## 2 Materials and Methods
### Cephalometric Analysis  
Lateral cephalosporgrams of patients belonging to both treated and control groups were traced and digitalized by one investigator ([PERSON]) using the Viewbox4 program (dHAL software, Kifissia, Greece). The accuracy of the landmark placement was verified by a second investigator ([PERSON]), resolving any discrepancies.  
The cephalometric measurements used were (airway variables were obtained from [PERSON], [PERSON] et al. 2020) [14]:  
1. SNA (\({}^{\circ}\)): angle between sella, nasion, and subspinale point A. It indicates the antero-posterior position of the maxilla relative to anterior cranial base (Figure 1, 1);
2. SNB (\({}^{\circ}\)): angle between sella, nasion, and supramentale point B. It indicates the antero-posterior position of the mandible to anterior cranial base (Figure 1, 2);
3. ANB (\({}^{\circ}\)): angle resulting from the difference between the SNA and SNB angles, which provide an indication of the sagittal skeletal relationships (Figure 1, 3);
4. Wits (mm): is the measure of the segment Ao-Bo where Ao and Bo indicate respectively the projection of point A and point B on the occlusal plane (Figure 2, a);
5. SN-Occlusal Plane (\({}^{\circ}\)): angle between the cranial base (SN) and the occlusal plane (Figure 1, 4);
6. SN-Palatal Plane (\({}^{\circ}\)): angle between the cranial base (SN) and the palatal plane (Figure 1, 5);
7. SN-Mandibular Plane (\({}^{\circ}\)): angle between the cranial base (SN) and the mandibular plane (Figure 1, 6);
8. Palatal Plane-Mandibular Plane (\({}^{\circ}\)): angle between the bispinal plane and the mandibular plane, expressing intermaximillary divergence (Figure 1, 7);
9. Co-Gn (mm): distance from condylion to anatomic gathion, expressing total mandibular length (Figure 2, b);
10. Co-Go (mm): distance from condylion to gonion, expressing the height of the mandibular ramus (Figure 2, c);
11. Co-Go-Me (\({}^{\circ}\)): mandibular angle (Figure 1, 8);
12. Overjet (mm): parameter indicating the measurement of the distance in the sagittal plane between the incision margin of the upper incisors and the vestibular surface of the lower incisors (Figure 2, d);
13. Overbite (mm): distance in the vertical plane between the incision margin of the upper and lower central incisors (Figure 2, e);
14. Molar relationship (mm): distance between the projections in the occlusal plane of the point of contact between the first permanent molars and the adjacent mesial tooth (second deciduous molar or second premolar) (Figure 2, f);
15. Inc. Sup.-Pal. Pl. (\({}^{\circ}\)): angle expressing the inclination of the axis of the upper central incisor relative to the palatal plane (Figure 1, 9);
16. Inc. Inf.-Mand. Pl. (\({}^{\circ}\)): angle expressing the inclination of the axis of the lower central incisor relative to the mandibular plane (Figure 1, 10);
17. PNS-AD1 (mm): lower airway dimension; distance between the PNS and the nearest adenoid tissue measured through the PNS-Ba line (AD1) (Figure 3, g);
18. AD1-Ba (mm): lower adenoid size; defined as the soft tissue thickness at the posterior nasopharynx wall through the PNS-Ba line (Figure 3, h);
19. PNS-AD2 (mm): upper airway dimension; distance between the PNS and the nearest adenoid tissue measured through a perpendicular line to S-Ba from PNS (AD2) (Figure 3, i);
20. AD2-H (mm): upper adenoid size; defined as the soft tissue thickness at the posterior nasopharynx wall through the PNS-H line (H, Hormion, point located at the intersection between the perpendicular line to S-Ba from PNS and the cranial base) (Figure 3, I);