Dependence of phonation threshold pressure on vocal tract acoustics and vocal fold tissue mechanics

Analytical and computer simulation studies have shown that the acoustic impedance of the vocal tract as well as the viscoelastic properties of vocal fold tissues are critical for determining the dynamics and the energy transfer mechanism of vocal fold oscillation. In the present study, a linear, small-amplitude oscillation theory was revised by taking into account the propagation of a mucosal wave and the inertive reactance (inertance) of the supraglottal vocal tract as the major energy transfer mechanisms for flow-induced self-oscillation of the vocal fold. Specifically, analytical results predicted that phonation threshold pressure (Pth) increases with the viscous shear properties of the vocal fold, but decreases with vocal tract inertance. This theory was empirically tested using a physical model of the larynx, where biological materials (fat, hyaluronic acid, and fibronectin) were implanted into the vocal fold cover to investigate the effect of vocal fold tissue viscoelasticity on Pth. A uniform-tube supraglottal vocal tract was also introduced to examine the effect of vocal tract inertance on Pth. Results showed that Pth decreased with the inertive impedance of the vocal tract and increased with the viscous shear modulus (G") or dynamic viscosity (eta') of the vocal fold cover, consistent with theoretical predictions. These findings supported the potential biomechanical benefits of hyaluronic acid as a surgical bioimplant for repairing voice disorders involving the superficial layer of the lamina propria, such as scarring, sulcus vocalis, atrophy, and Reinke's edema.     

Phonation thresholds as a function of laryngeal size in a two-mass model of the vocal folds

This letter analyzes the oscillation onset-offset conditions of the vocal folds as a function of laryngeal size. A version of the two-mass model of the vocal folds is used, coupled to a two-tube approximation of the vocal tract in configuration for the vowel /a/. The standard male configurations of the laryngeal and vocal tract models are used as reference, and their dimensions are scaled using a single factor. Simulations of the vocal fold oscillation and oral output are produced for varying values of the scaling factor. The results show that the oscillation threshold conditions become more restricted for smaller laryngeal sizes, such as those appropriate for females and children.     

The physics of small-amplitude oscillation of the vocal folds

A theory of vocal fold oscillation is developed on the basis of the body-cover hypothesis. The cover is represented by a distributed surface layer that can propagate a mucosal surface wave. Linearization of the surface-wave displacement and velocity, and further small-amplitude approximations, yields closed-form expressions for conditions of oscillation. The theory predicts that the lung pressure required to sustain oscillation, i.e., the oscillation threshold pressure, is reduced by reducing the mucosal wave velocity, by bringing the vocal folds closer together and by reducing the convergence angle in the glottis. The effect of vocal tract acoustic loading is included. It is shown that vocal tract inertance reduces the oscillation threshold pressure, whereas vocal tract resistance increases it. The treatment, which is applicable to falsetto and breathy voice, as well as onset or release of phonation in the absence of vocal fold collision, is harmonized with former treatments based on two-mass models and collapsible tubes.     

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.     

Using the Relaxation Oscillations Principle for Simple Phonation Modeling

Well-known multimass models of vocal folds are useful to describe main behavior observed in human voicing but their principle of functioning, based on harmonic oscillation, may appear complex. This work is designed to show that a simple one-mass model ruled by laws of relaxation oscillation can also depict main behavior of glottis dynamic. Theory of relaxation oscillation is detailed. A relaxation oscillation model is assessed through a numerical simulation using conventional values for tissue characteristics and subglottal pressure. As expected, raising the mass decreases the fundamental frequency and increases the amplitude of vocal fold vibration: for a mass ranging from 0.01 to 0.4 g, F0 decreased from 297.5 to 42.5 Hz and vibrational amplitude increased from 1.26 to 3.25 mm (for stiffness k=10Nm(-1), damping r=0.015 N s m(-1), and subglottal pressure=1 kPa). Stiffness value has the opposite effect. The subglottal pressure controls the fundamental frequency with a rate ranging from 20 to 50 Hz/kPa. The vibrational amplitude is also controlled linearly by subglottal pressure from 0.22 to 0.26 mm/kPa. The range of phonation threshold pressure (PTP) is close to the values currently proposed, that is, 0.1 to 1 kPa and varies with the fundamental frequency. The relaxation oscillator is a simple and useful tool for modeling vocal fold vibration.     

A theoretical study of f0-f1 interaction with application to resonant speaking and singing voice

An interactive source-filter system, consisting of a three-mass body-cover model of the vocal folds and a wave reflection model of the vocal tract, was used to test the dependence of vocal fold vibration on the vocal tract. The degree of interaction is governed by the epilarynx tube, which raises the vocal tract impedance to match the impedance of the glottis. The key component of the impedance is inertive reactance. Whenever there is inertive reactance, the vocal tract assists the vocal folds in vibration. The amplitude of vibration and the glottal flow can more than double, and the oral radiated power can increase up to 10 dB. As F0 approaches F1, the first formant frequency, the interactive source-filter system loses its advantage (because inertive reactance changes to compliant reactance) and the noninteractive system produces greater vocal output. Thus, from a voice training and control standpoint, there may be reasons to operate the system in either interactive and noninteractive modes. The harmonics 2F0 and 3F0 can also benefit from being positioned slightly below F1.     

Nonlinear source-filter coupling in phonation: vocal exercises

Nonlinear source-filter coupling has been demonstrated in computer simulations, in excised larynx experiments, and in physical models, but not in a consistent and unequivocal way in natural human phonations. Eighteen subjects (nine adult males and nine adult females) performed three vocal exercises that represented a combination of various fundamental frequency and formant glides. The goal of this study was to pinpoint the proportion of source instabilities that are due to nonlinear source-tract coupling. It was hypothesized that vocal fold vibration is maximally destabilized when F(0) crosses F(1), where the acoustic load changes dramatically. A companion paper provides the theoretical underpinnings. Expected manifestations of a source-filter interaction were sudden frequency jumps, subharmonic generation, or chaotic vocal fold vibrations that coincide with F(0)-F(1) crossovers. Results indicated that the bifurcations occur more often in phonations with F(0)-F(1) crossovers, suggesting that nonlinear source-filter coupling is partly responsible for source instabilities. Furthermore it was observed that male subjects show more bifurcations in phonations with F(0)-F(1) crossovers, presumably because in normal speech they are less likely to encounter these crossovers as much as females and hence have less practice in suppressing unwanted instabilities.     

Effect of vocal effort on spectral properties of vowels.

The effects of variations in vocal effort corresponding to common conversation situations on spectral properties of vowels were investigated. A database in which three degrees of vocal effort were suggested to the speakers by varying the distance to their interlocutor in three steps (close--0.4 m, normal--1.5 m, and far--6 m) was recorded. The speech materials consisted of isolated French vowels, uttered by ten naive speakers in a quiet furnished room. Manual measurements of fundamental frequency F0, frequencies, and amplitudes of the first three formants (F1, F2, F3, A1, A2, and A3), and on total amplitude were carried out. The speech materials were perceptually validated in three respects: identity of the vowel, gender of the speaker, and vocal effort. Results indicated that the speech materials were appropriate for the study. Acoustic analysis showed that F0 and F1 were highly correlated with vocal effort and varied at rates close to 5 Hz/dB for F0 and 3.5 Hz/dB for F1. Statistically F2 and F3 did not vary significantly with vocal effort. Formant amplitudes A1, A2, and A3 increased significantly; The amplitudes in the high-frequency range increased more than those in the lower part of the spectrum, revealing a change in spectral tilt. On the average, when the overall amplitude is increased by 10 dB, A1, A2, and A3 are increased by 11, 12.4, and 13 dB, respectively. Using "auditory" dimensions, such as the F1-F0 difference, and a "spectral center of gravity" between adjacent formants for representing vowel features did not reveal a better constancy of these parameters with respect to the variations of vocal effort and speaker. Thus a global view is evoked, in which all of the aspects of the signal should be processed simultaneously.     

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.     

Membranous and cartilaginous vocal fold adduction in singing

While vocal fold adduction is an important parameter in speech, relatively little has been known on the adjustment of the vocal fold adduction in singing. This study investigates the possibility of separate adjustments of cartilaginous and membranous vocal fold adduction in singing. Six female and seven male subjects, singers and non-singers, were asked to imitate an instructor in producing four phonation types: "aBducted falsetto" (FaB), "aDducted falsetto" (FaD), "aBducted Chest" (CaB), and "aDducted Chest" (CaD). The phonations were evaluated using videostroboscopy, videokymography (VKG), electroglottography (EGG), and audio recordings. All the subjects showed less posterior (cartilaginous) vocal fold adduction in phonation types FaB and CaB than in FaD and CaD, and less membranous vocal fold adduction (smaller closed quotient) in FaB and FaD than in CaB and CaD. The findings indicate that the exercises enabled the singers to separately manipulate (a) cartilaginous adduction and (b) membranous medialization of the glottis though vocal fold bulging. Membranous adduction (monitored via videokymographic closed quotient) was influenced by both membranous medialization and cartilaginous adduction. Individual control over these types of vocal fold adjustments allows singers to create different vocal timbres.     

A methodological and preliminary study on the acoustic effect of a trumpet player's vocal tract

A methodological study is presented to examine the acoustic role of the vocal tract in playing the trumpet. Preliminary results obtained for one professional player are also shown to demonstrate the effectiveness of the method. Images of the vocal tract with a resolution of 0.5 mm (2 mm in thickness) were recorded with magnetic resonance imaging to observe the tongue posture and estimate the vocal-tract area function during actual performance. The input impedance was then calculated for the player's air column including both the supra- and subglottal tracts using an acoustic tube model including the effect of wall losses. Finally, a time-domain blowing simulation by Adachi and Sato [J. Acoust. Soc. Am. 99, 1200-1209 (1996)] was performed with a model of the lips. In this simulation, the oscillating frequency of the lips was slightly affected by using different shapes of the vocal tract measured for the player. In particular, when the natural frequency of the lips was gradually increased, the transition to the higher mode occurred at different frequencies for different vocal-tract shapes. Furthermore, simulation results showed that the minimum blowing pressure required to attain the lip oscillation can be reduced by adjusting the vocal-tract shape properly.     

Vestibular vocal fold behavior during phonation in unilateral vocal fold paralysis

Voice quality in patients with vocal fold paralysis can be affected by several factors, such as the position of the paralyzed vocal fold, its degree of atrophy, the configuration of its free edge, and the level differences between both vocal folds. Depending on the related vocal deficiency the patient will attempt to compensate using different maneuvers, such as increment of vocal tract and neck muscle contraction to improve glottal closure. This is probably one of the reasons why ventricular folds are frequently requested. The objective of this study is to analyze the behavior of the homolateral and contralateral vestibular folds to delineate patterns of vestibular motion during sustained phonation, in cases of unilateral vocal fold paralysis.     

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.     

Mathematical model of acoustic speech production with mobile walls of the vocal tract

A mathematical speech production model is considered that describes acoustic oscillation propagation in a vocal tract with mobile walls. The wave field function satisfies the Helmholtz equation with boundary conditions of the third kind (impedance type). The impedance mode corresponds to a threeparameter pendulum oscillation model. The experimental research demonstrates the nonlinear character of how the mobility of the vocal tract walls influence the spectral envelope of a speech signal.     

Correspondence of electroglottographic closed quotient to vocal fold impact stress in excised canine larynges

The purpose of this study was to explore the possible use of the electroglottographic closed quotient (EGG CQ) as a noninvasive estimate of vocal fold impact stress (SI). Two excised canine larynges were used. Each larynx was mounted and vocal fold oscillation was induced using a humidified air source. Twentyseven experimental trials were conducted for each larynx. Trials involved variations in vocal process gap, vocal fold elongation, and subglottic pressure. Simultaneous measures were made of vocal fold SI at the midpoint of the membranous vocal folds, and EGG CQ (dimensionless ratio). The results indicated that when threshold and saturation effects were excluded, the SI and the CQ were strongly related (linear correlation r = .83 and .96 for the two individual larynges, and .81 for the combined data). Within the region of linear relation, an increase of .15 in the CQ corresponded to about 1 kPa increase in SI for the combined data. Discussion focuses on possible clinical implications and the likely reasons for threshold and saturation phenomena.     

马铁菊头蝠声道声学特性的数值分析

采用有限元数值计算得到了马铁菊头蝠声道内部的声场分布,给出了马铁菊头蝠声道内几种特殊的腔体结构在蝙蝠发声过程中的作用。通过微型CT扫描并经过三维重构得到了马铁菊头蝠声道的三维立体模型用于有限元数值计算,通过在声门处放置单位声源计算得到了整个声道内部以及鼻孔周围的声压分布。结果表明,马铁菊头蝠声道包含了鼻腔结构后声波在声门上方的声压幅度明显大于不含鼻腔结构的情况,从传输曲线来看,声门上方鼻腔的存在使得系统对声波传输在二次谐波频率处呈现低阻抗效果,同时鼻腔的改变还可影响二次谐波的位置。而声门下方的气管空腔主要影响声波的背向转播,声门下方的气管空腔的存在可明显降低蝙蝠发声时声场在声道声门下方的声压幅度,同时抑制声音背向传播时二次谐波成分的强度。      

Oral breathing increases Pth and vocal effort by superficial drying of vocal fold mucosa.

Oral breathing superficially dehydrates the airway lumen by decreasing the depth of the sol layer in humans and animals. Conversely, nasal breathing can increase the humidity of inspired air. We compared the effects of short-term oral and nasal breathing on Pth and perceived vocal effort in 20 female subjects randomly assigned to two groups: oral breathing (N = 10, age 21-32 years); nasal breathing (N = 10, age 20-36 years). We hypothesized that short-term oral breathing, but not nasal breathing, would increase Pth, and that subjects would perceive this change as an increase in vocal effort. Following 15 minutes of oral breathing, Pth increased at comfortable and low pitch (p < 0.01) with 6 of 10 subjects reporting increased vocal effort. Nasal breathing reduced Pth at all three pitches (p < 0.01), and 7 of 10 subjects reported decreased vocal effort. Over all subjects, 49% of the variance in treatment-induced change in Pth was accounted for by change in vocal effort (R = 0.70). We posit that obligatory oral breathing places healthy subjects at risk for symptoms of increased vocal effort. The facilitatory role of superficial hydration on vocal fold oscillation should be considered in biomechanical models of phonation and in the clinical prevention of laryngeal dryness.     

Two-mass model of the vocal folds: negative differential resistance oscillation

The vocal folds and glottis are analyzed as a single system rather than as two separate but interacting systems, i.e., an aerodynamic one (the glottis) and a mechanical one (the vocal folds). Simplified steady flow calculations based on the two-mass model, and similar to those of Ishizaka and Matsudaira [SCRL Monograph No. 8, Santa Barbara, CA (1972)], are made except that flexible walls are assumed for both dc and ac flows. A negative differential resistance is found for steady flow when the coupling spring is weak compared to that of the lower mass. Dynamic transverse motion of the masses is represented by two transverse series resonant circuits in parallel within the glottis. The vocal tract is represented by a lumped resistance and inertance in series. Sustained, self-excited, small-amplitude oscillations can be obtained when the magnitude of the negative differential resistance is equal to the real part of the impedance of the rest of the circuit. The oscillation frequency depends only on the elasticity and mass of the vocal folds. The present analysis differs from Ishizaka and Matsudaira's analysis because their oscillation frequency decreases as dc volume velocity increases.     

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.