Medial surface dynamics as a function of subglottal pressure in a canine larynx model

Abstract

During vocal fold vibration, there may be a mucosal wave in the superior-inferior (vertical) direction, resulting in a convergent shape during opening and a divergent shape during closing. Most of our understanding of the converging/diverging shape of the glottis has come from studies in a hemilarynx model. Previous work has shown that vibratory patterns in the full excised larynx are different than the hemilarynx. This study characterized the dynamics of the medial glottal wall geometry during vibrations in the full excised canine larynx model. Using particle image velocimetry, the intraglottal geometry was measured at the mid-membranous coronal plane in an excised canine larynx model. Measurements of the glottal area were taken simultaneously using high-speed imaging. The results show that skewing of the glottal area waveform occurs without the presence of a vocal tract and that the phase-lag of the superior edge relative to the inferior edge is smaller than reported and depends on the subglottal pressure. In addition, it shows that the glottal divergence angle during closing is proportional to the magnitude of the acoustic intensity and the intraglottal negative pressure. This preliminary data suggests that more studies are needed to determine the important mechanisms determining the relationship between intraglottal flow, intraglottal geometry and acoustics.

INTRODUCTION

In the classic linear source filter theory¹, flow modulation (or a change in the flow rate) at the glottal exit produces the source of sound which is then “filtered” by resonances of the vocal tract. Flow rate is defined as the volume of air per unit time and is calculated by multiplying the area of the glottis by the velocity of the airflow exiting the glottis (Q = A × V). During normal phonation, the flow rate waveform may be skewed to the right, such that the flow during the latter part of closing decreases more rapidly than it increases during opening. The majority of acoustic energy is produced during this rapid flow deceleration², which is quantified variable known as the maximum flow declination rate (MFDR). MFDR is clinically important because it is highly correlated with maximum acoustic intensity (usually measured the intensity of the higher harmonics (which are important for intelligibility in noise important to note that the rightward skewing is reduced or eliminated in vocal fold scaring³ and with different vocal techniques⁴.

Because the flow rate is a product of the glottal opening area and the jet velocity, MFDR can be increased by either increasing the maximum area declination rate (MADR) and/or increasing the maximum velocity declination rate (MVDR). The glottal area waveform (that determines MADR) is formed by both the medial-lateral (will be referred to as lateral) and superior-inferior (will be referred to as vertical) mucosal waves. The vertical mucosal wave produces the alternating convergent-divergent geometry shape of the glottis during vibration. During opening, the glottis in the coronal plane assumes a convergent shape (the width is narrower superiorly than inferiorly) whereas during closing the glottis, in the coronal plane, forms a divergent shape (wider superiorly than inferiorly). The converging-diverging shape of the glottis yields separate waveforms for the superior and inferior aspects of the fold in the coronal plane.

In order to measure the vertical wave, quantitative measures are required of the medial surface of the fold. This was first done in an excised canine hemilarynx model^{5, 6}. These studies found that the complex three-dimensional vibrations can be broken up primary into two “modes”; the first in the vertical direction (super-inferior) and the second in the medial-lateral direction. This pioneering work led to many important insights. However, there are some relatively important questions that still need to be addressed.

The first question arises about the validity of the hemilarynx model to study the closing mechanism during vibrations. From our previous work with the hemilarynx canine model⁷ we observed that the vibratory pattern of the folds and the glottal flow characteristics can be different than in the full larynx model. Specifically, we observed the closed phase (i.e., duration of glottal closure) to be very short, which is different than the full larynx. Also, the intraglottal gage pressures observed near the superior aspect of the folds were much more negative in the full larynx compared with the hemilarynx model (for similar subglottal pressures). This is important to note because the negative pressure near the superior aspect of the folds might affect the closing mechanisms of the folds.

The second question is how accurately can current clinical methods capture the vertical mucosal wave. Both stroboscopy and high-speed videography observe vibration of the folds from above and show the mucosal wave in the medial-lateral direction; the vertical wave can only be qualitatively estimated⁴. In addition, the one camera from above can only measure the minimum glottal area based on the difference (e.g., in pixel intensity) between the intraglottal airway and the medial surface. During opening, the smallest area is at the superior edge due to the convergent shape. During closing the smallest area is at the inferior edge. Thus, automated edge-detection algorithms that track the glottal area capture the smallest glottal area at different axial planes depending on the phase of vibration. The current assumption is that the dynamics of the superior and inferior edge differ only by a phase lag, but this assumption has not been validated in a full larynx model.

The third question is what the phase lag of the superior fold relative to the inferior fold is. It is quoted as varying between 60 to 90 degrees⁸ but this finding also has not been validated in a full larynx model.

The relationship between MADR and MFDR was analyzed theoretically by Titze⁸. He found that the main determinant of the glottal area curve skewing was the amplitude coefficient, QA, which is the ratio of the maximum amplitude of the inferior edge of the fold divided by the amplitude of the superior edge. He found that the area curve skewed to the right when Q_A is greater than 1 (i.e., larger displacement at the inferior edge compared with the superior). When it is less than 1, the area curve skews to the left. Titze stated that during modal phonation, the amplitude coefficient is greater than 1. This leads to the fourth question, which is what is the value for Q_A in the full canine larynx, and it correlates with the skewing of the glottal area waveform.

The purpose of this study is to address these questions by examining the dynamics of the medial glottal wall geometry during vibrations in a full canine larynx model. Our technique allows tracking of the superior aspect of the fold throughout both opening and closing and the inferior edge during closing.

METHODS

Experimental setup

The dynamics of the medial glottal walls were captured using particle image velocimetry (PIV). PIV is a well-established visualization technique that is used in aerospace engineering to measure flow velocity. The PIV uses laser to illuminates the flow, and a video camera that captures an image (of the flow) simultaneously with the laser illumination. In the classical setup for a 2-D PIV measurement, the camera is positioned orthogonal to the laser which is condensed into a thin sheet that specifically illuminates the focal plane of the camera.

In the current study, the laser was projected as a 1 millimeter thick sheet from above the larynx in the in the mid-coronal plane (Figure 1a). The camera was positioned in front and above the larynx and directed into the glottis. Using this configuration for the PIV enables measurements of the entire intraglottal flow during the closing phase of the vibration because of the divergent shape of the glottis.

Figure 1 –

a) The laser sheet for the PIV was projected from above the larynx to illuminate the glottis. The camera was position in front and above the larynx (the tip of the lens connected to the camera can be seen on the right). b) Schematics for the experimental setup

In addition to the PIV measurements, the dynamics of the vocal folds was captured using highspeed video (HSV) camera. The HSV camera was positioned about 1 m directly above the larynx and its image acquisition was synchronized with the acquisition of the PIV data using the same trigger and reference clock for both cameras. The external reference clock was provided by a National Instruments timing and synchronization module (NI PXIe-6672). In addition, acoustic measurements (Brüel & Kjær, 1/4 ” multi-field microphone, Model 4961) and electroglottograph (EGG) were collected simultaneously with the imaging data using a data acquisition system (NI, PXIe-6356). The EGG was collected by placing the electrodes on both sides at the superior lateral aspect of the paraglottic space. The sampling rates for the data acquisition, HSV and PIV were 200 kHz, 20 kHz and 5 kHz, respectively.

The larynx was held in space using a four-prong support attached to the cricoid and the trachea was connected to an aerodynamic nozzle. The nozzle was connected to a settling chamber where the subglottal pressure was measured using a pressure transducer (Honeywell, FPG). Upstream to the chamber, the flow was humidified (Hudson RCI, ConchaTherm III) and regulated using a flow controller (Parker, MPC series), a flow meter (MicroMotion Inc, CMF025 Coriolis Flow Meter), and a pressure regulator (ControlAir Inc, Type 100 Precision Air Pressure Regulator). An illustrative schematic for the experimental setup is shown in Figure 1b.

Four excised canine larynges were examined in this study. All cartilage and soft tissue above the folds were removed to in order to obtained unobscured view of the glottis. Phonation of the folds was obtained at two subglottal pressures (low and high) and the data acquisition for each test was initiated about 10sec after the onset of phonation to allow for the vibration frequency to stabilize.

Measurements of vocal fold displacement

The phase of each PIV/HSV image was determined using the EGG signal as a reference. The glottal cycle was defined as 0°–360°, where 0° and 360° mark the opening of the folds at the superior edge. The phase of each image in the glottal cycle was determined by matching a reference signal from the camera (TTL) to the phase of the EGG signal (see Oren et al.⁹ for details).

Although PIV measurements were used previously for glottal flow measurements, the shape of the glottis during closing can also be extracted from the PIV images by marking the edges of the glottal jet area (Figure 2a). The figure shows a representative PIV image taken during the closing phase with marking for glottal wall and its edges. Because of the divergent shape of the glottis during the closing phase of vocal fold vibration, the entire glottis is illuminated by the laser that is projected from above, and distance measurements could be made along the entire height of the glottis. On the other hand, during the opening phase, only the distance between the superior edge of the medial glottal surface could be measured because the inferior edge is hidden due to the convergent shape of the glottis (Figure 2b). The representative image from the opening phase shows that the medial glottal walls appear to be vertically straight because the illumination from the laser that is projected from above is being truncated at the superior edge.

Figure 2.

Sample images of the glottal opening a) Using PIV during the closing phase. The approximate locations of the superior and inferior edges are marked. b) Using PIV during the opening phase. Only the location of the superior edge can be determined. c) Using HSV camera for the same phase during closing shown in (a). The minimum glottal area is marked on the image. Images are showing from the same case and the same larynx.

Measurements of the medial glottal wall displacement (from the PIV images) were taken as half the distance between the folds and were extracted manually over 10 glottal cycles for each subglottal pressure, P_SG. The distance between the folds was measured along the superior and inferior aspect of the folds. The superior aspect can be easily identified by the vertical change in curvature of the fold (see Figs. 2a–b) and is always visible during the opening and closing phases. Unlike the superior aspect, the inferior aspect is visible in the PIV image only during the closing phase (due to the divergent shape of the glottis). The location for the inferior aspect measurement was determined based on the height of the folds, which was measured a- priori in each larynx. The rapidity of closing along the superior and inferior edges was quantified by the maximum line declination rate (MLDR). This quantity is proportional to MADR, and is based on the line distance measurements from the PIV images. The divergence angle of the glottis during closing was also measured as the angle that is formed between the vertical and the medial glottal wall.

The glottal opening area was computed from the HSV images by marking the edges of the glottal opening based on the difference in pixel intensity of the folds and the glottal opening (Figure 2c). The HSV image that is shown is the synchronous image to the PIV image that is shown during the closing phase in Fig. 2a. The rapidity of closing from the HSV images was quantified by the maximum area declination rate (MADR).

RESULTS

The dynamics of the medial glottal wall displacement that is extracted from the PIV measurements is comparable, but slightly different than to the dynamics of the glottal opening area that is extracted from the HSV (Figure 3). During the opening phase of vibration, the waveform of the glottal opening area (computed from the HSV images) matches well with the displacement of the superior aspect of the fold (measured in the PIV images). On the other hand, during closing the glottal area waveform matches with the inferior aspect of the fold. The switching between the match with the superior/inferior aspects stems from the location where the minimum glottal opening area is measured in the HSV image; during the opening phase, the minimum area occurs at the superior aspect due to the convergent shape of the glottis. Likewise, during closing, the minimum glottal area occurs at the inferior aspect due to the divergent shape of the glottis. The dynamics of the inferior and superior fold are different during closing in that the MADR is higher for the superior edge.

Figure 3.

Waveforms of the medial glottal wall measured in the PIV images (open and closed symbols) and the glottal opening area computed from the HSV images (half-closed symbols). Data is shown for the same larynx at a) Low P_SG, and b) High P_SG.

The plots for the medial wall displacement (using PIV) and glottal area (using HSV) also show that the waveforms decrease more rapidly than they increase, a phenomenon described earlier as rightward skewing. The plots also show that skewing of the superior aspect waveform differs relative to the glottal area waveforms. The difference can be observed using the skewing index (Table 1). The skewing index is defined as the ratio of the duration of increase in area/medial wall displacement to the duration of the decrease in area/medial wall displacement, SI=T_open/T_close. The values computed for SI from the HSV are different than the values computed from the PIV data because T_open and T_close are computed based on displacement at different aspects of the folds. For the HSV data the value for T_close is computed based on the displacement of the folds in the inferior aspect, which closes before the superior aspect (because of the divergent shape of the glottis) and thus is shorter. Therefore, the values computed for SI based on the HSV data will be higher than SI values computed from PIV because the SI from PIV is based on the displacement in the superior aspect only.

Table 1.

Data for skewing index and phase delay based on the subglottal pressure in each larynx. SI_{glottal area} is computed from the HSV images and SI_{superior edge} is computed from the PIV images. Open quotient = (opening + closing)/one glottal cycle

Larynx	PSG (cmH2O)	SIglottal area	SIsuperior edge	Open Quotient	Phase delay (deg)
L1	10.1	1.75	1.57	0.71	13
	25.5	1.85	1.68	0.45	22
L2	18.8	1.40	1.37	0.17	28
	27.2	1.77	1.66	0.39	63
L3	15.2	1.16	0.80	0.20	29
	27.5	1.42	0.87	0.28	54
L4	16.2	1.13	1.58	0.45	13
	25.6	1.35	2.47	0.52	22

The divergence angle of the medial glottal wall can also be extracted from the PIV images. The divergence angle was measured as the angle between the vertical plane and a straight line that approximated the glottal wall (see Fig. 2a). The divergence angle in the glottis begins to form soon after the beginning of the closing phase. The onset of the closing phase in the glottal cycle is normally marked by the beginning of the medial motion of the inferior aspect of the folds. The angle measurements were taken on both glottal walls because of the apparent asymmetry of the glottis. The asymmetry in the shape of the glottal opening should be taken with caution as this observation could stem from the uncertainty in the wall location due to reflections of the laser from the tissue.

The waveform of the divergence angle that develops in the glottis matches well with the aerodynamics of the intraglottal flow (Figure 4). The maximum value of the divergence angle during the closing phase was observed around θ = 108°, which matches the phase where the lowest negative pressure was computed near the superior aspect of the fold for the same larynx in the same case (pressure data is reproduced from Oren et al.¹⁰). The match in the phase for the maximum value of the divergence angle and the lowest value of the negative pressure was also observed in the other test cases and will be discussed further. Maximum values for the divergence angle from all the larynges in the current study show that these values are proportional to the subglottal pressures (Figure 5).

Figure 4.

Waveform of the divergence angle for larynx L4 at high P_SG. The closed and open symbols are measurements taken on the right and left folds, respectively. Dashed line showed the most negative intraglottal pressure that is computed for the same case (data reproduced from¹⁰).

Figure 5.

The maximum values of divergence angle in the glottis increase as a function of subglottal pressure, P_SG.

The phase delay of the superior edge relative to the inferior edge can vary during the closing phase. By taking the phase difference for maximum displacement (for the inferior and superior edges) the current data shows that the phase delay is constant in each larynx, rather it changes with the subglottal pressure (Table 1). A greater phase lag between the superior and inferior aspects is associated with a greater divergence angle.

The increase in the divergence angle of the glottis is also proportional to the increase in the acoustic intensity and the lowest negative pressure that is calculated between the folds, P_min (Figure 6). The acoustic intensity was calculated from the microphone data and is shown using the sound pressure level (SPL) value. The pressure in the superior aspect of the folds is negative relative to the atmospheric pressure. Thus P_min, which is negative in the superior half of the glottis during most of closing, is a measure of the pulling (or suction) force that acts on the folds during closing. The details on how these pressures between the folds were calculated from the PIV measurements can be found in Oren et al.¹⁰. The magnitude of this negative pressure changes during the closing phase (which is shown as the dashed line in Fig. 4) and P_min is taken as the value for the minimum peak on the pressure curve.

Figure 6.

Relation between maximum divergence angle in the glottis to a) lowest negative pressure computed between the folds (Note: The quality of the velocity fields data for L4 were not sufficient to compute the pressure from the PIV measurements) and b) acoustic intensity (measured by the sound pressure level, SPL).

DISCUSSION

The current study measures the medial surface dynamics of the folds in the mid-membranous plane and it shows that skewing of the glottal area waveform can occur without the presence of a vocal tract. In addition, it shows that the phase lag of the superior edge relative to the inferior edge is smaller than reported and depends on the subglottal pressure. It also shows that the glottal divergence angle during closing is correlated with the acoustic intensity, which was shown qualitatively in a previous study of singers⁴, and with the intraglottal negative pressure, which can act as a pulling force on the glottal walls during the closing phase.

We will now review the questions raised in the introduction. The first has to do with the hemilarynx versus full larynx model. The hemilarynx model is used to look at the different modes of vibration. The current study did not characterize these modes, but we did observe a significant vertical and medial-lateral mucosal waves, which is consistent with what is seen in the hemilarynx. However, the current study shows that in the larger part of the cases, the open quotient for the full larynx model is below 0.5, which means the folds are completely closed for the majority of the glottal cycle (Table 1). By comparison, the value for open quotient in our hemilarynx study was around 0.95. Thus, the period of glottal closure is greater in the full larynx and it varies as a function of the subglottal pressure.

The second question has to do with how accurate current visualization techniques, such as stroboscopy or HSV, can evaluate the vertical wave. Figure 3 shows that the HSV captures the dynamics of the inferior fold during closing. However, from the PIV measurements the superior fold has a higher MADR during the latter part of the closing relative to early closing; for the inferior fold, the MADR is the same value throughout closing. In addition, MlDR is greater at the superior edge relative to the inferior. Since the length of the glottis is not changing and since there is no anterior-posterior wave seen, the assumption is that the glottal width at the superior edge is proportional to the glottal area. This will result in a higher MFDR superiorly.

The third question is the amount of phase delay between the superior and inferior edge during closing. It is quoted as 60–90 degrees and it has been assumed that the phase delay has no dependence on subglottal pressure. As seen in Table 1, the phase delay at low subglottal pressures ranged from 13–29 degrees with an average of 20.75. At high subglottal pressures, the phase delay ranged from 22–63 degrees with an average of 40.25 degrees. We took the phase difference at the beginning of closing, but it does decrease during the closing cycle, approaching zero at the end of closing. This dependency on subglottal pressure and phase has not been discussed in the literature and the significance is not yet known. The difference in MADR of the superior fold relative to the inferior will affect the computation of the MFDR at the glottal exit.

The fourth question is whether area (or displacement) skewing (to the right) occurs and what is the value of Q_A, the amplitude coefficient. The current data show skewing of the area and displacement waveforms where more skewing is always observed in the superior fold aspect compared with the inferior. As discussed previously, Titze⁸ hypothesized that right skewing of the area curve will occur if the amplitude coefficient is greater than one; a condition that requires the displacement amplitude of the lower edge to be greater than the upper edge. However, in all larynges, the superior displacement was equal or greater to the inferior displacement (which is seen at maximal opening), which Titze’s theory predicts that the area curve will not skew to the right. Thus, this theory cannot be used to explain our findings. The superior aspect of the folds may displace more laterally than the inferior aspect because of to the difference in elasticity at higher subglottal pressure ^11,12. The vertical change in the elasticity of the medial glottal wall likely stems from the proximity of the conus elasticus to the inferior aspect.

If the amplitude coefficient is one or less, what explains our observations of area and displacement skewing to the right. This skewing implies that the forces causing closing are greater than the forces present during the opening phase. Traditionally, there are two classic forces that occur during closing. To understand the first, the fold can be modeled as a spring. During opening, the spring is compressed and stores energy; during closing, this energy, known as elastic recoil, is released. However, due to viscous forces, the released energy during closing is less than the energy used to compress the spring during opening. Thus, increasing recoil forces may increase closing speed, but it will not cause the skewing of the area curves that are seen in the experiments described above. The second proposed cause of an additional closing force is due to the interaction of vocal folds with the acceleration/deceleration of the supraglottal air column in the vocal tract¹³. However, the current work shows that skewing of the area waveform can occur without a vocal tract. While the interaction of the vocal folds with the air column in the vocal tract clearly plays a role in skewing and in vocal efficiency, the results of the current study suggest that other forces maybe involved. Our work hypothesizes these additional forces are due to the vortices formed in the divergent glottis during closing.

In fluid mechanics, it is known that vortices will form in a divergent duct when the divergence angle exceeds a certain threshold. When these vortices occur, Bernoulli’s law does not apply. It is also known that the strength of the vortices can increase as the divergence angle increases. Using PIV measurements in canine larynx model, it was shown that vortices form in a divergent glottis during phonation and these vortices can produce negative pressures, P _min^{7, 10}

A larger divergent angle between the folds during closing enables for more entrainment flow to enter the void that is formed between the glottal flow and the glottal wall. The increase in the entrainment flow can also increase strength of the intraglottal vortices that are formed and consequently increase the magnitude of P_min, that is formed near the superior aspect of the fold during closing (Fig. 6). P_min is hypothesized to act as additional aerodynamic force that contributes to the closing mechanism of the folds’ vibration. The magnitude of the divergent angle in the glottis, which affects the magnitude of P_min, can therefore be also considered to be a factor that can contribute to the closing mechanism of the folds.

The negative pressure produced by the intraglottal vortices acts as a pulling (or suction) force, causing more rapid reduction in the glottal area or an increase in the MADR. This rapid reduction in glottal area will first cause a rapid increase in velocity; then, as the glottal flow shuts off, a rapid reduction in velocity occurs, which increases the maximum velocity declination rate (MVDR)¹⁴. Both increases in MADR and MVDR will increase MFDR, resulting in higher SPL, increased acoustic energy in the higher harmonics, and improved vocal efficiency.

Even if the hypothesis about the role of the vortices during closing is true, it still remains to be seen how this knowledge can be used to improve care of patients with voice disorders. These vortices are formed inside the glottis due to the flow dynamics that develops during closing and cannot be measured directly in a clinical setting. On the other hand, their magnitude and affect are directly related to the magnitude of the glottal divergent angle. A divergent glottis is created in part by the fact that the glottis is stiffer inferiorly. Increasing the stiffness at the inferior aspect of the fold can increase the divergent angle of the glottis. As a footing to this claim, the acoustic intensity is plotted against the divergent angle of the glottis (Fig. 6b) and it shows that SPL is increased as the divergence angle of the glottis is increased. This preliminary data suggests that detailed study of the alternative convergent-divergent wave is necessary in order to determine important mechanisms determining the relationship between the vertical wave and acoustics.

CONCLUSION

The current study examines the dynamics of the medial glottal wall geometry during phonation in a canine larynx model. The phase lag varies with subglottal pressure and is less than previously reported. The results show that increase in MADR and skewing of the glottal area waveform can occur without the present of a vocal tract. The results also show the dynamics of the superior fold cannot be captured with current stroboscopic or high-speed methods. Skewing of area waveform and MADR are proportional to MFDR, which increases acoustic intensity. Without a vocal tract, the area skewing is likely related to the intraglottal vortices that form near the superior aspect of the folds.