoral and tibial elevation angles to quantitatively evaluate the symmetry of lower limb movement during the transition from a sitting position to a standing position. In kinematic analysis of the transition from sitting to standing, the angles of the three joints of the lower limb are often measured. However, due to the large number of variables, it is difﬁcult to evaluate the symmetry of the lower limb movement by comparing data from the six joints of the left and right lower limbs. In this study, therefore, we measured the femoral and tibial elevation angles of healthy participants and rehabilitation patients and visually and numerically evaluated the symmetry and asymmetry of the movement of the left and right lower limbs. We were able to identify the kinematically major lower limbs in the transition from sitting to standing and quantify the symmetry of the movement patterns of the left and right lower limbs. Furthermore, we examined the possibility that the method could be effectively used in the rehabilitation ﬁeld to evaluate the motor co-ordination that constitutes the lower limb movement pattern in the transition from the sitting to standing position, such as the gait plane rule.


Introduction
In our daily lives, we repeatedly travel to and from our destinations to accomplish our goals, often choosing walking as our means of transportation. However, disabled or elderly people who cannot walk safely may choose a wheelchair as their means of transportation [1]. When we walk or sit in a wheelchair, we need to perform a standing movement (sitting to standing (STS)). However, disabled and elderly people may not be able to perform the STS movement and may not be able to continue to live independently. Therefore, sometimes, the goal of rehabilitation in hospitals and nursing homes is to ensure that the patient achieves the STS ability [2]. Post-hip-fracture and post-stroke patients targeted for rehabilitation have been reported to have asymmetric STS movements due to muscle weakness and impaired sensory integration in the lower limbs [3,4]. Pao-Tsai et al. reported that post-stroke patients who had experienced falls had greater asymmetry in the weight distribution to the lower limbs during the STS movement [5]; the asymmetry of the STS movements is shaped by the associated muscle forces and joint moments. Previous studies examining weight bearing in the lower limbs of post-stroke patients have reported that patients often shift their center of gravity to the nonparalyzed lower limb [6]. However, mechanical asymmetry of the lower limb during the STS movement may reduce safety when the person is performing an even more advanced and dynamic gait [7]. Ryoichiro et al. reported an STS rehabilitation system that improves the functional asymmetry of the lower limb caused by disease [8]. These previous studies indicate that it is important for rehabilitation to improve the muscle strength, movement, and asymmetric STS movement of the asymmetric lower limb.
In previous studies on STS symmetry, lower limb joint torque and floor reaction force were selected as mechanical parameters and joint angle as a kinematic parameter, parameters that can be observed in measurement experiments [9][10][11]. These parameters are observed as a result of the human central nervous system controlling the muscles (the locomotion organs). In Japan today, cerebrovascular disorders are the leading cause of the need for long-term care [12] and normalization of muscle activity patterns and centerof-gravity trajectories during movement through rehabilitation-incorporating robots is becoming the treatment of choice [13]. In other words, rehabilitation of the central nervous system, which controls muscle activity temporally and spatially, rather than rehabilitation to increase motor muscle mass and the force exerted by the muscles, is attracting attention. Ningjia et al. analyzed muscle synergy during the STS movement in stroke patients [14]. However, this report mentions asymmetry based on the analysis of muscle synergy but does not propose a quantitative method for evaluating symmetry and asymmetry. Wendy et al. proposed a symmetry index in their report on STS symmetry evaluation [9]. This method measures the angles of the right and left (R-L) lower limb joints during the STS movement and calculates the ratio of the angles as a symmetry index. Michalina et al. selected ankle, knee, and hip joint angles, joint torque, and floor reaction force as symmetry indices [11]. These previous studies converted the observed information into a single value as an index of symmetry and cannot represent the motion patterns during the STS movement.
The planar law of gait (PLG) is a well-known evaluation method that allows us to observe the coordination patterns of the neurophysiological body movement based on changes in joint angles observed over time during movement [15,16]. The PLG involves the three-dimensional plotting of the elevation angles (EAs) of three segments (thigh, shin, and foot) during walking. Gianluca et al. used the PLG of the L-R lower limbs to present the symmetry of the walking motion as visual information [17]. They evaluated the symmetry; if the PLG could be applied to the STS movement and the STS movement symmetry could be quantitatively evaluated, it would be possible to geometrically evaluate the symmetry of the control by the central nervous system during the STS movement. However, there are different factors involved in the STS movement and gait. In the gait, the EAs of three segments (thigh, shank, and foot) are observed, but in the STS movement the EA of the foot is always constant because the foot is restrained above the floor and only changes in the EAs of two segments (thigh and shank) are observed. Therefore, the observed changes in the EAs of the two body segments in the STS movement cannot be plotted on 3D coordinates as in the gait. Furthermore, since the STS movement is not a periodic motion similar to a gait, the PLG cannot be directly adapted to the STS movement.

Participants
This study included 4 healthy participants (22.3 ± 0.5 years) and 4 rehabilitation patients (82.8 ± 3.1 years). The selection criterion for healthy participants was the absence of trauma or a disability that would affect the STS motion at the time of participation. In the case of patients, those who were judged by a rehabilitation specialist to be able to complete the STS movement unaided were included. The study was conducted after the participants were informed about the study and after they signed a consent form. Table 1 provides physical information about the healthy participants and the rehabilitation patients.

Experiment
In this study, motion capture experiments were conducted with healthy participants at Kwansei Gakuin University from 20 February 2019 to 24 February 2019 and with rehabilitation patients at Toyonaka Heisei Hospital on 7 March 2020. The 40 motion capture markers were placed on landmarks throughout the body [18]. In this study, four markers (the lateral ankle, the lateral 1/3 of the lower tibia, the lateral epicondyle of the knee, and the lateral 1/3 of the lower thigh) were placed on one lower extremity, and participants sat in a chair with a height of 43.5 cm and without a backrest. Participants were instructed to not allow their upper limbs to come into contact with their body or the external environment during the STS movement. The motion capture experiment was conducted as follows ( Figure 1).

1.
Each participant sat in a chair and maintained their posture to initiate the STS movement.

2.
When we judged that the participant's sitting posture was stationary, we signaled the start of STS.

3.
On hearing the cue, the participant initiated the STS movement.

4.
When the participant stood up and we judged that the standing posture was stationary, we signaled the end of the STS movement.

5.
The video images from the cue for the start of the movement to the cue for the end of the movement were included in the analysis.
A calibration space with an area of 150 cm × 150 cm and a height of 195 cm centered on the participant's feet was set up (Figure 2). The captured images were recorded using Capture-Ex (Library Co., Ltd., Tokyo, Japan) at a sampling frequency of 50 Hz. Move-tr/3D (Library Co., Ltd., Tokyo, Japan) was used to convert the marker information in the video into coordinate data, and KineAnalyzer (KISSEI COMTEC Co., Ltd., Nagano, Japan) was used to measure the EAs of the thigh and shank. A 2 Hz low-pass filter was applied to all marker data. The EA formed by the shank and the vertical axis was defined as θ S , and the EA formed by the thigh and the vertical axis was defined as θ T (Figure 3).      The angle between the vertical axis and the thigh axis was defined as θ T , and the angle between the vertical axis and the lower leg was defined as θ S .

Analysis
Data for each of the healthy and rehabilitation patient groups were analyzed, and statistical tests were performed on the results. Details of the analysis are provided below.

Definition of the EA error
During the STS motion, the shank EA was defined as θ S and the thigh EA was defined as θ T . In the first experiment of this study, the L-R errors of θ S and θ T were calculated. The indices of the L-R error were the shank EA error SE ave , the thigh EA error TE ave , and the overall error E sum . Formulas (1)-(3) provide the calculation of each index.
where n is the total number of samples for each participant and i is the i-th sample. The total number of samples was calculated by dividing the STS measurement time for each participant by the sampling frequency of 50 Hz.

Analysis of Measured EA changes
Two-dimensional Cartesian coordinates C 1 were created with the shank EA θ S as the y-axis and the thigh EA θ T as the x-axis, and n points F i (θ Si , θ Ti ) were recorded on these coordinates. Point F i was recorded on coordinate C 1 for the R-L lower limbs. The position vector norm pointing from the origin to point F i was then calculated. Another two-dimensional Cartesian coordinate C 2 was created, with the position vector norm a Ri of the right lower limb as the x-axis and the position vector norm a Li of the left lower limb as the y-axis. Thus, a line (the R-L vector line) consisting of n points f i (a Ri , a Li ) on the two-dimensional coordinate C 2 was illustrated. Finally, a symmetrical reference line y = x was created on the two-dimensional coordinate C 2 and the average error ME and the average error sum of squares MSE at each point of the target reference line and the R-L vector line were calculated using Equations (4) and (5):

Symmetrical Comparison Using Measured EAs
Figures 4 and 5 display the changes in shank EA θ S and thigh EA θ T during the STS motion. Figure 4 shows the results for each participant in the healthy group, and Figure 5 shows the results for each participant in the rehabilitation patient group.   Table 1.
On the basis of the measured EA changes in the healthy group, the following four phases were commonly observed in the healthy participants: -Phase 1: The STS start angle; -Phase 2: A decrease in the thigh EA and an increase in the shank EA; -Phase 3: A decrease in the thigh EA and a decrease in the shank EA; -Phase 4: The STS end angle. A common characteristic of the healthy group was a small L-R error in the decrease in the thigh EA corresponding to Phases 2 and 3 but a trend toward larger L-R errors in thigh and shank EAs for Phases 1 and 4.
The EA changes in the rehabilitation patient group were characterized by two features. The first was that irregular EA changes occurred with shifting STS phases, making it impossible to identify the Phases 1-4 observed in the healthy group. The second was that the R-L thigh EAs were not as close as in the healthy group during Phases 2 and 3, even though the EA changes were similar in appearance to those in the healthy group (e.g., Patients 1 and 3). Table 2 summarizes the R-L EA errors in the healthy group and the rehabilitation patient group. In this experiment, the mean and the standard deviation of each EA error , , and the error sum of the rehabilitation patient group were larger than those of the healthy group. A two-tailed Student's t-test (R-4.0.2) at the 5% level of significance for the above three errors showed no significant difference between the two groups.   Table 1.
On the basis of the measured EA changes in the healthy group, the following four phases were commonly observed in the healthy participants: A common characteristic of the healthy group was a small L-R error in the decrease in the thigh EA corresponding to Phases 2 and 3 but a trend toward larger L-R errors in thigh and shank EAs for Phases 1 and 4.
The EA changes in the rehabilitation patient group were characterized by two features. The first was that irregular EA changes occurred with shifting STS phases, making it impossible to identify the Phases 1-4 observed in the healthy group. The second was that the R-L thigh EAs were not as close as in the healthy group during Phases 2 and 3, even though the EA changes were similar in appearance to those in the healthy group (e.g., Patients 1 and 3). Table 2 summarizes the R-L EA errors in the healthy group and the rehabilitation patient group. In this experiment, the mean and the standard deviation of each EA error SE ave , TE ave , and the error sum E sum of the rehabilitation patient group were larger than those of the healthy group. A two-tailed Student's t-test (R-4.0.2) at the 5% level of significance for the above three errors showed no significant difference between the two groups.

Comparison of R-L Symmetry by the R-L Vector Line
Figures 6 and 7 present the R-L vector lines for the healthy participants and the rehabilitation patients, respectively. Here, the numbers 1-4 assigned to each participant refer to the same participant's results for the measured EAs (Figures 4 and 5). Table 3 shows the ME and the MSE obtained from the R-L vector line and the symmetric reference line; the ME is the error in the position vector norm of the R-L lower limbs, which approaches 0 if the motion patterns of the R-L lower limbs are symmetric ( a Ri = a Li ). habilitation patients, respectively. Here, the numbers 1-4 assigned to each participant refer to the same participant's results for the measured EAs (Figures 4 and 5). Table 3 shows the and the obtained from the R-L vector line and the symmetric reference line; the is the error in the position vector norm of the R-L lower limbs, which approaches 0 if the motion patterns of the R-L lower limbs are symmetric (‖ ‖ = ‖ ‖).
If 0, then the point ( , ) is distributed more on the y-axis side of the symmetry reference line, and if 0, then the point f_i is distributed more on the xaxis side of the symmetry reference line. In the healthy participants, four values were negative, while in the rehabilitation patient group, two were positive and the remaining two were negative. Next, the is a parameter that quantifies the asymmetry of movement patterns. The of the healthy participants was 4.2 ± 2.0, while the of the rehabilitation patient group was 6.8 ± 2.5. The of the rehabilitation patient group was approximately 1.6 times that of the healthy group, but a two-tailed Mann-Whitney U test (R-4.0.2) at the 5% significance level showed no significant difference between the two groups.  Table 1.  Table 1.   Table 1.

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  Table 1. If ME > 0, then the point f i (a Ri , a Li ) is distributed more on the y-axis side of the symmetry reference line, and if ME < 0, then the point f_i is distributed more on the x-axis side of the symmetry reference line. In the healthy participants, four ME values were negative, while in the rehabilitation patient group, two were positive and the remaining two were negative. Next, the MSE is a parameter that quantifies the asymmetry of movement patterns. The MSE of the healthy participants was 4.2 ± 2.0, while the MSE of the rehabilitation patient group was 6.8 ± 2.5. The MSE of the rehabilitation patient group was approximately 1.6 times that of the healthy group, but a two-tailed Mann-Whitney U test (R-4.0.2) at the 5% significance level showed no significant difference between the two groups.

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.

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.