## 3 Results
### Displacements of Selected Facial Skeleton Structures along the X, Y, Z Axes (mm)  
The smallest displacement along the X axis in the buccal direction was found on the facial skeleton model without osteotomy (model 1), on the model with Le Fort I osteotomy (model 3) and on the model with Le Fort I osteotomy and separation from the pterygoid process (model 4). Displacements on the above-mentioned models were in the 0.04-0.13 mm range. On the models with palatal incision, displacements along the X axis in the buccal direction ranged from 0.22 to 0.31 mm on model 2, from 0.22 to 0.31 mm on model 5, and from 0.22 to 0.4 mm on model 6. The largest displacement in the buccal direction was found at the mesial incisal angle of the central maxillary incisor (0.4 mm) on model 6 of the facial skeleton.  
On the model without osteotomy (model 1) displacements ranged from \(-\)0.05 to 0.1 mm along the Y axis. On model 2 they ranged from 0.05 to 0.03 mm, on model 3 from \(-\)0.5 to 0.03 mm, on model 4 from \(-\)0.05 to 0.05 mm, on model 5 from 0.03 to 0.05 mm, and on model 6 from \(-\)0.01 to 0.07 mm.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Anatomical Structures** &
\begin{tabular}{c} **Model I No** \\ **Surgery** \\ \end{tabular} & **Model II** & **Model III** & **Model IV** & **Model V** & **Model VI** \\ \hline Nasofrontal suture & 2.2 & 5.5 & 1.1 & 1.1 & 4.4 & 2.2 \\ \hline Zygomaticomaxillary suture & 3.3 & 5.5 & 4.4 & 1.1 & 4.4 & 2.2 \\ \hline Arcus superciliar—brow ridge & 2.2 & 8.8 & 2.2 & 2.2 & 7.7 & 3.3 \\ \hline Zygomaticofrontal suture & 4.4 & 7.7 & 3.3 & 2.2 & 7.7 & 3.3 \\ \hline Palatal suture anterior region & \(>\)25 & 1.1 & \(>\)25 & \(>\)25 & 1.1 & 1.1 \\ \hline Palatal suture posterior region & 13.8 & 1.1 & 13.8 & 13.8 & 1.1 & 1.1 \\ \hline Supraorbital margin & 2.2 & 4.4 & 2.2 & 1.1 & 4.4 & 2.2 \\ \hline Infraorbital margin & 4.4 & 5.5 & 2.2 & 1.1 & 7.7 & 2.2 \\ \hline Apertura piriformis—the lowest point & 5.5 & 1.1 & \(>\)10 & \(>\)10 & 1.1 & 1.1 \\ \hline Anterior wall of maxillary sinus & \(>\)10 & 4.4 & 7.7 & 1.1 & 3.3 & 2.2 \\ \hline Zygomaticoalveolar crest & \(>\)10 & \(>\)10 & 5.5 & 3.3 & 5.5 & 3.3 \\ \hline Processus alveolaris of maxillie & _7.7_ & 1.1 & 10 & \(>\)10 & 1.1 & 1.1 \\ \hline Processus alveolaris of maxillie & \(>\)10 & 8.8 & \(>\)10 & \(>\)10 & 7.7 & 3.3 \\ \hline regio premolars & \(5.5\) & 1.1 & 5.5 & _7.7_ & 3.3 & 3.3 \\ \hline Crown/column fifth maxilla tooth & \(>\)10 & 5.5 & \(>\)10 & \(>\)10 & 5.5 & 4.4 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Stress distribution according to [PERSON] on the craniofacial model (MPa) with various surgical procedures and tooth born orthodontic appliance using finite element analysis.  
The largest displacement in the anterior direction was found at the mesial incision angle of the central maxillary incisor (0.07 mm) on model 6 of the facial skeleton.  
On the model without osteotomy, displacements ranged from \(-\)0.03 to 0.1 mm along the Z axis. On model 2, they ranged from 0.01 to 1.0 mm, on model 3 from \(-\)0.01 to 0.03 mm, on model 4 from \(-\)0.03 to 0.07 mm, on model 5 from \(-\)0.05 to 0.07 mm, and on model 6 from \(-\)0.05 to 0.07 mm. The largest displacement in the superior direction was found on the posterolateral surface of the maxilla (1.0 mm) on model 2 of the facial skeleton.  
Detailed displacement values (mm) along the X, Y, Z axes at selected sites of the facial skeleton are shown in Table 4.