## 3 Results and Discussion
### Sgs Cases
#### 3.2.2 SGS Cases: Vocal Fold Vibration and Glottal Flow Dynamics
To better understand the differences between the current study and our previous work regarding peak glottal area timing, \(\tau_{o}\), and \(f_{0}\), we examine the x-z plane cross-section of vocal fold vibration at y = 7.6 cm during the initial opening phase. Figure 8 illustrates this comparison for both the baseline and 96% severity cases, with the z-axis magnified fivefold to emphasize the differences. In the baseline case, the opening process begins at the anterior section of the vocal fold (Step I), followed by a progressive movement towards the middle of the vocal folds in Steps II and III. This pattern is consistent with the findings of [PERSON] et al. [16] in their study of subject-specific laryngeal dynamics. The earlier opening at the anterior end, compared to the posterior end, can be attributed to the material incompressibility, which causes a delay in the overall opening process. In contrast, for the 96% severity case, the opening occurs more uniformly across the middle of the vocal fold throughout all steps. We hypothesize that this difference is due to the more focused jet resulting from the subglottic stenosis (SGS) narrowing, which applies higher pressure to the central portion of the vocal fold. This concentrated pressure causes a slightly faster opening for the 96% severity case, leading to a leftward shift in the timing of the peak glottal opening. Consequently, we observe slight decreases in \(\tau_{o}\) and corresponding increases in \(f_{0}\). This shift in dynamics highlights the impact of stenosis-induced airflow patterns on vocal fold vibration and the resultant phonatory characteristics. Figure 8: The x-z plane cross-section of the vocal fold vibration at y = 7.6 cm during the beginning of the opening for the baseline and 96% severity cases. The z-axis is magnified five times to visualize the difference between the two cases. Figure 7: **(a)** The phase-averaged glottal area waveform, (**b**) the mean glottal area, peak glottal area, open quotient, and fundamental frequency; (**c**) the phase-averaged flow rate waveform; and (**d**) the mean flow rate, peak flow rate, skewness quotient, and maximum flow deceleration rate (MFDR) for different SGS severity cases. This shows that the above discrepancies can be attributed to the use of patient-specific airway geometry and vocal folds. The more complex model captures subtle interactions between the airflow and the vocal fold surfaces that were not present in the simplified model [14]. Furthermore, the realistic geometry leads to different pressure distributions and flow patterns within the larynx, particularly in severe SGS cases. The focused jet in the patient-specific model creates a more concentrated pressure on the vocal folds, altering their vibratory patterns. This change in dynamics highlights the impact of stenosis-induced airflow patterns on vocal fold vibration and the resultant phonatory characteristics, emphasizing the importance of using detailed, patient-specific models for accurate predictions in cases of severe SGS. Figure 9 presents the results of the 1 st and 2 nd modes from the POD analysis for our current study, which together account for approximately 90% of the total energy. Figure 9a illustrates the energy distribution of each mode and the sum of the first two modes' energies across different SGS severities. For severities below 75%, the energy distribution remains relatively constant. However, in the 90% and 96% severity cases, significant changes are observed: the energy of the 1 st mode increases by 11% and 9%, respectively, while the energy of the 2 nd mode decreases by 23% and 16%. Despite these notable shifts, the combined total energy of the first two modes sees only a slight increase, remaining under 2%.