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

Subject-Specific Computational Fluid-Structure Interaction Modeling of Rabbit Vocal Fold Vibration

A full three-dimensional (3D) fluid-structure interaction (FSI) study of subject-specific vocal fold vibration is carried out based on the previously reconstructed vocal fold models of rabbit larynges. Our primary focuses are the vibration characteristics of the vocal fold, the unsteady 3D flow field, and comparison with a recently developed 1D glottal flow model that incorporates machine learning. The 3D FSI model applies strong coupling between the finite-element model for the vocal fold tissue and the incompressible Navier-Stokes equation for the flow. Five different samples of the rabbit larynx, reconstructed from the magnetic resonance imaging (MRI) scans after the in vivo phonation experiments, are used in the FSI simulation. These samples have distinct geometries and a different inlet pressure measured in the experiment. Furthermore, the material properties of the vocal fold tissue were determined previously for each individual sample. The results demonstrate that the vibration and the intraglottal pressure from the 3D flow simulation agree well with those from the 1D flow model based simulation. Further 3D analyses show that the inferior and supraglottal geometries play significant roles in the FSI process. Similarity of the flow pattern with the human vocal fold is discussed. This study supports the effective usage of rabbit larynges to understand human phonation and will help guide our future computational studies that address vocal fold disorders.

Vortex Formation Times in the Glottal Jet, Measured in a Scaled-Up Model

In this paper, the timing of vortex formation on the glottal jet is studied using previously published velocity measurements of flow through a scaled-up model of the human vocal folds. The relative timing of the pulsatile glottal jet and the instability vortices are acoustically important since they determine the harmonic and broadband content of the voice signal. Glottis exit jet velocity time series were extracted from time-resolved planar DPIV measurements. These measurements were acquired at four glottal flow speeds (u_SS = 16.1–38 cm/s) and four glottis open times (T_o = 5.67–23.7 s), providing a Reynolds number range Re = 4100–9700 and reduced vibration frequency f* = 0.01–0.06. Exit velocity waveforms showed temporal behavior on two time scales, one that correlates to the period of vibration and another characterized by short, sharp velocity peaks (which correlate to the passage of instability vortices through the glottis exit plane). The vortex formation time, estimated by computing the time difference between subsequent peaks, was shown to be not well-correlated from one vibration cycle to the next. The principal finding is that vortex formation time depends not only on cycle phase, but varies strongly with reduced frequency of vibration. In all cases, a strong high-frequency burst of vortex motion occurs near the end of the cycle, consistent with perceptual studies using synthesized speech.

Phase-averaged and cycle-to-cycle analysis of jet dynamics in a scaled up vocal-fold model

Phase-averaged and cycle-to-cycle analysis of key contributors to sound production in phonation is examined in a scaled-up vocal-fold model. Simultaneous temporally and spatially resolved pressure and velocity measurements permitted examination of each term in the streamwise integral momentum equation. The relative sizes of these terms were used to address the issue of whether transglottal pressure is a surrogate for vocal-fold drag, a quantity directly related to sound production. Further, time traces of transglottal pressure and volume flow rate provided insight into the role of cycle-to-cycle variations in voiced sound production which affect voice quality. Experiments were conducted using a 10× scaled-up model in a free-surface water tunnel. Two-dimensional vocal-fold models with semi-circular ends inside a square duct were driven with constant opening and closing speeds. The time from opening to closed, T_o , was half the oscillation period. Time-resolved digital particle image velocimetry (DPIV) and pressure measurements along the duct centreline were made for 3650 ≤ Re ≤ 8100 and equivalent life frequencies from 52.5 to 97.5 Hz. Results showed that transglottal pressure does serve as a surrogate for the vocal-fold drag. However, smaller but non-negligible momentum flux and inertia terms, caused by the jet and vocal-fold motions, may also contribute to vocal-fold drag. Further, cycle-to-cycle variations including jet switching and modulation are inherent in flows of this type despite their high degrees of symmetry and repeatability. The origins of these variations and their potential role in sound production and voice quality are discussed.

Cycle-to-cycle flow variations in a square duct with a symmetrically oscillating constriction

Spatially and temporally resolved Digital Particle Image Velocimetry (DPIV) measurements are presented of flow complexities in a nominally two-dimensional, symmetric, duct with an oscillating constriction. The motivation for this research lies in advancing the state-of-the-art in applying integral control volume analysis to modeling unsteady internal flows. The specific target is acoustic modeling of human phonation. The integral mass and momentum equations are directly coupled to the acoustic equations and provide quantitative insight into acoustic source strengths in addition to the dynamics of the fluid-structure interactions in the glottis. In this study, a square cross-section duct was constructed with symmetric, computer controlled, oscillating constrictions that incorporate both rocking as well as oscillatory open/close motions. Experiments were run in a free-surface water tunnel over a Strouhal number range, based on maximum jet speed and model length, of 0.012 - 0.048, for a fixed Reynolds number, based on maximum gap opening and maximum jet speed, of 8000. In this study, the constriction motions were continuous with one open-close cycle immediately following another. While the model and its motions were nominally two-dimensional and symmetric, flow asymmetries and oscillation frequency dependent cycle-to-cycle variations were observed. These are examined in the context of terms in the integral conservation equations.

Analysis of the aerodynamic sound of speech through static vocal tract models of various glottal shapes

The acoustic spectrum of our voice can be divided into harmonic and inharmonic sound components. While the harmonic components, generated by the oscillatory motion of the vocal folds, are well described by reduced-order speech models, the accurate computation of the inharmonic components requires high-order flow simulations, which predict the vortex shedding and turbulent structures present in the shear layers of the glottal jet. This study characterizes the dominant frequencies in the unsteady flow of the intra- and supraglottal region. A realistic vocal tract geometry obtained through magnetic resonance imaging (MRI) is applied for the numerical domain, which is locally modified to account for different convergent and divergent glottal angles. Both time-averaged and fluctuating values of the flow variables are computed and their distribution at various glottal shapes is compared. The impact of the registered modes in the unsteady flow on the acoustic far field is computed through direct compressible flow simulations. Furthermore, acoustic analogies are applied to localize the sources of the aerodynamically generated sound.

Magnetic resonance imaging-based measurement of internal deformation of vibrating vocal fold models

A method is presented for tracking the internal deformation of self-oscillating vocal fold models using magnetic resonance imaging (MRI). Silicone models scaled to four times life-size to lower the flow-induced vibration frequency were embedded with fiducial markers in a coronal plane. Candidate marker materials were tested using static specimens, and two materials, cupric sulfate and glass, were chosen for testing in the vibrating vocal fold models. The vibrating models were imaged using a gated MRI protocol wherein MRI acquisition was triggered using the subglottal pressure signal. Two-dimensional image slices at different phases during self-oscillation were captured, and in each phase the fiducial markers were clearly visible. The process was also demonstrated using a three-dimensional scan at two phases. The benefit of averaging to increase signal-to-noise ratio was explored. The results demonstrate the ability to use MRI to acquire quantitative deformation data that could be used, for example, to validate computational models of flow-induced vocal fold vibration and quantify deformation fields encountered by cells in bioreactor studies.

Fully-coupled aeroelastic simulation with fluid compressibility - For application to vocal fold vibration

In this study, a fully-coupled fluid-structure interaction model is developed for studying dynamic interactions between compressible fluid and aeroelastic structures. The technique is built based on the modified Immersed Finite Element Method (mIFEM), a robust numerical technique to simulate fluid-structure interactions that has capabilities to simulate high Reynolds number flows and handles large density disparities between the fluid and the solid. For accurate assessment of this intricate dynamic process between compressible fluid, such as air and aeroelastic structures, we included in the model the fluid compressibility in an isentropic process and a solid contact model. The accuracy of the compressible fluid solver is verified by examining acoustic wave propagations in a closed and an open duct, respectively. The fully-coupled fluid-structure interaction model is then used to simulate and analyze vocal folds vibrations using compressible air interacting with vocal folds that are represented as layered viscoelastic structures. Using physiological geometric and parametric setup, we are able to obtain a self-sustained vocal fold vibration with a constant inflow pressure. Parametric studies are also performed to study the effects of lung pressure and vocal fold tissue stiffness in vocal folds vibrations. All the case studies produce expected airflow behavior and a sustained vibration, which provide verification and confidence in our future studies of realistic acoustical studies of the phonation process.

Evaluation of aerodynamic characteristics of a coupled fluid-structure system using generalized Bernoulli's principle: An application to vocal folds vibration

In this work we explore the aerodynamics flow characteristics of a coupled fluid-structure interaction system using a generalized Bernoulli equation derived directly from the Cauchy momentum equations. Unlike the conventional Bernoulli equation where incompressible, inviscid, and steady flow conditions are assumed, this generalized Bernoulli equation includes the contributions from compressibility, viscous, and unsteadiness, which could be essential in defining aerodynamic characteristics. The application of the derived Bernoulli's principle is on a fully-coupled fluid-structure interaction simulation of the vocal folds vibration. The coupled system is simulated using the immersed finite element method where compressible Navier-Stokes equations are used to describe the air and an elastic pliable structure to describe the vocal fold. The vibration of the vocal fold works to open and close the glottal flow. The aerodynamics flow characteristics are evaluated using the derived Bernoulli's principles for a vibration cycle in a carefully partitioned control volume based on the moving structure. The results agree very well to experimental observations, which validate the strategy and its use in other types of flow characteristics that involve coupled fluid-structure interactions.

The mechanisms of subharmonic tone generation in a synthetic larynx model

The sound spectra obtained in a synthetic larynx exhibited subharmonic tones that are characteristic for diplophonia. Although the generation of subharmonics is commonly associated with asymmetrically oscillating vocal folds, the synthetic elastic vocal folds showed symmetrical oscillations. The amplitudes of the subharmonics decreased with an increasing lateral diameter of the supraglottal channel, which indicates a strong dependence of the supraglottal boundary conditions. Investigations of the supraglottal flow field revealed small cycle-to-cycle variations of the static pressure in the region of the pulsatile glottal jet as the origin of the first subharmonic tone. It is located at half the fundamental frequency of the vocal fold oscillation. A principle component analysis of the supraglottal flow field with the fully developed glottal jet revealed a large recirculation area in the second spatial eigenvector which deflected the glottal jet slightly in a perpendicular direction of the jet axis. The rotation direction of the recirculation area changed with different oscillation cycles between clockwise and counterclockwise. As both directions were uniformly distributed across all acquired oscillation cycles, a cycle-wise change can be assumed. It is concluded that acoustic subharmonics are generated by small fluctuations of the glottal jet location favored by small lateral diameters of the supraglottal channel.

Intraglottal velocity and pressure measurements in a hemilarynx model

Determining the mechanisms of self-sustained oscillation of the vocal folds requires characterization of the pressures produced by intraglottal aerodynamics. Because most of the intraglottal aerodynamic forces cannot be measured in a tissue model of the larynx, current understanding of vocal fold vibration mechanism is derived from mechanical, analytical, and computational models. Previous studies have computed intraglottal pressures from measured intraglottal velocity fields and intraglottal geometry; however, this technique for determining pressures is not yet validated. In this study, intraglottal pressure measurements taken in a hemilarynx model are compared with pressure values that are computed from simultaneous velocity measurements. The results showed that significant negative pressure formed near the superior aspect of the folds during closing, which agrees with previous measurements in other hemilarynx models. Intraglottal velocity measurements show that the flow near the superior aspect separates from the glottal wall during closing and may develop into a vortex, which further augments the magnitude of negative pressure. Intraglottal pressure distributions, computed by solving the pressure Poisson equation, showed good agreement with pressure measurements. The match between the pressure computations and its measurements validates the current technique, which was previously used to estimate intraglottal pressure distribution in a full larynx model.

Computational study of effects of tension imbalance on phonation in a three-dimensional tubular larynx model

OBJECTIVES

The present study explores the use of a continuum-based computational model to investigate the effect of left-right tension imbalance on vocal fold (VF) vibrations and glottal aerodynamics, as well as its implication on phonation. The study allows us to gain new insights into the underlying physical mechanism of irregularities induced by VF tension imbalance associated with unilateral cricothyroid muscle paralysis.

METHODS

A three-dimensional simulation of glottal flow and VF dynamics in a tubular laryngeal model with tension imbalance was conducted by using a coupled flow-structure interaction computational model. Tension imbalance was modeled by reducing by 20% the Young's modulus of one of the VFs, while holding VF length constant. Effects of tension imbalance on vibratory characteristic of the VFs and on the time-varying properties of glottal airflow as well as the aerodynamic energy transfer are comprehensively analyzed.

RESULTS AND CONCLUSIONS

The analysis demonstrates that the continuum-based biomechanical model can provide a good description of phonatory dynamics in tension imbalance conditions. It is found that although 20% tension imbalance does not have noticeable effects on the fundamental frequency, it does lead to a larger glottal flow leakage and asymmetric vibrations of the two VFs. A detailed analysis of the energy transfer suggests that the majority of the energy is consumed by the lateral motion of the VFs and the net energy transferred to the softer fold is less than the one transferred to the normal fold.

Intraglottal pressure distribution computed from empirical velocity data in canine larynx

Intraglottal velocity measurements were taken using particle image velocimetry and the corresponding estimates for the intraglottal pressure were computed using the pressure Poisson equation. Results from five canine larynges showed that when the flow separated from the divergent glottal walls during closing, the vortices that were formed in the separated region of the glottis created negative pressure near the superior aspect of the folds. The magnitude of the negative pressure was directly proportional to the subglottal pressure. At low subglottal pressure, negative pressures at the superior edge were not observed when the divergence angle of the wall was minimal and the glottal flow did not separate from the wall.

Influence of vortical flow structures on the glottal jet location in the supraglottal region

Within the fully coupled multiphysics phonation process, the fluid flow plays an important role for sound production. This study addresses phenomena in the flow downstream of synthetic self-oscillating vocal folds. An experimental setup consisting of devices for producing and conditioning the flow including the main test channel was applied. The supraglottal channel was designed to prevent an acoustic coupling to the vocal folds. Hence, the oscillations were aerodynamically driven. The cross-section of the supraglottal channel was systematically varied by increasing the distance between the lateral channel walls. The vocal folds consisted of silicone rubber of homogenous material distribution generating self-sustained oscillations. The airflow was visualized in the immediate supraglottal region using a laser-sheet technique and a digital high-speed camera. Furthermore, the flow was studied by measuring the static pressure distributions on both lateral supraglottal channel walls. The results clearly showed different flow characteristics depending on the supraglottal configuration. In all cases with supraglottal channel, the jet was located asymmetrical and bent in medial-lateral direction. Furthermore, the side to which the jet was deflected changed in between the consecutive cycles showing a bifurcational behavior. Previously, this phenomenon was explained by the Coanda effect. However, the present data suggest that the deflection of the jet was mainly caused by large air vortices in the supraglottal channel produced by the flow field of previous oscillations. In contrast, for the case without supraglottal channel, the air jet was found totally symmetrical stabilized by the constant pressure in the ambient region. The emitted sound signal showed additional subharmonic tonal peaks for the asymmetric flow cases, which are characteristics for diplophonia.

Computational modeling of phonatory dynamics in a tubular three-dimensional model of the human larynx

Simulation of the phonatory flow-structure interaction has been conducted in a three-dimensional, tubular shaped laryngeal model that has been designed with a high level of realism with respect to the human laryngeal anatomy. A non-linear spring-based contact force model is also implemented for the purpose of representing contact in more general conditions, especially those associated with three-dimensional modeling of phonation in the presence of vocal fold pathologies. The model is used to study the effects of a moderate (20%) vocal-fold tension imbalance on the phonatory dynamics. The characteristic features of phonation for normal as well as tension-imbalanced vocal folds, such as glottal waveform, glottal jet evolution, mucosal wave-type vocal-fold motion, modal entrainment, and asymmetric glottal jet deflection have been discussed in detail and compared to established data. It is found that while a moderate level of tension asymmetry does not change the vibratory dynamics significantly, it can potentially lead to measurable deterioration in voice quality.

Relation of structural and vibratory kinematics of the vocal folds to two acoustic measures of breathy voice based on computational modeling

PURPOSE

To relate vocal fold structure and kinematics to 2 acoustic measures: cepstral peak prominence (CPP) and the amplitude of the first harmonic relative to the second (H1-H2).

METHOD

The authors used a computational, kinematic model of the medial surfaces of the vocal folds to specify features of vocal fold structure and vibration in a manner consistent with breathy voice. Four model parameters were altered: degree of vocal fold adduction, surface bulging, vibratory nodal point, and supraglottal constriction. CPP and H1-H2 were measured from simulated glottal area, glottal flow, and acoustic waveforms and were related to the underlying vocal fold kinematics.

RESULTS

CPP decreased with increased separation of the vocal processes, whereas the nodal point location had little effect. H1-H2 increased as a function of separation of the vocal processes in the range of 1.0 mm to 1.5 mm and decreased with separation > 1.5 mm.

CONCLUSIONS

CPP is generally a function of vocal process separation. H1*-H2* (see paragraph 6 of article text for an explanation of the asterisks) will increase or decrease with vocal process separation on the basis of vocal fold shape, pivot point for the rotational mode, and supraglottal vocal tract shape, limiting its utility as an indicator of breathy voice. Future work will relate the perception of breathiness to vocal fold kinematics and acoustic measures.

Nonlinear vocal fold dynamics resulting from asymmetric fluid loading on a two-mass model of speech

Nonlinear vocal fold dynamics arising from asymmetric flow formations within the glottis are investigated using a two-mass model of speech with asymmetric vocal fold tensioning, representative of unilateral vocal fold paralysis. A refined theoretical boundary-layer flow solver is implemented to compute the intraglottal pressures, providing a more realistic description of the flow than the standard one-dimensional, inviscid Bernoulli flow solution. Vocal fold dynamics are investigated for subglottal pressures of 0.6 < p(s) < 1.5 kPa and tension asymmetries of 0.5 < Q < 0.8. As tension asymmetries become pronounced the asymmetric flow incites nonlinear behavior in the vocal fold dynamics at subglottal pressures that are associated with normal speech, behavior that is not captured with standard Bernoulli flow solvers. Regions of bifurcation, coexistence of solutions, and chaos are identified.

In vitro experimental investigation of voice production

The process of human phonation involves a complex interaction between the physical domains of structural dynamics, fluid flow, and acoustic sound production and radiation. Given the high degree of nonlinearity of these processes, even small anatomical or physiological disturbances can significantly affect the voice signal. In the worst cases, patients can lose their voice and hence the normal mode of speech communication. To improve medical therapies and surgical techniques it is very important to understand better the physics of the human phonation process. Due to the limited experimental access to the human larynx, alternative strategies, including artificial vocal folds, have been developed. The following review gives an overview of experimental investigations of artificial vocal folds within the last 30 years. The models are sorted into three groups: static models, externally driven models, and self-oscillating models. The focus is on the different models of the human vocal folds and on the ways in which they have been applied.

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.

Mechanism of and threshold biomechanical conditions for falsetto voice onset

The sound source of a voice is produced by the self-excited oscillation of the vocal folds. In modal voice production, a drastic increase in transglottal pressure after vocal fold closure works as a driving force that develops self-excitation. Another type of vocal fold oscillation with less pronounced glottal closure observed in falsetto voice production has been accounted for by the mucosal wave theory. The classical theory assumes a quasi-steady flow, and the expected driving force onto the vocal folds under wavelike motion is derived from the Bernoulli effect. However, wavelike motion is not always observed during falsetto voice production. More importantly, the application of the quasi-steady assumption to a falsetto voice with a fundamental frequency of several hundred hertz is unsupported by experiments. These considerations suggested that the mechanism of falsetto voice onset may be essentially different from that explained by the mucosal wave theory. In this paper, an alternative mechanism is submitted that explains how self-excitation reminiscent of the falsetto voice could be produced independent of the glottal closure and wavelike motion. This new explanation is derived through analytical procedures by employing only general unsteady equations of motion for flow and solids. The analysis demonstrated that a convective acceleration of a flow induced by rapid wall movement functions as a negative damping force, leading to the self-excitation of the vocal folds. The critical subglottal pressure and volume flow are expressed as functions of vocal fold biomechanical properties, geometry, and voice fundamental frequency. The analytically derived conditions are qualitatively and quantitatively reasonable in view of reported measurement data of the thresholds required for falsetto voice onset. Understanding of the voice onset mechanism and the explicit mathematical descriptions of thresholds would be beneficial for the diagnosis and treatment of voice diseases and the development of artificial vocal folds.

Intraglottal pressures in a three-dimensional model with a non-rectangular glottal shape

This study used a symmetric, three-dimensional, physical model of the larynx called M6 in which the transverse plane of the glottis is formed by sinusoidal arcs for each medial vocal fold surface, creating a maximum glottal width of 0.16 cm at the location of the minimal glottal area. Three glottal angles were studied: convergent 10 degrees, uniform (0 degrees), and divergent 10 degrees. Fourteen pressure taps were incorporated in the upstream-downstream direction on the vocal fold surface at three coronal locations, at the one-fourth, one-half, and three-fourths distances in the anterior-posterior direction of the glottis. The computational software FLUENT was used to compare and augment the data for these cases. Near the glottal entrance, the pressures were similar across the three locations for the uniform case; however, for the convergent case the middle pressure distribution was lower by 4% of the transglottal pressure, and lower by about 2% for the divergent case. Also, there were significant secondary velocities toward the center from both the anterior commissure and vocal process regions (of as much as approximately 10% of the axial velocities). Thus, the three dimensionality created relatively small pressure gradients and significant secondary velocities anteriorly-posteriorly within the glottis.

Dynamics of temporal variations in phonatory flow

This paper addresses the dynamic relevance of time variations of phonatory airflow, commonly neglected under the quasisteady phonatory flow assumption. In contrast to previous efforts, which relied on direct measurement of glottal impedance, this work uses spatially and temporally resolved measurements of the velocity field to estimate the unsteady and convective acceleration terms in the unsteady Bernoulli equation. Theoretical considerations suggest that phonatory flow is inherently unsteady when two related conditions apply: (1) that the unsteady and convective accelerations are commensurate, and (2) that the inertia of the glottal jet is non-negligible. Acceleration waveforms, computed from experimental data, show that unsteady and convective accelerations to be the same order of magnitude, throughout the cycle, and that the jet flow contributes significantly to the unsteady acceleration. In the middle of the cycle, however, jet inertia is negligible because the convective and unsteady accelerations nearly offset one another in the jet region. These results, consistent with previous findings treating quasisteady phonatory flow, emphasize that unsteady acceleration cannot be neglected during the final stages of the phonation cycle, during which voice sound power and spectral content are largely determined. Furthermore, glottal jet dynamics must be included in any model of phonatory airflow.

Three-dimensional nature of the glottal jet

The factors contributing to human voice production are not yet fully understood. Even normal human phonation with a symmetric glottal opening area is still the subject of extensive investigation. Among others, it has already been shown that fluid dynamics has a strong influence on the vocal process. The full characterization of the glottal jet has not been accomplished yet. Time-resolved measurement and visualization of the three-dimensional (3D) flow downstream the human vocal folds are difficult if not impossible to perform in vivo. Therefore, it is common to use mechanical and numerical models with a simplified shape and motion profile of the vocal folds. In this article, further results regarding the 3D flow structure obtained in a 3:1 up-scaled dynamic glottis model (cam model) in a water circuit are given, extending earlier work [M. Triep et al. (2005). Exp. Fluids 39, 232-245]. The model mimics the temporal variation in the 3D contour of the glottal gap while water flow reduces the characteristic frequencies by the order of 1/140. The unsteady flow processes downstream of the vocal folds are visualized in slow motion and analyzed in detail via particle imaging techniques. The visualization results show complex 3D flow behavior of lengthwise jet contraction and axis switching. In addition, the time-dependent flow rate during the phonatory oscillation cycle is measured in detail. It is shown that the pressure loss is decreased in the presence of a second constriction downstream of the glottis in form of ventricular folds and it is observed that for this case the jet is stabilized in the divergent phase of the cycle.

Analysis of flow-structure interaction in the larynx during phonation using an immersed-boundary method

A recently developed immersed-boundary method is used to model the flow-structure interaction associated with the human phonation. The glottal airflow is modeled as a two-dimensional incompressible flow driven by a constant subglottal pressure, and the vocal folds are modeled as a pair of three-layered, two-dimensional, viscoelastic structures. Both the fluid dynamics and viscoelasticity are solved on fixed Cartesian grids using a sharp-interface immersed boundary method. It is found that the vibration mode and frequency of the vocal fold model are associated with the eigenmodes of the structures, and that the transition of the vibration mode takes place during onset of the sustained vibration. The computed glottal waveforms of the volume flux, velocity, and pressure are reasonably realistic. The glottal flow features an unsteady jet whose direction is deflected by the large-scale vortices in the supraglottal region. A detailed analysis of the flow and vocal fold vibrations is conducted in order to gain insights into the biomechanics of phonation.

Theoretical consideration of the flow behavior in oscillating vocal fold

Self-excited oscillation of the vocal folds produces a source sound of the human voiced speech. The mechanism of the self-excitation remains elusive partly because characteristics of the flow in rapidly oscillating vocal folds are unclear. This paper deals with theoretical considerations of the flow behavior in oscillating constriction based on general flow equations. The cause-and-effect relationships between time-varying glottal width and physical variables such as glottal pressure, velocity, and volume flow are analytically derived as functions of oscillatory frequency through perturbation analysis. The result shows that the unsteady effect due to convective acceleration of vocal fold wall-induced flow becomes comparable in magnitude to the Bernoulli effect at a high but physiological frequency of phonation. Consequently, a phase difference between the vocal fold motion and glottal pressure appears, enabling self-excited oscillation. The phase-lead of the pressure compared to wall motion is described as a monotonically increasing function of the Strouhal number. The above two effects essentially play the dominant role in the glottal flow. These explicit descriptions containing flow-related variables are useful for understanding of the glottal aerodynamics particularly at high frequency range of the falsetto voice register.

Flow-structure-acoustic interaction in a human voice model

For the investigation of the physical processes of human phonation, inhomogeneous synthetic vocal folds were developed to represent the full fluid-structure-acoustic coupling. They consisted of polyurethane rubber with a stiffness in the range of human vocal folds and were mounted in a channel, shaped like the vocal tract in the supraglottal region. This test facility permitted extensive observations of flow-induced vocal fold vibrations, the periodic flow field, and the acoustic signals in the far field of the channel. Detailed measurements were performed applying particle-image velocimetry, a laser-scanning vibrometer, a microphone, unsteady pressure sensors, and a hot-wire probe, with the aim of identifying the physical mechanisms in human phonation. The results support the existence of the Coanda effect during phonation, with the flow attaching to one vocal fold and separating from the other. This behavior is not linked to one vocal fold and changes stochastically from cycle to cycle. The oscillating flow field generates a tonal sound. The broadband noise is presumed to be caused by the interaction of the asymmetric flow with the downstream-facing surfaces of the vocal folds, analogous to trailing-edge noise.

Chaotic component obscured by strong periodicity in voice production system

The effect of glottal aerodynamics in producing the nonlinear characteristics of voice is investigated by comparing the outputs of the asymmetric composite model and the two-mass model. The two-mass model assumes the glottal airflow to be laminar, nonviscous, and incompressible. In this model, when the asymmetric factor is decreased from 0.65 to 0.35, only 1:1 and 1:2 modes are detectable. However, with the same parameters, four vibratory modes (1:1, 1:2, 2:4, 2:6) are found in the asymmetric composite model using the Navier-Stokes equations to describe the complex aerodynamics in the glottis. Moreover, the amplitude of the waveform is modulated by a small-amplitude noiselike series. The nonlinear detection method reveals that this noiselike modulation is not random, but rather it is deterministic chaos. This result agrees with the phenomenon often seen in voice, in which the voice signal is strongly periodic but modulated by a small-amplitude chaotic component. The only difference between the two-mass model and the composite model is in their descriptions of glottal airflow. Therefore, the complex aerodynamic characteristics of glottal airflow could be important in generating the nonlinear dynamic behavior of voice production, including bifurcation and a small-amplitude chaotic component obscured by strong periodicity.