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.     

Adapted to roar: functional morphology of tiger and lion vocal folds

Vocal production requires active control of the respiratory system, larynx and vocal tract. Vocal sounds in mammals are produced by flow-induced vocal fold oscillation, which requires vocal fold tissue that can sustain the mechanical stress during phonation. Our understanding of the relationship between morphology and vocal function of vocal folds is very limited. Here we tested the hypothesis that vocal fold morphology and viscoelastic properties allow a prediction of fundamental frequency range of sounds that can be produced, and minimal lung pressure necessary to initiate phonation. We tested the hypothesis in lions and tigers who are well-known for producing low frequency and very loud roaring sounds that expose vocal folds to large stresses. In histological sections, we found that the Panthera vocal fold lamina propria consists of a lateral region with adipocytes embedded in a network of collagen and elastin fibers and hyaluronan. There is also a medial region that contains only fibrous proteins and hyaluronan but no fat cells. Young's moduli range between 10 and 2000 kPa for strains up to 60%. Shear moduli ranged between 0.1 and 2 kPa and differed between layers. Biomechanical and morphological data were used to make predictions of fundamental frequency and subglottal pressure ranges. Such predictions agreed well with measurements from natural phonation and phonation of excised larynges, respectively. We assume that fat shapes Panthera vocal folds into an advantageous geometry for phonation and it protects vocal folds. Its primary function is probably not to increase vocal fold mass as suggested previously. The large square-shaped Panthera vocal fold eases phonation onset and thereby extends the dynamic range of the voice.     

Physical simulation of laryngeal disorders using a multiple-mass vocal fold model

This paper reports on the use of a high-dimensional discrete vocal fold model for the simulation of voice production under the presence of laryngeal disorders. Specifically, the effect of increases in mass and stiffness, both unilateral and bilateral, has been analysed independently for both magnitudes. The glottal flow waveform and the mass displacement have been studied and the obtained results are coherent with clinical observations that relate mass increments with lowered fundamental frequencies and mass and stiffness increments with reduced vibratory amplitudes of vocal folds. The reported results also indicate that asymmetries in the physical properties of vocal folds result in asymmetries in their vibratory patterns, including phase, amplitude and behaviour on collision. These are also correlated with voice perturbation measures such as jitter, shimmer and normalised noise energy.     

A computational study of systemic hydration in vocal fold collision

Mechanical stresses develop within vocal fold (VF) soft tissues due to phonation-associated vibration and collision. These stresses in turn affect the hydration of VF tissue and thus influence voice health. In this paper, high-fidelity numerical computations are described, taking into account fully 3D geometry, realistic tissue and air properties, and high-amplitude vibration and collision. A segregated solver approach is employed, using sophisticated commercial solvers for both the VF tissue and glottal airflow domains. The tissue viscoelastic properties were derived from a biphasic formulation. Two cases were considered, whereby the tissue viscoelastic properties corresponded to two different volume fractions of the fluid phase of the VF tissue. For each case, hydrostatic stresses occurring as a result of vibration and collision were investigated. Assuming the VF tissue to be poroelastic, interstitial fluid movement within VF tissue was estimated from the hydrostatic stress gradient. Computed measures of overall VF dynamics (peak airflow velocity, magnitude of VF deformation, frequency of vibration and contact pressure) were well within the range of experimentally observed values. The VF motion leading to mechanical stresses within the VFs and their effect on the interstitial fluid flux is detailed. It is found that average deformation and vibration of VFs tend to increase the state of hydration of the VF tissue, whereas VF collision works to reduce hydration.     

Modeling viscous dissipation during vocal fold contact: the influence of tissue viscosity and thickness with implications for hydration

The mechanics of vocal fold contact during phonation is known to play a crucial role in both normal and pathological speech production, though the underlying physics is not well understood. Herein, a viscoelastic model of the stresses during vocal fold contact is developed. This model assumes the cover to be a poroelastic structure wherein interstitial fluid translocates in response to mechanical squeezing. The maximum interstitial fluid pressure is found to generally increase with decreasing viscous dissipation and/or decreasing tissue elasticity. A global minimum in the total contact stress, comprising interstitial fluid pressure and elastic stress in the tissue, is observed over the studied dimensionless parameter range. Interestingly, physiologically reasonable estimates for the governing parameters fall within this global minimum region. The model is validated against prior experimental and computational work, wherein the predicted contact stress magnitude and impact duration agree well with published results. Lastly, observations of the potential relationship between vocal fold hydration and increased risk of tissue damage are discussed based upon model predictions of stress as functions of cover layer thickness and viscosity.     

Predicting Achievable Fundamental Frequency Ranges in Vocalization Across Species

Vocal folds are used as sound sources in various species, but it is unknown how vocal fold morphologies are optimized for different acoustic objectives. Here we identify two main variables affecting range of vocal fold vibration frequency, namely vocal fold elongation and tissue fiber stress. A simple vibrating string model is used to predict fundamental frequency ranges across species of different vocal fold sizes. While average fundamental frequency is predominantly determined by vocal fold length (larynx size), range of fundamental frequency is facilitated by (1) laryngeal muscles that control elongation and by (2) nonlinearity in tissue fiber tension. One adaptation that would increase fundamental frequency range is greater freedom in joint rotation or gliding of two cartilages (thyroid and cricoid), so that vocal fold length change is maximized. Alternatively, tissue layers can develop to bear a disproportionate fiber tension (i.e., a ligament with high density collagen fibers), increasing the fundamental frequency range and thereby vocal versatility. The range of fundamental frequency across species is thus not simply one-dimensional, but can be conceptualized as the dependent variable in a multi-dimensional morphospace. In humans, this could allow for variations that could be clinically important for voice therapy and vocal fold repair. Alternative solutions could also have importance in vocal training for singing and other highly-skilled vocalizations.     

Non-invasive in vivo measurement of the shear modulus of human vocal fold tissue

Voice is the essential part of singing and speech communication. Voice disorders significantly affect the quality of life. The viscoelastic mechanical properties of the vocal fold mucosa determine the characteristics of the vocal folds oscillations, and thereby voice quality. In the present study, a non-invasive method was developed to determine the shear modulus of human vocal fold tissue in vivo via measurements of the mucosal wave propagation speed during phonation. Images of four human subjects' vocal folds were captured using high speed digital imaging (HSDI) and magnetic resonance imaging (MRI) for different phonation pitches, specifically fundamental frequencies between 110 and 440 Hz. The MRI images were used to obtain the morphometric dimensions of each subject's vocal folds in order to determine the pixel size in the high-speed images. The mucosal wave propagation speed was determined for each subject and at each pitch value using an automated image processing algorithm. The transverse shear modulus of the vocal fold mucosa was then calculated from a surface (Rayleigh) wave propagation dispersion equation using the measured wave speeds. It was found that the mucosal wave propagation speed and therefore the shear modulus of the vocal fold tissue were generally greater at higher pitches. The results were in good agreement with those from other studies obtained via in vitro measurements, thereby supporting the validity of the proposed measurement method. This method offers the potential for in vivo clinical assessments of vocal folds viscoelasticity from HSDI.     

Vocal fold tissue failure: preliminary data and constitutive modeling

In human voice production (phonation), linear small-amplitude vocal fold oscillation occurs only under restricted conditions. Physiologically, phonation more often involves large-amplitude oscillation associated with tissue stresses and strains beyond their linear viscoelastic limits, particularly in the lamina propria extracellular matrix (ECM). This study reports some preliminary measurements of tissue deformation and failure response of the vocal fold ECM under large-strain shear The primary goal was to formulate and test a novel constitutive model for vocal fold tissue failure, based on a standard-linear cohesive-zone (SL-CZ) approach. Tissue specimens of the sheep vocal fold mucosa were subjected to torsional deformation in vitro, at constant strain rates corresponding to twist rates of 0.01, 0.1, and 1.0 rad/s. The vocal fold ECM demonstrated nonlinear stress-strain and rate-dependent failure response with a failure strain as low as 0.40 rad. A finite-element implementation of the SL-CZ model was capable of capturing the rate dependence in these preliminary data, demonstrating the model's potential for describing tissue failure. Further studies with additional tissue specimens and model improvements are needed to better understand vocal fold tissue failure.     

Laryngeal muscle responses to mechanical displacement of the thyroid cartilage in humans.

Speakers may use laryngeal sensory feedback to adjust vocal fold tension and length before initiating voice. The mechanism for accurately initiating voice at an intended pitch is unknown, given the absence of laryngeal muscle spindles in animals and conflicting findings regarding their existence in humans. Previous reports of rapid changes in voice fundamental frequency following thyroid cartilage displacement suggest that changes in vocal fold length modulate laryngeal muscle contraction in humans. We tested the hypothesis that voice changes resulting from mechanical perturbation are due to rapid responses in the intrinsic laryngeal muscles. Hooked wire electrodes were used to record from the thyroarytenoid, cricothyroid, and sternothyroid muscles along with surface electrodes on the skin overlying the thyroid cartilage in 10 normal adults. Servomotor displacements produced consistent changes in the subjects' vocal fundamental frequency at 70-80 ms, demonstrating changes in vocal fold length and tension. No simultaneous electromyographic responses occurred in the thyroarytenoid or cricothyroid muscles in any subjects. Instead, short-latency responses at 25-40 ms following stimulus onset occurred in the sternothyroid muscles, simultaneous with responses in the surface recordings. The sternothyroid responses may modulate long-latency changes in voice fundamental frequency (approximately 150 ms). The absence of intrinsic laryngeal muscle responses is consistent with a lack of spindles in these muscles. Our results suggest that other sensory receptors, such as mucosal mechanoreceptors, provide feedback for voice control.     

Elasticity and stress relaxation of a very small vocal fold

Across mammals many vocal sounds are produced by airflow induced vocal fold oscillation. We tested the hypothesis that stress-strain and stress-relaxation behavior of rat vocal folds can be used to predict the fundamental frequency range of the species' vocal repertoire. In a first approximation vocal fold oscillation has been modeled by the string model but it is not known whether this concept equally applies to large and small species. The shorter the vocal fold, the more the ideal string law may underestimate normal mode frequencies. To accommodate the very small size of the tissue specimen, a custom-built miniaturized tensile test apparatus was developed. Tissue properties of 6 male rat vocal folds were measured. Rat vocal folds demonstrated the typical linear stress-strain behavior in the low strain region and an exponential stress response at strains larger than about 40%. Approximating the rat's vocal fold oscillation with the string model suggests that fundamental frequencies up to about 6 kHz can be produced, which agrees with frequencies reported for audible rat vocalization. Individual differences and time-dependent changes in the tissue properties parallel findings in other species, and are interpreted as universal features of the laryngeal sound source.     

Influence of asymmetric stiffness on the structural and aerodynamic response of synthetic vocal fold models

The influence of asymmetric vocal fold stiffness on voice production was evaluated using life-sized, self-oscillating vocal fold models with an idealized geometry based on the human vocal folds. The models were fabricated using flexible, materially-linear silicone compounds with Young's modulus values comparable to that of vocal fold tissue. The models included a two-layer design to simulate the vocal fold layered structure. The respective Young's moduli of elasticity of the “left” and “right” vocal fold models were varied to create asymmetric conditions. High-speed videokymography was used to measure maximum vocal fold excursion, vibration frequency, and left–right phase shift, all of which were significantly influenced by asymmetry. Onset pressure, a measure of vocal effort, increased with asymmetry. Particle image velocimetry (PIV) analysis showed significantly greater skewing of the glottal jet in the direction of the stiffer vocal fold model. Potential applications to various clinical conditions are mentioned, and suggestions for future related studies are presented.     

Synthetic,Multi-Layer,Self-Oscillating Vocal Fold Model Fabrication

Sound for the human voice is produced via flow-induced vocal fold vibration. The vocal folds consist of several layers of tissue, each with differing material properties ¹. Normal voice production relies on healthy tissue and vocal folds, and occurs as a result of complex coupling between aerodynamic, structural dynamic, and acoustic physical phenomena. Voice disorders affect up to 7.5 million annually in the United States alone ² and often result in significant financial, social, and other quality-of-life difficulties. Understanding the physics of voice production has the potential to significantly benefit voice care, including clinical prevention, diagnosis, and treatment of voice disorders.Existing methods for studying voice production include in vivo experimentation using human and animal subjects, in vitro experimentation using excised larynges and synthetic models, and computational modeling. Owing to hazardous and difficult instrument access, in vivo experiments are severely limited in scope. Excised larynx experiments have the benefit of anatomical and some physiological realism, but parametric studies involving geometric and material property variables are limited. Further, they are typically only able to be vibrated for relatively short periods of time (typically on the order of minutes).Overcoming some of the limitations of excised larynx experiments, synthetic vocal fold models are emerging as a complementary tool for studying voice production. Synthetic models can be fabricated with systematic changes to geometry and material properties, allowing for the study of healthy and unhealthy human phonatory aerodynamics, structural dynamics, and acoustics. For example, they have been used to study left-right vocal fold asymmetry ^3,4, clinical instrument development ⁵, laryngeal aerodynamics ^6-9, vocal fold contact pressure ¹⁰, and subglottal acoustics ¹¹ (a more comprehensive list can be found in Kniesburges et al. ¹²)Existing synthetic vocal fold models, however, have either been homogenous (one-layer models) or have been fabricated using two materials of differing stiffness (two-layer models). This approach does not allow for representation of the actual multi-layer structure of the human vocal folds ¹ that plays a central role in governing vocal fold flow-induced vibratory response. Consequently, one- and two-layer synthetic vocal fold models have exhibited disadvantages ^3,6,8 such as higher onset pressures than what are typical for human phonation (onset pressure is the minimum lung pressure required to initiate vibration), unnaturally large inferior-superior motion, and lack of a "mucosal wave" (a vertically-traveling wave that is characteristic of healthy human vocal fold vibration).In this paper, fabrication of a model with multiple layers of differing material properties is described. The model layers simulate the multi-layer structure of the human vocal folds, including epithelium, superficial lamina propria (SLP), intermediate and deep lamina propria (i.e., ligament; a fiber is included for anterior-posterior stiffness), and muscle (i.e., body) layers ¹. Results are included that show that the model exhibits improved vibratory characteristics over prior one- and two-layer synthetic models, including onset pressure closer to human onset pressure, reduced inferior-superior motion, and evidence of a mucosal wave.     

Design of a mechanical larynx with agarose as a soft tissue substitute for vocal fold applications

Mechanical and computational models consisting of flow channels with convergent and oscillating constrictions have been applied to study the dynamics of human vocal fold vibration. To the best of our knowledge, no mechanical model has been studied using a material substitute with similar physical properties to the human vocal fold for surgical experimentation. In this study, we design and develop a mechanical larynx with agarose as a vocal fold substitute, and assess its suitability for surgical experimentation. Agarose is selected as a substitute for the vocal fold as it exhibits similar nonlinear hyperelastic characteristics to biological soft tissue. Through uniaxial compression and extension tests, we determined that agarose of 0.375% concentration most closely resembles the vocal fold mucosa and ligament of a 20-year old male for small tensile strain with an R(2) value of 0.9634 and root mean square error of 344.05±39.84?Pa. Incisions of 10 mm lengthwise and 3 mm in depth were created parallel to the medial edge on the superior surface of agar phantom. These were subjected to vibrations of 80, 130, and 180 Hz, at constant amplitude of 0.9 mm over a period of 10 min each in the mechanical larynx model. Lateral expansion of the incision was observed to be most significant for the lower frequency of 80 Hz. This model serves as a basis for future assessments of wound closure techniques during microsurgery to the vocal fold.     

Mechanotransduction of vocal fold fibroblasts and mesenchymal stromal cells in the context of the vocal fold mechanome

The design of cell-based therapies for vocal fold tissue engineering requires an understanding of how cells adapt to the dynamic mechanical forces found in the larynx. Our objective was to compare mechanotransductive processes in therapeutic cell candidates (mesenchymal stromal cells from adipose tissue and bone marrow, AT-MSC and BM-MSC) to native cells (vocal fold fibroblasts-VFF) in the context of vibratory strain. A bioreactor was used to expose VFF, AT-MSC, and BM-MSC to axial tensile strain and vibration at human physiological levels. Microarray, an empirical Bayes statistical approach, and geneset enrichment analysis were used to identify significant mechanotransductive pathways associated with the three cell types and three mechanical conditions. Two databases (Gene Ontology, Kyoto Encyclopedia of Genes and Genomes) were used for enrichment analyses. VFF shared more mechanotransductive pathways with BM-MSC than with AT-MSC. Gene expression that appeared to distinguish the vibratory strain condition from polystyrene condition for these two cells types related to integrin activation, focal adhesions, and lamellipodia activity, suggesting that vibratory strain may be associated with cytoarchitectural rearrangement, cell reorientation, and extracellular matrix remodeling. In response to vibration and tensile stress, BM-MSC better mimicked VFF mechanotransduction than AT-MSC, providing support for the consideration of BM-MSC as a cell therapy for vocal fold tissue engineering. Future research is needed to better understand the sorts of physical adaptations that are afforded to vocal fold tissue as a result of focal adhesions, integrins, and lamellipodia, and how these adaptations could be exploited for tissue engineering.     

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.     

Optical measurements of vocal fold tensile properties: implications for phonatory mechanics

In voice research, in vitro tensile stretch experiments of vocal fold tissues are commonly employed to determine the tissue biomechanical properties. In the standard stretch-release protocol, tissue deformation is computed from displacements applied to sutures inserted through the thyroid and arytenoid cartilages, with the cartilages assumed to be rigid. Here, a non-contact optical method was employed to determine the actual tissue deformation of vocal fold lamina propria specimens from three excised human larynges in uniaxial tensile tests. Specimen deformation was found to consist not only of deformation of the tissue itself, but also deformation of the cartilages, as well as suture alignment and tightening. Stress-stretch curves of a representative load cycle were characterized by an incompressible Ogden model. The initial longitudinal elastic modulus was found to be considerably higher if determined based on optical displacement measurements than typical values reported in the literature. The present findings could change the understanding of the mechanics underlying vocal fold vibration. Given the high longitudinal elastic modulus the lamina propria appeared to demonstrate a substantial level of anisotropy. Consequently, transverse shear could play a significant role in vocal fold vibration, and fundamental frequencies of phonation should be predicted by beam theories accounting for such effects.     

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.     

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.