Physical mechanisms of phonation onset: a linear stability analysis of an aeroelastic continuum model of phonation

In an investigation of phonation onset, a linear stability analysis was performed on a two-dimensional, aeroelastic, continuum model of phonation. The model consisted of a vocal fold-shaped constriction situated in a rigid pipe coupled to a potential flow which separated at the superior edge of the vocal fold. The vocal fold constriction was modeled as a plane-strain linear elastic layer. The dominant eigenvalues and eigenmodes of the fluid-structure-interaction system were investigated as a function of glottal airflow. To investigate specific aerodynamic mechanisms of phonation onset, individual components of the glottal airflow (e.g., flow-induced stiffness, inertia, and damping) were systematically added to the driving force. The investigations suggested that flow-induced stiffness was the primary mechanism of phonation onset, involving the synchronization of two structural eigenmodes. Only under conditions of negligible structural damping and a restricted set of vocal fold geometries did flow-induced damping become the primary mechanism of phonation onset. However, for moderate to high structural damping and a more generalized set of vocal fold geometries, flow-induced stiffness remained the primary mechanism of phonation onset.     

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.     

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.     

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.     

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.     

Effect of inferior surface angle on the self-oscillation of a computational vocal fold model

Geometry of the human vocal folds strongly influences their oscillatory motion. While the effect of intraglottal geometry on phonation has been widely investigated, the study of the geometry of the inferior surface of the vocal folds has been limited. In this study the way in which the inferior vocal fold surface angle affects vocal fold vibration was explored using a two-dimensional, self-oscillating finite element vocal fold model. The geometry was parameterized to create models with five different inferior surface angles. Four of the five models exhibited self-sustained oscillations. Comparisons of model motion showed increased vertical displacement and decreased glottal width amplitude with decreasing inferior surface angle. In addition, glottal width and air flow rate waveforms changed as the inferior surface angle was varied. Structural, rather than aerodynamic, effects are shown to be the cause of the changes in model response as the inferior surface angle was varied. Supporting data including glottal pressure distribution, average intraglottal pressure, energy transfer, and flow separation point locations are discussed, and suggestions for future research are given.     

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.     

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.     

Chaotic vibrations of a vocal fold model with a unilateral polyp

A nonlinear model was proposed to study chaotic vibrations of vocal folds with a unilateral vocal polyp. The model study found that the vocal polyp affected glottal closure and caused aperiodic vocal fold vibrations. Using nonlinear dynamic methods, aperiodic vibrations of the vocal fold model with a polyp were attributed to low-dimensional chaos. Bifurcation diagrams showed that vocal polyp size, stiffness, and damping had important effects on vocal fold vibrations. An increase in polyp size tended to induce subharmonic patterns and chaos. This study provides a theoretical basis to model aperiodic vibrations of vocal folds with a laryngeal mass.     

Phonation threshold pressure and onset frequency in a two-layer physical model of the vocal folds

The influence of vocal fold geometry and stiffness on phonation onset was experimentally investigated using a body-cover physical model of the vocal folds. Results showed that a lower phonation threshold pressure and phonation onset frequency can be achieved by reducing body-layer or cover-layer stiffness, reducing medial surface thickness, or increasing cover-layer depth. Increasing body-layer stiffness also restricted vocal fold motion to the cover layer and reduced prephonatory glottal opening. Excitation of anterior-posterior modes was also observed, particularly for large values of the body-cover stiffness ratio. The results of this study were also discussed in relation to previous theoretical and experimental studies.     

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.     

Relationship among glottal area, static supraglottic compression, and laryngeal function studies in unilateral vocal fold paresis and paralysis

In this study, we evaluated the relationship between laryngeal function measures and glottal gap ratio and normalized measures of supraglottic behaviors in patients with unilateral vocal fold paresis (UVFP). Thirty-one patients were found to have unilateral vocal fold paresis by videoendoscopy and laryngeal electromyography, and 13 controls participated in this study. Patients with UVFP demonstrated significantly larger glottal gap ratios (p = 0.016) than control subjects. The nonparalyzed or contralateral vocal fold was associated with significantly more static false vocal fold compression (p = 0.03) compared with the paralyzed vocal fold or with the controls. Patients with unilateral vocal fold paresis were divided into subgroups: those with normal or abnormal maximum phonation time, flow, or pressure measures. Smaller glottal gap ratios were identified in patients with normal maximum phonation times and flow measures. Greater false vocal fold activity was identified in unilateral vocal fold paresis patients with normal laryngeal function measures than in unilateral vocal fold paresis patients with abnormal measures. These findings suggest that some patients with documented unilateral paresis and glottal incompetence can compensate for vocal fold weakness such that their acoustic and aerodynamic measures are normal.     

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.     

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.     

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 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.     

Vocal fold and ventricular fold vibration in period-doubling phonation: physiological description and aerodynamic modeling

Occurrences of period-doubling are found in human phonation, in particular for pathological and some singing phonations such as Sardinian A Tenore Bassu vocal performance. The combined vibration of the vocal folds and the ventricular folds has been observed during the production of such low pitch bass-type sound. The present study aims to characterize the physiological correlates of this acoustical production and to provide a better understanding of the physical interaction between ventricular fold vibration and vocal fold self-sustained oscillation. The vibratory properties of the vocal folds and the ventricular folds during phonation produced by a professional singer are analyzed by means of acoustical and electroglottographic signals and by synchronized glottal images obtained by high-speed cinematography. The periodic variation in glottal cycle duration and the effect of ventricular fold closing on glottal closing time are demonstrated. Using the detected glottal and ventricular areas, the aerodynamic behavior of the laryngeal system is simulated using a simplified physical modeling previously validated in vitro using a larynx replica. An estimate of the ventricular aperture extracted from the in vivo data allows a theoretical prediction of the glottal aperture. The in vivo measurements of the glottal aperture are then compared to the simulated estimations.     

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.