Flow separation in a computational oscillating vocal fold model

A finite-volume computational model that solves the time-dependent glottal airflow within a forced-oscillation model of the glottis was employed to study glottal flow separation. Tracheal input velocity was independently controlled with a sinusoidally varying parabolic velocity profile. Control parameters included flow rate (Reynolds number), oscillation frequency and amplitude of the vocal folds, and the phase difference between the superior and inferior glottal margins. Results for static divergent glottal shapes suggest that velocity increase caused glottal separation to move downstream, but reduction in velocity increase and velocity decrease moved the separation upstream. At the fixed frequency, an increase of amplitude of the glottal walls moved the separation further downstream during glottal closing. Increase of Reynolds number caused the flow separation to move upstream in the glottis. The flow separation cross-sectional ratio ranged from approximately 1.1 to 1.9 (average of 1.47) for the divergent shapes. Results suggest that there may be a strong interaction of rate of change of airflow, inertia, and wall movement. Flow separation appeared to be "delayed" during the vibratory cycle, leading to movement of the separation point upstream of the glottal end only after a significant divergent angle was reached, and to persist upstream into the convergent phase of the cycle.     

Identification of geometric parameters influencing the flow-induced vibration of a two-layer self-oscillating computational vocal fold model

Simplified models have been used to simulate and study the flow-induced vibrations of the human vocal folds. While it is clear that the models' responses are sensitive to geometry, it is not clear how and to what extent specific geometric features influence model motion. In this study geometric features that played significant roles in governing the motion of a two-layer (body-cover), two-dimensional, finite element vocal fold model were identified. The model was defined using a flow solver based on the viscous, unsteady, Navier-Stokes equations and a solid solver that allowed for large strain and deformation. A screening-type design-of-experiments approach was used to identify the relative importance of 13 geometric parameters. Five output measures were analyzed to assess the magnitude of each geometric parameter's effect on the model's motion. The measures related to frequency, glottal width, flow rate, intraglottal angle, and intraglottal phase delay. The most significant geometric parameters were those associated with the cover--primarily the pre-phonatory intraglottal angle--as well as the body inferior angle. Some models exhibited evidence of improved model motion, including mucosal wave-like motion and alternating convergent-divergent glottal profiles, although further improvements are still needed to more closely mimic human vocal fold motion.     

A canonical biomechanical vocal fold model

The present article aimed at constructing a canonical geometry of the human vocal fold (VF) from subject-specific image slice data. A computer-aided design approach automated the model construction. A subject-specific geometry available in literature, three abstractions (which successively diminished in geometric detail) derived from it, and a widely used quasi two-dimensional VF model geometry were used to create computational models. The first three natural frequencies of the models were used to characterize their mechanical response. These frequencies were determined for a representative range of tissue biomechanical properties, accounting for underlying VF histology. Compared with the subject-specific geometry model (baseline), a higher degree of abstraction was found to always correspond to a larger deviation in model frequency (up to 50% in the relevant range of tissue biomechanical properties). The model we deemed canonical was optimally abstracted, in that it significantly simplified the VF geometry compared with the baseline geometry but can be recalibrated in a consistent manner to match the baseline response. Models providing only a marginally higher degree of abstraction were found to have significant deviation in predicted frequency response. The quasi two-dimensional model presented an extreme situation: it could not be recalibrated for its frequency response to match the subject-specific model. This deficiency was attributed to complex support conditions at anterior-posterior extremities of the VFs, accentuated by further issues introduced through the tissue biomechanical properties. In?creating canonical models by leveraging advances in clinical imaging techniques, the automated design procedure makes VF modeling based on subject-specific geometry more realizable.     

Modeling vocal fold motion with a hydrodynamic semicontinuum model

Vocal fold (VF) motion is a fundamental process in voice production, and is also a challenging problem for numerical computation because the VF dynamics depend on nonlinear coupling of air flow with the response of elastic channels (VF), which undergo opening and closing, and induce internal flow separation. The traditional modeling approach makes use of quasisteady flow approximation or Bernoulli's law which ignores air compressibility, and is known to be invalid during VF opening. A hydrodynamic semicontinuum system for VF motion is presented. The airflow is modeled by a modified quasi-one-dimensional Euler system with coupling to VF velocity. The VF is modeled by a lumped two mass system with a built-in geometric condition on flow separation. The modified Euler system contains the Bernoulli's law as a special case, and is derivable from the two-dimensional compressible Navier-Stokes equations in the inviscid limit. The computational domain contains also solid walls next to VFs (flexible walls). It is shown numerically that several salient features of VFs are captured, especially transients such as the double peaks of the driving subglottal pressures at the opening and the closing stages of VF motion consistent with fully resolved two-dimensional direct simulations, and experimental data. The system is much simpler to compute than a VF model based on two-dimensional Navier-Stokes system.     

Characterization of chronic vocal fold scarring in a rabbit model

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

Chaotic vibrations of a vocal fold model with a unilateral polyp

A nonlinear model was proposed to study chaotic vibrations of vocal folds with a unilateral vocal polyp. The model study found that the vocal polyp affected glottal closure and caused aperiodic vocal fold vibrations. Using nonlinear dynamic methods, aperiodic vibrations of the vocal fold model with a polyp were attributed to low-dimensional chaos. Bifurcation diagrams showed that vocal polyp size, stiffness, and damping had important effects on vocal fold vibrations. An increase in polyp size tended to induce subharmonic patterns and chaos. This study provides a theoretical basis to model aperiodic vibrations of vocal folds with a laryngeal mass.     

A two-dimensional biomechanical model of vocal fold posturing

The forces and torques governing effective two-dimensional (2D) translation and rotation of the laryngeal cartilages (cricoid, thyroid, and arytenoids) are quantified on the basis of more complex three-dimensional movement. The motions between these cartilages define the elongation and adduction (collectively referred to as posturing) of the vocal folds. Activations of the five intrinsic laryngeal muscles, the cricothyroid, thyroarytenoid, lateral cricoarytenoid, posterior cricoarytenoid, and interarytenoid are programmed as inputs, in isolation and in combination, to produce the dynamics of 2D posturing. Parameters for the muscles are maximum active stress, passive stress, activation time, contraction time, and maximum shortening velocity. The model accepts measured electromyographic signals as inputs. A repeated adductory-abductory gesture in the form /hi-hi-hi-hi-hi/ is modeled with electromyographic inputs. Movement and acoustic outputs are compared between simulation and measurement.     

Effect of artificially lengthened vocal tract on vocal fold oscillation's fundamental frequency.

The fundamental frequency of vocal fold oscillation (F(0)) is controlled by laryngeal mechanics and aerodynamic properties. F(0) change per unit change of transglottal pressure (dF/dP) using a shutter valve has been studied and found to have nonlinear, V-shaped relationship with F(0). On the other hand, the vocal tract is also known to affect vocal fold oscillation. This study examined the effect of artificially lengthened vocal tract length on dF/dP. dF/dP was measured in six men using two mouthpieces of different lengths. Results: The dF/dP graph for the longer vocal tract was shifted leftward relative to the shorter one. Conclusion: Using the one-mass model, the nadir of the "V" on the dF/dP graph was strongly influenced by the resonance around the first formant frequency. However, a more precise model is needed to account for the effects of viscosity and turbulence.     

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.     

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.     

Studying vocal fold vibrations in Parkinson's disease with a nonlinear model

A nonlinear model is applied to study pathologic vocal vibratory characteristics and voice treatments of Parkinson's disease. We find that a number of pathologic vocal characteristics commonly observed in Parkinson's disease, including reduced vibratory intensity, incomplete vocal closure, increased phonation threshold pressure, glottal tremor, subharmonics, and chaotic vocal fold vibrations, can be studied with this nonlinear model. We also find that two kinds of clinical voice treatments for Parkinson's disease, including respiratory effort treatment and Lee Silverman voice treatment can be studied with this computer model. Results suggest that respiratory effort treatment, in which subglottal pressure is increased, might aid in enhancing vibratory intensity, improving glottal closure, and avoiding vibratory irregularity. However, the Lee Silverman voice treatment, in which both subglottal pressure and vocal fold adduction are increased, might be better than respiratory effort treatment. Increasing vocal fold thickness would be further helpful to improve these pathologic characteristics. The model studies show consistencies with clinical observations. Computer models may be of value in understanding the dynamic mechanism of disordered voices and studying voice treatment effects in Parkinson's disease.     

A three-dimensional model of vocal fold abduction/adduction

A three-dimensional biomechanical model of tissue deformation was developed to simulate dynamic vocal fold abduction and adduction. The model was made of 1721 nearly incompressible finite elements. The cricoarytenoid joint was modeled as a rocking-sliding motion, similar to two concentric cylinders. The vocal ligament and the thyroarytenoid muscle's fiber characteristics were implemented as a fiber-gel composite made of an isotropic ground substance imbedded with fibers. These fibers had contractile and/or passive nonlinear stress-strain characteristics. The verification of the model was made by comparing the range and speed of motion to published vocal fold kinematic data. The model simulated abduction to a maximum glottal angle of about 31 degrees. Using the posterior-cricoarytenoid muscle, the model produced an angular abduction speed of 405 degrees per second. The system mechanics seemed to favor abduction over adduction in both peak speed and response time, even when all intrinsic muscle properties were kept identical. The model also verified the notion that the vocalis and muscularis portions of the thyroarytenoid muscle play significantly different roles in posturing, with the muscularis portion having the larger effect on arytenoid movement. Other insights into the mechanisms of abduction/adduction were given.     

Rhabdomyoma of the true vocal fold

Rhabdomyomas of the larynx are exceedingly rare. The incidence, sites of occurrence in the larynx, and treatment of these benign striated muscle tumors are reviewed. A case of rhabdomyoma involving the vocalis muscle is presented with magnetic resonance imaging and video-stroboscopic documentation.     

Spatiotemporal classification of vocal fold dynamics by a multimass model comprising time-dependent parameters

A model-based approach is proposed to objectively measure and classify vocal fold vibrations by left-right asymmetries along the anterior-posterior direction, especially in the case of nonstationary phonation. For this purpose, vocal fold dynamics are recorded in real time with a digital high-speed camera during phonation of sustained vowels as well as pitch raises. The dynamics of a multimass model with time-dependent parameters are matched to vocal fold vibrations extracted at dorsal, medial, and ventral positions by an automatic optimization procedure. The block-based optimization accounts for nonstationary vibrations and compares the vocal fold and model dynamics by wavelet coefficients. The optimization is verified with synthetically generated data sets and is applied to 40 clinical high-speed recordings comprising normal and pathological voice subjects. The resulting model parameters allow an intuitive visual assessment of vocal fold instabilities within an asymmetry diagram and are applicable to an objective quantification of asymmetries.     

Infraglottic aspect of canine vocal fold vibration: Effect of increase of mean airflow rate and lengthening of vocal fold

The mucosal upheaval (MU), where the mucosal wave starts and propagates upward, appears only when the vocal fold vibrates. The location of the MU histologically and the effect of changes in mean air flow rate (MFR) and vocal fold length on occurrence of the MU were studied in twelve excised canine larynges. The lower surface of the vocal fold was marked to serve as a landmark for subsequent study. Cricothyroid approximation was performed to lengthen the vocal fold. After taking high-speed pictures or recording stroboscopic images from the tracheal side, a small cut wound was made at the mark. This wound served to compare the position of the MU with the histologically identified location of the mark. The larynx was then sectioned in the frontal plane. Before lengthening the vocal fold, the MU occurred on the area where the lamina propria became thinner and where the muscular layer neared the epithelial layer. After lengthening the vocal fold, the MU actually shifted medially compared with its original position. The subglottic area surrounded by the bilateral MUs became longer and thinner. Whether or not complete glottal closure during a vibratory cycle was achieved did not alter these findings. In contrast, with a fixed vocal fold length the MU appeared more laterally as MFR increased, but, based on the relation with the mark, its location on the vocal fold did not change from its original position before increase of MFR.     

Influence of supraglottal structures on the glottal jet exiting a two-layer synthetic, self-oscillating vocal fold model

A synthetic two-layer, self-oscillating, life-size vocal fold model was used to study the influence of the vocal tract and false folds on the glottal jet. The model vibrated at frequencies, pressures, flow rates, and amplitudes consistent with human phonation, although some differences in behavior between the model and the human vocal folds are noted. High-speed images of model motion and flow visualization were acquired. Phase-locked ensemble-averaged glottal jet velocity measurements using particle image velocimetry (PIV) were acquired with and without an idealized vocal tract, with and without false folds. PIV data were obtained with varying degrees of lateral asymmetric model positioning. Glottal jet velocity magnitudes were consistent with those measured using excised larynges. A starting vortex was observed in all test cases. The false folds interfered with the starting vortex, and in some cases vortex shedding from the false folds was observed. In asymmetric cases without false folds, the glottal jet tended to skew toward the nearest wall; with the false folds, the opposite trend was observed. rms velocity calculations showed the jet shear layer and laminar core. The rms velocities were higher in the vocal tract cases compared to the open jet and false fold cases.     

Vibration in a self-oscillating vocal fold model with left-right asymmetry in body-layer stiffness

This study compares the phonatory behavior of an asymmetric vocal fold model to that of each individual vocal fold model in a hemi-configuration. Although phonation frequencies of the two folds in hemi-configurations had a ratio close to 1:3, a subharmonic synchronization between the two folds was not observed in the asymmetric model. Instead, the vibratory behavior was dominated by the dynamics of one fold only, and the other fold was enslaved to vibrate at the same frequency. Increasing subglottal pressure induced a shift in relative dominance between the two folds, leading to abrupt changes in both vibratory pattern and frequency.