On the relation between the phonation threshold lung pressure and the oscillation frequency of the vocal folds

This Letter presents an extension of a previous equation for the phonation threshold pressure by Titze [I. R. Titze, J. Acoust. Soc. Am. 83, 1536-1552 (1988)]. The extended equation contains the vocal-fold oscillation frequency as an explicit factor. It is derived from the mucosal wave model of the vocal folds by considering the general case of an arbitrary time delay for the mucosal wave to travel the glottal height. The results are illustrated with a numerical example, which shows good qualitative agreement with experimental measures.     

The phonation critical condition in rectangular glottis with wide prephonatory gaps

The effect of the pressure recovery at glottal exit is introduced to modify the one-mass model. Using the modified one-mass model, the phonation critical condition, including phonation threshold pressure and phonation threshold flow, is analyzed by using the small-amplitude oscillation theory. It is found that the phonation threshold pressure is not sensitive to the change of the prephonatory glottal width at a wide glottal gap. This result agrees with previous experimental observations and suggests that the low slope of dependence of phonation threshold pressure on prephonatory gap found by Chan and Titze [J. Acoust. Soc. Am. 119, 2351-2362 (2006)] could be a consequence of the pressure recovery effect at the glottal exit. In addition, it is predicted that the phonation threshold flow is always significantly increased with the prephonatory gap even at a wide prephonatory glottal gap. Therefore, the phonation threshold flow has an advantage in assessing the phonatory system at a wide prephonatory gap in comparison with the phonation threshold pressure. The phonation threshold flow can be a useful aerodynamic parameter for pathological conditions in which the incomplete glottal gap is often seen.     

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.     

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.     

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 effects of rehydration on phonation in excised canine larynges

Experiments using excised canine larynges were conducted to study the restoration of vocal efficiency in dehydrated larynges. Excised larynges were dehydrated with warm, dry air to the point that airflow through the approximated vocal folds would not entrain the folds to produce phonation. The dehydrated vocal folds were then bathed in a saline solution. The rehydrated larynges were then remounted on the bench apparatus that enabled phonation with a constant humidified airflow, and measurements were made of phonation threshold pressure, glottal airflow, and amplitude. Hydration resulted in significantly increased efficiency and decrease in phonation threshold pressure. The findings confirm clinical impressions that hydration is critical in the physiology of normal phonation.     

A lumped mucosal wave model of the vocal folds revisited: recent extensions and oscillation hysteresis

This paper examines an updated version of a lumped mucosal wave model of the vocal fold oscillation during phonation. Threshold values of the subglottal pressure and the mean (DC) glottal airflow for the oscillation onset are determined. Depending on the nonlinear characteristics of the model, an oscillation hysteresis phenomenon may occur, with different values for the oscillation onset and offset threshold. The threshold values depend on the oscillation frequency, but the occurrence of the hysteresis is independent of it. The results are tested against pressure data collected from a mechanical replica of the vocal folds, and oral airflow data collected from speakers producing intervocalic /h/. In the human speech data, observed differences between voice onset and offset may be attributed to variations in voice pitch, with a very small or inexistent hysteresis phenomenon.     

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.     

The effect of viscosity changes in the vocal folds on the range of oscillation

Changes in vocal fold oscillation threshold pressure were induced in excised canine larynges by experimentally causing fluid movement into and out of the vocal folds. The transport was facilitated by exposing the vocal folds to various osmotic solutions, and it was assumed that changes in hydration caused changes in the internal tissue viscosity. A range of oscillation threshold pressures was measured for each condition of hydration by varying length and glottal width. The oscillation threshold pressure shifted as predicted. Decreased hydration (increased viscosity) raised the threshold of oscillation, and increased hydration (decreased viscosity) lowered the threshold of oscillation. This apparently represents the first in vitro model for the study of the effect of viscosity changes of the internal environment of the vocal folds on phonation.     

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.     

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.     

Phonation Threshold Power in Ex Vivo Laryngeal Models

This study hypothesized that phonation threshold power is measureable and sensitive to changes in the biomechanical properties of the vocal folds. Phonation threshold power was measured in three sample populations of 10 excised canine larynges treated with variable posterior glottal gap, variable bilateral vocal fold elongation, and variable vocal fold lesioning. Posterior glottal gap varied from 0 to 4 mm in 0.5 mm intervals. Bilateral vocal fold elongation varied from 0% to 20% in 5% intervals. Vocal fold lesion treatments included unilateral and bilateral vocal fold lesion groups. Each treatment was investigated independently in a sample population of 10 excised canine larynges. Linear regression analysis indicated that phonation threshold power was sensitive to posterior glottal gap (R² = 0.298, P < 0.001) and weakly to vocal fold elongation (R² = 0.052, P = 0.003). A one-way repeated measures analysis of variance indicated that phonation threshold power was sensitive to the presence of lesions (P < 0.001). Theoretical and experimental evidence presented here suggests that phonation threshold power could be used as a broad screening parameter sensitive to certain changes in the biomechanical properties of the larynx. It has not yet been measured in humans, but because it has the potential to represent the airflow-tissue energy transfer more completely than the phonation threshold pressure or flow alone, it may be a more useful parameter than these and could be used to indicate that laryngeal health is likely abnormal.     

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.     

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.     

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.     

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.     

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.     

Effect of a Single Injection of Basic Fibroblast Growth Factor into the Vocal Folds: A 36-Month Clinical Study

ObjectiveA single injection of basic fibroblast growth factor (bFGF) into the vocal folds of patients with glottal insufficiency has been shown to be effective for a few years. However, the long-term therapeutic effect of a single injection of bFGF into the vocal folds has yet to be demonstrated. In this study, the therapeutic effect of a single injection of bFGF into the vocal folds was investigated over several years by monitoring patients for 36 months following this treatment.MethodsNineteen patients with glottal insufficiency received injections of bFGF diluted to 20 μg/mL in the superficial layer of the lamina propria of the bilateral vocal folds. The following parameters were evaluated at preinjection baseline and 6, 12, 18, 24, and 36 months later, and statistical comparisons were performed. The parameters evaluated were: the Grade, Rough, Breathy, Asthenic, and Strained (GRBAS) scale score; maximum phonation time; acoustic analysis; and glottal wave analysis (GWA) and kymograph edge analysis (KEA) using high-speed digital imaging (HSDI). The amplitude perturbation quotient (APQ) and period perturbation quotient (PPQ) were measured by acoustic analysis. The mean minimum glottal area during vocalization and mean minimum distance between the vocal folds were measured by GWA. The amplitudes of the bilateral vocal folds were measured by KEA.ResultsPostinjection, the GRBAS scale score decreased from 6 months after injection, and maximum phonation time was prolonged. The mean minimum glottal area during vocalization and the mean minimum distance between the vocal folds calculated by GWA of HSDI decreased significantly after 6 months. These effects persisted until 36 months postinjection. APQ and PPQ derived from acoustic analysis tended to decrease, but not significantly. There was no clear change in the amplitudes of the bilateral vocal folds calculated by KEA of HSDI before and after injection.ConclusionsThese results suggest that the effects of a single injection of bFGF into the vocal folds persist for 36 months.     

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.