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.     

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.     

Approximating the vocal tract by conical horns

The transmission-line method is studied systematically as applied to the vocal tract approximated by a sequence of conical horns. The constructed scheme describes the propagation of plane waves in conical horns, with all factors interesting in terms of acoustic theory of speech production, viz., losses, nonrigid vocal tract walls, and potential side-branches, taken into account. The derived equations are tested on a cross-sectional areas of the vocal tract measured by magnetic-resonance tomography on a real speaker.     

A simplified model of mouth radiation impedance closed by mask cavity

Acoustic radiation impedance of the mouth is an important parameter when the vocal tract is modelled by the equivalent electrical circuit. If the vocal tract is closed by a cavity, as when the speaker wears some kind of mask, total impedance acoustically loading the vocal tract becomes serial connection of the mouth radiation impedance and the mask impedance. In that case the mouth radiation impedance has to be changed compared to free field conditions. This paper introduces a simplified approach to the modelling of that change by an appropriate reduction coefficient. The analysis based on an experiment preformed by measurement in the vocal tract physical model accompanied with analytical estimation has shown that the value of such reduction coefficient is 0.5. The results reveal that for a vocal tract closed with mask cavity the change in mouth radiation impedance introduced in an equivalent electrical circuit can be approximated by the value for free field radiation decreased by about 50%.     

Frequency modulations in the speech signal

The paper examines physical mechanisms of frequency modulations in acoustics of the vocal tract and methods of estimation of these modulations in the speech signal. It has been found that vibrations of the tract walls make a negligibly small effect on modulations of its resonance frequencies. The model of the process of speech formation with account for the subglottal cavity shows that a change in boundary conditions at the open glottis produces noticeable variations in resonance frequencies. Along with this type of modulations, modulations determined by the shape of the source of excitation also arise in the speech signal. They substantially depend on the ratio of the frequency of the fundamental tone to the resonance frequency and of the parameters of methods estimating modulations and methods of analysis of the speech signal. Overall, this may sometimes cause unstable and unpredictable modulations of estimated formant frequencies in the speech signal.     

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.     

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.     

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.     

Towards the Automatic Study of the Vocal Tract From Magnetic Resonance Images

Over the last few decades, researchers have been investigating the mechanisms involved in speech production. Image analysis can be a valuable aid in the understanding of the morphology of the vocal tract. The application of magnetic resonance imaging to study these mechanisms has been proven to be reliable and safe. We have applied deformable models in magnetic resonance images to conduct an automatic study of the vocal tract; mainly, to evaluate the shape of the vocal tract in the articulation of some European Portuguese sounds, and then to successfully automatically segment the vocal tract's shape in new images. Thus, a point distribution model has been built from a set of magnetic resonance images acquired during artificially sustained articulations of 21 sounds, which successfully extracts the main characteristics of the movements of the vocal tract. The combination of that statistical shape model with the gray levels of its points is subsequently used to build active shape models and active appearance models. Those models have then been used to segment the modeled vocal tract into new images in a successful and automatic manner. The computational models have thus been revealed to be useful for the specific area of speech simulation and rehabilitation, namely to simulate and recognize the compensatory movements of the articulators during speech production.     

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.     

Effect of artificially lengthened vocal tract on vocal fold oscillation's fundamental frequency.

The fundamental frequency of vocal fold oscillation (F(0)) is controlled by laryngeal mechanics and aerodynamic properties. F(0) change per unit change of transglottal pressure (dF/dP) using a shutter valve has been studied and found to have nonlinear, V-shaped relationship with F(0). On the other hand, the vocal tract is also known to affect vocal fold oscillation. This study examined the effect of artificially lengthened vocal tract length on dF/dP. dF/dP was measured in six men using two mouthpieces of different lengths. Results: The dF/dP graph for the longer vocal tract was shifted leftward relative to the shorter one. Conclusion: Using the one-mass model, the nadir of the "V" on the dF/dP graph was strongly influenced by the resonance around the first formant frequency. However, a more precise model is needed to account for the effects of viscosity and turbulence.     

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.     

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.     

Large scale data acquisition of simultaneous MRI and speech

We describe an arrangement for simultaneous recording of speech and vocal tract geometry in patients undergoing surgery involving this area. Experimental design is considered from an articulatory phonetic point of view. The speech signals are recorded with an acoustic-electrical arrangement. The vocal tract is simultaneously imaged with MRI. A MATLAB-based system controls the timing of speech recording and MR image acquisition. The speech signals are cleaned from acoustic MRI noise by an adaptive signal processing algorithm. Finally, a vowel data set from pilot experiments is qualitatively compared both with validation data from the anechoic chamber and with Helmholtz resonances of the vocal tract volume, obtained using FEM.     

Adaptive computation of articulatory parameters from the speech signal

An unconstrained optimization technique is used to find the values of parameters, of a combination of an articulatory and a vocal tract model, that minimize the difference between model spectra and natural speech spectra. The articulatory model is anatomically realistic and the vocal tract model is a "lossy" Webster equation for which a method of solution is given. For English vowels in the steady state, anatomically reasonable articulatory configurations whose corresponding spectra match those of human speech to within 2 dB have been computed in fewer than ten iterations. Results are also given which demonstrate a limited ability of the system to track the articulatory dynamics of voiced speech.     

Resonances of a branched vocal tract with compliant walls

The calculation of the resonance frequencies from experimental cross-sectional areas of a vocal tract under the assumption that its walls are perfectly rigid provides values that noticeably differ from the measured resonance frequencies. The compliance of the walls affects the first resonance and almost does not affect the higher-order resonances. The presence of branching in the tract at the level of the larynx affects the second and third resonances stronger than the first resonance. The parameters of the wall impedance (the loss, mass, and elasticity) and the length and cross-sectional area of the branchings are determined by minimizing the rms discrepancy between the measured and calculated resonance frequencies. The error in the frequency calculation with allowance for the wall compliance and branching in the tract proves to be within the accuracy of the formant estimation.     

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.     

Acoustic impedance of an artificially lengthened and constricted vocal tract

Voice training techniques often make use of exercises involving partial occlusion of the vocal tract, typically at the anterior part of the oral cavity or at the lips. In this study two techniques are investigated: a bilabial fricative and a small diameter hard-walled tube placed between the lips. Because the input acoustic impedance of the vocal tract is known to affect both the shaping of the glottal flow pulse and the vibrational pattern of the vocal folds, a study of the input impedance is an essential step in understanding the benefits of these two techniques. The input acoustic impedance of the vocal tract was investigated theoretically for cases of a vowel, bilabial occlusion (fully closed lips), a bilabial fricative, and artificially lengthening the tract with small diameter tubes. The results indicate that the tubes increase the input impedance in the range of the fundamental frequency of phonation by lowering the first formant frequency to nearly that of the bilabial occlusion (the lower bound on the first formant) while still allowing a continuous airflow. The bilabial fricative also has the effect of lowering the first formant frequency and increasing the low-frequency impedance, but not as effectively as the extension tubes.     

The occurrence of the Coanda effect in pulsatile flow through static models of the human vocal folds

Pulsatile flow through a one-sided diffuser and static divergent vocal-fold models is investigated to ascertain the relevance of viscous-driven flow asymmetries in the larynx. The models were 7.5 times real size, and the flow was scaled to match Reynolds and Strouhal numbers, as well as the translaryngeal pressure drop. The Reynolds number varied from 0-2000, for flow oscillation frequencies corresponding to 100 and 150 Hz life-size. Of particular interest was the development of glottal flow skewing by attachment to the bounding walls, or Coanda effect, in a pulsatile flow field, and its impact on speech. The vocal folds form a divergent passage during phases of the phonation cycle when viscous effects such as flow separation are important. It was found that for divergence angles of less than 20 degrees, the attachment of the flow to the vocal-fold walls occurred when the acceleration of the forcing function was zero, and the flow had reached maximum velocity. For a divergence angle of 40 degrees, the fully separated central jet never attached to the vocal-fold walls. Inferences are made regarding the impact of the Coanda effect on the sound source contribution in speech.