## 3 Results  
All of the performed simulations were effective in distalization movements; differences between models were detected mostly in the anterior region of the arch. Considering the anchorage of a Class I elastic on the first premolar, the resulting side effect was a buccal movement of the canine. This result was confirmed by the anti-clockwise deformation detected on the aligner in the canine region. This deformation became larger as the angle between the elastic vector and the occlusal plane increased: the deformation registered was 0.044 mm when the elastic was applied parallel to the occlusal plane; it became 0.058 mm and 0.06 mm when the angle was 20\  
When the Class I elastic was anchored on the canine, distal displacement (from 0.04 to 0.06, depending on elastic inclination) of the canine, as well as a deformation of the aligner in the distal direction, were observed.  
Figure 4: Tooth displacement.  
Figure 3: Aligner deformation.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Configuration** & **X (mm)** & **Y (mm)** & **Z (mm)** & **Total (mm)** \\ \hline \(\alpha\) 90 & \(-\)0.002 & 0.062 & \(-\)0.016 & 0.064 \\ \(\alpha\) 20 & \(-\)0.007 & 0.060 & \(-\)0.015 & 0.062 \\ \(\alpha\) 30 & \(-\)0.009 & 0.058 & \(-\)0.014 & 0.060 \\ \(\beta\) 90 & \(-\)0.009 & 0.068 & \(-\)0.017 & 0.071 \\ \(\beta\) 20 & \(-\)0.010 & 0.065 & \(-\)0.017 & 0.068 \\ \(\beta\) 30 & \(-\)0.011 & 0.063 & \(-\)0.016 & 0.066 \\ \(\alpha\) 90 anch & \(-\)0.0001 & 0.064 & \(-\)0.017 & 0.066 \\ \(\beta\) 90 anch & \(-\)0.008 & 0.069 & \(-\)0.018 & 0.072 \\ \(\beta\) 30 anch & \(-\)0.009 & 0.065 & \(-\)0.017 & 0.068 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Element 1.6 meso-buccal cusp displacement.  
As the angle between the elastic and the occlusal plane increased, a more intrusive movement of the canine was highlighted. Interestingly, while this vertical component was null in the configuration with the elastic parallel to the occlusal plane (\(\alpha\)90), it was maximum (0.016 mm) when the elastic was tilted at 30\({}^{\circ}\), with respect to the occlusal plane.  
The distalization movements of the second premolars and first molars were more efficient when the elastics were parallel to the occlusal plane. Values registered were similar in both elements: the distalization movement of 1.6 ranged from 0.062 with \(\alpha\)90 to 0.058 with \(\alpha\)30 while ranged from 0.072 with \(\alpha\)90 to 0.70 with \(\alpha\)30 in 1.5. Moreover, with these configurations, the pressure between the teeth and aligner on the second premolar attachment mesial surface reaches the maximum value (3435.42 g/cm\({}^{2}\) in \(\alpha\)90 situation), while it decreases as the angle between the elastic and the occlusal plane increases (2744.57 g/cm\({}^{2}\) in \(\alpha\)20 and 2681.34 g/cm\({}^{2}\) in \(\alpha\)30 configuration).  
A greater anterior anchorage loss was observed when the elastic was anchored on the canine, with a proclination (0.015 mm) of the upper central incisor, 30% higher than in the simulation in which the elastic was anchored on the first premolar (0.026 mm).  
No significant changes in the pattern of teeth movement were detected in the pseudo-ankylosis simulation, with the exclusion of any mesial movement of the upper second molar. However, a slightly better performance was measured in terms of distalization of the second premolar and first molar, and a greater contact pressure on the mesial surface of the second premolar attachment was revealed (3680.05 g/cm\({}^{2}\) in \(\alpha\)90, 5155.89 g/cm\({}^{2}\) in \(\beta\)90, and 3812.31 g/cm\({}^{2}\) in \(\beta\)30).