## 4 Conclusions  
In this study, a 3D laryngeal model was employed to study the effects of subglottic stenosis on dynamics of glottal flow, vocal fold vibration, and acoustics during voice production. The results show that the SGS starts to have a noticeable effect on glottal flow rate only when the area reduction is beyond 75% and has an effect on vocal fold vibration when the area reduction is beyond 90%. Specifically, when the SGS area reduction is below this threshold, varying the SGS area reduction had little effect on glottal flow, vocal fold vibration, and acoustics; when it is beyond this threshold, increasing the SGS area reduction quickly decreases the flow rate, vocal fold vibration amplitude, and vocal efficiency; it slightly decreases the skewness quotient, vibration frequency, signal-to-noise ratio, and vocal intensity; and it slightly increases the open quotient. Furthermore, our results show that large SGS area reduction can also affect vocal fold dynamics by affecting the energy percentage of the vibration modes or generating different vibration modes. Changing SGS location shows no effect on the dynamics. The detailed analysis on the trans-stenosis flow resistance, trans-glottis flow resistance, and total flow resistance shows that the effects of SGS are related to its effect on the total flow resistance, which is further related to the ratio of the cycle-averaged glottal area to SGS area. When the SGS area reduction is below 75%, the area ratio was nearly zero, meaning that the glottis opening is much smaller than the SGS opening. In these cases, the trans-stenosis resistance is nearly zero, and the total flow resistance is almost the same as the trans-glottis flow resistance, suggesting that the SGS does not generate additional flow  
Figure 14: The cycle-averaged trans-glottis, trans-stenosis, and tract flow resistance of the 2.1 and 3.13 cm SGS distances for the 90% and 96% SGS severities. resistance. As a result, the SGS shows nearly no effect on the dynamics. By increasing the SGS severity beyond 75%, the area ratio starts to increase rapidly with the SGS severity, and the trans-stenosis flow resistance is observed to increase rapidly too, resulting in the quick increase of the total flow resistance. As a result, the flow rate and vocal fold vibration reduce quickly. In the meantime, increasing SGS severity also causes a decrease in the trans-glottis resistance and trans-glottis pressure drop, which further causes a drop in the fundamental frequency. Therefore, our results indicate that the effect of SGS on phonatory dynamics is largely determined by the area ratio between the glottis and SGS. A threshold area ratio exists, below which the SGS has nearly no effect on the dynamics, and, beyond which, the effect of SGS grows rapidly with its severity. In our results, the threshold area ratio is around 0.1, corresponding to an SGS area reduction of 75%. The results are found to be consistent with clinical observations that Grades I and II SGS (area reduction below 70%) had very minor effects on both voice production, and respiration and normally no treatment is needed; only at Grades III and IV SGS, effects on breathing and voice production become significant and treatments are needed. Conceptualization, X.Z. and S.T. ; methodology, D.B., Q.X., and X.Z. ; formal analysis, D.B., Q.X., and X.Z. ; investigation, D.B., Q.X., and X.Z. ; writing--original draft preparation, D.B., Q.X., and X.Z. ; writing--review and editing, Q.X., X.Z., and S.T. ; supervision, Q.X. and X.Z. ; project administration, X.Z. and S.T. ; funding acquisition, S.T. All authors have read and agreed to the published version of the manuscript. This research was partially funded by the National Institute on Deafness and Other Communication Disorders (NIDCD), Grant No. 5R01 DC009616. The numerical simulation used the Extreme Science and Engineering Discovery Environment (XSEDE) (allocation award number TG-BIO150055). Not applicable. The data presented in this study are available upon request.