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 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.     

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.     

Characterization of chronic vocal fold scarring in a rabbit model

The purpose of the current study was to assess the histologic and rheologic properties of the scarred vocal fold lamina propria during a chronic phase of wound repair in a rabbit model. Eighteen rabbit larynges were scarred using a procedure that involved stripping the vocal fold lamina propria down to the thyroarytenoid muscle, using 3-mm microforceps. The approximate dimension of injury to the vocal fold was 3 x 1.5 x 0.5 mm [length x width x depth]. At 6 months postoperatively, histologic analysis of the scarred and control lamina propria in eight of these rabbits was completed for collagen, procollagen, elastin, and hyaluronic acid. Compared with control samples, scarred tissue samples revealed fragmented and disorganized elastin fibers. Additionally, collagen was significantly increased, organized, and formed thick bundles in the scarred vocal fold lamina propria. Measurements of the viscoelastic shear properties of the scarred and control lamina propria in the remaining 10 rabbits revealed increased elastic shear modulus (G') in 8 of 10 scarred samples and increased dynamic viscosity (eta') in 9 of 10 scarred samples. Although rheologic differences were not statistically significant, they revealed that on average, scarred samples were stiffer and more viscous than the normal controls. Histologic data are interpreted as indicating that by 6 months postinjury, the scarred rabbit vocal fold has reached a mature phase of wound repair, characterized by an increased, organized, and thick bundle collagen matrix. Rheologic data are interpreted as providing support for the potential role of increased, thick bundle collagen, and a disorganized elastin network on shear stiffness and dynamic viscosity in the chronic vocal fold scar. Based on these results, a 6-month postoperative time frame is proposed for future studies of chronic vocal fold scarring using the rabbit animal model.     

Nonlinear source-filter coupling in phonation: theory

A theory of interaction between the source of sound in phonation and the vocal tract filter is developed. The degree of interaction is controlled by the cross-sectional area of the laryngeal vestibule (epilarynx tube), which raises the inertive reactance of the supraglottal vocal tract. Both subglottal and supraglottal reactances can enhance the driving pressures of the vocal folds and the glottal flow, thereby increasing the energy level at the source. The theory predicts that instabilities in vibration modes may occur when harmonics pass through formants during pitch or vowel changes. Unlike in most musical instruments (e.g., woodwinds and brasses), a stable harmonic source spectrum is not obtained by tuning harmonics to vocal tract resonances, but rather by placing harmonics into favorable reactance regions. This allows for positive reinforcement of the harmonics by supraglottal inertive reactance (and to a lesser degree by subglottal compliant reactance) without the risk of instability. The traditional linear source-filter theory is encumbered with possible inconsistencies in the glottal flow spectrum, which is shown to be influenced by interaction. In addition, the linear theory does not predict bifurcations in the dynamical behavior of vocal fold vibration due to acoustic loading by the vocal tract.     

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.     

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.     

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.     

Measurements of vocal fold tissue viscoelasticity: approaching the male phonatory frequency range

Viscoelastic shear properties of human vocal fold tissues have been reported previously. However, data have only been obtained at very low frequencies (< or = 15 Hz). This necessitates data extrapolation to the frequency range of phonation based on constitutive modeling and time-temperature superposition. This study attempted to obtain empirical measurements at higher frequencies with the use of a controlled strain torsional rheometer, with a design of directly controlling input strain that introduced significantly smaller system inertial errors compared to controlled stress rheometry. Linear viscoelastic shear properties of the vocal fold mucosa (cover) from 17 canine larynges were quantified at frequencies of up to 50 Hz. Consistent with previous data, results showed that the elastic shear modulus (G'), viscous shear modulus (G"), and damping ratio (zeta) of the vocal fold mucosa were relatively constant across 0.016-50 Hz, whereas the dynamic viscosity (eta') decreased monotonically with frequency. Constitutive characterization of the empirical data by a quasilinear viscoelastic model and a statistical network model demonstrated trends of viscoelastic behavior at higher frequencies generally following those observed at lower frequencies. These findings supported the use of controlled strain rheometry for future investigations of the viscoelasticity of vocal fold tissues and phonosurgical biomaterials at phonatory frequencies.     

Vocal Warm-up Increases Phonation Threshold Pressure in Soprano Singers at High Pitch

Vocal warm-up is thought to optimize singing performance. We compared effects of short-term, submaximal, vocal warm-up exercise with those of vocal rest on the soprano voice (n = 10, ages 19-21 years). Dependent variables were the minimum subglottic air pressure required for vocal fold oscillation to occur (phonation threshold pressure, Pth), and the maximum and minimum phonation fundamental frequency. Warm-up increased Pth for high pitch phonation (p = 0.033), but not for comfortable (p = 0.297) or low (p = 0.087) pitch phonation. No significant difference in the maximum phonation frequency (p = 0.193) or minimum frequency (p = 0.222) was observed. An elevated Pth at controlled high pitch, but an unchanging maximum and minimum frequency production suggests that short-term vocal exercise may increase the viscosity of the vocal fold and thus serve to stabilize the high voice.     

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.     

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.     

Influence of acoustic loading on an effective single mass model of the vocal folds

Three-way interactions between sound waves in the subglottal and supraglottal tracts, the vibrations of the vocal folds, and laryngeal flow were investigated. Sound wave propagation was modeled using a wave reflection analog method. An effective single-degree-of-freedom model was designed to model vocal-fold vibrations. The effects of orifice geometry changes on the flow were considered by enforcing a time-varying discharge coefficient within a Bernoulli flow model. The resulting single-degree-of-freedom model allowed for energy transfer from flow to structural vibrations, an essential feature usually incorporated through the use of higher order models. The relative importance of acoustic loading and the time-varying flow resistance for fluid-structure energy transfer was established for various configurations. The results showed that acoustic loading contributed more significantly to the net energy transfer than the time-varying flow resistance, especially for less inertive supraglottal loads. The contribution of supraglottal loading was found to be more significant than that of subglottal loading. Subglottal loading was found to reduce the net energy transfer to the vocal-fold oscillation during phonation, balancing the effects of the supraglottal load.     

The shear modulus of the human vocal fold in a transverse direction

The aim of this study was to measure the shear modulus of the vocal fold in a human hemilarynx, such that the data can be related to direction of applied stress and anatomical context. Dynamic spring rate data were collected using a modified linear skin rheometer using human hemilarynges, and converted to estimated shear modulus via application of a simple shear model. The measurement probe was attached to the epithelial layer of the vocal fold cover using suction. A sinusoidal force of 3g was applied to the epithelium, and the resultant displacement logged at a rate of 1kHz. Force measurement accuracy was 20microg and position measurement accuracy was 4microm. The force was applied in a transverse direction at the midmembranous point between the vocal process and the anterior commissure. The shear modulus of the three female vocal folds ranged from 814 to 1232Pa. The shear modulus of the three male vocal folds ranged from 1021 to 1796Pa. These data demonstrate that it is possible to obtain estimates for the shear modulus of the vocal fold while preserving anatomical context. The modulus values reported here are higher than those reported using parallel plate rheometry. This is to be expected as the tissue is attached to surrounding structures, and is under natural tension.     

A simple-shear rheometer for linear viscoelastic characterization of vocal fold tissues at phonatory frequencies

Previous studies reporting the linear viscoelastic shear properties of the human vocal fold cover or mucosa have been based on torsional rheometry, with measurements limited to low audio frequencies, up to around 80 Hz. This paper describes the design and validation of a custom-built, controlled-strain, linear, simple-shear rheometer system capable of direct empirical measurements of viscoelastic shear properties at phonatory frequencies. A tissue specimen was subjected to simple shear between two parallel, rigid acrylic plates, with a linear motor creating a translational sinusoidal displacement of the specimen via the upper plate, and the lower plate transmitting the harmonic shear force resulting from the viscoelastic response of the specimen. The displacement of the specimen was measured by a linear variable differential transformer whereas the shear force was detected by a piezoelectric transducer. The frequency response characteristics of these system components were assessed by vibration experiments with accelerometers. Measurements of the viscoelastic shear moduli (G' and G") of a standard ANSI S2.21 polyurethane material and those of human vocal fold cover specimens were made, along with estimation of the system signal and noise levels. Preliminary results showed that the rheometer can provide valid and reliable rheometric data of vocal fold lamina propria specimens at frequencies of up to around 250 Hz, well into the phonatory range.     

Vocal tract changes caused by phonation into a tube: a case study using computer tomography and finite-element modeling

Phonation into a glass tube is a voice training and therapy method that leads to beneficial effects in voice production. It has not been known, however, what changes occur in the vocal tract during and after the phonation into a tube. This pilot study examined the vocal tract shape in a female subject before, during, and after phonation into a tube using computer tomography (CT). Three-dimensional finite-element models (FEMs) of the vocal tract were derived from the CT images and used to study changes in vocal tract input impedance. When phonating on vowel [a:] the data showed tightened velopharyngeal closure and enlarged cross-sectional areas of the oropharyngeal and oral cavities during and after the tube-phonation. FEM calculations revealed an increased input inertance of the vocal tract and an increased acoustic energy radiated out of the vocal tract after the tube-phonation. The results indicate that the phonation into a tube causes changes in the vocal tract which remain also when the tube is removed. These effects may help improving voice production in patients and voice professionals.     

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.     

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.