## 3 Results and Discussion
### Sgs Cases
#### 3.2.2 SGS Cases: Vocal Fold Vibration and Glottal Flow Dynamics  
The phase-averaged glottal area waveform for all cases is shown in Figure 7a. The waveform remains unchanged for severities below 90%, indicating that the threshold for significant changes in the glottal area occurs at 90% severity. For the 96% severity case, there is a noticeable decrease in both the mean and peak glottal areas, along with a slight leftward shift in the peak glottal area. The open quotient \(\tau_{o}\) and fundamental frequency \(f_{0}\) both decrease as the severity increases beyond 90%, with the most significant changes occurring at the 96% severity level (Figure 7b). The phase-averaged volumetric flow rate at the glottis  
Figure 6: (**a**) The SGS location and the axial distance between the narrowest section of the SGS and superior surface of the vocal folds; (**b**) schematics of the cross-section of an idealized SGS geometry and the parameters used in the Equation (8) to create the SGS. is shown in Figure 7c. Changes in the flow rate remain negligible for SGS severities up to 75%. However, beyond 75% severity, the flow rate begins to drop significantly. The mean and peak flow rates decrease rapidly as SGS severity increases, with a 22% reduction in the mean flow rate and a 26% reduction in the peak flow rate for the 96% severity case. Additionally, there is a slight leftward shift in both the peak flow rate (by 0.04T) and the closure instance (by 0.02T) for severe SGS cases. This leads to a shorter flow acceleration duration and a longer flow deceleration duration. The decreases in peak flow rate and the increased closure duration for high SGS severities suggest a drop in the maximum flow declination rate (MFDR). Figure 7b confirms this, showing a maximum MFDR reduction of 30% for the most severe case. Significant changes in the flow rate begin at 75% SGS severity, which corresponds to Grade III and Grade IV SGS categories. This threshold differs from the changes observed in vocal fold dynamics, where significant alterations do not occur until 90% severity. This difference is consistent with our earlier findings, likely resulting from the distinct physical mechanisms governing these phenomena. The flow rate is more sensitive to stenosis due to increased viscous losses as air passes through the narrowing airway, making flow characteristics change at lower severities. In contrast, vocal fold vibration depends primarily on pressure distribution around the folds, which remains stable enough to maintain consistent vibration patterns until more severe stenosis occurs (90% and above). In comparison with our previous study using simplified geometry [14], several differences emerge, primarily due to the use of patient-specific airway geometry and the inclusion of a realistic environmental flow domain with an anatomically accurate facial structure. In the previous study, the peak glottal area for the 96% severity case exhibited a slight rightward shift, whereas in this study, it shifts to the left. Likewise, the open quotient \(\tau_{o}\) increased for 96% and 99% SGS severities in the previous study, but in the current work, it decreases for the 96% severity case. Additionally, the fundamental frequency \(f_{0}\) decreased for both 96% and 99% severities in the earlier study, whereas it increases for the 96% severity case in the present study. Regarding glottal flow, the previous study demonstrated a constant flow acceleration duration across all SGS severities, with only a slight increase in deceleration duration. In contrast, the current study reveals a reduction in flow acceleration duration and a more pronounced decrease in deceleration duration for severe SGS cases. These combined effects lead to a larger drop in the speed quotient \(\tau_{s}\) for the 96% severity case in this study (0.162) compared to the previous study (0.035).