A computational study of asymmetric glottal jet deflection during phonation

Fluid-Structure Interaction Analysis of Aerodynamic and Elasticity Forces During Vocal Fold Vibration

The effect of the intraglottal vortices on the glottal flow waveform was explored using flow-structure-interaction (FSI) modeling. These vortices form near the superior aspect of the vocal folds during the closing phase of the folds' vibration. The geometry of the vocal fold was based on the well-known M5 model. The model did not include a vocal tract to remove its inertance effect on the glottal flow. Material properties for the cover and body layers of the folds were set using curve fit to experimental data of tissue elasticity. A commercially available FSI solver was used to perform simulations at low and high values of subglottal input pressure. Validation of the FSI results showed a good agreement for the glottal flow and the vocal fold displacement data with measurements taken in the excised canine larynx model. The simulations result further support the hypothesis that intraglottal vortices can affect the glottal flow waveform, specifically its maximum flow declination rate (MFDR). It showed that MFDR occurs at the same phase when the highest intraglottal vortical strength and the negative pressure occur. It also showed that when MFDR occurs, the magnitude of the aerodynamic force acting on the glottal wall is greater than the elastic recoil force predicted in the tissue. These findings are significant because nearly all theoretical and computational models that study the vocal fold vibrations mechanism do not consider the intraglottal negative pressure caused by the vortices as an additional closing force acting on the folds.

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.

Variability in expiratory trajectory angles during consonant production by one human subject and from a physical mouth model: Application to respiratory droplet emission

The COVID-19 pandemic has highlighted the need to improve understanding of droplet transport during expiratory emissions. While historical emphasis has been placed on violent events such as coughing and sneezing, the recognition of asymptomatic and presymptomatic spread has identified the need to consider other modalities, such as speaking. Accurate prediction of infection risk produced by speaking requires knowledge of both the droplet size distributions that are produced, as well as the expiratory flow fields that transport the droplets into the surroundings. This work demonstrates that the expiratory flow field produced by consonant productions is highly unsteady, exhibiting extremely broad inter- and intra-consonant variability, with mean ejection angles varying from ≈+30° to -30°. Furthermore, implementation of a physical mouth model to quantify the expiratory flow fields for fricative pronunciation of [f] and [θ] demonstrates that flow velocities at the lips are higher than previously predicted, reaching 20-30 m/s, and that the resultant trajectories are unstable. Because both large and small droplet transport are directly influenced by the magnitude and trajectory of the expirated air stream, these findings indicate that prior investigations of the flow dynamics during speech have largely underestimated the fluid penetration distances that can be achieved for particular consonant utterances.

Vocal fold dynamics in a synthetic self-oscillating model: Intraglottal aerodynamic pressure and energy

Self-sustained oscillations of the vocal folds (VFs) during phonation are the result of the energy exchange between the airflow and VF tissue. Understanding this mechanism requires accurate investigation of the aerodynamic pressures acting on the VF surface during oscillation. A self-oscillating silicone VF model was used in a hemilaryngeal flow facility to measure the time-varying pressure distribution along the inferior-superior thickness of the VF and at four discrete locations in the anterior-posterior direction. It was found that the intraglottal pressures during the opening and closing phases of the glottis are highly dependent on three-dimensional and unsteady flow behaviors. The measured aerodynamic pressures and estimates of the medial surface velocity were used to compute the intraglottal energy transfer from the airflow to the VFs. The energy was greatest at the anterior-posterior midline and decreased significantly toward the anterior/posterior endpoints. The findings provide insight into the dynamics of the VF oscillation and potential causes of some VF disorders.

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.

Effect of Longitudinal Variation of Vocal Fold Inner Layer Thickness on Fluid-Structure Interaction During Voice Production

A three-dimensional fluid-structure interaction computational model was used to investigate the effect of the longitudinal variation of vocal fold inner layer thickness on voice production. The computational model coupled a finite element method based continuum vocal fold model and a Navier-Stokes equation based incompressible flow model. Four vocal fold models, one with constant layer thickness and the others with different degrees of layer thickness variation in the longitudinal direction, were studied. It was found that the varied thickness resulted in up to 24% stiffness reduction at the middle and up to 47% stiffness increase near the anterior and posterior ends of the vocal fold; however, the average stiffness was not affected. The fluid-structure interaction simulations on the four models showed that the thickness variation did not affect vibration amplitude, glottal flow rate, and the waveform related parameters. However, it increased glottal angles at the middle of the vocal fold, suggesting that vocal fold vibration amplitude was determined by the average stiffness of the vocal fold, while the glottal angle was determined by the local stiffness. The models with longitudinal variation of layer thickness consumed less energy during the vibrations compared with the constant layer thickness one.

Characteristics of the pulsating jet flow through a dynamic glottal model with a lens-like constriction

A computational study of the pulsating jet in a squared channel with a dynamic glottal-shaped constriction is presented. It follows the model experiments of Triep and Brücker (J Acoust Soc Am 127(2):1537-1547, 2010) with the cam-driven model that replicates the dynamic glottal motion in the process of human phonation. The boundary conditions are mapped from the model experiment onto the computational model and the three dimensional time resolved velocity and pressure fields are numerically calculated. This study aims to provide more details of flow separation and pressure distribution in the glottal gap and in the supraglottal flow field. Within the glottal gap a 'vena contracta' effect is generated in the mid-sagittal plane. The flow separation in the mid-coronal plane is therefore delayed to larger diffuser angles which leads to an 'axis-switching' effect from mid-sagittal to mid-coronal plane. The location of flow separation in mid-sagittal cross section moves up- and downwards along the vocal folds surface in streamwise direction. The generated jet shear layer forms a chain of coherent vortex structures within each glottal cycle. These vortices cause characteristic velocity and pressure fluctuations in the supraglottal region, that are in the range of 10-30 times of the fundamental frequency.

Computational Models of Laryngeal Aerodynamics: Potentials and Numerical Costs

Human phonation is based on the interaction between tracheal airflow and laryngeal dynamics. This fluid-structure interaction is based on the energy exchange between airflow and vocal folds. Major challenges in analyzing the phonatory process in-vivo are the small dimensions and the poor accessibility of the region of interest. For improved analysis of the phonatory process, numerical simulations of the airflow and the vocal fold dynamics have been suggested. Even though most of the models reproduced the phonatory process fairly well, development of comprehensive larynx models is still a subject of research. In the context of clinical application, physiological accuracy and computational model efficiency are of great interest. In this study, a simple numerical larynx model is introduced that incorporates the laryngeal fluid flow. It is based on a synthetic experimental model with silicone vocal folds. The degree of realism was successively increased in separate computational models and each model was simulated for 10 oscillation cycles. Results show that relevant features of the laryngeal flow field, such as glottal jet deflection, develop even when applying rather simple static models with oscillating flow rates. Including further phonatory components such as vocal fold motion, mucosal wave propagation, and ventricular folds, the simulations show phonatory key features like intraglottal flow separation and increased flow rate in presence of ventricular folds. The simulation time on 100 CPU cores ranged between 25 and 290 hours, currently restricting clinical application of these models. Nevertheless, results show high potential of numerical simulations for better understanding of phonatory process.

Computational Modeling of Fluid-Structure-Acoustics Interaction during Voice Production

The paper presented a three-dimensional, first-principle based fluid-structure-acoustics interaction computer model of voice production, which employed a more realistic human laryngeal and vocal tract geometries. Self-sustained vibrations, important convergent-divergent vibration pattern of the vocal folds, and entrainment of the two dominant vibratory modes were captured. Voice quality-associated parameters including the frequency, open quotient, skewness quotient, and flow rate of the glottal flow waveform were found to be well within the normal physiological ranges. The analogy between the vocal tract and a quarter-wave resonator was demonstrated. The acoustic perturbed flux and pressure inside the glottis were found to be at the same order with their incompressible counterparts, suggesting strong source-filter interactions during voice production. Such high fidelity computational model will be useful for investigating a variety of pathological conditions that involve complex vibrations, such as vocal fold paralysis, vocal nodules, and vocal polyps. The model is also an important step toward a patient-specific surgical planning tool that can serve as a no-risk trial and error platform for different procedures, such as injection of biomaterials and thyroplastic medialization.

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.

Non-stationary Bayesian estimation of parameters from a body cover model of the vocal folds

The evolution of reduced-order vocal fold models into clinically useful tools for subject-specific diagnosis and treatment hinges upon successfully and accurately representing an individual patient in the modeling framework. This, in turn, requires inference of model parameters from clinical measurements in order to tune a model to the given individual. Bayesian analysis is a powerful tool for estimating model parameter probabilities based upon a set of observed data. In this work, a Bayesian particle filter sampling technique capable of estimating time-varying model parameters, as occur in complex vocal gestures, is introduced. The technique is compared with time-invariant Bayesian estimation and least squares methods for determining both stationary and non-stationary parameters. The current technique accurately estimates the time-varying unknown model parameter and maintains tight credibility bounds. The credibility bounds are particularly relevant from a clinical perspective, as they provide insight into the confidence a clinician should have in the model predictions.

Subject-Specific Computational Modeling of Evoked Rabbit Phonation

When developing high-fidelity computational model of vocal fold vibration for voice production of individuals, one would run into typical issues of unknown model parameters and model validation of individual-specific characteristics of phonation. In the current study, the evoked rabbit phonation is adopted to explore some of these issues. In particular, the mechanical properties of the rabbit's vocal fold tissue are unknown for individual subjects. In the model, we couple a 3D vocal fold model that is based on the magnetic resonance (MR) scan of the rabbit larynx and a simple one-dimensional (1D) model for the glottal airflow to perform fast simulations of the vocal fold dynamics. This hybrid three-dimensional (3D)/1D model is then used along with the experimental measurement of each individual subject for determination of the vocal fold properties. The vibration frequency and deformation amplitude from the final model are matched reasonably well for individual subjects. The modeling and validation approaches adopted here could be useful for future development of subject-specific computational models of vocal fold vibration.

Regulation of glottal closure and airflow in a three-dimensional phonation model: implications for vocal intensity control

Maintaining a small glottal opening across a large range of voice conditions is critical to normal voice production. This study investigated the effectiveness of vocal fold approximation and stiffening in regulating glottal opening and airflow during phonation, using a three-dimensional numerical model of phonation. The results showed that with increasing subglottal pressure the vocal folds were gradually pushed open, leading to increased mean glottal opening and flow rate. A small glottal opening and a mean glottal flow rate typical of human phonation can be maintained against increasing subglottal pressure by proportionally increasing the degree of vocal fold approximation for low to medium subglottal pressures and vocal fold stiffening at high subglottal pressures. Although sound intensity was primarily determined by the subglottal pressure, the results suggest that, to maintain small glottal opening as the sound intensity increases, one has to simultaneously tighten vocal fold approximation and/or stiffen the vocal folds, resulting in increased glottal resistance, vocal efficiency, and fundamental frequency.

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.

Subject-specific computational modeling of human phonation

A direct numerical simulation of flow-structure interaction is carried out in a subject-specific larynx model to study human phonation under physiological conditions. The simulation results compare well to the established human data. The resulting glottal flow and waveform are found to be within the normal physiological ranges. The effects of realistic geometry on the vocal fold dynamics and the glottal flow are extensively examined. It is found that the asymmetric anterior-posterior laryngeal configuration produces strong anterior-posterior asymmetries in both vocal fold vibration and glottal flow which has not been captured in the simplified models. It needs to be pointed out that the observations from the current numerical simulation are only valid for the flow conditions investigated. The limitations of the study are also discussed.

The influence of material anisotropy on vibration at onset in a three-dimensional vocal fold model

Although vocal folds are known to be anisotropic, the influence of material anisotropy on vocal fold vibration remains largely unknown. Using a linear stability analysis, phonation onset characteristics were investigated in a three-dimensional anisotropic vocal fold model. The results showed that isotropic models had a tendency to vibrate in a swing-like motion, with vibration primarily along the superior-inferior direction. Anterior-posterior (AP) out-of-phase motion was also observed and large vocal fold vibration was confined to the middle third region along the AP length. In contrast, increasing anisotropy or increasing AP-transverse stiffness ratio suppressed this swing-like motion and allowed the vocal fold to vibrate in a more wave-like motion with strong medial-lateral motion over the entire medial surface. Increasing anisotropy also suppressed the AP out-of-phase motion, allowing the vocal fold to vibrate in phase along the entire AP length. Results also showed that such improvement in vibration pattern was the most effective with large anisotropy in the cover layer alone. These numerical predictions were consistent with previous experimental observations using self-oscillating physical models. It was further hypothesized that these differences may facilitate complete glottal closure in finite-amplitude vibration of anisotropic models as observed in recent experiments.

Influence of numerical model decisions on the flow-induced vibration of a computational vocal fold model

Computational vocal fold models are often used to study the physics of voice production. In this paper the sensitivity of predicted vocal fold flow-induced vibration and resulting airflow patterns to several modeling selections is explored. The location of contact lines used to prevent mesh collapse and assumptions of symmetry were found to influence airflow patterns. However, these variables had relatively little effect on the vibratory response of the vocal fold model itself. Model motion was very sensitive to Poisson's ratio. The importance of these parameter sensitivities in the context of vocal fold modeling is discussed.

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.

Asymmetric vibration in a two-layer vocal fold model with left-right stiffness asymmetry: experiment and simulation

Vibration characteristics of a self-oscillating two-layer vocal fold model with left-right asymmetry in body-layer stiffness were experimentally and numerically investigated. Two regimes of distinct vibratory pattern were identified as a function of left-right stiffness mismatch. In the first regime with extremely large left-right stiffness mismatch, phonation onset resulted from an eigenmode synchronization process that involved only eigenmodes of the soft fold. Vocal fold vibration in this regime was dominated by a large-amplitude vibration of the soft fold, and phonation frequency was determined by the properties of the soft fold alone. The stiff fold was only enslaved to vibrate at a much reduced amplitude. In the second regime with small left-right stiffness mismatch, eigenmodes of both folds actively participated in the eigenmode synchronization process. The two folds vibrated with comparable amplitude, but the stiff fold consistently led the soft fold in phase for all conditions. A qualitatively good agreement was obtained between experiment and simulation, although the simulations generally underestimated phonation threshold pressure and onset frequency. The clinical implications of the results of this study are also discussed.

Asymmetric glottal jet deflection: differences of two- and three-dimensional models

Flow is studied through a channel with an oscillating orifice mimicking the motion of the glottal-gap during phonation. Simulations with prescribed flow and wall-motion are carried out for different orifice geometries, a 2D slit-like and a 3D lens-like one. Although the jet emerges from a symmetric orifice a significant deflection occurs in case of the slit-like geometry, contrary to the 3D lens-like one. The results demonstrate the dependency of jet entrainment and vortex dynamics on the orifice geometry and the interpretation of asymmetric jet deflection with regard to the relevance of the Coanda effect in the process of human phonation.

Direct-numerical simulation of the glottal jet and vocal-fold dynamics in a three-dimensional laryngeal model

An immersed-boundary method based flow solver coupled with a finite-element solid dynamics solver is employed in order to conduct direct-numerical simulations of phonatory dynamics in a three-dimensional model of the human larynx. The computed features of the glottal flow including mean and peak flow rates, and the open and skewness quotients are found to be within the normal physiological range. The flow-induced vibration pattern shows the classical "convergent-divergent" glottal shape, and the vibration amplitude is also found to be typical for human phonation. The vocal fold motion is analyzed through the method of empirical eigenfunctions and this analysis indicates a 1:1 modal entrainment between the "adduction-abduction" mode and the "mucosal wave" mode. The glottal jet is found to exhibit noticeable cycle-to-cycle asymmetric deflections and the mechanism underlying this phenomenon is examined.