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-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.     

Nonlinear behavior of vocal fold vibration: The role of coupling between the vocal folds

Coupling between the vocal folds is one of the nonlinear mechanisms allowing regulation and synchronization of mucosal vibration. The purpose of this study was to establish that modulations such as diplophonia and abnormalities observed in vocal signals that may be observed in some cases of laryngeal pathology can be considered as nonlinear behavior due to the persistence of some physical interaction (coupling). An experimental model using excised porcine larynx was designed to create tension asymmetry between the vocal folds and to obtain vocal signals with modulations. Signals were analyzed by spectral analysis and the phase portrait method. Results were compared with computer-generated synthetic signals corresponding to nonlinear combinations of sinusoid signals. Under these conditions, evidence of nonlinear behavior was detected in 85% of experimental signals. These findings were interpreted as a demonstration of vocal fold interaction. Based on these findings, the authors conclude that (1) coupling must be taken into account in physical models of laryngeal physiology, and that (2) methods of nonlinear dynamics may be used for objective voice analysis.     

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.     

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.     

Sex-related differences in vocal responses to pitch feedback perturbations during sustained vocalization

The present study assessed the effect of sex on voice fundamental frequency (F(0)) responses to pitch feedback perturbations during sustained vocalization. Sixty-four native-Mandarin speakers heard their voice pitch feedback shifted at ± 50, ± 100, or ± 200 cents for 200 ms, five times during each vocalization. The results showed that, as compared to female speakers, male speakers produced significantly larger but slower vocal responses to the pitch-shifted stimuli. These findings reveal a modulation of vocal response as a function of sex, and suggest that there may be a differential processing of vocal pitch feedback perturbations between men and women.     

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.     

Observation of perturbations in a lumped-element model of the vocal folds with application to some pathological cases

In this paper a mass-spring model is developed that is a hybrid of the two-mass and the longitudinal string models, proposed by Ishizaka and Flanagan [Bell Sys. Tech. J. 51, 1233-1268 (1972)] and Titze [Phonetica 28, 129-170 (1973)], respectively. The model is used to simulate the vibratory motion of both the normal and asymmetric vocal folds. Mouth-output pressure, lateral tissue displacement, phase plots, and energy diagrams are presented to demonstrate the interaction between vocal fold tissue and the aerodynamic flow between the folds. The results of the study suggest that this interaction is necessary for sustained large amplitude oscillation because the flow supplies the energy lost by the tissue damping. Tissue mass and stiffness were varied locally or uniformly. Decreased stress in the longitudinal string tension produced subharmonic and chaotic vibrations in the displacement, velocity and acceleration phase diagrams. Similar vibratory characteristics also appeared in pathological speech data analyzed using time domain jitter and shimmer measures and a harmonics-to-noise ratio metric. The subharmonics create an effect that has been perceptually described as diplophonia.     

The dynamics of length change in canine vocal folds

The time courses of vocal fold elongation and contraction have beenmeasured as a function of intrinsic laryngeal muscle activity. The superior and recurrent laryngeal nerves of anesthetized canines were stimulated supramaximally (on-off in all combinations) while the vocal folds were surgically exposed and illuminated for conventional and higher speed (300 frames per second) video recording. Microsutures were placed on various points on the vocal folds to measure elongation and contraction. Vocal fold strain, defined as elongation divided by rest length, ranged from −17% to +45%. The typical time constant for exponential increase or decrease in strain was about 30 ms. This reflects primarily the intrinsic muscle activation times rather than a passive (inertial or viscoelastic) response of cricothyroid joint rotation or translation.     

Stroboscopic signs associated with benign lesions of the vocal folds

Stroboscopic signs were systematically rated for a group of 80 patients with benign vocal fold lesions, most of whom had either a nodule or a polyp. Each group revealed a characteristic pattern of ranking of signs and exhibited differences of most predominant signs. The results of the ratings were submitted to a multiple discriminant analysis to determine if post hoc stroboscopic ratings could be used to correctly classify patients into one of four diagnostic groups and into one of two treatment groups. All patients except one were correctly classified into the diagnostic groups, and all were correctly classified into the treatment groups. The important signs for classifying patients into the diagnostic groups were roughness of the edge of the affected vocal fold, phase closure pattern, and phase symmetry. The important signs for classifying patients into the treatment groups were roughness of the edge of the affected vocal fold, glottal closure configuration, and vibration characteristics of the affected (or more affected) vocal fold. The results suggest that objective evaluation of stroboscopic examinations can be valuable in correctly diagnosing patients and in selecting the proper treatment regimen for the patient.     

Unsteady behavior of flow in a scaled-up vocal folds model

Measurements of the fluid flow through a scaled-up model of the human glottis are presented to determine whether glottal flow may be approximated as unsteady. Time- and space-resolved velocity vector fields from digital particle image velocimetry (DPIV) measurements of the flow through the gap between two moving, rigid walls are presented in four cases, over a range of Strouhal numbers: 0.010, 0.018, 0.035, 0.040, corresponding to life-scale f(0) of 30, 58, 109, and 126 Hz, respectively, at a Reynolds number of 8000. It is observed that (1) glottal flow onset is delayed after glottal opening and (2) glottal flow shutoff occurs prior to closure. A comparison between flow through a fully open, nonmoving glottis and that through the moving vocal folds shows a marked difference in spatial structure of the glottal jet. The following features of the flow are seen to exhibit strong dependence on cycle frequency: (a) glottal exit plane velocity, (b) volume flow, (c) vortex shedding rates, and (d) vortex amplitude. Vortex shedding appears to be a factor both in controlling flow resistance and in cycle-to-cycle volume flow variations. All these observations strongly suggest that glottal flow is inherently unsteady.     

Mechanisms of irregular vibration in a physical model of the vocal folds

Previous investigations have shown that one mechanism of irregular vocal fold vibration may be a desynchronization of two or more vibratory modes of the vocal fold tissues. In the current investigation, mechanisms of irregular vibration were further examined using a self-oscillating, physical model of vocal fold vibration, a hemi-model methodology, and high-speed, stereoscopic, digital imaging. Using the method of empirical eigen-functions, a spatiotemporal analysis revealed mechanisms of irregular vibration in subharmonic phonation and biphonation, which were not disclosed in a standard acoustic spectrum.     

Rijke热声振荡的非线性效应

本文研究了Rjike管热声振荡的非线性效应,指出了引起非线性效应的两个因素,即热声相互作用的非线性和声波在管子末端的非线性辐射声阻,并通过计算声波振幅的增长率和实验分析声波的频谱,发现非线性效应限制了管内声波振幅的增长,并且导致了二次及高阶谐波的产生。     

Botox for hyperadduction of the false vocal folds: A case report

We present a patient with severe hyperadduction of the false vocal folds (FVF) treated with Botulinum Toxin injections to each FVF. This patient presented with severe dysphonia and was found to demonstrate severe hyperadduction of the FVF's with all phonatory tasks. The patient was treated with extensive speech therapy without improvement in voice quality nor FVF motion pattern. He was then injected with Botox A bilaterally using a peroral approach to the FVFs. Shortly after treatment the patient experienced dramatic improvement in voice quality. Videolaryngoscopy revealed no adduction of the FVFs with phonation and essentially normal true vocal fold motion. He remained with normal voice quality one year after treatment without any further treatment. Possible mechanism of action of this type of treatment are discussed.     

Model for vocalization by a bird with distensible vocal cavity and open beak

Some birds make use of a distensible oral cavity to produce nearly pure-tone song. Songbirds such as the Northern cardinal (Cardinalis cardinalis) have a muscularly distended oropharyngeal-esophageal cavity between the top of the trachea and the open beak. The present paper analyzes the acoustics of this vocal system. It is shown that the resonance of the oropharyngeal-esophageal cavity, vented through the beak, introduces a dominant peak in the radiation efficiency, the frequency of which can be adjusted by varying the volume of the cavity, the beak gape, and perhaps the position of the tongue in the mouth. To produce nearly pure-tone song, the bird adjusts the frequency of this peak to coincide with the fundamental of the syringeal oscillation. The present paper provides the acoustical analysis underlying this behavior.     

Verification of two minimally invasive methods for the estimation of the contact pressure in human vocal folds during phonation

The contact pressure on the vocal fold surface during high pitch or amplitude voice production is believed to be one major source of phonotrauma. Models for the quantitative estimate of the contact pressure may be valuable for prevention and treatment. Various indirect and minimally invasive approaches have been purported to estimate contact pressure. But the accuracy of these methods has not yet been objectively verified in controlled laboratory settings. In the present study, two indirect approaches for the estimation of the contact pressure were investigated. One is based on a Hertzian impact model, and the other on a finite element model. A probe microphone was used for direct measurements of the contact pressure and verifications of the indirect approaches. A silicone replica of human vocal folds was used as a test bed. Consistent contact pressure estimations were obtained using all three methods. The advantages and disadvantages of each approach for eventual clinical applications are described.     

The effects of excessive vocalization on acoustic and videostroboscopic measures of vocal fold condition

Although dysphonia is a recognized consequence of acute vocal abuse, associated changes in vocal fold appearance and function are not well understood. To document these presumed effects of vocal abuse, audio recordings of sustained vowel production were obtained from 42 drill sergeants daily during the first 6 days of a vocally demanding training exercise. Acoustic analysis showed abnormal levels of jitter and shimmer on Day 1 in 16 of the 42 subjects. Considering only the 26 subjects who showed normal voice acoustics on Day 1, the median levels of jitter and shimmer varied little over the course of training, and significant increases in jitter and shimmer were not seen during the study period. However, the distributions for both jitter and shimmer became more positively skewed and showed a greater number of positive outliers over the course of training. This trend was attributed to 11 subjects who showed two or more instances of abnormal voice acoustics over Days 2 through 6. Laryngeal videostroboscopic recordings of sustained vowel production also were obtained prior to and following training. Perceptual ratings of these recordings by 2 observers revealed significant increases in vocal fold edema, erythema, and edge irregularity, and decreases in vocal fold mucosal wave and amplitude of excursion following the 5-day training period. In general, there was considerable intersubject variability in the extent of acoustic and videostroboscopic effects over the course of training. Of the two types of data, videostroboscopy appears to provide a more sensitive indication of the effects of excessive vocalization.