Effects of poroelastic coefficients on normal vibration modes in vocal-fold tissues

The vocal-fold tissue is treated as a transversally isotropic fluid-saturated porous material. Effects of poroelastic coefficients on eigenfrequencies and eigenmodes of the vocal-fold vibration are investigated using the Ritz method. The study demonstrates that the often-used elastic model is only a particular case of the poroelastic model with an infinite fluid-solid mass coupling parameter. The elastic model may be considered appropriate for the vocal-fold tissue when the absolute value of the fluid-solid mass coupling parameter is larger than 10(5) kg/m(3). Otherwise, the poroelastic model may be more accurate. The degree of compressibility of the vocal tissue can also been described by the poroelastic coefficients. Finally, it is revealed that the liquid and solid components in a poroelastic model could have different modal shapes when the coupling between them is weak. The mode decoupling could cause desynchronization and irregular vibration of the folds.     

A mechanical model of vocal-fold collision with high spatial and temporal resolution

The tissue mechanics governing vocal-fold closure and collision during phonation are modeled in order to evaluate the role of elastic forces in glottal closure and in the development of stresses that may be a risk factor for pathology development. The model is a nonlinear dynamic contact problem that incorporates a three-dimensional, linear elastic, finite-element representation of a single vocal fold, a rigid midline surface, and quasistatic air pressure boundary conditions. Qualitative behavior of the model agrees with observations of glottal closure during normal voice production. The predicted relationship between subglottal pressure and peak collision force agrees with published experimental measurements. Accurate predictions of tissue dynamics during collision suggest that elastic forces play an important role during glottal closure and are an important determinant of aerodynamic variables that are associated with voice quality. Model predictions of contact force between the vocal folds are directly proportional to compressive stress (r2 = 0.79), vertical shear stress (r2 = 0.69), and Von Mises stress (r2 = 0.83) in the tissue. These results guide the interpretation of experimental measurements by relating them to a quantity that is important in tissue damage.     

What happens during vocal warm-up?

Most singers prefer to warm up their voices before performing. Although the subjective effect is often considerable, the underlying physiological effects are largely unknown. Because warm-up tends to increase blood flow in muscles, it seems likely that vocal warm-up might induce decreased viscosity in the vocal folds. According to the theory of vocal-fold vibration, such a decrease should lead to a lower phonation threshold pressure. In this investigation the effect of vocal warm-up on the phonation threshold pressure was examined in a group of male and female singers. The effect varied considerably between subjects, presumably because the vocal-fold viscosity was not a dominating factor for the phonation-threshold pressure.     

Parameter estimation of an asymmetric vocal-fold system from glottal area time series using chaos synchronization

In this paper, we apply an iterative parameter adaption scheme based on chaos synchronization to estimate system parameters of the asymmetric vocal folds from glottal area time series. The original asymmetric vocal-fold system associated with recurrent laryngeal paralysis shows chaotic vibrations with positive Lyapunov exponents. Aperiodic glottal area time series from the original system will be applied as the feedback variable coupling the simulative and the original vocal-fold systems. The parameter adaption technique based on chaos synchronization is employed to manipulate the simulative system parameters. The chaotic vibrations, system parameters, and the bifurcation diagram of the original vocal-fold system can be exactly reproduced in the simulative system, and the two chaotic systems can be synchronized. Furthermore, the effects of noise, sampling rate, and equation difference due to nonlinear spring terms on vocal-fold parameter estimations are investigated. Despite large noise perturbations, large equation differences, and low sampling rate, the parameter adaption scheme can effectively estimate the original vocal-fold system parameters. This study provides a theoretical base to apply chaos synchronization to estimate the vocal-fold system parameters from the glottal area data and show its potential application in laryngeal physiology.     

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 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.     

Two parametric voice source models and their asymptotic analysis

The paper studies the asymptotic behavior of the function for the area of the glottis near moments of its opening and closing for two mathematical voice source models. It is shown that in the first model, the asymptotics of the area function obeys a power law with an exponent of no less that 1. Detailed analysis makes it possible to refine these limits depending on the relative sizes of the intervals of a closed and open glottis. This work also studies another parametric model of the area of the glottis, which is based on a simplified physical-geometrical representation of vocal-fold vibration processes. This is a special variant of the well-known two-mass model and contains five parameters: the period of the main tone, equivalent masses on the lower and upper edge of vocal folds, the coefficient of elastic resistance of the lower vocal fold, and the delay time between openings of the upper and lower folds. It is established that the asymptotics of the obtained function for the area of the glottis obey a power law with an exponent of 1 both for opening and closing.     

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.     

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.     

A flow waveform-matched low-dimensional glottal model based on physical knowledge

The purpose of this study is to explore the possibility for physically based mathematical models of the voice source to accurately reproduce inverse filtered glottal volume-velocity waveforms. A low-dimensional, self-oscillating model of the glottal source with waveform-matching properties is proposed. The model relies on a lumped mechano-aerodynamic scheme loosely inspired by the one- and multimass lumped models. The vocal folds are represented by a single mechanical resonator and a propagation line which takes into account the vertical phase differences. The vocal-fold displacement is coupled to the glottal flow by means of an aerodynamic driving block which includes a general parametric nonlinear component. The principal characteristics of the flow-induced oscillations are retained, and the overall model is able to match inverse-filtered glottal flow signals. The method offers in principle the possibility of performing transformations of the glottal flow by acting on the physiologically based parameters of the model. This is a desirable property, e.g., for speech synthesis applications. The model was tested on a data set which included inverse-filtered glottal flow waveforms of different characteristics. The results demonstrate the possibility of reproducing natural speech waveforms with high accuracy, and of controlling important characteristics of the synthesis such as pitch.     

Anterior-posterior biphonation in a finite element model of vocal fold vibration

In this paper, a finite-element model is used to simulate anterior-posterior biphonation [Neubauer et al., J. Acoust. Soc. Am. 110(6), 3179-3192 (2001)]. The anterior-posterior stiffness asymmetric factor and the anterior-posterior shape asymmetric factor describe the asymmetry properties of vocal folds. Spatiotemporal plot, spectral analysis, anterior-posterior fundamental frequency ratio, cross covariation function, and correlation length quantitatively estimate the spatial asymmetry of vocal fold oscillations. Calculation results show that the anterior-posterior stiffness asymmetry decreases the spatial coherence of vocal fold vibration. When the stiffness asymmetry reaches a certain level, the drop in spatial coherence desynchronizes the vibration modes. The anterior and posterior sides of the vocal fold oscillate with two independent fundamental frequencies (f(a) and f(p)). The complex spectral characteristics of vocal fold vibration under biphonation conditions can be explained by the linear combination of f(a) and f(p). Empirical orthogonal eigenfunctions prove the existence of higher-order anterior-posterior modes when anterior-posterior biphonation occurs. Then, it is found that the anterior-posterior shape asymmetry also decreases the spatial coherence of vocal fold vibration, and shape asymmetry is a possible reason for anterior-posterior biphonation.     

Unsteady flow through in-vitro models of the glottis

The unsteady two-dimensional flow through fixed rigid in vitro models of the glottis is studied in some detail to validate a more accurate model based on the prediction of boundary-layer separation. The study is restricted to the flow phenomena occurring within the glottis and does not include effects of vocal-fold movement on the flow. Pressure measurements have been carried out for a transient flow through a rigid scale model of the glottis. The rigid model with a fixed geometry driven by an unsteady pressure is used in order to achieve a high accuracy in the specification of the geometry of the glottis. The experimental study is focused on flow phenomena as they might occur in the glottis, such as the asymmetry of the flow due to the Coanda effect and the transition to turbulent flow. It was found that both effects need a relatively long time to establish themselves and are therefore unlikely to occur during the production of normal voiced speech when the glottis closes completely during part of the oscillation cycle. It is shown that when the flow is still laminar and symmetric the prediction of the boundary-layer model and the measurement of the pressure drop from the throat of the glottis to the exit of the glottis agree within 40%. Results of the boundary-layer model are compared with a two-dimensional vortex-blob method for viscous flow. The difference between the results of the simpiflied boundary-layer model and the experimental results is explained by an additional pressure difference between the separation point and the far field within the jet downstream of the separation point. The influence of the movement of the vocal folds on our conclusions is still unclear.     

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.     

Measurement of Characteristic Leap Interval Between Chest and Falsetto Registers

A markedly smaller time constant distinguishes a chest-falsetto leap from the more usual execution of a sung interval by muscular adjustments in the length and tension of the vocal folds. The features of such a chest-falsetto leap are examined in detail with respect to F0, peak-to-peak amplitude of the vocal-fold contact area signal (EGG), and the closed quotient. A method is proposed to standardize and quantify this chest-falsetto leap in the characteristic leap interval (CLI), a measure of the separation between the natural registers in a given singing voice. The measure is applied to a varied group of experienced singers. Preliminary results include a suggested dimorphic pattern with respect to sex, with female voices exhibiting smaller CLIs and less individual diversity than male voices.     

Irregular vocal-fold vibration--high-speed observation and modeling

Direct observations of nonstationary asymmetric vocal-fold oscillations are reported. Complex time series of the left and the right vocal-fold vibrations are extracted from digital high-speed image sequences separately. The dynamics of the corresponding high-speed glottograms reveals transitions between low-dimensional attractors such as subharmonic and quasiperiodic oscillations. The spectral components of either oscillation are given by positive linear combinations of two fundamental frequencies. Their ratio is determined from the high-speed sequences and is used as a parameter of laryngeal asymmetry in model calculations. The parameters of a simplified asymmetric two-mass model of the larynx are preset by using experimental data. Its bifurcation structure is explored in order to fit simulations to the observed time series. Appropriate parameter settings allow the reproduction of time series and differentiated amplitude contours with quantitative agreement. In particular, several phase-locked episodes ranging from 4:5 to 2:3 rhythms are generated realistically with the model.     

Material parameter computation for multi-layered vocal fold models

Today, the prevention and treatment of voice disorders is an ever-increasing health concern. Since many occupations rely on verbal communication, vocal health is necessary just to maintain one's livelihood. Commonly applied models to study vocal fold vibrations and air flow distributions are self sustained physical models of the larynx composed of artificial silicone vocal folds. Choosing appropriate mechanical parameters for these vocal fold models while considering simplifications due to manufacturing restrictions is difficult but crucial for achieving realistic behavior. In the present work, a combination of experimental and numerical approaches to compute material parameters for synthetic vocal fold models is presented. The material parameters are derived from deformation behaviors of excised human larynges. The resulting deformations are used as reference displacements for a tracking functional to be optimized. Material optimization was applied to three-dimensional vocal fold models based on isotropic and transverse-isotropic material laws, considering both a layered model with homogeneous material properties on each layer and an inhomogeneous model. The best results exhibited a transversal-isotropic inhomogeneous (i.e., not producible) model. For the homogeneous model (three layers), the transversal-isotropic material parameters were also computed for each layer yielding deformations similar to the measured human vocal fold deformations.     

Nonlinear analysis of irregular animal vocalizations

Animal vocalizations range from almost periodic vocal-fold vibration to completely atonal turbulent noise. Between these two extremes, a variety of nonlinear dynamics such as limit cycles, subharmonics, biphonation, and chaotic episodes have been recently observed. These observations imply possible functional roles of nonlinear dynamics in animal acoustic communication. Nonlinear dynamics may also provide insight into the degree to which detailed features of vocalizations are under close neural control, as opposed to more directly reflecting biomechanical properties of the vibrating vocal folds themselves. So far, nonlinear dynamical structures of animal voices have been mainly studied with spectrograms. In this study, the deterministic versus stochastic (DVS) prediction technique was used to quantify the amount of nonlinearity in three animal vocalizations: macaque screams, piglet screams, and dog barks. Results showed that in vocalizations with pronounced harmonic components (adult macaque screams, certain piglet screams, and dog barks), deterministic nonlinear prediction was clearly more powerful than stochastic linear prediction. The difference, termed low-dimensional nonlinearity measure (LNM), indicates the presence of a low-dimensional attractor. In highly irregular signals such as juvenile macaque screams, piglet screams, and some dog barks, the detectable amount of nonlinearity was comparatively small. Analyzing 120 samples of dog barks, it was further shown that the harmonic-to-noise ratio (HNR) was positively correlated with LNM. It is concluded that nonlinear analysis is primarily useful in animal vocalizations with strong harmonic components (including subharmonics and biphonation) or low-dimensional chaos.     

Effects of consonant manner and vowel height on intraoral pressure and articulatory contact at voicing offset and onset for voiceless obstruents

In obstruent consonants, a major constriction in the upper vocal tract yields an increase in intraoral pressure (P(io)). Phonation requires that subglottal pressure (P(sub)) exceed P(io) by a threshold value, so as the transglottal pressure reaches the threshold, phonation will cease. This work investigates how P(io) levels at phonation offset and onset vary before and after different German voiceless obstruents (stop, fricative, affricates, clusters), and with following high vs low vowels. Articulatory contacts, measured using electropalatography, were recorded simultaneously with P(io) to clarify how supraglottal constrictions affect P(io). Effects of consonant type on phonation thresholds could be explained mainly in terms of the magnitude and timing of vocal-fold abduction. Phonation offset occurred at lower values of P(io) before fricative-initial sequences than stop-initial sequences, and onset occurred at higher levels of P(io) following the unaspirated stops of clusters compared to fricatives, affricates, and aspirated stops. The vowel effects were somewhat surprising: High vowels had an inhibitory effect at voicing offset (phonation ceasing at lower values of P(io)) in short-duration consonant sequences, but a facilitating effect on phonation onset that was consistent across consonantal contexts. The vowel influences appear to reflect a combination of vocal-fold characteristics and vocal-tract impedance.