To ensure that there was no airflow leakage within the setup, the relation between subglottal pressure and applied airflow was tested. Because of the linear correlation between these two parameters, as displayed in the top row of Fig. 3, which has also been reported by Alipour and colleagues, flow leakage in the setup was ruled out for all three larynges. The control variable for the succeeding measurements was subglottal pressure PS, which was kept constant during each experimental run. In the following, the parameters being analyzed are introduced. Global parameters: Direct current airflow and SPL were measured. Fundamental frequencies of the vocal fold oscillations were computed on the basis of the high-speed video data. The laryngeal flow resistance was determined using the definitions of van den Berg and Alipour and colleagues. Whereas RB is equal to the ratio between the transglottal pressure difference and the mean glottal flow rate, Alipour and colleagues proposed the flow resistance RA as a derivative of the subglottal pressure with respect to the mean flow rate. In the context of vocal fold adduction, different studies reported similar systematic results for both definitions of glottal flow resistance, i.e., increased glottal adduction resulted in increased flow resistance. However, when investigating the impact of the ventricular folds, package of blueberries different behaviors for RA and RB were reported: Whereas Alipour et al. found increased flow resistance RA in the presence of the ventricular folds compared with configurations without ventricular vocal folds, Zhang et al. reported a decrease of glottal flow resistance RB.

In a later study, Zheng et al. showed that these different findings, for small flow rates, result from the different definitions of RA and RB. Local parameters were determined on the basis of the high-speed video data. The three local parameters, maximal lateral and vertical displacements and the maximal velocity, were computed over all sutures. Here, displacement means the actual distance moved by the sutures in the corresponding direction. Displacements in the longitudinal direction of the vocal folds were not considered, since they are in the range of random noise and therefore have been shown to be negligible. The mucosal wave propagation from inferior to superior was investigated and will be shown along the vertical suture row r3; sutures are highlighted by o in Fig. 2. For assessing mucosal wave propagation along the medial surface, phase delays in degrees for reaching minimal lateral displacement values were computed between the lowest suture and the suture at the vocal fold edge covering a vertical distance of approximately 8 mm; distance is indicated by the white arrow aside suture row r3 in Fig. 2. The higher the degree values, the longer the time delay and the slower the mucosal wave propagation along the medial surface . For computing the mucosal phase delay, we concentrated on the medially positioned vertical suture row r3 where the dynamics are most distinctive. Considering only one vertical suture row is also justified by previous work that had shown that along the medial surface only a negligible anterior-posterior mucosal wave phase delay of the lateral dynamics is present . 

EEFs: Because of the large amount of data, EEF analysis and visualization over the three different adduction levels will be restricted to high PS values with equal air- flow where the dynamics are most distinct. For presenting the EEFs, the vertical row r3 is chosen where dynamics were found to be largest. Also, as seen before, the EEF geometry and shape are qualitatively similar along vertical suture rows. Further, only EEFs with at least 10% of the total energy were analyzed, resulting in up to three EEFs per single test case. The evaluation contains the angle of the moving direction and the absolute displacement of each suture in addition to the shape and the relative energy captured by each EEF.According to the definition by van den Berg et al., the flow resistance RB increases with an increase in subglottal pressure PS. Additionally, for larynges L1 and L2, the resistance also increases with an increase in adduction level. In contrast, for L3, RB shows the opposite behavior and decreases with rising adduction level. The absolute values of RB are found to be smaller for L3 than L1 and L2. Because of the linear dependence that exists between flow rate and subglottal pressure, the flow resistance RA for a given adduction level is represented by one value. As Fig. 5 shows, the basic trend of RA is equal to the trend of RB for larynges L1 and L2, Fig. 4, i.e., flow resistance increases with adduction. However, for larynx L3, RA also rises for increasing adduction levels in contrast to RB. The absolute values of RB are found to be smaller than the RA values for all three larynges. In summary, for global parameters, L1 and L2 show similar basic behavior, whereas L3 responds differently, especially with increasing adduction levels. Local parameters are given in Fig. 6. For all three larynges, the lateral and vertical displacements , and the absolute velocities are in physiological ranges. L3 shows the smallest vertical displacements. L2 exhibits the largest velocities by a factor of two compared with L1 and L3.

For all three larynges, the lateral displacement is more dominant than the vertical component. In the case of L3, the lateral motion is much more pronounced compared to larynges L1 and L2. This can be shown by computing the ratio between lateral and vertical displacements, which is higher for L3 than for L1 and L2 . For all three larynges, no systematic trend for lateral and vertical displacements as a function of PS could be found. However, velocity tends to increase with increase in PS. For increasing adduction, the basic trend of local parameters is similar for larynges L1 and L2. The displacements in both directions and the velocity tend to increase with the rising adduction level, especially for high PS values. Again, L3 shows the opposite behavior: the higher the adduction, the smaller the dynamic values, i.e., maximum amplitudes and velocities are always found at the lowest adduction level MP10. For each larynx, the dynamic phase delay of the mucosal wave propagation along suture row r3 along the medial surface is given as a function of the adduction level, see Fig. 7. The corresponding PS and airflow are given in Table III. For L1 and L2, the phase delay increases at higher adduction levels, reflecting a decrease in the propagation velocity of the mucosal wave. In contrast, for L3, the phase delay remains almost constant at around 170 , corresponding to an unchanging wave propagation velocity at different adduction levels. The corresponding trajectories for the adduction level MP100 along suture row r3 are given in Fig. 8. Larynges L2 and L3 show almost perfect periodicity, whereas the trajectories for L1 are more perturbed. Finally, L3 exhibits almost exclusively lateral motion, in contrast to L1 and L2, both of which also have a significant vertical component. EEFs: The EEFs of the vocal fold dynamics were determined for the three different adduction levels . The calculations were performed on the basis of the displacements of sutures in the centrally located vertical row r3; see Fig. 2. In Figs. 9, 10, and 11, the EEFs for larynges L1, L2m and L3, respectively, are displayed. The EEFs correspond to the test cases with PS values as given in Table III, i.e., high PS with equal airflow. Furthermore, square plant pots only EEFs with an energy level of more than 10% of the entire dynamic energy are discussed. According to Fig. 8, the flow direction is upwardly directed. The glass plate of the setup is located upright at position zero of the x axis. Figures 9, 10, and 11 are composed as follows: the mean vocal fold surface position , the minimal displacement , the maximal displacement , and the displacement vector of the EEF at the corresponding sutures. The contour of the vocal fold surface between the sutures is interpolated by cubic B-splines, since these functions tend to minimize the curvature and are therefore appropriate for interpolating tissue surfaces. Furthermore, the numerical values of the angle and the length of the displacement vector are depicted for each suture having displacements of more than 0.1 mm.

The displacement of a suture is defined by the length of displacement and the angle of the moving direction, with 0 representing horizontal motion. Thus, angles with large absolute degree values reflect a high vertical component in the EEF. The higher the absolute degree value, the larger the vertical component. The angles determine the spatial shape of the EEF and its contribution to the entire dynamics. Higher absolute degree values reflect an alternating divergent-convergent shape and dynamics of the medial surface. Angles close to zero are approximately orthogonal to the glass plate, which indicates that these dynamics primarily govern the lateral movement of the vocal fold, which is responsible for modulating the glottal airflow and producing the acoustic signal. The amount of energy governed by a given EEF reflects the percentage of the total energy represented by this EEF. For all three larynges, the vocal fold edge is near the second highest suture, where the offset curve exhibits a location closest to the glass plate. EEF1: The largest eigenfunction is given in the first row in Figs. 9, 10, and 11 corresponding to larynges L1, L2, and L3, respectively. For all three larynges, it shows qualitatively the same behavior. The vocal fold dynamics exhibit a distinctive convergent-divergent shape change of the glottal duct during motion between maximum and minimum positions. This is characterized by the Fig. 8-shape of the area enclosed by the Max and Min curves of EEF1. Thereby, the Min and Max curves cross each other slightly below the vocal fold edge near the second highest suture. Concerning the direction of motion in EEF1, L1 and L2 show significantly higher vertical components than L3, represented by higher absolute values of the angle of the displacement vector, especially near the vocal fold edge. The energy level within EEF1 differs between the three larynges: whereas for L2 and L3 the energy level is fairly high, the energy level for L1 is significantly lower in EEF1. For increasing adduction levels accompanied with increasing PS for equal airflow, the Fig. 8-shape of the enclosed area in EEF1 becomes more developed for L1 and L2, i.e., the lateral displacement components clearly increase. In contrast, for L3, the lateral components become smaller with increasing adduction levels, i.e., the Fig. 8- shape becomes more compressed. EEF2: The energy levels of EEF2 are much lower for L1 and L2 than for L3 . For L1 and L2, the vertical components are fairly high, being in the same range as or even larger than for EEF1. For L3, EEF2 is characterized by predominantly lateral displacement, which is again in contrast to L1 and L2. For increasing adduction level, the absolute displacements in all suture positions decrease for L2 and L3. Furthermore, for L2, an energy shift from EEF2 to EEF1 occurs whereas the energy levels of EFF1 and EEF2 for L3 remain constant. For larynx L1, no systematic trend concerning EFF2 could be established. EEF3: Only for L1 does EEF3 contain more than 10% of the entire dynamic energy, Fig. 9. Comparable to the EEFs accounting for more variance, it exhibits vertical and lateral components. With an increase in the adduction level, the energy percentage increases slightly from 10% to 12%,which is also visible in slightly increased displacement values . The distribution of the entire energy captured by EEFs with more than 2% is reflected in the trajectories given in Fig. 8. The least periodicity is reflected by a low energy portion of the two largest EEFs, between 47% and 56%. In contrast, L2 reaches 72%–87% of the entire energy in the two largest EEFs; as a result, the trajectories are much more periodic. L3 shows the highest periodicity, being reflected in energy levels of 93% in the two largest EEFs.Global parameters: First, it should be mentioned that basic phonatory relations were reproduced. An increase in subglottal pressure resulted in an increase in the fundamental frequency, as demonstrated by Alipour et al. and Jiang and Titze. Furthermore, higher airflow, f0, and SPL were found with increasing PS values. Based on a preliminary, single ex-vivo hemilarynx study, D€ollinger & Berry hypothesized that subglottal pressure and flow rate were not significantly influenced by increasing vocal fold adduction .