## 3 Results
### Moments  
3.2.1 Mx (Mesiodistal Angulation Moment, (+): Distal Tipping Moment, (\(-\)): Mesial Tipping Moment)  
Mx represents the mesiodistal rotational force along the long axis of the tooth. Groups 3 and 4 with enhanced structures had significantly smaller mesial tipping moments than Groups 1 and 2. Group 2, which only added an intrusive force, had the largest mesial  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Measurements** & **Group 1** & **Group 2** & **Group 3** & **Group 4** & **\(p\)-Value** \\
**(Total 80 Sample)** & **(Median, IQR)** & **(Median, IQR)** & **(Median, IQR)** & **(Median, IQR)** & **\(p\)-Value** \\ \hline Fz & 0.31, 0.16 \({}^{\text{a}}\) & \(-\)0.01, 0.20 \({}^{\text{b}}\) & 0.39, 0.09 \({}^{\text{a}}\) & \(-\)0.19, 0.57 \({}^{\text{b}}\) & H = 47.129 \\ Mx (Nmm) & \(-\)10.70, 1.69 \({}^{\text{a}}\) & \(-\)12.43, 1.83 \({}^{\text{b}}\) & \(-\)8.98, 6.46 \({}^{\text{ac}}\) & \(-\)7.91, 4.54 \({}^{\text{c}}\) & H = 29.465 \\ My & 2.27, 3.88 \({}^{\text{a}}\) & \(-\)2.27, 3.55 \({}^{\text{b}}\) & 2.97, 5.21 \({}^{\text{a}}\) & 0.97, 8.01 \({}^{\text{a}}\) & H = 17.114 \\ Mz & \(-\)23.21, 4.20 \({}^{\text{a}}\) & \(-\)23.36, 3.87 \({}^{\text{a}}\) & \(-\)18.87, 26.17 \({}^{\text{a}}\) & \(-\)12.50, 20.24 \({}^{\text{b}}\) & \(<\)0.001 *** \\ \hline \end{tabular}  
* A total of 80 samples were tested, 20 for each group. Different superscripts indicate statistical differences at a significance level of \(p\) < 0.05. ***, statistical difference at \(p\) < 0.001. The Kruskal–Wallis test was used to compare the differences between the groups, with post hoc tests conducted using the Dunn test. Abbreviations: IQR, Interquartile range; Fx (+), buccal force; Fy (+), mesial force; Fz (+), extrusive force; Mx, mesiodistal angulation moment; My, buccolingual inclination moment; Mx, rotation moment.  
\end{table}
Table 2: _Cont._tipping moment of \(-12.43\) Nmm, followed by Group 1 with \(-10.70\) Nmm. Therefore, the application of enhanced structures can reduce mesiodistal tipping.  
2.2 My (Labiolingual Inclination Moment, (+): Labial Inclination Moment, (\(-\)): Linequal Inclination Moment)  
Group 2, which was given only the intrusive movement, had the only lingual inclination moment value of \(-2.273\) Nmm, which was significantly different (\(p<0.001\)). In other words, when the intrusive movement was added, a lingual inclination moment occurred. However, in Group 4, which was given structural enhancement even with the intrusive movement, a labial inclination moment occurred. Group 3, which only applied structural reinforcement, had the largest labial inclination moment of 2.97 Nmm, indicating that the structural enhancement contributed to increasing the net labial rotation force.  
2.3 Mz (Rotational Moment, (+): Mesial (Mesial-In) Rotational Moment, (\(-\)): Distal (Mesial-Out) Rotational Moment)  
Mz represents the rotation moment in the occlusal plane of the tooth. Group 4, with both the enhanced structure and 0.1 mm of intrusive movement, recorded the smallest rotational moment, significantly at \(-12.50\) Nmm, indicating a decrease in mesial-out rotational force. Groups 3 and 4 with enhanced structures observed relatively smaller rotation moments compared to Groups 1 and 2.