## 3 Results
### Change in the Angle of the Occlusal Plane  
The angular change of the occlusal plane was investigated through the coordinate values of the incisal edge of the maxillary central incisor and the mesio-palatal cusp of the maxillary first molar. The position of the maxillary first molar mesio-palatal cusp intruded 1.00-1.51 mm in the +Z direction, and the incisal edge of the maxillary central incisor extruded or intruded by \(-1.19\)-\(+1.85\) mm in the +Z direction under six conditions (Figure 8). The initial occlusal plane angle was \(-0.16^{\circ}\). After space closure, only HOMS1 had a positive value (CCW) of \(+0.42^{\circ}\). Under the remaining conditions, the occlusal plane angle after space closure had a negative value (CW). The absolute value increased from HOMS2 to LOMS3 (Table 7).  
In the case of LOMS, according to the intrusion of the first molar and extrusion of the anterior teeth, the occlusal plane rotated clockwise (CW). However, in the HOMS1 group,  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**HOMS1**} & \multicolumn{2}{c}{**HOMS2**} & \multicolumn{2}{c}{**HOMS3**} \\ \cline{2-7}  & \(\Delta\)**CY (mm)** & \(\Delta\)**CZ (mm)** & \(\Delta\)**CY (mm)** & \(\Delta\)**CZ (mm)** & \(\Delta\)**CY (mm)** & \(\Delta\)**CZ (mm)** \\ \hline Mesio palatal cusp tip & \(-1.45\times 10^{-3}\) & \(1.52\times 10^{0}\) & \(-1.53\times 10^{-1}\) & \(1.39\times 10^{0}\) & \(-2.83\times 10^{-1}\) & \(1.29\times 10^{0}\) \\ Root apex & \(-1.10\times 10^{0}\) & \(1.50\times 10^{0}\) & \(-8.56\times 10^{-1}\) & \(1.39\times 10^{0}\) & \(-6.38\times 10^{-1}\) & \(1.27\times 10^{0}\) \\ \hline \multirow{4}{*}{Mesio palatal cusp tip \(\Delta\)CZ (mm)} & \multicolumn{2}{c}{**LOMS1**} & \multicolumn{2}{c}{**LOMS2**} & \multicolumn{2}{c}{**LOMS3**} \\ \cline{2-7}  & \(\Delta\)**CY (mm)** & \(\Delta\)**CZ (mm)** & \(\Delta\)**CY (mm)** & \(\Delta\)**CZ (mm)** & \(\Delta\)**CY (mm)** & \(\Delta\)**CZ (mm)** \\ \hline Mesio palatal cusp tip & \(-6.95\times 10^{-1}\) & \(1.23\times 10^{0}\) & \(-7.61\times 10^{-1}\) & \(1.14\times 10^{0}\) & \(-7.93\times 10^{-1}\) & \(1.00\times 10^{0}\) \\ Root apex & \(-3.04\times 10^{-1}\) & \(1.19\times 10^{0}\) & \(-1.93\times 10^{-1}\) & \(1.06\times 10^{0}\) & \(-2.64\times 10^{-2}\) & \(8.51\times 10^{-1}\) \\ \hline \multirow{4}{*}{Mesio palatal cusp tip \(\Delta\)CZ (mm)} & \multicolumn{2}{c}{**HOMS2**} & \multicolumn{2}{c}{**LOMS3**} & \multicolumn{2}{c}{**LOMS1**} & \multicolumn{2}{c}{**LOMS2**} \\ \cline{2-7}  & \(\Delta\)**CZ (mm)** & & & & & \\ Change of Mesio & \multirow{2}{*}{Intrusion} & \multicolumn{2}{c}{Intrusion} & \multicolumn{2}{c}{Intrusion} & \multicolumn{2}{c}{Intrusion} & \multicolumn{2}{c}{Intrusion} \\ \cline{1-1} \cline{4-6} \cline{7-7}  & \(\Delta\)**CZ (mm)** & \(+\) **means intrusion** & \(-\) **means extrusion** & & \\ \hline \hline \end{tabular}
\end{table}
Table 6: Changes in maxillary first molar’s mesio-palatal cusp tip and root apex until the extraction space is closed for each case.  
Figure 7: Changes in tooth axis of maxillary first molar after initial tooth movement and completion of space closure.  
counterclockwise (CCW) rotation of the occlusal plane was observed due to more intrusion of the anterior teeth than that of the first molar.