## Appendix C NDT Intervention for Improving Pelvic Rotation  
Since the original intervention method did not improve the subjects' pelvic rotation (see Table 7), we further analyzed the therapists' intervention during the clinical NDT rehabilitation in [14; 15; 16]. The results are illustrated in Table 11, where the pelvic rotation, in general, was improved in all subjects during the treatment (stage B) and the effectsremained after the treatment (stage \(\overline{\text{A}}\)). Therefore, we analyzed the relationship between the therapists' interventions and the subjects' pelvic rotations in the following three scenarios: (1) the applied forces when the pelvic rotation was better; (2) the pelvic rotation when the applied forces were larger; and (3) the influences of larger forces on the asymmetry of the swing phases. (Figures: 20% forces and 20% pelvic rotation).  
\begin{tabular}{c c c c c} \hline \hline
**Subject** & **A** & \multicolumn{2}{c}{**B (imp%)**} & \multicolumn{2}{c}{**A (imp%)**} \\ \hline P1 & 8.9 & 16.7 & (87) & 10.0 & (12) \\ P2 & 18.0 & 23.1 & (28) & 18.7 & (4) \\ P3 & 11.3 & 16.3 & (45) & 11.4 & (2) \\ P4 & 12.1 & 16.9 & (39) & 15.8 & (31) \\ P5 & 19.9 & 26.5 & (34) & 22.6 & (14) \\ P6 & 17.3 & 21.6 & (25) & 15.1 & (\(-\)12) \\ P7 & 21.9 & 35.9 & (65) & 24.4 & (12) \\ P8 & 15.6 & 31.6 & (103) & 17.9 & (15) \\ P9 & 9.4 & 25.9 & (175) & 17.7 & (87) \\ P10 & 9.2 & 18.2 & (98) & 12.8 & (39) \\ \hline \hline \end{tabular}  
* The applied forces when the pelvic rotation was better: we analyzed the applied forces when the pelvic rotation was better. For example, Figure A2 illustrates the intervention forces when the pelvic rotation \(Amp_{PR}\) was the largest (20%). We noted that: (i) the average pelvic rotation is 22.98\({}^{\circ}\), where the average applied force was \(F_{\text{max}}=2.79\) lb; (ii) for the largest \(Amp_{PR}\)(20%), the average pelvic rotation was 28.24\({}^{\circ}\) and the average applied force was \(F_{\text{max}}=3.07\) lb.  
That is, the therapists' intervention forces were greater when the pelvic rotation was larger.  
* The pelvic rotation when the applied forces were larger: we analyzed the impacts of the magnitudes of applied forces on pelvic rotation, as follows: (i) the average applied force was \(F_{\text{max}}=2.79\) lb, where the average pelvic rotation was 22.98\({}^{\circ}\); (ii) when the applied forces were the largest (20%), the average applied force was \(F_{\text{max}}=3.8\) lb and the average pelvic rotation was 23.81\({}^{\circ}\).  
That is, the pelvic rotation was larger when the intervention forces were larger.  
* The influences of larger forces on the asymmetry of the swing phases: we analyzed the influences of the magnitudes of the applied forces on the gait symmetry \(Asym_{SP}\)The results shown in Table 16 indicate that the magnitudes of the applied forces had no significant influence on the gait symmetry index \(Asym_{SP}\). That is, the modified intervention method had no significant influence on the gait symmetry.  
From the above analyses, changing the magnitudes of applied forces can improve the pelvic rotation \(Amp_{PR}\) without influencing the gait symmetry \(Asym_{SP}\). Therefore, we propose the modified intervention method as follows:  
_increasing the intervention forces \(\overline{F}_{\max}\) when the pelvic rotation \(Amp_{PR}\) is less than a threshold of, as illustrated in Figure 7_