# Effects of Vertical Glottal Duct Length on Intraglottal Pressures in the Convergent Glottis
## 5 Conclusions  
In an earlier study, the vertical glottal duct length played an important role in determining intraglottal aerodynamic parameters for the uniform glottal angle [7]. This study continues the examination of the effects of the length of the vertical convergent glottal duct on the transglottal and intraglottal pressures. The computational fluid dynamics code Fluent was used (for laminar, incompressible flow). Four vertical glottal duct lengths (0.108, 0.308, 0.608, 0.908 cm) were studied for three glottal minimal diameters (0.01, 0.04, 0.16 cm), three transglottal pressures (500, 1000, 1500 Pa), and three glottal angles (\(-5^{\circ}\), \(-10^{\circ}\), \(-20^{\circ}\)). The results suggest that the vertical glottal duct length has significant effects on glottal aerodynamic parameters:  
(1) A longer vertical glottal duct length increases the intraglottal pressures, causing greater aerodynamic forces that act upon the vocal fold medial surfaces, and more so for smaller glottal minimal diameters. (2) The vertical glottal duct length typically has a direct relation to the glottal entrance loss coefficient (\(k_{e}\)). (3) For the smallest diameter, the entrance loss coefficient was the largest, and the coefficient value decreased as the Reynolds number or convergent glottal angle increased. (4) The transglottal pressure coefficient is somewhat increased as the vertical glottal duct length is increased, especially for low flows and small glottal minimal diameters. (5) The transglottal pressure coefficient was largest for the smallest diameter, ranging between approximately 1.1 and 2.2, and decreased as the diameter or Reynolds number increased. (6) Compared to other parameters such as the glottal minimal diameter, transglottal pressure, and the convergent glottal angle, the vertical glottal duct length has only small effects on the exit coefficient and volume flow. (7) A longer vertical glottal duct length results in a less abrupt increase of both the intraglottal flow velocity and the wall shear stress along the vertical glottal duct.  
The results of this study suggest that current mathematical and physical models of glottal aerodynamics should take into consideration the vertical glottal duct length, especially under different conditions of normal voicing. For example, the chest voice (or modal register) corresponds to having a relatively long vertical glottal duct length, and the falsetto voice corresponds to having a relatively short vertical glottal duct length. The results are relevant to surgical interventions (reconstruction, injection, thyroplasty) of the vocal fold, where a longer glottal duct may be advantageous for a normal phonation threshold pressure, mucosal wave, and source acoustics, and are also relevant to why vocal fold atrophy may result in a shorter glottal duct and a higher phonation threshold pressure.  
Conceptualization, S.L., R.C.S. and M.W.; methodology, S.L. and R.C.S.; writing S.L. and R.C.S. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (NSFC, No. 11974289) and the Key Research and Development Program of Shaanxi Province, China (No. 2019 SF-103).  
The authors declare no conflict of interest.