# Effects of Vertical Glottal Duct Length on Intraglottal Pressures in the Convergent Glottis
## 4 Discussion  
The longer vertical glottal duct length caused by short vocal folds (low cricothyroid muscle contraction), higher levels of vocalis muscle contraction (to promote bulging), or greater excursion of vocal fold motion (via higher levels of subglottal pressure) should result in a more rectangular glottal shape, whereas a short vertical glottal duct length is caused by relatively high levels of cricothyroid muscle contraction (and for high falsetto, minimal activity of the vocalis muscle) and lower subglottal pressures, resulting in a more convergent glottal shape [8; 35]. Thus, the vocal fold contour, glottal length, and glottal angles may vary over a wide range, even during conversational speech, as prosody changes follow the coordination of cricothyroid muscle contraction, vocalis muscle contraction, and subglottal pressure. In addition, as the size of the larynx increases developmentally and differs by sex post-puberty, the vertical length of the glottis should be longer for larger larynxes. This study suggests that vertical glottal duct length is an important variable that is part of the governing of intraglottal pressures during phonation. In general, an increase of the vertical glottal duct length should increase the intraglottal aerodynamic forces acting to separate the vocal folds during glottal opening and increase the entrance loss coefficient (\(k_{e}\)) for minimal glottal diameters smaller than 0.04 cm for the convergent glottis. The results also suggest that a change of the vertical glottal duct length appears to have only small effects on the exit coefficient (\(k_{ex}\)), transglottal pressure coefficient, volume flow, and tangential forces that act upon the vocal folds. The basic changes of the intraglottal pressure and the transglottal pressure coefficient with changes of the glottal minimal diameter, transglottal pressure, and the convergent glottal angle were consistent with prior modeling work with model M5. For example, both the entrance loss coefficient and the exit coefficient tend to decrease as the transglottal pressure increases and as the minimal diameter increases for convergent glottal angle cases [29]. In addition, the transglottal pressure coefficient increases greatly as diameter and flow decrease (consistent with [PERSON] [36; 37] and [PERSON] et al. [29]). The four parameters studied in this paper--vertical glottal duct length, glottal minimal diameter, convergent glottal angle, and transglottal pressure--have complex and integrated effects on intraglottal aerodynamic parameters. Table 3 shows the effects of these parameters on intraglottal aerodynamics. In general, compared to the other parameters, glottal minimal diameter has the greatest effect on the aerodynamic parameters. For some conditions, the change of minimal diameter may also synchronously increase (or induce) the effects of other parameters onto the aerodynamic parameters, thus creating complex integrated effects. For example, glottal angle and transglottal pressure have fewer effects on \(k_{t}\) and \(k_{e}\) when the minimal diameter is larger than 0.04 cm (and Reynolds number is larger than 500, especially larger than 2000), but these effects are induced (increased) for minimal diameters smaller than 0.04 cm (Reynolds number less than 500 conditions). Another example is the volume flow; the transglottal pressure has a small effect on volume flow for small minimal diameters but large effects on the flow for the larger (0.16 cm) minimal diameter (the volume flow increased by 74% when the transglottal pressure increased from 500 Pa to 1500 Pa). The effects of the vertical glottal duct length on the glottal aerodynamic parameters are smaller than those of the minimal glottal diameter but larger than those for the convergent glottal angle and transglottal pressure.