The vocal membrane, i.e., an extended part of the vocal fold, is observed in a wide range of species including bats and primates. A theoretical study [Mergell, Fitch, and Herzel (1999). J. Acoust. Soc. Am. 105(3), 2020–2028] predicted that the vocal membranes can make the animal vocalizations more efficient by lowering the phonation threshold pressure. To examine this prediction, a synthetic model of the vocal membrane was developed, and its oscillation properties were examined. The experiments revealed that the phonation threshold pressure was lower in the vocal membrane model compared to that in a model with no vocal membrane. Chaotic oscillations were observed as well.

The vocal membrane, known as an accessory extension from the vocal fold, has been observed in a range of species such as bats and primates (Fitch, 2000; Nishimura, 2020; Nishimura et al., 2022; Suthers, 2004). It is attached to a supero-medial portion of the vocal fold and extends superiorly along the medial surface of the vocal fold. Because of its close location to the vocal folds, involvement of the vocal membrane in the animal voice production has been a matter of great interest. Understanding the role of vocal membrane in animal vocalizations may not only clarify why the animals possess such a small appendage but also lead to an insight into why this feature was lost in the human lineage. Acoustic functions of the vocal membrane, however, have not yet been extensively investigated due to the limited availability of animals in experiments. Mergell et al. (1999) presented a theoretical model of the vocal membrane and demonstrated that it makes the animal vocalizations more efficient by lowering the phonation threshold pressure. Brown et al. (2003) carried out an excised larynx experiment of squirrel monkey (Saimiri boliviensis) and observed a variety of vocalizations, including irregular calls, that lack a clear fundamental frequency. The empirical data from marmosets also suggested that this feature improves efficiency in phonation (Zhang et al., 2019). In these two animal studies, however, presence of the vocal membrane, which should be distinguished from the vocal fold, was not clearly identified in the larynges. In vivo and ex vivo observations of primate species (Nishimura et al., 2022), on the other hand, showed that irregular oscillations of the vocal membrane can easily occur by interacting with the vocal fold vibrations. Although the in vivo and ex vivo studies provide an important hint on how the vocal membranes influence the vocal fold oscillations, configuration of the vocal membranes cannot be precisely controlled in such experiments and their results may not be always reproducible due to the individuality of the animal samples.

The aim of the present paper is to develop a synthetic model of the vocal membrane and to examine the oscillation properties of the vocal membrane and the vocal fold. The synthetic model is advantageous in the sense that it can be controlled much more precisely than real animals and the experiment can be reproduced. Based on representative anatomical features of the vocal membrane in primates, we have designed the vocal membrane, which was attached to a supero-medial portion of the vocal fold. The synthetic model for the vocal fold, as well as the vocal membrane, was made of flexible silicone compounds with material properties comparable to those of the vocal fold tissues. In the present study, the phonation threshold pressure and other acoustic quantities were measured experimentally for the vocal fold model having a vocal membrane (hereafter, the vocal membrane model) and compared with those of the vocal fold model having no vocal membrane (hereafter, the vocal fold model).

As a synthetic model of the vocal fold and the vocal membrane, the model geometry was designed as shown in Fig. 1(b). The vocal membrane is attached to a supero-medial portion of the vocal fold and extends along the inferior–superior axis in the vocal membrane model. This design is consistent with the representative anatomical features of the vocal membrane (Nishimura et al., 2022; Suthers, 2004) and is also compatible to the design of the computational model [see Mergell et al., 1999]. To examine the effect of the vocal membrane, the vocal fold model was also constructed according to the design of Fig. 1(a) (Murray and Thomson, 2012; Thomson et al., 2005), which was based on the M5 geometry of Scherer et al. (2001). In contrast to the vocal membrane model, the M5 model had a rounded medio-superior surface of the vocal fold. As summarized in Table 1, the two models had similar dimensions except for the part of the vocal membrane. The vocal folds are structured with the body and cover layers in non-human primates as well as in humans, despite their differences in layered histological compositions (Ishii et al., 1999; Kurita et al., 1983; Nishimura et al., 2022; Riede, 2010). To realize such body-cover structure of the vocal folds, two molds were created to fabricate the body and cover layers [see Fig. 1(c)]. According to an anatomical investigation (Riede, 2010), the vocal membrane has been considered as a part of the cover layer. Following the basic methodology of Murray and Thomson, 2012, both models were created [Figs. 1(d) and 1(e) show a sample]. The models were fabricated using liquid two-part silicone (EcoFlex® 00–30, Smooth-On, Inc., Easton, PA), stiffer two-part silicone mixture (Dragon Skin® 10 Fast, Smooth-On, Inc.), and silicone thinner compounds (Silicone Thinner®, Smooth-On, Inc.). Stiffnesses of the individual layers were controlled by the mixture ratio of these materials. The mixture ratio was 1:1:2 (EcoFlex part A, EcoFlex part B, and Silicone Thinner) for the body layer, while it was 1:1:4 for the cover layer. Upon the cover layer, a thin epithelium layer with 1:1:1 ratio was further attached. For our experiment of flow-induced oscillations, three model instances composed of left and right vocal membranes were created [see Fig. 1(f)]. To visualize the movements of the vocal membrane more clearly, the membrane part was colored in red in one model instance. Three instances of the vocal fold model without vocal membranes were also created.

Fig. 1.

(a) Geometry of the M5 vocal fold model, to which no vocal membrane is attached. (b) Geometry of the M5 vocal fold model, to which vocal membrane is attached. Detailed dimensions of (a) and (b) are summarized in Table 1. (c) Molds for fabricating the body and cover layers of the vocal membrane model. (d) Fabricated vocal membrane model. (e) Vocal membrane model attached to a rigid plate. (f) Left and right vocal membrane models that are located closely to each other during the phonation experiment.

Fig. 1.

(a) Geometry of the M5 vocal fold model, to which no vocal membrane is attached. (b) Geometry of the M5 vocal fold model, to which vocal membrane is attached. Detailed dimensions of (a) and (b) are summarized in Table 1. (c) Molds for fabricating the body and cover layers of the vocal membrane model. (d) Fabricated vocal membrane model. (e) Vocal membrane model attached to a rigid plate. (f) Left and right vocal membrane models that are located closely to each other during the phonation experiment.

Close modal
TABLE 1.

Dimensions of the vocal fold model with and without the vocal membranes. r1c and r2c represent radius of curvature.

DimensionWith vocal membraneWithout vocal membrane
H 8.665 mm 8.4 mm 
T 0 mm 0.1 mm 
I 7.413 mm  
J 2 mm  
δ1 0 mm  
δ2 1.077 mm  
θ1c 50° 50° 
θ2c 5° 5° 
θ3c 90° 90° 
r1c 6 mm 6 mm 
r2c  0.987 mm 
DimensionWith vocal membraneWithout vocal membrane
H 8.665 mm 8.4 mm 
T 0 mm 0.1 mm 
I 7.413 mm  
J 2 mm  
δ1 0 mm  
δ2 1.077 mm  
θ1c 50° 50° 
θ2c 5° 5° 
θ3c 90° 90° 
r1c 6 mm 6 mm 
r2c  0.987 mm 

Oscillation properties of the two models were examined by injecting an air-flow. As shown in Fig. 1(f), the model was attached to a rigid acrylic plate (1.2 cm thick). Under a default situation, pre–phonatory medial–lateral distance between the left and right vocal folds was set to zero so that the two folds slightly touched each other when no flow was injected. By inserting a thin plate between the left and right model plates, their distance was also controlled.

A polyvinyl chloride (PVC) tube (length: 25 cm, inner diameter: 2.5 cm) was connected to the model as a trachea, where the tracheal length was in accordance with Zanartu et al. (2007). Since this setting avoids resonance effect of the subglottis, it should aerodynamically drive the model (Zhang et al., 2006). No supraglottal tube was attached. To transfer an air-flow from an air compressor (SilentAirCompressor Sc820, Hitachi Koki Co., Ltd., Tokyo, Japan) to the tracheal tube, an expansion chamber (inner cross sectional diameter: 30 cm, length: 50 cm) was inserted between them. The flow rate from the air compressor was controlled by a pressure regulator (10202 U, Fairchild, Winston-Salem, NC) and a digital mass flow controller (CMQ–V, Azbil, Santa Clara, CA).

The subglottal pressure was measured by a differential pressure transducer (DP15-28-N1S4A, Validyne Engineering, Northridge, CA) and a pressure amplifier (PA501, KRONE Corporation, Tokyo, Japan), which was mounted flush onto the inner wall of the tracheal tube, 2 cm upstream of the model. The acoustic sound and the sound pressure level (SPL) were measured by an omnidirectional microphone (type 4192, Nexus conditioning amplifier, Brüel and Kjaer, Tokyo, Japan) and a sound level meter (type 2250–A, Brüel and Kjaer), respectively, both located 10 cm away from the model. All signals were stored into a digital recorder (Controller, PXIe-8840, National Instruments; input/output card, BNC-2110, National Instruments; Software, Labview, National Instruments, Tokyo, Japan) with a sampling frequency of 12.5 kHz.

To measure the vibration patterns of the vocal folds and/or the vocal membranes in each model, a high-speed video (VW-9000, Keyence, Osaka, Japan) was used (160 X 112 pixel resolution; 10 kHz sampling rate).

To measure the phonation onset pressure, the flow rate was linearly increased from 0 l/min to a maximum rate in 5 s (the maximum flow rate was adjusted between 40 l/min and 160 l/min depending upon the individual model instance). The phonation onset was detected at the pressure, where the difference between the maximum and minimum of the oscillating subglottal pressure exceeded a threshold value. After the onset point, the flow-induced oscillations of the model were continued to be measured for 10 s by the microphone, from which the fundamental frequency fo and jitter were computed by the Praat software (Boersma and Weenink, 2022). The vocal efficiency was also calculated as E=10log104πr2IUPs, where r m represents distance from the vocal fold model to the microphone, I=10(SPL/10)12 W/m2 is the sound intensity obtained from the sound pressure level SPL dB, U is the flow rate m3/s, and Ps kg/m s2 is the subglottal pressure (Jiang et al., 2004; Titze, 1992). Next, the flow rate was linearly decreased from the maximum level to 0 l/min in 5 s and the phonation offset was detected when the oscillation amplitude of the subglottal pressure became less than the threshold.

The phonation onset, constant flow oscillations, and phonation offset were all measured within a single experimental procedure, which was fully automated. This procedure was repeated twice for each model instance, where averaging over the two runs provided the representative values (i.e., onset and offset pressures and other acoustic quantities) for each model instance. To examine statistical difference between the vocal fold and vocal membrane models, Welch's t-test was applied using ttest2 function of the Matlab software (R2020a; MathWorks, Natick, MA). The group size was n = 3 (i.e., number of instances created for each model type).

Figure 2 shows the results of the flow-induced oscillations of the vocal membrane and vocal fold models. In panel (a), the phonation onset pressures are compared between the vocal membrane model (red, 1.63 ± 0.16 kPa, n = 3) and the vocal fold model (blue, 2.90 ± 0.03 kPa, n = 3). The onset pressure was significantly decreased in the presence of the vocal membranes (t-test: p = 0.0042). Panel (b), on the other hand, shows the results on the offset pressure. Again, the offset pressure was significantly decreased in the presence of the vocal membranes (vocal membrane model: 1.37 ± 0.24 kPa, n = 3; vocal fold model: 2.64 ± 0.01 kPa, n = 3; t-test: p = 0.006). In each model, the offset pressure was slightly lower than the onset pressure due to the hysteresis of the vocal fold system, implying that the phonation onset is governed by a subcritical Hopf bifurcation.

Fig. 2.

Comparative experiment of the vocal fold models with (red) and without (blue) vocal membranes. For each model, the measurements were made for three instances (circles) and their average was plotted with a bar chart. In (a)–(e), distance between the left and right vocal folds was set to 0 mm. (a) Phonation onset pressure detected by the subglottal pressure signal. (b) Phonation offset pressure detected by the subglottal pressure signal. (c) Fundamental frequency fo computed from the microphone signal. (d) Jitter computed from the microphone signal. (e) Vocal efficiency computed from the subglottal pressure and the sound pressure level. (f) Phonation onset and offset pressures detected in the case that the distance between the left and right vocal folds was set to 1 mm.

Fig. 2.

Comparative experiment of the vocal fold models with (red) and without (blue) vocal membranes. For each model, the measurements were made for three instances (circles) and their average was plotted with a bar chart. In (a)–(e), distance between the left and right vocal folds was set to 0 mm. (a) Phonation onset pressure detected by the subglottal pressure signal. (b) Phonation offset pressure detected by the subglottal pressure signal. (c) Fundamental frequency fo computed from the microphone signal. (d) Jitter computed from the microphone signal. (e) Vocal efficiency computed from the subglottal pressure and the sound pressure level. (f) Phonation onset and offset pressures detected in the case that the distance between the left and right vocal folds was set to 1 mm.

Close modal

Panels (c)–(e) show results on the acoustic quantities. The fundamental frequency was slightly lowered by the vocal membrane, possibly because of the change in the oscillation pattern, but the difference was rather small (vocal membrane model: 122.5 ± 0.9 Hz, n = 3; vocal fold model: 132.9 ± 3.4 Hz, n = 3; t-test: p = 0.026). The jitter (vocal membrane model: 3.2 ± 0.2%, n = 3; vocal fold model: 2.6 ± 0.8%, n = 3; t-test: p = 0.31) and the vocal efficiency (vocal membrane model: −42.1 ± 5.6 dB, n = 3; vocal fold model: −37.3 ± 2.2 dB, n = 3; t-test: p = 0.27), on the other hand, did not show a significant effect of the vocal membranes. It should be noted that, since within-group variance is large in the jitter and the vocal efficiency, the present statistical test has a limited reliability.

To confirm that the results are independent of the level of adduction, the medial–lateral distance between the left and right vocal folds was extended to 1 mm by inserting a thin plate between the left and right model plates. As shown in panel (f), both phonation onset pressure (vocal membrane model: 1.82 ± 0.35 kPa, n = 3; vocal fold model: 2.51 ± 0.04 kPa, n = 3; t-test: p = 0.075) and offset pressure (vocal membrane model: 1.18 ± 0.18 kPa, n= 3; vocal fold model: 2.02 ± 0.10 kPa, n = 3; t-test: p = 0.005) were again lowered by the vocal membranes. Noteworthy is the fact that the phonation was observed in the vocal membrane model up to the vocal fold distance of 4 mm, while it was observed in the vocal fold model only up to 2 mm. This implies that the vocal membranes worked efficiently to lower the phonation threshold pressures, independently of the level of adduction.

Figure 3(a) shows a sequence of images measured by the high-speed camera. On the medial–lateral and anterior–posterior axes, movements of the vocal folds as well as the vocal membranes, which are in a dark color, are discernible. Initially, the vocal folds are closed at 2.6 ms. Next, they start to open, reach to the maximal opening area at 4.6 ms, and then start to close. The vocal membranes, on the other hand, start to open simultaneously with the vocal folds, reach to the maximal at 6.6 ms and then start to close. Compared to the vocal folds, the vocal membranes display much larger amplitudes. Their movements follow those of the vocal folds with a time-lag of about 2 ms. Figure 3(b), on the other hand, shows a sequence of images measured for the vocal fold model without vocal membranes. While the vocal membrane model tends to close completely, the vocal fold model does not show a complete glottal closure. Such an incomplete closure with air leaks could make the vocal fold oscillations less efficient. The existence of the vocal membrane may realize a complete glottal closure more easily and consequently improve the efficiency of the vocal fold oscillations.

Fig. 3.

(a) Sequence of high-speed images that captured surface movement of the vocal membrane model. The vocal fold distance was set to 0 mm. In each image, the vocal folds as well as the vocal membranes (dark color) are displayed on the medial–lateral and anterior–posterior axes. (b) Sequence of high-speed images that captured surface movement of the vocal fold model. The vocal fold distance was set to 0 mm. In each image, the vocal folds are displayed on the medial–lateral and anterior–posterior axes. In (a) and (b), the labels indicate the recording time corresponding to the images.

Fig. 3.

(a) Sequence of high-speed images that captured surface movement of the vocal membrane model. The vocal fold distance was set to 0 mm. In each image, the vocal folds as well as the vocal membranes (dark color) are displayed on the medial–lateral and anterior–posterior axes. (b) Sequence of high-speed images that captured surface movement of the vocal fold model. The vocal fold distance was set to 0 mm. In each image, the vocal folds are displayed on the medial–lateral and anterior–posterior axes. In (a) and (b), the labels indicate the recording time corresponding to the images.

Close modal

In Fig. 4(a), a kymogram (Svec and Schutte, 1996) was drawn by extracting the line images from the medial–lateral axis of the high-speed images [blue line in Fig. 3(a)]. The horizontal axis represents time, whereas the vertical axis indicates the pixel location. The middle dark area corresponds to the opening area of the glottis, while the gray/white area indicates surface of the vocal folds. It can be confirmed again that the vocal membranes (dark color) follow the trajectories of the vocal folds with a larger amplitude. Figure 4(b) shows a kymogram of the vocal fold model [extracted from blue line in Fig. 3(b)]. Oscillation pattern of the vocal folds looks similar to that of the vocal membrane model. As a quantity to characterize the oscillation pattern, the closed quotient (CQ) (i.e., percentage of the glottal cycle in which the vocal folds are closed) was computed from the kymogram. The CQ was 18.2 ± 0.6% and 26.1 ± 0.7% for the vocal fold model and the vocal membrane model, respectively. The extended CQ implies that the glottal waveform is more deformed to generate higher harmonics in the vocal membrane model.

Fig. 4.

(a) Kymogram extracted from the high-speed images of the vocal membrane model on the medial–lateral axis [blue line of Fig. 3(a)]. (b) Kymogram extracted from the high-speed images of the vocal fold model on the medial–lateral axis [blue line of Fig. 3(b)]. (c) Kymogram measured from another instance of the vocal membrane model (vocal fold distance: 0 mm). (d) Two-dimensional delay-coordinate representation {Ps(t),Ps(tτ)} (τ=1.5 ms) of the subglottal pressure corresponding to the kymogram of (c).

Fig. 4.

(a) Kymogram extracted from the high-speed images of the vocal membrane model on the medial–lateral axis [blue line of Fig. 3(a)]. (b) Kymogram extracted from the high-speed images of the vocal fold model on the medial–lateral axis [blue line of Fig. 3(b)]. (c) Kymogram measured from another instance of the vocal membrane model (vocal fold distance: 0 mm). (d) Two-dimensional delay-coordinate representation {Ps(t),Ps(tτ)} (τ=1.5 ms) of the subglottal pressure corresponding to the kymogram of (c).

Close modal

Overall, both vocal membrane and vocal fold models showed mostly periodic stable oscillations. There were, however, few cases, in which the vocal membrane model showed an irregular behavior. Figure 4(c) provides such an example with a left–right asymmetric pattern. According to the spectral analysis of the kymogram as well as the simultaneously measured subglottal pressure, this oscillation pattern had a strong frequency component at around 170 Hz. Figure 4(d) displays a two-dimensional delay-coordinate representation {Ps(t),Ps(tτ)} (τ=1.5 me) (Takens, 1981) of the subglottal pressure, revealing a geometry that underlies the irregular oscillations. Existence of such chaotic dynamics associated with the vocal membranes has been also predicted by the preceding theoretical study (Mergell et al., 1999) and also reported by the excised larynx experiment (Nishimura et al., 2022). So far, this sort of irregular dynamics was not frequent in the present experiment. Among three instances of the vocal membrane models, one instance exhibited this sort of chaotic behavior under the condition that the vocal fold distance was set to 0 mm.

To study the effect of the vocal membranes on the vocal fold oscillations, synthetic models of the vocal membranes were constructed. The M5 model of the vocal fold was modified by adding a vocal membrane, which extends superiorly along the medial surface of the vocal folds. Our experiment of the flow-induced vocal fold oscillations indicated that the phonation threshold pressures (both onset and offset) have been lowered significantly by the vocal membranes. This provides an experimental confirmation of the theoretical study (Mergell et al., 1999), which predicted that the vocal membranes can lower the subglottal pressure by supporting the vocal fold oscillations. Our experiment also showed that the vocal membranes did not have a strong influence on acoustic quantities such as jitter and vocal efficiency, while they slightly lowered the fundamental frequency. Concerning the oscillation patterns, the kymogram indicated that the vocal membranes gave rise to a larger oscillation amplitude with some time-lag from the vocal folds. Such a time-delayed movement of the vocal membranes might have compensated for the diminished convergent–divergent motion that is needed for an efficient vocal fold oscillation in the original M5 model. Also, despite its rare occurrences, irregular chaotic dynamics was also observed in the kymogram for one instance of the vocal membrane model.

From the viewpoint of animal bioacoustics, the present study suggests that the vocal membranes can support the vocalization by lowering the phonation threshold pressure, thereby facilitating the vocal fold oscillations. Such property can be advantageous for animals to produce various calls with less power from the lungs. Chaotic phonations induced by the vocal membrane can also increase their vocal repertories (Fitch et al., 2002; Nishimura et al., 2022).

In this study, we have examined only a single design of the vocal membrane model. On the other hand, in vivo and ex vivo experiments showed that the vocal membrane can exhibit various oscillation patterns (e.g., in-phase and out-of-phase oscillations of the vocal membrane and the vocal fold, and sole oscillations of the vocal membrane) (Nishimura et al., 2022). To reproduce such patterns, varying the length, thickness, angle, and stiffness of the vocal membrane model should add more insight into the functions of the vocal membrane in a future study.

This work was partially supported by Grant–in–Aid for Scientific Research (Grant Nos. 17H06313, 19H01002, and 20K11875) from Japan Society for the Promotion of Science.

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