## 2 Materials and Methods
### Reference Planes and Measurements  
All CBCTs were aligned in InVivo5(r) (Anatomage, San Jose, CA, USA) so that the plane through the nasion, basion, and anterior nasal spine (ANS) was the midsagittal plane, and the transverse plane was perpendicular to the midsagittal plane and through the posterior nasal spine (PNS). The coronal plane was perpendicular to the mid-sagittal and transverse planes.  
Skeletal (ANS-Ex, amount of expansion of the midpalatal suture at the ANS site; Mx6-Ex, amount of expansion of the midpalatal suture at the maxillary first molar area; PNS-Ex, amount of expansion of the midpalatal suture at the PNS site; UNW, anterior nasal width at the level of the buccal bone vertically; IZW, inter-zygomatic width; NSdev, nasal septum deviation; NW-lower, lower nasal width; NW-upper, upper nasal width; MxBBW, maxillary basal bone width), and dentoalveolar (Mx6W, maxillary interpolar width; Mx6 Ax, maxillary first molar axis) measurements were analyzed. The landmarks, reference planes, and measurements used for CBCT in this study are depicted in Table 1 and Figures 3-5.  
\begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt}} \hline \hline
**Reference Points** & **Definitions** \\ \hline Coronal plane & \\ \hline NSdev (Figure 5) & Nasal septum deviation; the angle between the top and bottom of the nasal septum (\({}^{\circ}\)). \\ \hline NW-lower (Figure 5) & Lower nasal width; width of the lower nasal cavity, length of the line connecting the maximum convexity of the left and right nasal cavities (mm). \\ \hline NW-upper (Figure 5) & Upper nasal width; length of the line connecting the uppermost points of the left and right nasal cavities (mm). \\ \hline MxBBW (Figure 5) & Maximillary basal bone width; distance from the line connecting the roots of the left and right maxillary first molars to the tangent of the outer surface of the cortical bone of the left and right basal bones (mm). \\ \hline Mx6W (Figure 5) & Maximillary intermolar width; length of the line connecting the palatal cusps of the left and right maxillary first molars (mm). \\ \hline Mx6 Ax (Figure 5) & Maximillary first molar axis; the medial angle (\({}^{\circ}\)) between the line extending the long axis of the palatal root of the maxillary first molar and the MxBBW (\({}^{\circ}\)). \\ \hline \hline \end{tabular}
\end{table}
Table 1: _Cont._  
Figure 3: Measurements in a cross-sectional slice of the palatal root apex of the maxillary left first molar: ANS-Ex, amount of expansion of the midpalatal suture at the anterior nasal spine (ANS) site; Mx6-Ex, amount of expansion of the midpalatal suture at the maxillary first molar area; PNS-Ex, amount of expansion of the midpalatal suture at the posterior nasal spine (PNS) site.  
Figure 4: Measurements in a cross-sectional slice of the zygomatocmaximillary suture: UNW, anterior nasal width at the level of the buccal bone vertically; IZW, inter-zygomatic width.  
Figure 5: Measurements in a slice of the root apex of the palatal side of the left maxillary first molar in the coronal plane: Nsdev, nasal septum deviation; NW-lower, lower nasal width; NW-upper, upper nasal width; Mx8 BW, maxillary basal bone width; Mx6W, maxillary interpolar width; Mx6 Ax, maxillary first molar axis.