Clarification of the Acoustic Characteristics of Velopharyngeal Insufficiency by Acoustic Simulation Using the Boundary Element Method: A Pilot Study

Abstract

A model of the vocal tract that mimicked velopharyngeal insufficiency was created, and acoustic analysis was performed using the boundary element method to clarify the acoustic characteristics of velopharyngeal insufficiency. The participants were six healthy adults. Computed tomography (CT) images were taken from the frontal sinus to the glottis during phonation of the Japanese vowels /i/ and /u/, and models of the vocal tracts were created from the CT data. To recreate velopharyngeal insufficiency, coupling of the nasopharynx was carried out in vocal tract models with no nasopharyngeal coupling, and the coupling site was enlarged in models with nasopharyngeal coupling. The vocal tract models were extended virtually for 12 cm in a cylindrical shape to represent the region from the lower part of the glottis to the tracheal bifurcation. The Kirchhoff–Helmholtz integral equation was used for the wave equation, and the boundary element method was used for discretization. Frequency response curves from 1 to 3000 Hz were calculated by applying the boundary element method. The curves showed the appearance of a pole–zero pair around 500 Hz, increased intensity around 250 Hz, decreased intensity around 500 Hz, decreased intensities of the first and second formants (F1 and F2), and a lower frequency of F2. Of these findings, increased intensity around 250 Hz, decreased intensity around 500 Hz, decreased intensities of F1 and F2, and lower frequency of F2 agree with the previously reported acoustic characteristics of hypernasality.

1. Introduction

Patients sometimes fail to achieve velopharyngeal function after cleft palate surgery. Velopharyngeal insufficiency is a proximal cause of articulatory disorders, such as the substitution of glottal stops for certain consonants. Leakage of exhaled air into the nasal cavity impairs the ability to increase the intraoral pressure, resulting in abnormal sound production, such as distorted consonants. In addition, it has been pointed out that the speech of post-cleft palate surgery patients may also be affected by abnormalities in palatal morphology and related posteriorization of the tongue [1]. Research to date into the acoustic characteristics of the speech of cleft palate patients has focused mainly on techniques such as frequency analysis. For example, characteristics such as a lower second formant (F2) frequency of /i/ [2,3] and lower F2 frequency due to posteriorization of the tongue [4] have been noted, but the characteristics of the speech of cleft palate patients have not been fully identified.

Recently, many studies have been using magnetic resonance imaging (MRI) to analyze the movement and shape of the velopharynx during speech [5,6], and attempts to perform three-dimensional analysis of nasopharyngeal movement during swallowing have also been reported using computed tomography (CT) [7]. Although these methods enable detailed analysis of the movement of the nasopharynx during speech and swallowing, the relationships between the state of velopharyngeal closure or the shape of the articulatory organs and the sounds produced there cannot be analyzed.

We have been aiming to establish a simulation method using the boundary element method to clarify the relationship between the morphology of the articulatory organs and the speech that is produced. In previous studies, we applied the boundary element method to develop a simulation of the Japanese vowels /a/, /i/, and /u/ using a model of the vocal tract from the frontal sinus to the trachea, and verification of its validity showed that it is capable of simulation with sufficient accuracy [8,9]. This approach makes it possible to predict with high accuracy the changes in acoustic characteristics that result from modifying vocal tract morphology.

The present study sought to clarify the acoustic changes and characteristics of velopharyngeal insufficiency by modifying a vocal tract model created from computed tomography (CT) data during phonation of /i/ and /u/ into a model that recreates velopharyngeal insufficiency and then using the modified model for acoustic analysis with the boundary element method.

2. Materials and Methods

2.1. Participants

The study participants were six healthy adults (three males and three females; age range of 26–45 years) with a normal occlusal relationship and no abnormalities in the articulatory organs, including the tongue, palate, velum, and pharynx. The Institutional Review Board of Yamaguchi University Hospital approved this study (H26-22-4), and written, informed consent was obtained from all participants.

2.2. Simulation Method

The vocal tract model that we described previously [9] was used for the six participants. A SOMATOM Force (Siemens Healthineers, Munich, Germany) CT scanner was used for imaging. The scanning conditions were as follows: tube voltage, 100 (+Tin filter) kV; tube current, 96 mA; slice thickness, 0.6 mm; and CTDI vol., 0.23 mGy. The CT scanner used had the advantage of being able to maintain a low exposure dose. Namely, whereas the exposure dose for an ordinary chest CT examination is 5–30 mSv, it was only 0.1 mSv with the present CT scanner. CT imaging was carried out only once during phonation of the Japanese vowels /i/ and /u/ in the supine position. Using Amira 3D visualization software (version 5.6.0; Maxnet, Tokyo, Japan), the frontal, ethmoid, sphenoid, and maxillary sinuses; the nasal and oral cavities; and the pharynx, larynx, and glottis were extracted from the CT data. They were then used to create a three-dimensional model of the vocal tract, which was extended virtually for 12 cm in a cylindrical shape to represent the region from the lower part of the glottis to the tracheal bifurcation. To equalize and adjust the mesh size and remove unnecessary meshes, a direct modeler (Space Claim Direct Modeler, version 2021R1; ANSYS, Canonsburg, PA, USA) was used to modify the vocal tract model. The meshes of the nostril and oral aperture were removed, and the nasal and oral cavities and tracheal bifurcation were then opened. Using the method previously described [8], acoustic analysis was performed from 1 to 3000 Hz at 1 Hz intervals by software (WAON; version 4.55; Cybernet Systems Co., Ltd., Tokyo, Japan) using the Kirchhoff–Helmholtz integral equation and the boundary element method. The parameters of the acoustic analysis model were set as follows: The wall of the vocal tract model was regarded as rigid, so that the sound absorption coefficient was set to 0% with a specific acoustic impedance of ∞; the bottom of the virtual trachea was regarded as nonrigid after being extended cylindrically between the tracheal bifurcation and the lower part of the glottis [10]; the acoustic medium temperature was set to 37 °C; at this temperature, the sound velocity was 352.85 m/s and the density was 1.1468 kg/m³; and the sound source and observation point were set as points corresponding to the vocal cords and a location 10 cm in front of the lips, respectively. A frequency response curve was then drawn at the sound pressure level to calculate the first formant (F1) and F2.

2.3. Analysis Method

The condition of velopharyngeal insufficiency was recreated in the vocal tract models to investigate the acoustic characteristics. Of the vocal tract models created from the CT data, those with no nasopharyngeal coupling were modified to become models in which the nasopharynx was coupled (Figure 1). For the modification, a 2-milimeter mesh model of the vocal tract was created. A 1–3-mesh hole was opened in the nasal cavity side and in the oral cavity side of the mesh corresponding to the nasopharyngeal coupling site so that the cavities were coupled. For models with nasopharyngeal coupling, the part of the nasopharyngeal coupling site that coupled with the nasal cavity and the part that coupled with the oral cavity were each enlarged by 1–3 meshes (Figure 2). One to three meshes was the minimum number of meshes at which the cross-sectional area of the nasopharyngeal coupling site changed. In the preliminary experiments, vocal tract models enlarged by four or more mesh holes were created and simulated, but there was no difference in the results. Therefore, 1–3 mesh holes were opened for the models with no nasopharyngeal coupling, and the nasopharyngeal coupling sites were enlarged by 1–3 meshes for the models with nasopharyngeal coupling. The changes in cross-sectional area of the nasopharyngeal coupling site as a result of the modifications are shown in

Table 1. Minimum cross-sectional areas of the nasopharyngeal coupling site in the vocal tract models.

		Minimum Cross-Sectional Area of the Coupling Site in the Vocal Tract Model During Phonation of /i/ (mm2)		Minimum Cross-Sectional Area of the Coupling Site in the Vocal Tract Model During Phonation of /u/ (mm2)
Participant No.	Sex	Before Modification	After Modification	Before Modification	After Modification
1	Male	2.82	14.52	7.91	13.55
2	Male	0	0.37	0	3.35
3	Male	0	15.86	0	1.58
4	Female	0.45	3.54	12.01	14.47
5	Female	0	6.34	0	2.55
6	Female	1.44	13.99	4.12	10.74

. Acoustic analysis was performed using modified models.

3. Results

The results of acoustic simulation in the six participants are shown in

Table 2. Three cases with nasopharyngeal coupling during phonation of the Japanese vowel /i/, in which nasopharyngeal insufficiency was recreated by enlarging the nasopharyngeal coupling site.

/i/				F1						F2
Participant No.	Sex	Intensity Around 250 Hz	Intensity Around 500 Hz	Simulation Value (Hz)	Actual Voice (Hz)	Discrimination Threshold (%)	Enlarged	Percent Change (%)	Intensity	Simulation Value (Hz)	Actual Voice (Hz)	Discrimination Threshold (%)	Enlarged	Percent Change (%)	Intensity
1	Male	Increase	Decrease	356	351	1.4	365↑	2.5↑	Decrease	2196	2031	7.5	1992↓	9.3↑	Decrease
4	Female	Increase	Decrease	374	370	1.1	378↑	1.1↑	Increase	2510	2649	5.5	2511↑	0.0↑	Decrease
6	Female	Increase	Increase	401	442	10.2	381↓	5.0↓	Increase	2775	2882	3.9	2315↓	16.6↓	Decrease

“↑” and “↓” mean increase and decrease, respectively.

,

Table 3. Three cases with no nasopharyngeal coupling during phonation of the Japanese vowel /i/, in which nasopharyngeal insufficiency was recreated by coupling the nasopharyngeal coupling site.

/i/				F1						F2
Participant No.	Sex	Intensity Around 250 Hz	Intensity Around 500 Hz	Simulation Value (Hz)	Actual Voice (Hz)	Discrimination Threshold (%)	Coupled	Percent Change (%)	Intensity	Simulation Value (Hz)	Actual Voice (Hz)	Discrimination Threshold (%)	Coupled	Percent Change (%)	Intensity
2	Male	Increase	Decrease	365	342	6.3	360↓	1.4↓	Increase	2204	2356	6.9	2191↓	0.6↓	Increase
3	Female	Increase	Decrease	317	336	6	349↑	10.1↑	Decrease	2347	2180	7.1	2368↑	0.9↑	Decrease
5	Female	Increase	Decrease	368	358	2.7	389↑	5.7↑	Decrease	2451	2579	5.2	2416↓	1.4↓	Decrease

“↑” and “↓” mean increase and decrease, respectively.

,

Table 4. Three cases with nasopharyngeal coupling during phonation of the Japanese vowel /u/, in which nasopharyngeal insufficiency was recreated by enlarging the nasopharyngeal coupling site.

/u/				F1						F2
Participant No.	Sex	Intensity Around 250 Hz	Intensity Around 500 Hz	Simulation Value (Hz)	Actual Voice (Hz)	Discrimination Threshold (%)	Enlarged	Percent Change (%)	Intensity	Simulation Value (Hz)	Actual Voice (Hz)	Discrimination Threshold (%)	Enlarged	Percent Change (%)	Intensity
1	Male	Decrease	Decrease	371	364	1.9	385↑	3.8↑	Decrease	1127	1198	6.3	1135↑	0.7↑	Decrease
4	Female	Decrease	Increase	449	447	0.4	478↑	6.5↑	Decrease	1403	1333	5.0	1705↑	21.5↑	Decrease
6	Female	Increase	Increase	432	472	9.3	426↓	1.4↓	Increase	2072	1906	8.0	1997↓	3.6↓	Increase

“↑” and “↓” mean increase and decrease, respectively.

and

Table 5. Three cases with no nasopharyngeal coupling during phonation of the Japanese vowel /u/, in which nasopharyngeal insufficiency was recreated by coupling the nasopharyngeal coupling site.

/u/				F1						F2
Participant No.	Sex	Intensity Around 250 Hz	Intensity Around 500 Hz	Simulation Value (Hz)	Actual Voice (Hz)	Discrimination Threshold (%)	Coupled	Percent Change (%)	Intensity	Simulation Value (Hz)	Actual Voice (Hz)	Discrimination Threshold (%)	Coupled	Percent Change (%)	Intensity
2	Male	Decrease	Decrease	445	436	2.0	478↑	7.4↑	Decrease	1102	1222	11.0	1018↓	7.6↓	Decrease
3	Male	Increase	Decrease	381	375	1.6	360↓	5.5↓	Increase	1121	1261	12.5	993↓	11.4↓	Increase
5	Female	Increase	Decrease	495	464	6.3	527↑	6.5↑	Decrease	1220	1292	6.0	1136↓	6.9↓	Increase

“↑” and “↓” mean increase and decrease, respectively.

. With the Japanese vowel /i/, participants 1, 4, and 6 had nasopharyngeal coupling, and participants 2, 3, and 5 had no nasopharyngeal coupling during phonation. With /i/, two of the three participants with nasopharyngeal coupling showed a decrease in the frequency of F2 as a result of enlargement of the coupling site, and two of the three participants with no nasopharyngeal coupling showed a decrease in the frequency of F2 as a result of coupling being created.

The frequency response curves obtained from the results of simulation with the models of the Japanese vowel /i/ before and after modification of the nasopharyngeal coupling site are shown in Figure 3 and Figure 4. In the models with no nasopharyngeal coupling, pole–zero pairs around 500 Hz were observed with /i/ in all participants when coupling was created at the nasopharyngeal coupling site. An increase in intensity around 250 Hz was found with /i/ in all participants. A decrease in intensity around 500 Hz was found with /i/ in five of six participants. A decrease in intensity of the formant frequency was found for F2 with /i/ in five of six participants.

With the Japanese vowel /u/, participants 1, 4, and 6 had nasopharyngeal coupling, and participants 2, 3, and 5 had no nasopharyngeal coupling during phonation. With /u/, one of the three participants with nasopharyngeal coupling showed a decrease in the frequency of F2 as a result of enlargement of the coupling site, and all three participants with no nasopharyngeal coupling showed a decrease in the frequency of F2 as a result of coupling being created.

The frequency response curves obtained from the results of simulation with the models of the Japanese vowel /u/ before and after modification of the nasopharyngeal coupling site are shown in Figure 5 and Figure 6. In the models with no nasopharyngeal coupling, pole–zero pairs around 500 Hz were observed with /u/ in all participants with coupling created at the nasopharyngeal coupling site. An increase in intensity around 250 Hz was found with /u/ in three of six participants. A decrease in intensity around 500 Hz was found with /u/ in four of six participants. A decrease in intensity of the formant frequency was found for F1 with /u/ in four of six participants.

For both vowels, pole–zero pairs around 500 Hz were observed due to the presence of nasopharyngeal coupling. Although the frequency of occurrence differed between the two vowels, increased intensity around 250 Hz, decreased intensity around 500 Hz, lower frequency of F2, and decreased intensities of F1 with /u/ and F2 with /i/ were observed by mimicking velopharyngeal insufficiency.

4. Discussion

A comparative study in which acoustic analysis of vocal tract models that recreate velopharyngeal functional insufficiency, using the boundary element method with the same parameter settings as in our previous studies, was performed [8,9].

Prior studies have reported a range of acoustic characteristics of hypernasality, such as increased intensity around 250 Hz [11], decreased intensity around 500 Hz [11], decreased formant intensity [2,11], increased intensity in the band between F1 and F2 [12,13], broadened F1 bandwidth [13,14], resonance around 1000 Hz [2], and loss of or decreased F3 or high-frequency formants [2,13].

The results of simulation on models with modification of the nasopharyngeal coupling site showed a pole–zero pair around 500 Hz, increased intensity around 250 Hz, decreased intensity around 500 Hz, decreased intensity of F1 and F2, and decreased F2 formant frequency.

First, the pole–zero pair around 500 Hz is produced by coupling of the nasal and oral cavities, and there are a number of reports of this, including our own prior reports [8,9,15]. In the present analysis, there was a pole–zero pair around 500 Hz with /i/ and /u/ in all cases, including those originally with nasopharyngeal coupling and those with no nasopharyngeal coupling in which coupling was created at the nasopharyngeal coupling site.

Next, the increase in intensity around 250 Hz is reported to be caused by resonance in the overall cavity, from the pharynx, nasal cavity, and glottis to the nostrils, and because sounds emitted from the nostrils are particularly intensified in this domain [11]. A characteristic of nasalization reported in prior studies is that the component in the extremely low-frequency range becomes more intense [11], and Hattori et al. suggested that this is the case with the increased intensity around 250 Hz. The vocal tract model that we have been using for some time extends from the glottis to the oral cavity, nasal cavity, and paranasal sinus. This is a similar range to the overall cavity from the pharynx, nasal cavity, and glottis to the nostrils that Hattori et al. reported increases the intensity at around 250 Hz, and it therefore appears that it was possible to recreate this characteristic.

The reduction in intensity around 500 Hz has been described together with the increase in intensity around 250 Hz as a characteristic of nasalization of vowels [11]. Hattori et al. stated that the cause of this is resonance in the nasal cavity, and considering the pathway of the voice from the pharynx to the oral cavity, it is likely that the branch along the way causes antiresonance. This would mean that sounds of this frequency are selectively absorbed by the nasal cavity on the way to the mouth. There is some emission of sound from the nostrils when they are open, but the emissivity from the mouth is far greater (with the exception of narrow vowels), and this is probably because the F1 of vowels, which is the resonance from the pharynx to the oral cavity, is often in this vicinity.

There have been reports of decreases in the intensity of formant frequencies, which include reports for all formants [2,11], for F2 [16], and for F3 and above [11,12]. However, there is also a report that, because formant frequencies depend greatly on the level of vocalization, and there are considerable individual differences, rather than a decrease in formant frequency, there is an increase in the level of the bandwidth around 1000 Hz between F1 and F2 [17]. In the present simulation, a decrease in the formant frequency was seen with the Japanese vowel /i/ at F2 in five of six cases and with the Japanese vowel /u/ at F1 in four of six cases, with no increase in the level around 1000 Hz.

The decrease in F2 formant frequency is likely to be due to the appearance of resonance at around 1000 Hz with no overlap with the formant [2]. Imai et al. [3] explained this resonance around 1000 Hz as a nasalization component that appears due to leakage of exhaled air into the nasal cavity and is probably related to the shift in F2 toward lower frequencies. However, the present simulations and those in our prior studies showed a peak around 1000 Hz with the Japanese vowel /i/, regardless of nasopharyngeal coupling. It therefore appears that the resonance around 1000 Hz is not a nasalization component as explained by Imai et al. Instead, it is produced by one or another of the resonances from the oral cavity to the glottis. At the same time, it is likely that the decrease in F2 frequency is the result not only of nasal cavity resonance but also of the effects of the difference in palatal morphology between cleft palate patients, even after palatoplasty, and people without cleft palate [18], as well as a tendency for the tongue to be pulled back, which is a common articulatory maneuver in cleft palate patients [1]. If the tongue is pulled back, there is likely to be a resulting shift in F2 toward lower frequencies [2,3]. Since it has been reported that this tendency is not seen with vowels because the tongue is more readily pulled back with consonants [19], and also the present study used CT data taken in the supine position, there is therefore a need for further study of tongue position.

As mentioned above, the increased intensity around 250 Hz, decreased intensity around 500 Hz, decreased intensities of F1 and F2, and lower frequency of F2 agree with the previously reported acoustic characteristics of hypernasality. We believe that these may be acoustic characteristics resulting from velopharyngeal insufficiency, but the results need to be verified by analyzing actual cleft palate patients with velopharyngeal insufficiency. It is difficult to make any further physiological interpretation based on the results of this study alone.

To create a vocal tract model that mimics the state of velopharyngeal insufficiency, the nasopharyngeal coupling site was opened or expanded by one to three meshes. In the preliminary experiments, vocal tract models with holes of four or more meshes were created, and a simulation was performed, but there was no difference in the results. This mesh size was then used. It is considered necessary to compare this with the actual velopharyngeal shape of patients with velopharyngeal insufficiency after cleft palate surgery in the future.

5. Conclusions

A vocal tract model that recreates velopharyngeal functional insufficiency was created, and wave acoustic analysis using the boundary element method was performed. The findings included the appearance of pole–zero pairs around 500 Hz, increased intensity around 250 Hz, decreased intensity around 500 Hz, decreased intensity of F1 and F2, and lower frequency of F2. Of these findings, the increased intensity around 250 Hz, decreased intensity around 500 Hz, decreased intensity of F1 and F2, and lower frequency of F2 agree with the previously reported acoustic characteristics of hypernasality.