## 3 Results
### Forces and Moments
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline  & \multicolumn{8}{c}{**ATMOS**} & \multicolumn{4}{c}{_p-Value_} \\ \cline{2-10}  & \multicolumn{4}{c}{**0.25 mm**} & \multicolumn{4}{c}{**0.50 mm**} & \multicolumn{2}{c}{_p-Value_**} \\ \cline{2-10}  & \multicolumn{4}{c}{**Mean \(\pm\) SD**} & \multicolumn{4}{c}{**Mean \(\pm\) SD**} & \multicolumn{4}{c}{**Mean \(\pm\) SD**} \\ \hline Fx (N) & 0.86 & L & \(\pm\) & 2.11 & 0.54 & F & \(\pm\) & 0.58 & \textless{}0.001 \\ \hline Fy (N) & 0.63 & D & \(\pm\) & 3.47 & 0.51 & M & \(\pm\) & 0.42 & \textless{}0.001 \\ \hline Fz (N) & 1.05 & O & \(\pm\) & 1.59 & 0.19 & O & \(\pm\) & 0.23 & \textless{}0.001 \\ \hline Mx (Nmm) & 17.49 & M & \(\pm\) & 25.91 & 6.30 & M & \(\pm\) & 1.27 & \textless{}0.001 \\ \hline My (Nmm) & 20.62 & L & \(\pm\) & 23.66 & 8.27 & L & \(\pm\) & 3.21 & \textless{}0.001 \\ \hline Mz (Nmm) & 18.39 & D & \(\pm\) & 72.60 & 5.38 & M & \(\pm\) & 8.85 & \textless{}0.001 \\ \hline \multicolumn{10}{c}{**Zendura FLX**} & \multicolumn{4}{c}{_p-Value_} \\ \cline{2-10}  & \multicolumn{4}{c}{**0.25 mm**} & \multicolumn{4}{c}{**0.50 mm**} & \multicolumn{4}{c}{**_p-Value_**} \\ \cline{2-10}  & \multicolumn{4}{c}{**Mean \(\pm\) SD**} & \multicolumn{4}{c}{**Mean \(\pm\) SD**} & \multicolumn{4}{c}{**_p-Value_**} \\ \hline Fx (N) & 0.21 & L & \(\pm\) & 0.84 & 0.41 & F & \(\pm\) & 0.54 & \textless{}0.001 \\ \hline Fy (N) & 0.34 & M & \(\pm\) & 0.81 & 0.93 & M & \(\pm\) & 0.58 & \textless{}0.001 \\ \hline Fz (N) & 1.02 & O & \(\pm\) & 1.61 & 0.32 & O & \(\pm\) & 0.27 & \textless{}0.001 \\ \hline Mx (Nmm) & 16.90 & M & \(\pm\) & 23.18 & 5.52 & M & \(\pm\) & 2.71 & \textless{}0.001 \\ \hline My (Nmm) & 15.28 & L & \(\pm\) & 15.50 & 5.83 & L & \(\pm\) & 5.22 & \textless{}0.001 \\ \hline Mz (Nmm) & 4.64 & D & \(\pm\) & 11.87 & 6.95 & M & \(\pm\) & 8.88 & \textless{}0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparisons of initial forces and moments exerted on the maxillary left lateral incisor (22) by activation amount for ATMOS, Zendura FLX, and TC-85 materials. The magnitude of lingual force experienced by tooth 21 increased with increasing activation of lingual bodily movement. For ATMOS, a two-fold increase in activation from 0.25 mm to 0.50 mm resulted in a two-fold increase in the mean lingual force from 3.82 N to 7.70 N; for Zendura FLX, the same increase in activation resulted in a 2.7-fold increase in mean lingual force from 3.00 N to 8.23 N; and for TC-85, the same increase in activation resulted in a 1.5-fold increase in mean lingual force from 0.99 N to 1.53 N.  
In addition to expected lingual forces, the aligners generated unplanned forces in the mesiodistal and occlusogingival directions on tooth 21. There were mesial forces measured for all three materials at all activations, although the magnitudes were lower with TC-85 than with ATMOS or Zendura FLX. For example, with ATMOS and Zendura FLX at 0.25 mm lingual activation, there were 4.09 N and 3.32 N of extrusive force, respectively. However, at 0.50 mm activation, these force directions became intrusive. With TC-85, the occlusogingival forces were relatively minor, ranging from 0.06 to 0.10 N for both activations. When tooth 21 was activated lingually, the right central incisor (tooth 11) also experienced a force in the lingual direction with all material types. When the activation was increased from 0.25 mm to 0.50 mm, the force level remained relatively constant with TC-85 (0.52 N to 0.51 N), whereas with ATMOS and Zendura FLX, the force level increased (2.01 N to 2.58 N, 1.59 N to 2.25 N, respectively). Extrusive forces were noted with all three materials at the different activations, and the force magnitudes were lowest with TC-85 (0.09-0.16 N) versus ATMOS (0.94-1.47 N) and Zendura FLX (0.28-0.63 N). The effect of lingual activation on tooth 21 and the maxillary left central incisor (tooth 22) was different compared to its effect on tooth 11. Whereas ATMOS and Zendura FLX generated a mean lingual force, TC-85 generated a mean facial force.