**2. Methods**

#### *2.1. 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.


**Table 1.** Summary of the participants' physical information.

<sup>1</sup> Number of participants. <sup>2</sup> Standard deviation

#### *2.2. 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).

(**a**) (**b**) (**c**) (**d**)

**Figure 1.** STS measurement experiment. The upper extremity did not touch the body or the outside environment. The plantar was fixed in an arbitrary position that was not interchanged from the beginning to the end of the STS motion. (**a**) The start of the STS motion from the stationary starting posture at the signal, (**b, c**) the STS motion in progress, and (**d**) the end of the STS motion when the ending posture is stationary.


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 *θS*, and the EA formed by the thigh and the vertical axis was defined as *θ<sup>T</sup>* (Figure 3).

**Figure 2.** Experimental setup. A calibration space (150 cm × 150 cm × 195 cm) photographed with four CCD cameras.

**Figure 3.** Definition of EAs for the thigh and the lower leg. The EA was measured using KineAnalyzer. The angle between the vertical axis and the thigh axis was defined as *θT*, and the angle between the vertical axis and the lower leg was defined as *θS*.

#### *2.3. 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.

#### 2.3.1. Definition of the EA error

During the STS motion, the shank EA was defined as *θ<sup>S</sup>* and the thigh EA was defined as *θT*. In the first experiment of this study, the L–R errors of *θ<sup>S</sup>* and *θ<sup>T</sup>* were calculated. The indices of the L–R error were the shank EA error *SEave*, the thigh EA error *TEave*, and the overall error *Esum*. Formulas (1)–(3) provide the calculation of each index.

$$E\_{sum} = SE\_{\text{avw}} + TE\_{\text{avw}} \tag{1}$$

$$SE\_{\text{ave}} = \frac{\sum |\text{Right } \theta\_{Si} - Lcf \; \theta\_{Si}|}{n},\tag{2}$$

$$TE\_{\text{ave}} = \frac{\sum |Right\,\,\theta\_{Ti} - Left\,\,\theta\_{Ti}|}{n},\tag{3}$$

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.

#### 2.3.2. Analysis of Measured EA changes

Two-dimensional Cartesian coordinates *C*<sup>1</sup> were created with the shank EA *θ<sup>S</sup>* as the y-axis and the thigh EA *θ<sup>T</sup>* as the x-axis, and n points *Fi* (*θSi*, *θTi*) were recorded on these coordinates. Point *Fi* was recorded on coordinate *C*<sup>1</sup> for the R–L lower limbs. The position vector norm pointing from the origin to point *Fi* was then calculated. Another two-dimensional Cartesian coordinate *C*<sup>2</sup> was created, with the position vector norm *aRi* of the right lower limb as the x-axis and the position vector norm *aLi* of the left lower limb as the y-axis. Thus, a line (the R–L vector line) consisting of n points *fi* (*aRi*, *aLi*) on the two-dimensional coordinate *C*<sup>2</sup> was illustrated. Finally, a symmetrical reference line y = x was created on the two-dimensional coordinate *C*<sup>2</sup> 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):

$$ME = \frac{\sum(||a\_{Li}|| - ||a\_{Ri}||)}{n},\tag{4}$$

$$MSE = \frac{\sum \sqrt{ME^2}}{n}.\tag{5}$$

#### **3. Results**

#### *3.1. Symmetrical Comparison Using Measured EAs*

Figures 4 and 5 display the changes in shank EA *θ<sup>S</sup>* and thigh EA *θ<sup>T</sup>* 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.

**Figure 4.** Measured angular changes in thigh and shank EAs in the healthy group. The horizontal axis is the STS time (in seconds) of each participant. H-1 through H-4 in the figure refer to each healthy participant in Table 1.

**Figure 5.** Measured angular changes in thigh and shank EAs in the rehabilitation patient group. The horizontal axis is the STS time (in seconds) of each participant. P-1 through P-4 in the figure refer to each rehabilitated patient in 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 *SEave*, *TEave*, and the error sum *Esum* 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 2.** EA error in both groups.

<sup>1</sup> Number of participants. <sup>2</sup> Number of samples. <sup>3</sup> Standard deviation. A significance test for the above three errors showed no significant difference between the two groups.

#### *3.2. 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 ( *aRi* = *aLi* ).

**Figure 6.** R–L vector line in the healthy group. The lower limb movement pattern is symmetrical enough to be drawn near the central symmetry reference line. H-1 through H-4 in the figure refer to each healthy participant in Table 1.



**Figure 7.** R–L vector line in the rehabilitation patient group. The lower limb movement pattern is symmetrical enough to be drawn near the central symmetry reference line. P-1 through P-4 in the figure refer to each rehabilitated patient in Table 1.

If *ME* > 0, then the point *fi* (*aRi*, *aLi*) 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.
