## 4 Discussion  
Many finite element studies have looked at changes in teeth based on their initial responses when an orthodontic force is applied [1; 2; 3]. However, during orthodontic treatment, tooth movement occurs, and the force system changes accordingly. To compensate for these shortcomings, [PERSON] et al. [10] have conducted a study by dividing the start and end time points of tooth movement. In the present study, the space closing in the maxillary first premolar extraction model was simulated through continuous finite element analysis. As a result of the study by [PERSON] et al. [10], in the case of HOMS, the incisal edge of the maxillary central incisor extruded in M1 (model immediately after extraction model). However, in M2 (model with 1 mm of extraction space left), the incisal edge of the maxillary central incisor intruded. These results could be confirmed through a continuous process of changes in the present study. Moreover, in LOMS, extrusion of the incisal edge of the maxillary central incisors was observed in both M1 and M2 models, and the continuous process of changes was confirmed in this study (Figure 6). The axis of the maxillary central incisors showed a more upright tendency in LOMS (Figure 5), which was also consistent with the results of [PERSON] et al. [10]. The rotation of the occlusal plane in CW in the M1 model was also confirmed through the tooth movement pattern before 'bounce,' as shown in Figure 6. In LOMS, the occlusal plane was rotated in CW larger than in HOMS. In the M2 model, the rotation of the occlusal plane by CCW for HOMS and CW for LOMS was also consistent with the results of the present study. If there was a difference between the results of [PERSON] et al. [10] and the results of the present study, rotation of the occlusal plane was observed with CCW only in HOMS1 in the present study. The reason for this difference might be because a significant amount of first molar intrusion was observed in continuous finite element analysis. In the M2 condition, the maxillary central incisors intruded in all HOMS conditions. In the case of HOMS1, which had the largest vertical component of retraction force due to the shortest ARH (\(-1\) mm), CCW rotation of the occlusal plane was found, as shown in Figure 8.  
In a study by [PERSON] [24], HOMS was used for patients with gummy smiles, ARH was placed at \(-1\) mm, and en masse retraction was performed to complete the treatment \begin{table}
\begin{tabular}{l c c c} \hline  & **Angle of Initial Occlusal Plane** & **Angle of Occlusal Plane** & **Angle Differences (Deg.)** \\  & **Plane (Deg.)** & **after Space Closing (Deg.)** & **Angle Differences (Deg.)** \\ \hline HOMS1 & & \(+0.42\) & \(+0.58\) \\ HOMS2 & & \(-0.60\) & \(-0.43\) \\ HOMS3 & \(-0.16\) & \(-1.44\) & \(-1.27\) \\ LOMS1 & & \(-3.54\) & \(-3.37\) \\ LOMS2 & & \(-3.87\) & \(-3.71\) \\ LOMS3 & & \(-4.34\) & \(-4.17\) \\ \hline \end{tabular}
\end{table} 
Table 7: Angle and difference in angle value of occlusal plane after initial and space closing. Figure 8: Changes of occlusal plane. aesthetically. In the FEA results of the present study, intrusion of the maxillary central incisor was the largest in the ARH \(-\)1 mm condition of HOMS1, and the occlusal plane was rotated the most by CCW. Therefore, actual clinical results and FEA analysis results were consistent. [PERSON] et al. [25] have studied the effect of OMS position on tooth movement. When the OMS was placed mesial to the second premolar and a short hook (+1 mm) was used, the maxillary central incisor was moved posteriorly by 7.23 mm and intruded by 1.59 mm after space closing, similar to results of our study (HOMS2: the maxillary central incisor was moved posteriorly by 8.92 mm and intruded by 1.19 mm after space closing).