A three-dimensional model of vocal fold abduction/adduction

A viscoelastic laryngeal muscle model with active components

Accurate definitions of both passive and active tissue characteristics are important to laryngeal muscle modeling. This report tested the efficacy of a muscle model which added active stress components to an accurate definition of passive properties. Using the previously developed three-network Ogden model to simulate passive stress, a Hill-based contractile element stress equation was utilized for active stress calculations. Model input parameters were selected based on literature data for the canine cricothyroid muscle, and simulations were performed in order to compare the model behavior to published results for the same muscle. The model results showed good agreement with muscle behavior, including appropriate tetanus response and contraction time for isometric conditions, as well as accurate stress predictions in response to dynamic strain with activation.

Strain modulations as a mechanism to reduce stress relaxation in laryngeal tissues

Vocal fold tissues in animal and human species undergo deformation processes at several types of loading rates: a slow strain involved in vocal fold posturing (on the order of 1 Hz or so), cyclic and faster posturing often found in speech tasks or vocal embellishment (1–10 Hz), and shear strain associated with vocal fold vibration during phonation (100 Hz and higher). Relevant to these deformation patterns are the viscous properties of laryngeal tissues, which exhibit non-linear stress relaxation and recovery. In the current study, a large strain time-dependent constitutive model of human vocal fold tissue is used to investigate effects of phonatory posturing cyclic strain in the range of 1 Hz to 10 Hz. Tissue data for two subjects are considered and used to contrast the potential effects of age. Results suggest that modulation frequency and extent (amplitude), as well as the amount of vocal fold overall strain, all affect the change in stress relaxation with modulation added. Generally, the vocal fold cover reduces the rate of relaxation while the opposite is true for the vocal ligament. Further, higher modulation frequencies appear to reduce the rate of relaxation, primarily affecting the ligament. The potential benefits of cyclic strain, often found in vibrato (around 5 Hz modulation) and intonational inflection, are discussed in terms of vocal effort and vocal pitch maintenance. Additionally, elderly tissue appears to not exhibit these benefits to modulation. The exacerbating effect such modulations may have on certain voice disorders, such as muscle tension dysphonia, are explored.

The influence of thyroarytenoid and cricothyroid muscle activation on vocal fold stiffness and eigenfrequencies

The influence of the thyroarytenoid (TA) and cricothyroid (CT) muscle activation on vocal fold stiffness and eigenfrequencies was investigated in a muscularly controlled continuum model of the vocal folds. Unlike the general understanding that vocal fold fundamental frequency was determined by vocal fold tension, this study showed that vocal fold eigenfrequencies were primarily determined by vocal fold stiffness. This study further showed that, with reference to the resting state of zero strain, vocal fold stiffness in both body and cover layers increased with either vocal fold elongation or shortening. As a result, whether vocal fold eigenfrequencies increased or decreased with CT/TA activation depended on how the CT/TA interaction influenced vocal fold deformation. For conditions of strong CT activation and thus an elongated vocal fold, increasing TA contraction reduced the degree of vocal fold elongation and thus reduced vocal fold eigenfrequencies. For conditions of no CT activation and thus a resting or slightly shortened vocal fold, increasing TA contraction increased the degree of vocal fold shortening and thus increased vocal fold eigenfrequencies. In the transition region of a slightly elongated vocal fold, increasing TA contraction first decreased and then increased vocal fold eigenfrequencies.

Influence of subglottic stenosis on the flow-induced vibration of a computational vocal fold model

The effect of subglottic stenosis on vocal fold vibration is investigated. An idealized stenosis is defined, parameterized, and incorporated into a two-dimensional, fully-coupled finite element model of the vocal folds and laryngeal airway. Flow-induced responses of the vocal fold model to varying severities of stenosis are compared. The model vibration was not appreciably affected by stenosis severities of up to 60% occlusion. Model vibration was altered by stenosis severities of 90% or greater, evidenced by decreased superior model displacement, glottal width amplitude, and flow rate amplitude. Predictions of vibration frequency and maximum flow declination rate were also altered by high stenosis severities. The observed changes became more pronounced with increasing stenosis severity and inlet pressure, and the trends correlated well with flow resistance calculations. Flow visualization was used to characterize subglottal flow patterns in the space between the stenosis and the vocal folds. Underlying mechanisms for the observed changes, possible implications for human voice production, and suggestions for future work are discussed.

Arytenoid abduction for bilateral vocal fold immobility

PURPOSE OF REVIEW

The pathophysiology of bilateral vocal fold immobility includes two broad categories: mechanical fixation and neurogenic paralysis. A mobile arytenoid can be surgically abducted, and this procedure has been reported as a treatment for patients with bilateral neurogenic laryngeal paralysis. This article reviews the theoretical basis and clinical outcomes of this procedure.

RECENT FINDINGS

Two concepts form the theoretical basis for arytenoid abduction. First, in most cases of neurogenic paralysis, laryngeal muscles are not denervated; there is considerable residual or regenerated function of adductor muscles. The vocal fold lies near the midline, because there is inadequate force to abduct the vocal fold. Second, the cricoarytenoid joint is multiaxial. The posterior cricoarytenoid (PCA) muscle rotates the arytenoid about an oblique axis to pull the vocal process laterally and superiorly, while the axis of adduction is nearly vertical. Thus, surgical abduction of the arytenoid, by simulating contraction of the PCA muscle, should not preclude active adduction during phonation or swallow. Surgical arytenoid abduction has been reported to improve the airway in many patients with bilateral laryngeal paralysis, with little or no impairment of vocal function. It is less successful in patients with inspiratory adductor muscle activity, long-term immobility, or previous procedures to statically enlarge the glottis.

SUMMARY

Arytenoid abduction is a promising treatment for selected patients with bilateral neurogenic laryngeal paralysis.

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.

2D/3D hybrid structural model of vocal folds

The spatial dimensionality of the vocal fold vibration is a common challenge in creating parsimonious models of vocal fold vibration. The ideal model is one that is accurate, with the lowest possible computational expense. Inclusion of full 3D flow and structural vibration typically requires massive amounts of computation, whereas reduction of either the flow or the structure to two dimensions eliminates certain aspects of physical reality, thus making the resulting models less accurate. Previous 2D models of the vocal fold structure have utilized a plane strain formulation, which is shown to be an erroneous modeling approach since it ignores influential stress components. We herein present a 2D/3D hybrid vocal fold model that preserves three-dimensional effects of length and longitudinal shear stresses, while taking advantage of a two-dimensional computational domain. The resulting model exhibits static and dynamic responses comparable to a 3D model, and retains the computational advantage of a two-dimensional model.

Cooperative regulation of vocal fold morphology and stress by the cricothyroid and thyroarytenoid muscles

Voice is produced by vibrations of vocal folds that consist of multiple layers. The portion of the vocal fold tissue that vibrates varies depending primarily on laryngeal muscle activity. The effective depth of tissue vibration should significantly influence the vibrational behavior of the tissue and resulting voice quality. However, thus far, the effect of the activation of individual muscles on the effective depth is not well understood. In this study, a three-dimensional finite element analysis is performed to investigate the effect of the activation of two major laryngeal muscles, the cricothyroid (CT) and thyroarytenoid (TA) muscles, on vocal fold morphology and stress distribution in the tissue. Because structures that bear less stress can easily be deformed and involved in vibration, information on the morphology and stress distribution may provide a useful estimate of the effective depth. The results of the analyses indicate that the two muscles perform distinct roles, which allow cooperative control of the morphology and stress. When the CT muscle is activated, the tip region of the vocal folds becomes thinner and curves upward, resulting in the elevation of the stress magnitude all over the tissue to a certain degree that depends on the stiffness of each layer. On the other hand, the TA muscle acts to suppress the morphological change and controls the stress magnitude in a position-dependent manner. Thus, the present analyses demonstrate quantitative relationships between the two muscles in their cooperative regulation of vocal fold morphology and stress.

Toward a simulation-based tool for the treatment of vocal fold paralysis

Advances in high-performance computing are enabling a new generation of software tools that employ computational modeling for surgical planning. Surgical management of laryngeal paralysis is one area where such computational tools could have a significant impact. The current paper describes a comprehensive effort to develop a software tool for planning medialization laryngoplasty where a prosthetic implant is inserted into the larynx in order to medialize the paralyzed vocal fold (VF). While this is one of the most common procedures used to restore voice in patients with VF paralysis, it has a relatively high revision rate, and the tool being developed is expected to improve surgical outcomes. This software tool models the biomechanics of airflow-induced vibration in the human larynx and incorporates sophisticated approaches for modeling the turbulent laryngeal flow, the complex dynamics of the VFs, as well as the production of voiced sound. The current paper describes the key elements of the modeling approach, presents computational results that demonstrate the utility of the approach and also describes some of the limitations and challenges.

Membranous and cartilaginous vocal fold adduction in singing

While vocal fold adduction is an important parameter in speech, relatively little has been known on the adjustment of the vocal fold adduction in singing. This study investigates the possibility of separate adjustments of cartilaginous and membranous vocal fold adduction in singing. Six female and seven male subjects, singers and non-singers, were asked to imitate an instructor in producing four phonation types: "aBducted falsetto" (FaB), "aDducted falsetto" (FaD), "aBducted Chest" (CaB), and "aDducted Chest" (CaD). The phonations were evaluated using videostroboscopy, videokymography (VKG), electroglottography (EGG), and audio recordings. All the subjects showed less posterior (cartilaginous) vocal fold adduction in phonation types FaB and CaB than in FaD and CaD, and less membranous vocal fold adduction (smaller closed quotient) in FaB and FaD than in CaB and CaD. The findings indicate that the exercises enabled the singers to separately manipulate (a) cartilaginous adduction and (b) membranous medialization of the glottis though vocal fold bulging. Membranous adduction (monitored via videokymographic closed quotient) was influenced by both membranous medialization and cartilaginous adduction. Individual control over these types of vocal fold adjustments allows singers to create different vocal timbres.

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.

Biomechanics of fundamental frequency regulation: Constitutive modeling of the vocal fold lamina propria

Accurate characterization of biomechanical characteristics of the vocal fold is critical for understanding the regulation of vocal fundamental frequency (F(0)), which depends on the active control of the intrinsic laryngeal muscles as well as the passive biomechanical response of the vocal fold lamina propria. Specifically, the tissue stress-strain response and viscoelastic properties under cyclic tensile deformation are relevant, when the vocal folds are subjected to length and tension changes due to posturing. This paper describes a constitutive modeling approach quantifying the relationship between vocal fold stress and strain (or stretch), and establishes predictions of F(0) with the string model of phonation based on the constitutive parameters. Results indicated that transient and time-dependent changes in F(0), including global declinations in declarative sentences, as well as local F(0) overshoots and undershoots, can be partially attributed to the time-dependent viscoplastic response of the vocal fold cover.

A cervid vocal fold model suggests greater glottal efficiency in calling at high frequencies

Male Rocky Mountain elk (Cervus elaphus nelsoni) produce loud and high fundamental frequency bugles during the mating season, in contrast to the male European Red Deer (Cervus elaphus scoticus) who produces loud and low fundamental frequency roaring calls. A critical step in understanding vocal communication is to relate sound complexity to anatomy and physiology in a causal manner. Experimentation at the sound source, often difficult in vivo in mammals, is simulated here by a finite element model of the larynx and a wave propagation model of the vocal tract, both based on the morphology and biomechanics of the elk. The model can produce a wide range of fundamental frequencies. Low fundamental frequencies require low vocal fold strain, but large lung pressure and large glottal flow if sound intensity level is to exceed 70 dB at 10 m distance. A high-frequency bugle requires both large muscular effort (to strain the vocal ligament) and high lung pressure (to overcome phonation threshold pressure), but at least 10 dB more intensity level can be achieved. Glottal efficiency, the ration of radiated sound power to aerodynamic power at the glottis, is higher in elk, suggesting an advantage of high-pitched signaling. This advantage is based on two aspects; first, the lower airflow required for aerodynamic power and, second, an acoustic radiation advantage at higher frequencies. Both signal types are used by the respective males during the mating season and probably serve as honest signals. The two signal types relate differently to physical qualities of the sender. The low-frequency sound (Red Deer call) relates to overall body size via a strong relationship between acoustic parameters and the size of vocal organs and body size. The high-frequency bugle may signal muscular strength and endurance, via a 'vocalizing at the edge' mechanism, for which efficiency is critical.

Developing a 3D model of the laryngeal cartilages using HRCT data and MIMICS's segmentation software

Discussions relating to the biomechanics of the larynx are still generally controversial. The purpose of this study is to develop a 3D model of the larynx based on high-resolution computer tomography (HRCT) data identifying and visualizing anatomical landmarks and structures of the larynx. We examined four fresh cadaver larynges with HRCT. The DICOM (Digital Imaging and Communication in Medicine) data were post-processed with the software package MIMICS for three-dimensional visualization. All relevant structures of the laryngeal cartilages could be identified on HRCT and visualized in a 3D model. We conclude that 1) HRCT provides excellent data for three-dimensional visualization of the laryngeal anatomy, and 2) the combined technology of HRCT and MIMICS is useful to study the biomechanics on 3D images and for preoperative planning of laryngeal framework surgery.

A virtual trajectory model predicts differences in vocal fold kinematics in individuals with vocal hyperfunction

A simple, one degree of freedom virtual trajectory model of vocal fold kinematics was developed to investigate whether kinematic features of vocal fold movement confirm increased muscle stiffness. Model simulations verified that increases in stiffness were associated with changes in kinematic parameters, suggesting that increases in gesture rate would affect kinematic features to a lesser degree in vocal hyperfunction patients given the increased levels of muscle tension they typically employ to phonate. This hypothesis was tested experimentally in individuals with muscle tension dysphonia (MTD; N = 10) and vocal nodules (N = 10) relative to controls with healthy normal voice (N = 10) who were examined with trans-nasal endoscopy during a simple vocal fold abductory-adductory task. Kinematic measures in MTD patients were less affected by increased gesture rate, consistent with the hypothesis that these individuals have elevated typical laryngeal muscle tension. Group comparisons of the difference between medium and fast gesture rates (Mann-Whitney, one-tailed) showed statistically significant differences between the control and MTD individuals on the two kinematic features examined (p<0.05). Results in nodules participants were mixed and are discussed independently. The findings support the potential use of vocal fold kinematics as an objective clinical assay of vocal hyperfunction.

Cervids with different vocal behavior demonstrate different viscoelastic properties of their vocal folds

The authors test the hypothesis that vocal fold morphology and biomechanical properties covary with species-specific vocal function. They investigate mule deer (Odocoileus hemionus) vocal folds, building on, and extending data on a related cervid, the Rocky Mountain elk (Cervus elaphus nelsoni). The mule deer, in contrast to the elk, is a species with relatively little vocal activity in adult animals. Mule deer and elk vocal folds show the typical three components of the mammalian vocal fold (epithelium, lamina propria and thyroarytenoid muscle). The vocal fold epithelium and the lamina propria were investigated in two sets of tensile tests. First, creep rupture tests demonstrated that ultimate stress in mule deer lamina propria is of the same magnitude as in elk. Second, cyclic loading tests revealed similar elastic moduli for the vocal fold epithelium in mule deer and elk. The elastic modulus of the lamina propria is also similar between the two species in the low-strain region, but differs at strains larger than 0.3. Sex differences in the stress-strain response, which have been reported for elk and human vocal folds, were not found for mule deer vocal folds. The laminae propriae in mule deer and elk vocal folds are comparatively large. In general, a thick and uniformly stiff lamina propria does not self-oscillate well, even when high subglottic pressure is applied. If the less stiff vocal fold seen in elk is associated with a differentiated lamina propria it would allow the vocal fold to vibrate at high tension and high subglottic pressure. The results of this study support the hypothesis that viscoelastic properties of vocal folds varies with function and vocal behavior.

Ranking vocal fold model parameters by their influence on modal frequencies

The purpose of this study was to identify, using computational models, the vocal fold parameters which are most influential in determining the vibratory characteristics of the vocal folds. The sensitivities of vocal folds modal frequencies to variations model parameters were used to determine the most influential parameters. A detailed finite element model of the human vocal fold was created. The model was defined by eight geometric and six material parameters. The model included transitional boundary regions to idealize the complex physiological structure of real human subjects. Parameters were simultaneously varied over ranges representative of actual human vocal folds. Three separate statistical analysis techniques were used to identify the most and least sensitive model parameters with respect to modal frequency. The results from all three methods consistently suggest that a set of five parameters are most influential in determining the vibratory characteristics of the vocal folds.

Liquid accumulation in vibrating vocal fold tissue: a simplified model based on a fluid-saturated porous solid theory

The human vocal fold is treated as a continuous, transversally isotropic, porous solid saturated with liquid. A set of mathematical equations, based on the theory of fluid-saturated porous solids, is developed to formulate the vibration of the vocal fold tissue. As the fluid-saturated porous tissue model degenerates to the continuous elastic tissue model when the relative movement of liquid in the porous tissue is ignored, it can be considered a more general description of vocal fold tissue than the continuous, elastic model. Using the fluid-saturated porous tissue model, the vibration of a bunch of one-dimensional fibers in the vocal fold is analytically solved based on the small-amplitude assumption. It is found that the vibration of the tissue will lead to the accumulation of excess liquid in the midmembranous vocal fold. The degree of liquid accumulation is positively proportional to the vibratory amplitude and frequency. The correspondence between the liquid distribution predicted by the porous tissue theory and the location of vocal nodules observed in clinical practice, provides theoretical evidence for the liquid accumulation hypothesis of vocal nodule formation (Jiang, Ph.D., dissertation, 1991, University of Iowa).

A fluid-saturated poroelastic model of the vocal folds with hydrated tissue

The purpose of this study is to develop a continuous model to describe the vibration of the vocal fold with hydrated tissue. This model is unique because it is based on the fluid-saturated porous solid theory. Therefore, this new model can be used to study some vocal fold characteristics that would be difficult to predict using previous models. Numerical simulations show that this model can generate self-oscillation and that its phonation threshold pressure (PTP) is 0.555 kPa. The basic outputs of this model, including fundamental frequency, maximum lateral displacement, surface dynamics, and empirical eigenfunctions, agree with previous models and experimental studies, which validates this new model. The ability to simulate the flow of liquid through the tissue is one of the important advantages of this new model. It was found that the liquid in the vocal fold tissue could be accumulated at the anterior-posterior midpoint during phonation, which could cause a pressure increase in the liquid. The liquid pressure increased from 0.033 to 0.150 kPa when the subglottal pressure increased from 0.555 kPa (PTP) to 0.7 kPa. It was believed that the liquid dynamics in the tissue during phonation could be related to the development of some vocal diseases, such as vocal nodules, edema, and so on. Therefore, we expect that this model might not only provide a more appropriate description of the vocal fold vibration, but that it could also have clinical value in investigating certain vocal fold diseases.

A self-oscillating biophysical computer model of the elongated vocal fold

A new three-dimensional model is developed to simulate the self-oscillation of the elongated vocal folds. This model allows for large deformation and longitudinal displacement. The displacement boundary condition is applied on the posterior side to represent the elongation of vocal fold length by the cricothyroid or the thyroarytenoid muscles. After this model is verified by comparing its outputs using modal analysis and principle component analysis with those of previous models and experimental studies, it is applied to simulate the vibration of elongated vocal fold. Numerical simulation showed that longitudinal elongation increases the y-direction normal stress, decreases the lateral maximum displacement, and increases the fundamental frequency. These results agree with experimental measurements from an excised larynx setup, which suggests that the proposed elongation vocal fold model could be a useful tool to investigate voice production and the control of vocal fold vibration.

Modeling of the transient responses of the vocal fold lamina propria

The human voice is produced by flow-induced self-sustained oscillation of the vocal fold lamina propria. The mechanical properties of vocal fold tissues are important for understanding phonation, including the time-dependent and transient changes in fundamental frequency (F(0)). Cyclic uniaxial tensile tests were conducted on a group of specimens of the vocal fold lamina propria, including the superficial layer (vocal fold cover) (5 male, 5 female) and the deeper layers (vocal ligament) (6 male, 6 female). Results showed that the vocal fold lamina propria, like many other soft tissues, exhibits both elastic and viscous behavior. Specifically, the transient mechanical responses of cyclic stress relaxation and creep were observed. A three-network constitutive model composed of a hyperelastic equilibrium network in parallel with two viscoplastic time-dependent networks proves effective in characterizing the cyclic stress relaxation and creep behavior. For male vocal folds at a stretch of 1.4, significantly higher peak stress was found in the vocal ligament than in the vocal fold cover. Also, the male vocal ligament was significantly stiffer than the female vocal ligament. Our findings may help explain the mechanisms of some widely observed transient phenomena in F(0) regulation during phonation, such as the global declination in F(0) during the production of declarative sentences, and local F(0) changes such as overshoot and undershoot.

Reducing the number of vocal fold mechanical tissue properties: evaluation of the incompressibility and planar displacement assumptions

The incompressibility and planar displacement assumptions were used to reduce the number of independent tissue parameters required for the characterization of a structural model of the vocal folds. The influence of these simplifying assumptions on the vibratory properties of the model was investigated. The purpose was to provide estimates of the error introduced by these assumptions. The variability in human tissue properties was accounted for through systematic variation of several material parameters. The modal properties of a vocal fold structural model were computed with each assumption and, in turn, were relaxed to determine their respective effects. The results indicated that the incompressibility assumption introduces little error. Errors introduced by the planar displacement assumption were found to depend on the ratio of the longitudinal stiffness and the transverse stiffness. Criteria for determining the compatibility of tissue property values from independent studies are also presented.

An immersed-boundary method for flow-structure interaction in biological systems with application to phonation

A new numerical approach for modeling a class of flow-structure interaction problems typically encountered in biological systems is presented. In this approach, a previously developed, sharp-interface, immersed-boundary method for incompressible flows is used to model the fluid flow and a new, sharp-interface Cartesian grid, immersed boundary method is devised to solve the equations of linear viscoelasticity that governs the solid. The two solvers are coupled to model flow-structure interaction. This coupled solver has the advantage of simple grid generation and efficient computation on simple, single-block structured grids. The accuracy of the solid-mechanics solver is examined by applying it to a canonical problem. The solution methodology is then applied to the problem of laryngeal aerodynamics and vocal fold vibration during human phonation. This includes a three-dimensional eigen analysis for a multi-layered vocal fold prototype as well as two-dimensional, flow-induced vocal fold vibration in a modeled larynx. Several salient features of the aerodynamics as well as vocal-fold dynamics are presented.

Vocal fold elasticity of the Rocky Mountain elk (Cervus elaphus nelsoni) - producing high fundamental frequency vocalization with a very long vocal fold

The vocal folds of male Rocky Mountain elk (Cervus elaphus nelsoni) are about 3 cm long. If fundamental frequency were to be predicted by a simple vibrating string formula, as is often done for the human larynx, such long vocal folds would bear enormous stress to produce the species-specific mating call with an average fundamental frequency of 1 kHz. Predictions would be closer to 50 Hz. Vocal fold histology revealed the presence of a large vocal ligament between the vocal fold epithelium and the thyroarytenoid muscle. In tensile tests, the stress-strain response of vocal fold epithelium and the vocal ligament were determined. Elasticity of both tissue structures reached quantitative values similar to human tissue. It seems unlikely that the longitudinal stress in elk vocal folds can exceed that in human vocal folds by an order of magnitude to overcome the drop in fundamental frequency due to a 3:1 increase in vocal fold length. Alternative hypotheses of how the elk produces high fundamental frequency utterances, despite its very long vocal fold, include a reduced effective vocal fold length in vibration, either due to bending properties along the vocal fold, or by actively moving the boundary point with muscle stiffening. The relationships between an individual's average fundamental frequency, vocal fold length and body size are discussed.

Predictions of fundamental frequency changes during phonation based on a biomechanical model of the vocal fold lamina propria

This study examines the local and global changes of fundamental frequency (F(0)) during phonation and proposes a biomechanical model of predictions of F(0) contours based on the mechanics of vibration of vocal fold lamina propria. The biomechanical model integrates the constitutive description of the tissue mechanical response with a structural model of beam vibration. The constitutive model accounts for the nonlinear and time-dependent response of the vocal fold cover and the vocal ligament. The structural model of the vocal fold lamina propria is based on a composite beam model with axial stress. Results show that local fluctuations such as F(0) overshoots and undershoots can be characterized by the biomechanical model and might be related to the processes of stress relaxation of vocal fold tissues during length changes. The global changes of F(0) declination in declarative sentence production can also be characterized by the model. Such F(0) declination is partially attributed to the peak stress decay associated with stress relaxation of the vocal fold lamina propria and partially to neuromuscular control of the vocal fold length.

A muscle controlled finite-element model of laryngeal abduction and adduction

A three-dimensional finite-element model was developed to simulate the complex movement of the laryngeal cartilages during vocal fold abduction and adduction. The model consists of cricoid and arytenoid cartilages, as well as the intralaryngeal muscles and vocal folds. The active and passive properties of the muscles were idealised by one-dimensional elements based on the Hill theory. Its controlling input value is a time dependent stimulation rate. Optimisation loops have been carried out for the arrangement of the individual stimulation rates. Since in vivo measurements are not feasible, the developed biomechanical model shall be used to analyse the force distribution within the laryngeal muscles during phonatory manoeuvres. Simulations of abduction and adduction in different pitches of voice lead to realistic tensions of the vocal folds. The model is a first step to analyse motional vocal fold diseases and to predict the consequences of phonosurgical interventions.

A numerical study of the flow-induced vibration characteristics of a voice-producing element for laryngectomized patients

A computational model for exploring the design of a voice-producing voice prosthesis, or voice-producing element (VPE), is presented. The VPE is intended for use by laryngectomized patients who cannot benefit from current speech rehabilitation techniques. Previous experiments have focused on the design of a double-membrane voice generator as a VPE. For optimization studies, a numerical model has been developed. The numerical model introduced incorporates the finite element (FE) method to solve for the flow-induced vibrations of the VPE system, including airflow coupled with a mass-loaded membrane. The FE model includes distinct but coupled fluid and solid domains. The flow solver is governed by the incompressible, laminar, unsteady Navier-Stokes equations. The solid solver allows for large deformation, large strain, and collision. It is first shown that the model satisfactorily represents previously published experimental results in terms of frequency and flow rate, enabling the model for use as a design tool. The model is then used to study the influence of geometric scaling, membrane thickness, membrane stiffness, and slightly convergent or divergent channel geometry on the model response. It is shown that physiological allowable changes in the latter three device parameters alone will not be sufficient to generate the desired reduction in fundamental frequency. However, their effects are quantified and it is shown that membrane stiffness and included angle should be considered in future designs.

Relative contributions of collagen and elastin to elasticity of the vocal fold under tension

This study examined the contributions of collagen and elastin to the tensile elastic properties of the vocal fold lamina propria. Uniaxial stress-strain responses of vocal fold cover and vocal ligament specimens from 20 human larynges (12 males, 8 females) were quantified with sinusoidal stretch-release deformation in vitro. Mid-coronal sections of 12 specimens were examined histologically with Masson's trichrome and elastin van Gieson stain to quantify the relative densities of collagen and elastin fibers. Results showed that significantly higher levels of collagen were found in the male vocal fold than female, for both the cover and the ligament. For male there was a significantly higher level of elastin in the cover than in the ligament. On average, the elastic modulus of the male cover was about twice that of the female at high-tensile strain (35-40%), whereas the male ligament was 3-5 times stiffer than the female in the same range. The ligament was stiffer than the cover for male, but the opposite was observed for female. These findings suggested that collagen and elastin could contribute differentially to elasticity of the cover and the ligament. The data may provide guidance for surgical reconstruction and tissue engineering of different lamina propria layers.

Refinements in modeling the passive properties of laryngeal soft tissue

The nonlinear viscoelastic passive properties of three canine intrinsic laryngeal muscles, the lateral cricoarytenoid (LCA), the posterior cricoarytenoid (PCA), and the interarytenoid (IA), were fit to the parameters of a modified Kelvin model. These properties were compared with those of the thyroarytenoid (TA) and cricothyroid (CT) muscles, as well as previously unpublished viscoelastic characteristics of the human vocal ligament. Passive parameters of the modified Kelvin model were summarized for the vocal ligament, mucosa, and all five laryngeal muscles. Results suggest that the LCA, PCA, and IA muscles are functionally different from the TA and CT muscles in their load-bearing capacity. Furthermore, the LCA, PCA, and IA have a much larger stress-strain hysteresis effect than has been previously reported for the TA and CT or the vocal ligament. The variation in this effect suggests that the connective tissue within the TA and CT muscles is somehow similar to the vocal ligament but different from the LCA, PCA, or IA muscles. Further demonstrating the potential significance of grouping tissues in the laryngeal system by functional groups in the laryngeal system was the unique finding that, over their working elongation range, the LCA and PCA were nearly as exponentially stiff as the vocal ligament. This paper was written in conjunction with an online technical report (http://www.ncvs.org/ncvs/library/tech) in which comprehensive muscle data and sensitivity analysis, as well as downloadable data files and computer scripts, are made available.

Sensitivity of a continuum vocal fold model to geometric parameters, constraints, and boundary conditions

The influence of key dimensional parameters, motion constraints, and boundary conditions on the modal properties of an idealized, continuum model of the vocal folds was investigated. The Ritz method and the finite element method were used for the analysis. The model's vibratory modes were determined to be most sensitive to changes in the anterior-posterior length of the vocal fold model, due to the influence of three-dimensional stress components acting in the transverse plane. Anterior/ posterior boundary conditions were found to have a significant influence on the vibratory response. Overestimation of modal frequencies resulted when vibration of the structure was restricted to the transverse plane. The overestimation of each modal frequency was proportional to the ratio of longitudinal to transverse Young's modulus, and was significant for ratio values less than 20.

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.

An in vitro setup to test the relevance and the accuracy of low-order vocal folds models

An experimental setup and human vocal folds replica able to produce self-sustained oscillations are presented. The aim of the setup is to assess the relevance and the accuracy of theoretical vocal folds models. The applied reduced mechanical models are a variation of the classical two-mass model, and a simplification inspired on the delayed mass model for which the coupling between the masses is expressed as a fixed time delay. The airflow is described as a laminar flow with flow separation. The influence of a downstream resonator is taken into account. The oscillation pressure threshold and fundamental frequency are predicted by applying a stability analysis to the mechanical models. The measured frequency response of the mechanical replica together with the initial (rest) area allows us to determine the model parameters (spring stiffness, damping, geometry, masses). Validation of theoretical model predictions to experimental data shows the relevance of low-order models in gaining a qualitative understanding of phonation. However, quantitative discrepancies remain large due to an inaccurate estimation of the model parameters and the crudeness in either flow or mechanical model description. As an illustration it is shown that significant improvements can be made by accounting for viscous flow effects.

Mechanical stress during phonation in a self-oscillating finite-element vocal fold model

The stress information during phonation in the vocal folds is helpful in understanding the etiologies of vocal trauma and its related vocal diseases, such as nodules. In this paper, a self-oscillating finite-element model, which combines aerodynamic properties, tissue mechanics, airflow-tissue interactions, and vocal fold collisions, was used to simulate the vocal fold vibration during phonation. The spatial and temporal characteristics of mechanical stress in the vocal folds were predicted by this model. Temporally, it was found that mechanical stress periodically undulates with vibration of the vocal folds and that vocal fold impact causes a jump in the normal stress value. Spatially, the normal stress is significantly higher on the vocal fold surface than inside of the vocal folds. At the midpoint of the medial surface, the peak-to-peak amplitude of the normal stress reaches its maximum value. Using different lung pressures (0-1.5kPa) to drive the self-oscillating model, we found that lower lung pressure can effectively decrease the mechanical stress in the vocal folds. This study supports the fatigue damage hypothesis of vocal trauma. With this hypothesis and the numerical simulation in this study, the clinical observations of vocal fold trauma risk can be explained. This implies the mechanical stress predicted by this self-oscillating model could be valuable for predicting, preventing, and treating vocal fold injury.

Sensitivity of elastic properties to measurement uncertainties in laryngeal muscles with implications for voice fundamental frequency prediction

This paper discusses the effects of measurement uncertainties when calculating elastic moduli of laryngeal tissue. Small dimensions coupled with highly nonlinear elastic properties exacerbate the uncertainties. The sensitivity of both tangent and secant Young's Modulus was quantified in terms of the coefficient of variation, which depended on measurement of reference length and cross-sectional area. Uncertainties in the measurement of mass, used to calculate cross-sectional area of a small tissue sample, affected Young's Modulus calculations when tissue absorption of the hydrating solution was not accounted for. Uncertainty in reference length had twice the effect on elasticity than other measures. The implication of these measurement errors on predicted fundamental frequency of vocalization is discussed. Refinements on isolated muscle experimental protocols are proposed that pay greatest attention to measures of highest sensitivity.

Proteomic profiling of rat thyroarytenoid muscle

PURPOSE

Proteomic methodologies offer promise in elucidating the systemwide cellular and molecular processes that characterize normal and diseased thyroarytenoid (TA) muscle. This study examined methodological issues central to the application of 2-dimensional sodium dodecyl sulfate polyacrylamide gel electrophoresis (2D SDS-PAGE) to the study of the TA muscle proteome using a rat model.

METHOD

2D SDS-PAGE was performed using 4 chemically skinned rat TA muscle samples. Gel images were analyzed and compared. Protein spot detection and matching were performed using computational image analysis algorithms only and computational image analysis followed by visual inspection and manual error correction. A synthetic master gel, constructed to control for uninteresting biological variation and technical artifact due to differences in protein loading and staining, was evaluated against its constituent gels.

RESULTS

Manual error correction resulted in a consistent increase in the number of protein spots detected (between 5.8% and 40.9%) and matched (from 25.8% to 70.8%) across all gels. Sensitivity and specificity of the automatic (computational) spot detection procedure, evaluated against the manual correction procedure, were 74.1% and 97.9%, respectively. Evaluation of protein quantitation parameter values revealed statistically significant differences (p < .0001) in optical density, area, and volume for matched protein spots across gels. The synthetic master gel successfully compensated for these intergel differences.

CONCLUSIONS

Valid and reliable proteomic data are dependant on well-controlled manageable variability and well-defined unmanageable variability. Manual correction of spot detection and matching errors and the use of a synthetic master gel appear to be useful strategies in addressing these issues. With these issues accounted for, 2D SDS-PAGE may be applied to quantitative experimental comparisons of normal and disease conditions affecting voice, speech, and swallowing function.

Review of range of arytenoid cartilage motion

Vocal fold abduction/adduction posturing is key to phonation control. As biomechanical models of the larynx increase in complexity, there is a need to verify them with laboratory data. To help experimental cross-validation of models, ranges of vocal process displacement were reviewed and combined. Although general inter-study agreement was found, there was substantial variation. Using a model of vocal fold posturing, insights were uncovered that could not otherwise be made; best-practice guidelines and research avenues for future studies of vocal posturing were also outlined.

Computational simulations of vocal fold vibration: Bernoulli versus Navier-Stokes

The use of the mechanical energy (ME) equation for fluid flow, an extension of the Bernoulli equation, to predict the aerodynamic loading on a two-dimensional finite element vocal fold model is examined. Three steady, one-dimensional ME flow models, incorporating different methods of flow separation point prediction, were compared. For two models, determination of the flow separation point was based on fixed ratios of the glottal area at separation to the minimum glottal area; for the third model, the separation point determination was based on fluid mechanics boundary layer theory. Results of flow rate, separation point, and intraglottal pressure distribution were compared with those of an unsteady, two-dimensional, finite element Navier-Stokes model. Cases were considered with a rigid glottal profile as well as with a vibrating vocal fold. For small glottal widths, the three ME flow models yielded good predictions of flow rate and intraglottal pressure distribution, but poor predictions of separation location. For larger orifice widths, the ME models were poor predictors of flow rate and intraglottal pressure, but they satisfactorily predicted separation location. For the vibrating vocal fold case, all models resulted in similar predictions of mean intraglottal pressure, maximum orifice area, and vibration frequency, but vastly different predictions of separation location and maximum flow rate.

A constitutive model of the human vocal fold cover for fundamental frequency regulation

The elastic as well as time-dependent mechanical response of the vocal fold cover (epithelium and superficial layer of the lamina propria) under tension is one key variable in regulating the fundamental frequency. This study examines the hyperelastic and time-dependent tensile deformation behavior of a group of human vocal fold cover specimens (six male and five female). The primary goal is to formulate a constitutive model that could describe empirical trends in speaking fundamental frequency with reasonable confidence. The constitutive model for the tissue mechanical behavior consists of a hyperelastic equilibrium network in parallel with an inelastic, time-dependent network and is combined with the ideal string model for phonation. Results showed that hyperelastic and time-dependent parameters of the constitutive model can be related to observed age-related and gender-related differences in speaking fundamental frequency. The implications of these findings on fundamental frequency regulation are described. Limitations of the current constitutive model are discussed.

Biofluid Mechanics of the Pulmonary System

Presents an overview of leading areas of discovery in bio-fluid mechanics related to the pulmonary system, with particular reference to the airways. Areas briefly reviewed include airway gas dynamics, impedance studies, collapsible-tube studies, and airway liquid studies. Emphasis is placed on promising further directions, such as analysis of interacting fluid-mechanical or fluid-structure phenomena, multi-scale modeling across widely varying length and time scales, and integration of advanced simulations into respiratory investigation and pulmonary medicine.

Medial surface dynamics of an in vivo canine vocal fold during phonation

Quantitative measurement of the medial surface dynamics of the vocal folds is important for understanding how sound is generated within the larynx. Building upon previous excised hemilarynx studies, the present study extended the hemilarynx methodology to the in vivo canine larynx. Through use of an in vivo model, the medial surface dynamics of the vocal fold were examined as a function of active thyroarytenoid muscle contraction. Data were collected using high-speed digital imaging at a sampling frequency of 2000 Hz, and a spatial resolution of 1024 x 1024 pixels. Chest-like and fry-like vibrations were observed, but could not be distinguished based on the input stimulation current to the recurrent laryngeal nerve. The subglottal pressure did distinguish the registers, as did an estimate of the thyroarytenoid muscle activity. Upon quantification of the three-dimensional motion, the method of Empirical Eigenfunctions was used to extract the underlying modes of vibration, and to investigate mechanisms of sustained oscillation. Results were compared with previous findings from excised larynx experiments and theoretical models.