## 2 Materials and Methods
### Quantitative Point-Based Assessment of Airway: PAS, MPH, Radius, and Perimeter  
As reported by [PERSON] et al., the evaluation of cephalometric parameters can detect the early development of sleep disorders. However, lateral cephalograms are two-dimensional (2D) X-rays and can be influenced by instrumental bias due to the superimposition of anatomical structures [5]. In contrast, nuclear magnetic resonance (NMR) provides a three-dimensional (3D) analysis of the upper airway, avoiding exposure to ionizing radiation. Nonetheless, the evaluation of airways can be affected by the patient's head posture during both imaging methods [17].  
In the present study, lateral cephalograms and NMR scans were retrieved. A quantitative 2D point-based assessment of the airway's sagittal and vertical dimensions was conducted using the lateral cephalograms taken before and after ENT surgery (T0 and T1) and orthodontic camouflage. Measurements were taken using Dolphin Imaging Software (version 10.5, Canoga Park, CA, USA). In accordance with [PERSON] et al. [18], the posterior airway space (PAS) was measured as the linear sagittal distance between the base of the tongue and the posterior wall of the pharynx (at the level of the inferior border of the second vertebra). Additionally, as proposed by [PERSON] et al., the mandibular plane-hyoid distance (MPH) was measured as the perpendicular vertical distance from the hyoid point (H) to the mandibular plane. The hyoid point is defined as the most superior and anterior point on the body of the hyoid bone [19].  
Moreover, the evaluation of the radius and perimeter of the upper airway space was performed using NMR scans acquired before the ENT surgery (N0) in 2010 and during a follow-up in 2022 (N1), which was requested to check for papilledema. Both NMR scans were performed at the Department of< Radiology, \"Agostino Gemelli IRCSS\" Policlinic in Rome, using an Ingenia 3.0 Tesla (T) MR system (Philips Healthcare, Best, The Netherlands). The acquired data from N0 and N1 were imported into MIMICS 19 software (Materialise(r), Leuven, Belgium). A custom-made mask was created according to the protocol suggested by [PERSON] et al. [17]: the lower limit of the mask was set to \(-\)1024 HU, and the upper limit ranged from \(-\)400 HU to \(-\)161 HU. Landmarks and planes are summarized in Table 1.  
The obtained masks were modified to delineate the retropalatal and oropharyngeal volumes: airway superior border 1 plane (AS1) and airway superior border 2 plane (AS2) define the upper and lower borders of the retropalatal volume, respectively. AS2 and the airway inferior border plane (AI) define the upper and lower borders of the oropharyngeal volume. AS1 passes through the midpoint of the sella-basion line (So) and is perpendicular to the SBa coronal and sagittal SN planes. AS2 passes through the basion (Ba) and is parallel to AS1. AI passes through the most superior point of the epiglottis (E) and is parallel to the Frankfurt plane (Figure 4).  
The segmented masks of the retropalatal and retropharyngeal volumes at N0 and N1 were imported from Mimics as independent STL files into 3-Matic Medical Version 11.0 software (Materialise(r), Leuven, Belgium). For each STL file, the perimeter and radius of the upper and lower borders were measured. All procedures were repeated twice by two operators (D.G. and E.S.), with an interval of at least one week between the measurements.