In Vivo Quantification of the Intraglottal Pressure: Modal Phonation and Voice Onset

Intraglottal pressure is the driving force of vocal fold vibration. Its time course during the open phase of the vibratory cycle is essential in the mechanics of phonation, but measuring it directly is difficult and may hinder spontaneous voicing. However, it can be computed from the in vivo measured transglottal flow and glottal area (hence the air particle velocity) on the basis of the Bernoulli energy law and the interaction with the inertance of the vocal tract. As to sustained modal phonation, calculations are presented for the two possible shapes of glottal duct: convergent and divergent, including absolute calibration in order to obtain quantitative physical values. Whatever the glottal duct configuration, the calculations based on measured values of glottal area and air flow show that the integrated intraglottal pressure during the opening phase systematically exceeds that during the closing phase, which is the basic condition for sustaining vocal fold oscillation. The key point is that the airflow curve is skewed to the right relative to the glottal area curve. The skewing results from air compressibility and vocal tract inertance. The intraglottal pressure becomes negative during the closing phase. As to the soft (or physiological) voice onset, a similar approach shows that the integrated pressure differences (opening phase − closing phase) actually increase as the onset progresses, and this applies to the results based on Bernoulli's energy law as well as to those based on the interaction with the inertance of the vocal tract. Furthermore and similarly, the phase lead of the pressure wave with respect to the glottal opening progressively increases. The underlying explanation lies in the progressively increasing skewing of the airflow curve to the right with respect to the glottal area curve.     

Medial Surface Dynamics as a Function of Subglottal Pressure in a Canine Larynx Model

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 midmembranous 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.     

Two-mass models of the vocal cords for natural sounding voice synthesis

Three new two-mass models of the vocal cords are treated. First, the features, structure, and differential equations of motion are described for each of the new models and compared with those of previous models. Second, performances of the models are discussed in terms of glottal volume flow, glottal area, radiated sound pressure, trajectories of mass movement, running spectra of the output sound pressure, and perceptual naturalness of the output sound. Finally, the major effects of glottal source-vocal tract interaction including skewing, truncation, and superposition are investigated, using one of the simplest types of two-mass models and two types of load representing the vocal tract.     

Measures of spectral slope using an excised larynx model

Spectral measures of the glottal source were investigated using an excised canine larynx (CL) model for various aerodynamic and phonatory conditions. These measures included spectral harmonic difference H1-H2 and spectral slope that are highly correlated with voice quality but not reported in a systematic manner using an excised larynx model. It was hypothesized that the acoustic spectra of the glottal source were significantly influenced by the subglottal pressure, glottal adduction, and vocal fold elongation, as well as the resulting vibration pattern. CLs were prepared, mounted on the bench with and without false vocal folds, and made to oscillate with a flow of heated and humidified air. Major control parameters were subglottal pressure, adduction, and elongation. Electroglottograph, subglottal pressure, flow rate, and audio signals were analyzed using custom software. Results suggest that an increase in subglottal pressure and glottal adduction may change the energy balance between harmonics by increasing the spectral energy of the first few harmonics in an unpredictable manner. It is suggested that changes in the dynamics of vocal fold motion may be responsible for different spectral patterns. The finding that the spectral harmonics do not conform to previous findings was demonstrated through various cases. Results of this study may shed light on phonatory spectral control when the larynx is part of a complete vocal tract system.     

A theoretical model of the pressure field arising from asymmetric intraglottal flows applied to a two-mass model of the vocal folds

A theoretical flow solution is presented for predicting the pressure distribution along the vocal fold walls arising from asymmetric flow that forms during the closing phases of speech. The resultant wall jet was analyzed using boundary layer methods in a non-inertial reference frame attached to the moving wall. A solution for the near-wall velocity profiles on the flow wall was developed based on a Falkner-Skan similarity solution and it was demonstrated that the pressure distribution along the flow wall is imposed by the velocity in the inviscid core of the wall jet. The method was validated with experimental velocity data from 7.5 times life-size vocal fold models, acquired for varying flow rates and glottal divergence angles. The solution for the asymmetric pressures was incorporated into a widely used two-mass model of vocal fold oscillation with a coupled acoustical model of sound propagation. Asymmetric pressure loading was found to facilitate glottal closure, which yielded only slightly higher values of maximum flow declination rate and radiated sound, and a small decrease in the slope of the spectral tilt. While the impact on symmetrically tensioned vocal folds was small, results indicate the effect becomes more significant for asymmetrically tensioned vocal folds.     

Phonological systems in bilinguals: age of learning effects on the stop consonant systems of Korean-English bilinguals

Interaction of Korean and English stop systems in Korean-English bilinguals as a function of age of acquisition (AOA) of English was investigated. It was hypothesized that early bilinguals (mean AOA=3.8 years) would more likely be native-like in production of English and Korean stops and maintain greater independence between Korean and English stop systems than late bilinguals (mean AOA=21.4 years). Production of Korean and English stops was analyzed in terms of three acoustic-phonetic properties: voice-onset time, amplitude difference between the first two harmonics, and fundamental frequency. Late bilinguals were different from English monolinguals for English voiceless and voiced stops in all three properties. As for Korean stops, late bilinguals were different from Korean monolinguals for fortis stops in voice-onset time. Early bilinguals were not different from the monolinguals of either language. Considering the independence of the two stop systems, late bilinguals seem to have merged English voiceless and Korean aspirated stops and produced English voiced stops with similarities to both Korean fortis and lenis stops, whereas early bilinguals produced five distinct stop types. Thus, the early bilinguals seem to have two independent stop systems, whereas the late bilinguals likely have a merged Korean-English system.     

Two-dimensional model of vocal fold vibration for sound synthesis of voice and soprano singing

Voiced sounds were simulated with a computer model of the vocal fold composed of a single mass vibrating both parallel and perpendicular to the airflow. Similarities with the two-mass model are found in the amplitudes of the glottal area and the glottal volume flow velocity, the variation in the volume flow waveform with the vocal tract shape, and the dependence of the oscillation amplitude upon the average opening area of the glottis, among other similar features. A few dissimilarities are also found in the more symmetric glottal and volume flow waveforms in the rising and falling phases. The major improvement of the present model over the two-mass model is that it yields a smooth transition between oscillations with an inductive load and a capacitive load of the vocal tract with no sudden jumps in the vibration frequency. Self-excitation is possible both below and above the first formant frequency of the vocal tract. By taking advantage of the wider continuous frequency range, the two-dimensional model can successfully be applied to the sound synthesis of a high-pitched soprano singing, where the fundamental frequency sometimes exceeds the first formant frequency.     

Laryngeal Gestures During Stop Production Using High-Speed Digital Images

On acoustic and fiberscopic studies of stop consonants, voice onset time and glottal width have been shown to be greatest in heavily aspirated stops, next greater for slightly aspirated stops, and least for unaspirated stops. Integrated activity of the thyroarytenoid and posterior cricoarytenoid muscles has been reported to be involved in differentiating aspirate characteristics of the stops. However, the fine movement of mucosal edges of vocal folds during the production of stops has not been well documented. In recent years, a new method for high-speed digital recording of laryngeal dynamics has made this possible. In the current study, the movements of vocal fold edges were documented during the period of stop production using a fiberscopic system of high-speed digital images. By observing the glottal width and the visual vibratory movements of vocal folds before voice onset, the heavily aspirated stop was characterized as being more prominent and dynamic than the slightly aspirated and unaspirated stops.     

Glottal flow through a two-mass model: comparison of Navier-Stokes solutions with simplified models

A new numerical model of the vocal folds is presented based on the well-known two-mass models of the vocal folds. The two-mass model is coupled to a model of glottal airflow based on the incompressible Navier-Stokes equations. Glottal waves are produced using different initial glottal gaps and different subglottal pressures. Fundamental frequency, glottal peak flow, and closed phase of the glottal waves have been compared with values known from the literature. The phonation threshold pressure was determined for different initial glottal gaps. The phonation threshold pressure obtained using the flow model with Navier-Stokes equations corresponds better to values determined in normal phonation than the phonation threshold pressure obtained using the flow model based on the Bernoulli equation. Using the Navier-Stokes equations, an increase of the subglottal pressure causes the fundamental frequency and the glottal peak flow to increase, whereas the fundamental frequency in the Bernoulli-based model does not change with increasing pressure.     

Pressure and velocity profiles in a static mechanical hemilarynx model

This study examined pressure and velocity profiles in a hemilarynx mechanical model of phonation. The glottal section had parallel walls and was fabricated from hard plastic. Twelve pressure taps were created in the vocal fold surface and connected to a differential pressure transducer through a pressure switch. The glottal gap was measured with feeler gauges and the uniform glottal duct was verified by use of a laser system. Eight pressure transducers were placed in the flat wall opposite the vocal fold. Hot-wire anemometry was used to obtain velocity profiles upstream and downstream of the glottis. The results indicate that the pressure distribution on the vocal fold surface was consistent with pressure change along a parallel duct, whereas the pressures on the opposite flat wall typically were lower (by 8%-40% of the transglottal pressure just past mid-glottis). The upstream velocity profiles were symmetric regardless of the constriction shape and size. The jet flow downstream of the glottis was turbulent even for laminar upstream conditions. The front of the jet was consistently approximately 1.5 mm from the flat wall for glottal gaps of 0.4, 0.8 and 1.2 mm. The turbulence intensity also remained approximately at the same location of about 4 mm from the flat wall for the two larger gaps.     

Voice production model integrating boundary-layer analysis of glottal flow and source-filter coupling

A voice production model is created in this work by considering essential aerodynamic and acoustic phenomena in human voice production. A precise flow analysis is performed based on a boundary-layer approximation and the viscous-inviscid interaction between the boundary layer and the core flow. This flow analysis can supply information on the separation point of the glottal flow and the thickness of the boundary layer, both of which strongly depend on the glottal configuration and yield an effective prediction of the flow behavior. When the flow analysis is combined with the modified two-mass model of the vocal fold [Pelorson et al. (1994). J. Acoust. Soc. Am. 96, 3416-3431], the resulting acoustic wave travels through the vocal tract and a pressure change develops in the vicinity of the glottis. This change can affect the glottal flow and the motion of the vocal folds, causing source-filter coupling. The property of the acoustic feedback is explicitly expressed in the frequency domain by using an acoustic tube model, allowing a clear interpretation of the coupling. Numerical experiments show that the vocal-tract input impedance and frequency responses representing the source-filter coupling have dominant peaks corresponding to the fourth and fifth formants. Results of time-domain simulations also suggest the importance of these high-frequency peaks in voice production.     

Influence of supraglottal structures on the glottal jet exiting a two-layer synthetic, self-oscillating vocal fold model

A synthetic two-layer, self-oscillating, life-size vocal fold model was used to study the influence of the vocal tract and false folds on the glottal jet. The model vibrated at frequencies, pressures, flow rates, and amplitudes consistent with human phonation, although some differences in behavior between the model and the human vocal folds are noted. High-speed images of model motion and flow visualization were acquired. Phase-locked ensemble-averaged glottal jet velocity measurements using particle image velocimetry (PIV) were acquired with and without an idealized vocal tract, with and without false folds. PIV data were obtained with varying degrees of lateral asymmetric model positioning. Glottal jet velocity magnitudes were consistent with those measured using excised larynges. A starting vortex was observed in all test cases. The false folds interfered with the starting vortex, and in some cases vortex shedding from the false folds was observed. In asymmetric cases without false folds, the glottal jet tended to skew toward the nearest wall; with the false folds, the opposite trend was observed. rms velocity calculations showed the jet shear layer and laminar core. The rms velocities were higher in the vocal tract cases compared to the open jet and false fold cases.     

Analytic Representation of Volume Flow as a Function of Geometry and Pressure in a Static Physical Model of the Glottis

A static physical model of the larynx (model M5) was used to obtain a large set of volume flows as a function of symmetric glottal geometry and transglottal pressure. The measurements cover ranges of these variables relevant to human phonation. A generalized equation was created to accurately estimate the glottal volume flow given specific glottal geometries and transglottal pressures. Both the data and the generalized formula give insights into the flow behavior for different glottal geometries, especially the contrast between convergent and divergent glottal angles at different glottal diameters. The generalized equation produced a fit to the entire M5 dataset (267 points) with an average accuracy of 3.4%. The accuracy was about seven times better than that of the Ishizaka-Flanagan approach to glottal flow and about four times better than that of a pressure coefficient approach. Thus, for synthesis purposes, the generalized equation presented here should provide more realistic glottal flows (based on steady flow conditions) as suitable inputs to the vocal tract, for given values of transglottal pressure and glottal geometry. Applications of the generalized formula to pulses generated by vocal fold motions typical of those produced by the Ishizaka-Flanagan coupled-oscillator model and the more recent body-cover model of Story and Titze are also included.     

Phonation threshold pressure: a missing link in glottal aerodynamics.

Phonation threshold pressure has previously been defined as the minimum lung pressure required to initiate phonation. By modeling the dependence of this pressure on fundamental frequency, it is shown that relatively simple aerodynamic relations for time-varying flow in the glottis are obtained. Lung pressure and peak glottal flow are nearly linearly related, but not proportional. For this reason, traditional power law relations between vocal power and lung pressure may not hold. Glottal impendance for time-varying flow should be defined differentially rather than as a simple ratio between lung pressure and peak flow. It is shown that the peak flow, the peak flow derivative, the open quotient, and the speed quotient of inverse-filtered glottal flow waveforms all depend explicitly on phonation threshold pressure. Data from singers are compared with those from nonsingers. The primary difference is that singers obtain two to three times greater peak flow for a given lung pressure, suggesting that they adjust their glottal or vocal tract impedance for optimal flow transfer between the source and the resonantor.     

Computational Simulations of Vocal Fold Vibration: Bernoulli Versus Navier–Stokes

The use of the mechanical energy (ME) equation for fluid flow, an extension of the Bernoulli equation, to predict the aerodynamic loading on a two-dimensional finite element vocal fold model is examined. Three steady, one-dimensional ME flow models, incorporating different methods of flow separation point prediction, were compared. For two models, determination of the flow separation point was based on fixed ratios of the glottal area at separation to the minimum glottal area; for the third model, the separation point determination was based on fluid mechanics boundary layer theory. Results of flow rate, separation point, and intraglottal pressure distribution were compared with those of an unsteady, two-dimensional, finite element Navier-Stokes model. Cases were considered with a rigid glottal profile as well as with a vibrating vocal fold. For small glottal widths, the three ME flow models yielded good predictions of flow rate and intraglottal pressure distribution, but poor predictions of separation location. For larger orifice widths, the ME models were poor predictors of flow rate and intraglottal pressure, but they satisfactorily predicted separation location. For the vibrating vocal fold case, all models resulted in similar predictions of mean intraglottal pressure, maximum orifice area, and vibration frequency, but vastly different predictions of separation location and maximum flow rate.     

Objective Analysis of Vocal Warm-Up with Special Reference to Ergonomic Factors

Vocal warm-up was studied in terms of changes in voice parameters during a 45-minute vocal loading session in the morning. The voices of a randomly chosen group of 40 female and 40 male young students were loaded by having them read a novel aloud. The exposure groups (5 females and 5 males per cell) consisted of eight combinations of the following factors: (1) low (25 +/- 5%) or high (65 +/- 5%) relative humidity of ambient air; (2) low [< 65 dB(SPL)] or high [> 65 dB(SPL)] speech output level during vocal loading; (3) sitting or standing posture during vocal loading. Two sets of voice samples were recorded: a resting sample before the loading session and a loading sample after the loading session. The material recorded consisted of /pa:ppa/ words produced normally, as softly and as loudly as possible in this order by all subjects. The long /a/ vowel of the test word was inverse-filtered to obtain the glottal flow waveform. Time domain parameters of the glottal flow [open quotient (OQ), closing quotient (CQ), speed quotient (SQ), fundamental frequency (F0)], amplitude domain parameters of the glottal flow [glottal flow (fAC) and its logarithm, minimum of the first derivative of the glottal flow (dpeak) and its logarithm, amplitude quotient (AQ), and a new parameter, CQAQ], intraoral pressure (p), and sound pressure level (SPL) values of the phonations were analyzed. Voice range profiles (VRP) and the singer's formant (g/G, a/A, cl/c, e1/e, g1/g for females/males) of the loud phonation were also measured. Statistically significant differences between the preloading and postloading samples could be seen in many parameters, but the differences depended on gender and the type of phonation. In females the values of CQ, AQ, and CQAQ decreased and the values of SQ and p increased in normal phonations; the values of fAC, dpeak, and SPL increased in soft phonations; the values of AQ and CQAQ decreased in loud phonations; the harmonic energy in the singer's formant region increased significantly at every pitch. In males the values of OQ and AQ decreased and the values of dpeak, F0, p, and SPL increased in normal phonations; the values of fAC and p increased in soft phonations. The changes could be interpreted as signs of a shift toward hyperfunctional voice production. Low humidity was associated with more hyperfunctional changes than high humidity. High output was associated with more hyperfunctional changes than low output. Sitting position was associated with an increasing trend at both margins of male VRP, whereas the case was the opposite for standing position.     

Pressure-flow relationships during phonation in the canine larynx

Measurements of air pressure and flow were made using an in vivo canine model of the larynx. Subglottic pressures at varying flow rates were taken during phonation induced by laryngeal nerve stimulation. Results showed that during constant vocal fold stiffness, subglottic pressure rose slightly with increased air flow. The larynx in the in vivo canine model exhibited a flow-dependent decrease in laryngeal airway resistance. Increasing flow rate was associated with an increase in frequency of phonation and open quotient, as measured glottographically. Results from this experiment were compared with a theoretical two-mass model of the larynx and other theoretical models of phonation. The influence of aerodynamic forces on glottal vibration is explained by increased lateral excursion of the vocal folds during the open interval and shortening of the closed interval during the glottal cycle.     

Theoretical simulation and experimental validation of inverse quasi-one-dimensional steady and unsteady glottal flow models

In physical modeling of phonation, the pressure drop along the glottal constriction is classically assessed with the glottal geometry and the subglottal pressure as known input parameters. Application of physical modeling to study phonation abnormalities and pathologies requires input parameters related to in vivo measurable quantities commonly corresponding to the physical model output parameters. Therefore, the current research presents the inversion of some popular simplified flow models in order to estimate the subglottal pressure, the glottal constriction area, or the separation coefficient inherent to the simplified flow modeling for steady and unsteady flow conditions. The inverse models are firstly validated against direct simulations and secondly against in vitro measurements performed for different configurations of rigid vocal fold replicas mounted in a suitable experimental setup. The influence of the pressure corrections related to viscosity and flow unsteadiness on the flow modeling is quantified. The inversion of one-dimensional glottal flow models including the major viscous effects can predict the main flow quantities with respect to the in vitro measurements. However, the inverse model accuracy is strongly dependent on the pertinence of the direct flow modeling. The choice of the separation coefficient is preponderant to obtain pressure predictions relevant to the experimental data.     

Optimal glottal configuration for ease of phonation

Recent experimental studies have shown the existence of optimalvalues of the glottal width and convergence angle, at which the phonation threshold pressure is minimum. These results indicate the existence of an optimal glottal configuration for ease of phonation, not predicted by the previous theory. In this paper, the origin of the optimal configuration is investigated using a low dimensional mathematical model of the vocal fold. Two phenomena of glottal aerodynamics are examined: pressure losses due to air viscosity, and air flow separation from a divergent glottis. The optimal glottal configuration seems to be a consequence of the combined effect of both factors. The results agree with the experimental data, showing that the phonation threshold pressure is minimum when the vocal folds are slightly separated in a near rectangular glottis.     

Vocal intensity in speakers and singers.

Vocal intensity is studied as a function of fundamental frequency and lung pressure. A combination of analytical and empirical models is used to predict sound pressure levels from glottal waveforms of five professional tenors and twenty five normal control subjects. The glottal waveforms were obtained by inverse filtering the mouth flow. Empirical models describe features of the glottal flow waveform (peak flow, peak flow derivative, open quotient, and speed quotient) in terms of lung pressure and phonation threshold pressure, a key variable that incorporates the Fo dependence of many of the features of the glottal flow. The analytical model describes the contributions to sound pressure levels SPL by the vocal tract. Results show that SPL increases with Fo at a rate of 8-9 dB/octave provided that lung pressure is raised proportional to phonation threshold pressure. The SPL also increases at a rate of 8-9 dB per doubling of excess pressure over threshold, a new quantity that assumes considerable importance in vocal intensity calculations. For the same excess pressure over threshold, the professional tenors produced 10-12 dB greater intensity than the male nonsingers, primarily because their peak airflow was much higher for the same pressure. A simple set of rules is devised for predicting SPL from source waveforms.