# For Patients with Stroke, Balance Ability Affects the Leg Extension Angle on the Affected Side
## 3 Results  
The BBS, FMA-LL, and MI-LL in the study participants were assessed to be 45.0 \(\pm\) 5.5 points, 23.3 \(\pm\) 6.4 points, and 54.2 \(\pm\) 12.3 points, respectively, and gait speed was 0.48 \(\pm\) 0.19 m/s (Table 1). Addressing the affected side, the leg extension angle (10.0 \(\pm\) 7.1\({}^{\circ}\), \(p\) = 0.009) and the velocity increment at the late stance (0.18 \(\pm\) 0.09 m/s, \(p\) < 0.001) were significantly lower than those on the non-affected side (leg extension angle, 14.1 \(\pm\) 4.8\({}^{\circ}\); velocity increment, 0.32 \(\pm\) 0.11 m/s).  
The correlation between the leg extension angle, BBS, FMA-LL, MI-LL, velocity increment of the affected side, and gait speed are given in Table 2. The leg extension angle showed a significant positive correlation with BBS (\(r\) = 0.757, \(p\) < 0.001), FMA-LL (\(r\) = 0.393, \(p\) = 0.047), MI-LL (\(r\) = 0.532, \(p\) = 0.005), velocity increment (\(r\) = 0.863, \(p\) < 0.001), and gait speed (\(r\) = 0.732, \(p\) < 0.001) (Table 2).  
BBS, FMA-LL, and MI-LL were included in the multiple regression analysis to identify the factors determining the leg extension angle on the affected side (Table 3); BBS was the only factor that showed a significant association (\(\beta\) = 0.757, \(p\) < 0.001).  
The results of the path analysis based on an exploratory regression analysis (Appendix A, Tables A1-A4) were used to derive the model shown in Figure 2. The model fitted well (chi-square test: \(\chi\)2 = 4.219, df = 8, \(p\) = 0.837; CFI: 1.000; GFI: 0.949; RMSEA: \(<\) 0.001). The leg extension angle on the affected side was directly associated with BBS (\(\beta\) = 0.757, \(p\) < 0.001) and indirectly affected by MI-LL via BBS (\(\beta\) = 0.668, \(p\) < 0.001). The leg extension angle on the affected side modulated gait speed via the increment of velocity on the affected side (\(\beta\) = 0.863, \(p\) < 0.001). The BBS also directly affected the gait speed (\(\beta\) = 0.356, \(p\) = 0.027).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variable** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline
1. Leg extension & - & 0.757 ** & 0.393 * & 0.532 ** & 0.863 ** & 0.732 ** \\
2. BBS & & - & 0.487 ** & 0.594 ** & 0.597 ** & 0.709 ** \\
3. FMA-LL & & & - & 0.793 ** & 0.109 & 0.605 ** \\
4. MI-LL & & & & - & 0.399 * & 0.619 ** \\
5. Increment of & & & & & - & 0.622 ** \\ velocity & & & & & - \\
6. Gait speed & & & & & - \\ \hline \hline \end{tabular}  
* \(p\) < 0.05, ** \(p\) < 0.01. BBS: Berg balance scale; FMA-LL: Fugl-Meyer assessment-lower limb; MI-LL: mortality index-lower limb.  
\end{table}
Table 2: Correlations among leg extension angle, physical impairments, and gait parameters on the affected side.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Independent Variable** & **B** & \(\beta\) & \(t\)**Value** & \(p\)**Value** & **95\% CI** & **VIF** \\ \hline BBS & 0.984 & 0.757 & 5.675 & \textless{}0.001 & 0.626–1.342 & 1.000 \\ \hline \hline \end{tabular}  
\(R^{2}\) = 0.555 (F = 32.209, \(p\) < 0.001). B: unstandardized coefficient; \(\beta\): standardized coefficient; CI: confidence interval; VIF: variance inflation factor; \(R^{2}\): adjusted coefficient of determination; BBS: Berg balance scale.  
\end{table}
Table 3: Clinical factors associated with the leg extension angle on the affected side in stepwise multiple regression analysis.