## 2 Materials and Methods
### Nasal Airway Volume  
The method utilized in this research project is similar to the previously published protocol [18]. In summary, to create 3D nasal airway models from the CBCT scan images, the scans were imported into Materialise Mimics (Materialise(r), Leuven, Belgium) (Figure 1a). A color mask was created by thresholding (Min: \(-\)1024 Hounsfield unit (HU), Max: \(-\)600 HU) in Mimics(r) (Figure 1b). Then, manual segmentation was used to remove unnecessary features slice by slice, such as the frontal sinus, maxillary sinus, pharynx, etc., to isolate the nasal airway model (Figure 1c). Additionally, to standardize the study methods, we removed the indeterminate apical parts of the nasal airway, which could be part of both the sinus and the nasal airway. The starting point of the anterior nasal airway boundary was defined as the most anterior slice where the boundary was closed (Figure 1d--upper ones). As shown in (Figure 1d--lower ones), the posterior boundary of the nasal airway was identified as the most posterior slice where the two parts are connected. The upper part belongs to the nasopharynx region, while the lower part belongs to the laryngopharynx region. Finally, the 3D nasal airway model was exported as an STL file.  
The T1 and T2 nasal airway 3D models were imported into Geomagic(r) Control(tm) 2015 (3D Systems, Rock Hill, SC, USA). The models were cleaned to remove spikes using the tool available in the software, and the process was standardized to minimize investigator bias (smoothness level set to 70). The two models (T1 and T2) were aligned using the best-fit alignment function with T1 as the reference model and T2 as the floating (test) model. The best-fit alignment is a built-in function that minimizes the distance between reference and test models by means of an iterative closest point algorithm. After aligning the models, there was imperfect alignment at the anterior and posterior boundary parts so the edges were trimmed with planes to ensure perfectly aligned boundaries. Under the trim with the plane tool, the position and the angle of the plane can be set to cut off the model to ensure that there is no excess at the anterior and posterior boundary parts of the T1 and T2 models.  
The geometrical differences between the T1 and T2 models were determined by conducting a 3D deviation analysis in Geomagic(r). This provides a deviation map that can give a visual and quantitative representation of the degree of difference between the surfaces of the models (Figure 2).  
The deviation map shows both positive and negative deviation areas. This indicates that the surface of the test model (T2 model) is above or below the reference model (T1 model). The lower threshold value for the deviation color map was set to \(\pm\)0.3 mm indicating that any areas with deviations within these limits would be considered negligible and colored green. The upper threshold value for the deviation color map was set to \(\pm\)5.0 mm, which captured the larger deviations between the models where there were corresponding points. The root mean square (RMS) error, the maximum upper deviation, and the maximum lower deviation were also output as outcome metrics from the 3D deviation analysis. In addition, the volume and surface area of the nasal airway models can be measured in Geomagic(r).  
Figure 1: (**a**) Importing cone-beam computed tomography (CBCT) scan images into Mimics(r). (**b**) Creating a red color mask. (**c**) The nasal airway model. (**d**) The definition of the anterior and posterior nasal airway boundaries.