## 2 Normal Material and Methods
### Cbct  
All CBCT examinations were taken at T0 and T1, and were performed by the Planmeca Promax(r) 3D MID unit (Planmeca Oy, Helsinki, Finland) according to the low-dose protocol [15] with these parameters: an acquisition time of 15 s, 80 kVp, 5 mA, 35 microSievert (\(\upmu\)Sv), and a field of view (FOV) of 240 \(\times\) 190.  
The patients' CBCTs were performed with the head oriented according to the natural head position (NHP); the patients were in a sitting position with the back perpendicular to the floor as much as possible. The head was stabilized with ear rods in the external auditory meatus. The patients were instructed to look into their own eyes in a mirror 1.5 m in front of them to obtain NHP. The NHP is a physiological and reproducible posture defined for the morphological analysis described in orthodontic and anthropological literature. The 3D image of the cranium was oriented in the Dolphin software according to NHP posture before taking cephalometric measurements. The NHP orientation was carried out by the widgets present in Dolphin; hard- and soft-tissue views were checked for orientation in the software by visualizing the head from the front, right, and left sides. In the NHP, there are three reference planes perpendicular to each other, which are identified in the software for the patients' cephalometric measurements (Figure 1).  
\begin{table}
\begin{tabular}{l l l} \hline \hline  & **Inclusion Criteria** & \multicolumn{2}{c}{**Exclusion Criteria**} \\ \hline - & age ranged from 10 to 14 years (early & \\  & adolescence) [16] & - & lack of any diagnostic data (including \\  - & presence of a transverse & & CBCT images at T0 and T1) \\  - & maxillary deficiency & - & poor quality CBCT images \\  - & presence of a unilateral or bilateral & - & impacted or missing teeth \\  - & posterior crossbite & - & previous orthodontic treatment \\  - & presence of a complete CBCT exam at T0 & - & dentofacial abnormalities \\  & and T1 & - & skeletal asymmetry \\  - & success of the therapy with an & - & any syndromes or pathologies involving \\  & RPE appliance & bone metabolism. \\ \hline \hline \end{tabular}
\end{table}
Table 1: Inclusion and exclusion criteria.  
1. The transverse plane coincides with the Frankfurt plane (FH), a plane passing through two points: Orbital (Or) and Porion (Po);
2. The sagittal plane coincides with the mid-sagittal plane (MSP), a plane perpendicular to plane FH and passing through two points: Crista Galli (Cg) and Basin (Ba);
3. The coronal plane coincides with the anteroposterior (PO) plane, perpendicular to the FH and MSP, passing through the right and left Porion.  
The examiners manually defined the ROI and used it to calculate the bone density of the MPS in Hounsfield units (HU), twice. The ROI [18] for all patients is the delimited area (Figure 2):  
Figure 1: Spatial orientation of the CBCT scans according to the natural head position (NHP). The frontal view scan (Figure 1A) and lateral view scan (Figure 1B) are from the same patient. (**A**) The red line in the coronal orientation coincides with the mid-sagittal plane (MSP), a plane perpendicular to plane FH and passing through Crista Galli (Cg) and Basin (Ba) points. (**B**) The blue line in the sagittal orientation coincides with the Frankfurt plane (FH), a plane passing through Orbital (Or) and Porion (Po) points; the green line coincides with the anteroposterior (PO) plane, perpendicular to the FH and MSP, passing through the Porion.  
* superiorly by the upper central incisors' apex
* laterally by the upper central incisors' medial root surface
* inferiorly by the cementoenamel junction
* posteriorly by the anterior edge of the nasopalatine foramen  
Sex and vertical and sagittal skeletal patterns were used to categorize the sample into eight groups as reported in Table 2:  
Each measurement was performed twice by the same examiners at the first (T0) and second (T1) CBCT scan for all patients.