## 3 Modified NDT Intervention
The amplitude of pelvic rotation \(Amp_{PR}\) is defined as the maximum rotation angle between two consecutive HS events on the paretic side, as follows:  
\[Amp_{PR}=\theta_{\text{max}}-\theta_{\text{min}} \tag{3}\]  
where \(\theta_{\text{max}}\) and \(\theta_{\text{min}}\) represent the maximum and minimum pelvic angles during a complete gait cycle, respectively, as shown in Figure 6. Since stroke patients' muscles are usually weakened on the paretic side, their pelvic rotation is limited and less than in healthy persons. Therefore, we can evaluate the effectiveness of the NDT rehabilitation by \(Amp_{PR}\), and we regard the training as effective if \(Amp_{PR}\) is increased. We attached an IMU to the subjects' waists (see Figure 5) to record their pelvic rotations. The results are illustrated in Table 5; only 6 of the 10 subjects had an improvement in \(Amp_{PR}\) during the treatment (B stage) and after the treatment (\(\overline{\text{A}}\) stage). That is, the current intervention method can improve the subjects' gait symmetry but not their pelvic rotation. Therefore, we analyzed the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Subject** & **A** & **B (imp\%)** & **A (imp\%)** \\ \hline H1 & 41.4 & 35.7 (14) & 30.9 (25) \\ H2 & 34.4 & 40.2 (\(-\)17) & 31.5 (8) \\ H3 & 61.9 & 66.8 (\(-\)8) & 50.8 (18) \\ H4 & 38.4 & 27.3 (29) & 30.2 (21) \\ H5 & 59.7 & 42.2 (29) & 43.7 (44) \\ H6 & 20.4 & 15.9 (22) & 6.7 (67) \\ H7 & 17.3 & 18.9 (\(-\)10) & 12.4 (28) \\ H8 & 39.9 & 14.9 (63) & 18.9 (52) \\ H9 & 14.9 & 38.9 (\(-\)160) & 18.8 (\(-\)25) \\ H10 & 11.0 & 5.6 (17) & 4.7 (57) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The asymmetry of the swing phase. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Subject** & **Gender** & **Age** & **Height (cm)** & **Weight (kg)** \\ \hline H1 & Male & 25 & 172 & 76 \\ H2 & Female & 58 & 164 & 64 \\ H3 & Male & 25 & 170 & 65 \\ H4 & Male & 23 & 172 & 70 \\ H5 & Male & 23 & 178 & 70 \\ H6 & Male & 24 & 164 & 70 \\ H7 & Male & 22 & 166 & 61 \\ H8 & Male & 25 & 165 & 50 \\ H9 & Female & 24 & 158 & 45 \\ H10 & Male & 23 & 185 & 85 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Information of the healthy subjects. therapists' interventions during the clinical NDT training in [14; 15; 16], as those interventions were manually conducted by the therapists. The analyses are illustrated in Appendix C and show that the therapist tended to increase the intervention forces on the non-paretic side when the subject's pelvic rotation was small. Based on that analysis, we proposed a modified NDT intervention algorithm that can improve the gait asymmetry and the pelvic rotation simultaneously. The modified intervention method is shown in Figure 7, where the maximum intervention forces on the non-paretic side are increased by 50% if the pelvic rotation is less than a given threshold. For example, we applied the rehabilitation gaiter to the subjects' right knee so that the left motor was controlled according to the following procedures:  
1. The motor tracked a minimum force of \(\overline{F}_{\min}\) to keep the rope straight. 2. The motor was activated to follow the intervention force pattern of (2), when the right HS was detected. 3. The maximum intervention force \(\overline{F}_{\max}\) was increased if the pelvic rotation \(Amp_{PR}\) was less than a threshold value. \begin{table}
\begin{tabular}{c|c c c|c c} \hline \hline \multirow{2}{*}{**Subject**} & \multirow{2}{*}{**A**} & \multirow{2}{*}{**B (imp\%)**} & \multicolumn{2}{c}{–} \\  & & & & **A (imp\%)** \\ \hline H1 & 7.6 & 13.9 & (82) & 9.6 & (27) \\ H2 & 12.9 & 7.7 & (\(-41\)) & 10.5 & (\(-19\)) \\ H3 & 6.0 & 11.2 & (86) & 6.4 & (5) \\ H4 & 7.5 & 11.9 & (59) & 8.0 & (7) \\ H5 & 12.4 & 14.5 & (17) & 15.3 & (23) \\ H6 & 6.7 & 6.5 & (\(-3\)) & 4.5 & (\(-33\)) \\ H7 & 7.8 & 8.2 & (5) & 9.1 & (17) \\ H8 & 15.6 & 15.4 & (\(-1\)) & 16.5 & (6) \\ H9 & 12.7 & 7.3 & (\(-42\)) & 7.1 & (\(-44\)) \\ H10 & 9.9 & 17.0 & (\(72\)) & 9.1 & (\(-8\)) \\ \hline \hline \end{tabular}
\end{table}