Flow visualization and pressure distributions in a model of the glottis with a symmetric and oblique divergent angle of 10 degrees

Modeling the human larynx can provide insights into the nature of the flow and pressures within the glottis. In this study, the intraglottal pressures and glottal jet flow were studied for a divergent glottis that was symmetric for one case and oblique for another. A Plexiglas model of the larynx (7.5 times life size) with interchangeable vocal folds was used. Each vocal fold had at least 11 pressure taps. The minimal glottal diameter was held constant at 0.04 cm. The glottis had an included divergent angle of 10 degrees. In one case the glottis was symmetric. In the other case, the glottis had an obliquity of 15 degrees. For each geometry, transglottal pressure drops of 3, 5, 10, and 15 cm H2O were used. Pressure distribution results, suggesting significantly different cross-channel pressures at glottal entry for the oblique case, replicate the data in another study by Scherer et al. [J. Acoust. Soc. Am. 109, 1616-1630 (2001b)]. Flow visualization using a LASER sheet and seeded airflow indicated separated flow inside the glottis. Separation points did not appear to change with flow for the symmetric glottis, but for the oblique glottis moved upstream on the divergent glottal wall as flow rate increased. The outgoing glottal jet was skewed off-axis for both the symmetric and oblique cases. The laser sheet showed asymmetric circulating regions in the downstream region. The length of the laminar core of the glottal jet was less than approximately 0.6 cm, and decreased in length as flow increased. The results suggest that the glottal obliquity studied here creates significantly different driving forces on the two sides of the glottis (especially at the entrance to the glottis), and that the skewed glottal jet characteristics need to be taken into consideration for modeling and aeroacoustic purposes.     

Flow separation in a computational oscillating vocal fold model

A finite-volume computational model that solves the time-dependent glottal airflow within a forced-oscillation model of the glottis was employed to study glottal flow separation. Tracheal input velocity was independently controlled with a sinusoidally varying parabolic velocity profile. Control parameters included flow rate (Reynolds number), oscillation frequency and amplitude of the vocal folds, and the phase difference between the superior and inferior glottal margins. Results for static divergent glottal shapes suggest that velocity increase caused glottal separation to move downstream, but reduction in velocity increase and velocity decrease moved the separation upstream. At the fixed frequency, an increase of amplitude of the glottal walls moved the separation further downstream during glottal closing. Increase of Reynolds number caused the flow separation to move upstream in the glottis. The flow separation cross-sectional ratio ranged from approximately 1.1 to 1.9 (average of 1.47) for the divergent shapes. Results suggest that there may be a strong interaction of rate of change of airflow, inertia, and wall movement. Flow separation appeared to be "delayed" during the vibratory cycle, leading to movement of the separation point upstream of the glottal end only after a significant divergent angle was reached, and to persist upstream into the convergent phase of the cycle.     

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.     

Intraglottal pressure profiles for a symmetric and oblique glottis with a divergence angle of 10 degrees

Human phonation does not always involve symmetric motions of the two vocal folds. Asymmetric motions can create slanted or oblique glottal angles. This study reports intraglottal pressure profiles for a Plexiglas model of the larynx with a glottis having a 10-degree divergence angle and either a symmetric orientation or an oblique angle of 15 degrees. For the oblique glottis, one side was divergent and the other convergent. The vocal fold surfaces had 14 pressure taps. The minimal glottal diameter was held constant at 0.04 cm. Results indicated that for either the symmetric or oblique case, the pressure profiles were different on the two sides of the glottis except for the symmetric geometry for a transglottal pressure of 3 cm H2O. For the symmetric case, flow separation created lower pressures on the side where the flow stayed attached to the wall, and the largest pressure differences between the two sides of the channel were 5%-6% of the transglottal pressure. For the oblique case, pressures were lower on the divergent glottal side near the glottal entry and exit, and the cross-channel pressures at the glottis entrance differed by 27% of the transglottal pressure. The empirical pressure distributions were supported by computational results. The observed aerodynamic asymmetries could be a factor contributing to normal jitter values and differences in vocal fold phasing.     

On the role of glottis-interior sources in the production of voiced sound

The voice source is dominated by aeroacoustic sources downstream of the glottis. In this paper an investigation is made of the contribution to voiced speech of secondary sources within the glottis. The acoustic waveform is ultimately determined by the volume velocity of air at the glottis, which is controlled by vocal fold vibration, pressure forcing from the lungs, and unsteady backreactions from the sound and from the supraglottal air jet. The theory of aerodynamic sound is applied to study the influence on the fine details of the acoustic waveform of "potential flow" added-mass-type glottal sources, glottis friction, and vorticity either in the glottis-wall boundary layer or in the portion of the free jet shear layer within the glottis. These sources govern predominantly the high frequency content of the sound when the glottis is near closure. A detailed analysis performed for a canonical, cylindrical glottis of rectangular cross section indicates that glottis-interior boundary/shear layer vortex sources and the surface frictional source are of comparable importance; the influence of the potential flow source is about an order of magnitude smaller.     

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.     

The effect of glottal angle on intraglottal pressure

Intraglottal pressure distributions depend upon glottal shape, size, and diameter. This study reports the effects of varying glottal angle on intraglottal and transglottal pressures using a three-dimensional Plexiglas model with a glottis having nine symmetric glottal angles and a constant minimal glottal diameter of 0.06 cm. The empirical data were supported by computational results using FLUENT. The results suggested that (1) the greater the convergent glottal angle, the greater outward driving forces (higher intraglottal pressures) on the vocal folds; (2) flow resistance was greatest for the uniform glottis, and least for the 10 degrees divergent glottis; (3) the greatest negative pressure in the glottis and therefore the greatest pressure recovery for diverging glottal shapes occurred for an angle of 10 degrees; (4) the smaller the convergent angle, the greater the flow resistance; (5) FLUENT was highly accurate in predicting the empirical pressures of this model; (6) flow separation locations (given by FLUENT) for the divergent glottis moved upstream for larger flows and larger glottal angles. The results suggest that phonatory efficiency related to aerodynamics may be enhanced with vocal fold oscillations that include large convergent angles during glottal opening and small (5 degrees - 10 degrees) divergent angles during glottal closing.     

The membranous contact quotient: A new phonatory measure of glottal competence

The membranous contact quotient (MCQ) is introduced as a measure of dynamic glottal competence. It is defined as the ratio of the membranous contact glottis (the anterior-posterior length of contact between the two membranous vocal folds) and the membranous vocal fold length. An elliptical approximation to the vocal fold contour during phonation was used to predict MCQ values as a function of vocal process gap (adduction), maximum glottal width, and membranous glottal length. MCQ is highly dependent on the vocal process gap and the maximum glottal width, but not on vocal fold length. Five excised larynges were used to obtain MCQ data for a wide range of vocal process gaps and maximum glottal widths. Predicted and measured MCQ values had a correlation of 0.93, with an average absolute difference of 9.6% (SD = 10.5%). The model is better at higher values of MCQ. The theory for MCQ is also expressed as a function of vocal process gap and subglottal pressure to suggest production control potential. The MCQ measure is obtainable with the use of stroboscopy and appears to be a potentially useful clinical measure.     

Theoretical assessment of unsteady aerodynamic effects in phonation

This paper ranks the importance of unsteady aerodynamic mechanisms in glottal flow. Particular emphasis is given to separation point motion, acceleration of glottal airflow by vocal fold motion, and viscous blockage. How nondimensional parameters such as the Reynolds, Strouhal, and Womersley numbers help in this ranking is also addressed. An equation of motion is derived which includes terms explicitly describing the effects of interest, assuming (1) a symmetrical glottis, (2) zero pressure recovery downstream of the vocal folds, and (3) a quasisteady glottal jet. Estimating the order of magnitude of the terms in this equation, it is shown that the flow is characterized by two temporal regimes: (1) a flow initiation/shutoff regime where local unsteady acceleration and wall motion dominate, and (2) a "quasisteady" regime where the flow is dominated by convective acceleration. In the latter case, separation point motion and viscous blockage are shown to be out of phase with motion of the vocal folds, thereby impacting the shape of the glottal volume flow waveform. The analysis suggests that glottal flow may be considered quasisteady only insofar as traditional assumptions concerning glottal jet behavior can be confirmed.     

Dynamic glottal pressures in an excised hemilarynx model

During phonation, air pressures act upon the vocal folds to help maintain their oscillation. The air pressures vary dynamically along the medial surface of the vocal folds, although no live human or excised studies have shown how those pressure profiles vary in time. The purpose of this study was to examine time-dependent glottal pressure profiles using a canine hemilarynx approach. The larynx tissue was cut in the midsaggital plane from the top to about 5 mm below the vocal folds. The right half was replaced with a Plexiglas pane with imbedded pressure taps. Simultaneous recordings were made of glottal pressure signals, subglottal pressure, particle velocity, and average airflow at various levels of adduction. The data indicate that the pressures in the glottis (on the Plexiglas) vary both vertically and longitudinally throughout the phonatory cycle. Pressures vary most widely near the location of maximum vibratory amplitude, and can include negative pressures during a portion of the cycle. Pressures anterior and posterior to the maximum amplitude location may have less variation and may remain positive throughout the cycle, giving rise to a new concept called dynamic bidirectional pressure gradients in the glottis. This is an important concept that may relate strongly to tissue health as well as basic oscillatory mechanics.     

A preliminary study of particle velocity during phonation in an in vivo canine model

The particle velocity across the glottis was measured with simultaneous electroglottography, photoglottography, and subglottic pressure in an in vivo canine model of phonation. A constant temperature anemometer measured flow velocity at five midline anterior to posterior glottal positions. Tracheal input air flow was varied in five steps from 175 to 500 cc/s, while vocal fold approximation was achieved by constant electrical stimulation of the laryngeal nerves. For all levels of air flow, a decreasing peak velocity gradient was observed from the anterior commissure to the arytenoids. Time-varying features of the flow velocity are discussed in relation to glottal vibratory events and aerodynamics.     

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.     

Simulation of vocal fold impact pressures with a self-oscillating finite-element model

Vocal fold impact pressures were studied using a self-oscillating finite-element model capable of simulating vocal fold vibration and airflow. The calculated airflow pressure is applied on the vocal fold as the driving force. The airflow region is then adjusted according to the calculated vocal fold displacement. The interaction between airflow and the vocal folds produces a self-oscillating solution. Lung pressures between 0.2 and 2.5 kPa were used to drive this self-oscillating model. The spatial distribution of the impact pressure was studied. Studies revealed that the tissue collision during phonation produces a very large impact pressure which correlates with the lung pressure and glottal width. Larger lung pressure and a narrower glottal width increase the impact pressure. The impact pressure was found to be roughly the square root of lung pressure. In the inferior-superior direction, the maximum impact pressure is related to the narrowest glottis. In the anterior-posteriorfirection, the greatest impact pressure appears at the midpoint of the vocal fold. The match between our numerical simulations and clinical observations suggests that this self-oscillating finite-element model might be valuable for predicting mechanical trauma of the vocal folds.     

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.     

Characterizing glottal jet turbulence

Air pressure associated with airflow from the lungs drives the vocal folds into oscillation and allows the air to exit the glottis as a turbulent jet, even though laminar flow may enter the glottis from the trachea. The separation of the turbulence from the deterministic portion of the glottal jet was investigated in the excised canine larynx model. The present study is methodological in that the main goal was to examine three methods of obtaining reasonable representations of both the deterministic signal and the residual turbulence portion: (a) smoothing, (b) wavelet denoising, and (c) ensemble averaging. Ensemble averaging resulted in a deterministic signal that disregarded gross cyclic alterations while exaggerating the turbulence intensity. Wavelet denoising can perform an excellent analysis and synthesis of the glottal velocity, but was problematic in determining which levels of analysis to choose to represent both the deterministic and turbulence appropriately. Smoothing appeared to be the most appropriate for phonation velocities because it preserved gross cyclic variations important to perturbations and modulations, while extracting turbulence at what appears to be reasonable levels.     

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.     

The effect of entrance radii on intraglottal pressure distributions in the divergent glottis

Modeling laryngeal aerodynamics requires specification of the glottal geometry. Changing the glottal exit radius alters the intraglottal pressure distributions in the converging glottis [Scherer et al., J. Acoust. Soc. Am. 110, 2267-2269 (2001)]. This study examined the effects of the glottal entrance radius on the intraglottal pressure distributions for divergent angles of 5°, 10°, 20°, 30°, and 40°. Glottal airflow and minimal glottal diameter were held constant at 73.2 cm(3)/s and 0.02 cm, respectively. The computational code FLUENT was used to obtain the pressure distributions. Results suggest that a smaller glottal entrance radius tends to (1) lower the transglottal pressure (reduce glottal flow resistance), although this is angle dependent, (2) make the pressure dip near the glottal entrance more negative in value, (3) increase the slope of the pressure distribution just upstream of the glottal entrance, and (4) make the initial pressure recovery (rise) in the glottis steeper. A general empirical equation for transglottal pressure as a function of radius, angle, and separation point location is offered. These results suggest that glottal entrance curvature for the divergent glottis significantly affects the driving pressures on the vocal folds, and needs to be well specified when building computational and physical models.     

On the difference between negative damping and eigenmode synchronization as two phonation onset mechanisms

Negative damping and eigenmode synchronization as two different mechanisms of phonation onset are distinguished. Although both mechanisms lead to a favorable phase relationship between the flow pressure and the vocal fold motion as required for a net energy transfer into the vocal folds, the underlying mechanisms for this favorable phase relationship are different. The negative damping mechanism relies on glottal aerodynamics or acoustics to establish before onset and maintain after onset the favorable phase relationship, and therefore has minimum requirements on vocal fold geometry and biomechanics. A single degree-of-freedom vocal fold model is all that is needed for self-oscillation in the presence of a negative damping mechanism. In contrast, the mechanism of eigenmode synchronization critically depends on the geometrical and biomechanical properties of the vocal folds (at least 2-degrees-of-freedom are required), and has little requirement on the glottal aerodynamics other than flow separation. The favorable phase relation is established once synchronization occurs, regardless of the phase relationship imposed by glottal aerodynamics before onset. Unlike that of the negative damping mechanism, initiation of eigenmode synchronization requires neither a velocity-dependent flow pressure nor an alternating convergent-divergent glottis. The clinical implications of the distinctions between these two mechanisms are discussed.     

Physiologic and acoustic differences between male and female voices

Comparison is drawn between male and female larynges on the basis of overall size, vocal fold membranous length, elastic properties of tissue, and prephonatory glottal shape. Two scale factors are proposed that are useful for explaining differences in fundamental frequency, sound power, mean airflow, and glottal efficiency. Fundamental frequency is scaled primarily according to the membranous length of the vocal folds (scale factor of 1.6), whereas mean airflow, sound power, glottal efficiency, and amplitude of vibration include another scale factor (1.2) that relates to overall larynx size. Some explanations are given for observed sex differences in glottographic waveforms. In particular, the simulated (computer-modeled) vocal fold contact area is used to infer male-female differences in the shape of the glottis. The female glottis appears to converge more linearly (from bottom to top) than the male glottis, primarily because of medial surface bulging of the male vocal folds.