## 2 Materials and Methods
### Cbct  
A low-radiation dose dental CBCT scanner (NewTom 5G, QR, Verona, Italy) was used to acquire the 3D morphology of the facial skeleton and the nasal and upper airway (110 kVp, 5 mA, 0.3 mm isotropic voxel dimension, 18 s of scanning time with 3.6 s of exposure time, a field of vision (FOV) of \(18\times 16\) cm). Scanning protocols for acquisition ensured that the subjects were in centric occlusion with their lips and tongue in a resting position; during scanning, the subjects were also instructed to lie still to prevent motion artefacts. Raw data obtained from the CBCT scanner were exported in the DICOM format and imported into a specific software (Mimics 21, Materialise, Leuven, Belgium). The segmentation was performed following the same method as described elsewhere [25]. Landmark definitions for the dental, skeletal, and airway parameters, as well as plane definitions, are presented in Table 1. Four linear measurements were assessed to evaluate the transverse skeletal  
Figure 2: Flow chart for protocol. changes after expansion (Table 2 and Figure 3). Two reference planes were defined: Frankfort Horizontal, used as the horizontal plane, and Sagittl SN plane, used as the sagittal plane. The total pharyngeal airway (PA) was divided into three parts according to the location of PNS-So, PNS-Ba, and occlusal and E planes, and their volumes were assessed (Table 2 and Figure 4). Based on the midline of the total PA, the cross-sectional area (CS) and hydraulic diameter (D\({}_{\text{H}}\)) were assessed, both perpendicular to the center line. All measurements were conducted by one operator (X.N. ). \begin{table}
\begin{tabular}{l l} \hline
**Points** & **Description** \\ \hline ANS & The most anterior point on the nasal spine \\ Ba & The most posteriorier point on the clivus \\ E & Most superior point of the epiglottis \\ LD-L & The most inferior point of the left lacrimal duct \\ LD-R & The most inferior point of the right lacrimal duct \\ LF-L & Centroid of the Lacrimal foramen left \\ LF-R & Centroid of the Lacrimal foramen right \\ MoL & The distal-palatal tip of the first left molar in the upper jaw \\ MoR & The distal-palatal tip of the first right molar in the upper jaw \\ N & The intersection of the intranasal and frontonasal sutures in the midsagittal plane \\ Ntip & The tip of the nasal bone \\ OrL & Orbital left, the most inferior anterior point on left orbit’s margin \\ OrR & Orbital right, the most inferior anterior point on right orbit’s margin \\ PNS & The most posterior point on the nasal spine \\ Pl & Centroid of the greater palatine foramen left \\ Pr & Centroid of the greater palatine foramen right \\ PoL & Porion Left: the most upper point on the left bony external auditory meatus \\ PoR & Porion Left: the most upper point on Right bony external auditory meatus \\ S & The midpoint of the sella turcica \\ So & The midpoint of the sella-basion line \\ ii & The point midway between the incisal edges of the maxillary central incisors \\ \hline
**References Planes** & **Description** \\ \hline Frankfurt plane & A plane passing through the inferior borders of the bony orbits, encompassed by OrR and OrL, and the upper margin of the auditory meatus encompassed by PoL \\ Sagittl SN plane & Plane perpendicular to Frankfurt plane passing through S and N points \\ Ntip-ANS plane & Plane through Ntip and ANS points, perpendicular to Sagittl SN plane \\ PNS-So plane & Plane through PNS and So points, perpendicular to Sagittl SN plane \\ PNS-Ba plane & Plane through PNS and Ba points, perpendicular to Sagittl SN plane \\ Occlusion plane & Plane through MoL, MoR, and ii points \\ E plane & Plane through E point, parallel to Frankfurt plane \\ \hline \end{tabular}
\end{table} 
Table 2: NC and PA volumes and cross-sections.