Modeling mechanical stresses as a factor in the etiology of benign vocal fold lesions

Vocal fold tissue lesions such as nodules and polyps are thought to develop in response to mechanical stress that occurs during vocal fold collision. Two computational models of vocal fold collision during voice production are used to investigate this hypothesis. A one-dimensional lumped mass model, whose parameters are derived from vocal fold tissue dimensions and material properties, predicts stress perpendicular to the direction of impact (normal stress). A previously published three-dimensional finite element model that incorporates the same dimensions and properties predicts the entire stress tensor. The hypothesis is supported by predictions from the finite element model that three components of normal stress and one component of shear stress are increased during collision in the typical location of lesions (i.e. the center of the superior medial edge of the vocal fold in the middle of the vibrating and contact region). The lumped mass model predicts that mechanical stress is negatively correlated with mucosal thickness (increased by voice warm-up and hydration), is positively correlated with driving force (proportional to voice intensity), and is affected by voice production method. These relationships are consistent with clinical observations of vocal fold lesion risk factors and have implications for improving prevention and treatment of benign vocal fold lesions.     

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.     

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.     

A model for mechanics of primary lymphatic valves

Recent experimental evidence indicates that lymphatics have two valve systems, a set of primary valves in the wall of the endothelial cells of initial lymphatics and a secondary valve system in the lumen of the lymphatics. While the intralymphatic secondary valves are well described, no analysis of the primary valves is available. We propose a model for primary lymphatics valves at the junctions between lymphatic endothelial cells. The model consists of two overlapping endothelial extensions at a cell junction in the initial lymphatics. One cell extension is firmly attached to the adjacent connective tissue while the other cell extension is not attached to the interstitial collagen. It is free to bend into the lumen of the lymphatic when the lymphatic pressure falls below the adjacent interstitial fluid pressure. Thereby the cell junction opens a gap permitting entry of interstitial fluid into the lymphatic lumen. When the lymphatic fluid pressure rises above the adjacent interstitial fluid pressure, the endothelial extensions contact each other and the junction is closed preventing fluid reflow into the interstitial space. The model illustrates the mechanics of valve action and provides the first time a rational analysis of the mechanisms underlying fluid collection in the initial lymphatics and lymph transport in the microcirculation.     

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.     

A microstructurally based continuum model of cartilage viscoelasticity and permeability incorporating measured statistical fiber orientations

The remarkable mechanical properties of cartilage derive from an interplay of isotropically distributed, densely packed and negatively charged proteoglycans; a highly anisotropic and inhomogeneously oriented fiber network of collagens; and an interstitial electrolytic fluid. We propose a new 3D finite strain constitutive model capable of simultaneously addressing both solid (reinforcement) and fluid (permeability) dependence of the tissue’s mechanical response on the patient-specific collagen fiber network. To represent fiber reinforcement, we integrate the strain energies of single collagen fibers—weighted by an orientation distribution function (ODF) defined over a unit sphere—over the distributed fiber orientations in 3D. We define the anisotropic intrinsic permeability of the tissue with a structure tensor based again on the integration of the local ODF over all spatial fiber orientations. By design, our modeling formulation accepts structural data on patient-specific collagen fiber networks as determined via diffusion tensor MRI. We implement our new model in 3D large strain finite elements and study the distributions of interstitial fluid pressure, fluid pressure load support and shear stress within a cartilage sample under indentation. Results show that the fiber network dramatically increases interstitial fluid pressure and focuses it near the surface. Inhomogeneity in the tissue’s composition also increases fluid pressure and reduces shear stress in the solid. Finally, a biphasic neo-Hookean material model, as is available in commercial finite element codes, does not capture important features of the intra-tissue response, e.g., distributions of interstitial fluid pressure and principal shear stress.     

Influence of interstitial bone microcracks on strain-induced fluid flow

It is well known that microcracks act as a stimulus for bone remodelling, initiating resorption by osteoclasts and new bone formation by osteoblasts. Moreover, microcracks are likely to alter the fluid flow and convective transport through the bone tissue. This paper proposes a quantitative evaluation of the strain-induced interstitial fluid velocities developing in osteons in presence of a microcrack in the interstitial bone tissue. Based on Biot theory in the low-frequency range, a poroelastic model is carried out to study the hydro-mechanical behaviour of cracked osteonal tissue. The finite element results show that the presence of a microcrack in the interstitial osteonal tissue may drastically reduce the fluid velocity inside the neighbouring osteons. This fluid inactive zone inside osteons can cover up to 10% of their surface. Consequently, the fluid environment of bone mechano-sensitive cells is locally modified.     

A synthesis of interstitial fluid regulation and lymph formation.

The interstitial fluid spaces are filled with a mat of collagen fibers, and the interstices of this mat contain a mucopolysaccharide gel ground substance. Both the collagen fibers and the gel are elastic structures that can be expanded or compacted. In the expanded state the collagen fibers are pushed far apart and pockets of free fluid develop witin the gel. In the compacted state the elastic recoil of the compressed collagen fibers and gel reticular fibrillae seems to cause suction on the fluid within the tissue spaces, thus creating a subatmospheric pressure. Measurements of interstitial fluid pressure using a perforated capsule method indicate that this is normally slightly negative (subatmospheric) in most soft tissues. However, even very slight extra filtration of fluid into the tissue spaces increases the interstitial fluid pressure toward more positive values, which in turn increases lymph flow. The increased lymph flow then decreases the interstitial fluid volume and pressure back toward normal because of two mechanism, 1) direct removal of fluid from the tissue spaces in the lymph, and 2) removal of protein from the interstitial fluid in the lymph, thus decreasing the interstitial fluid colloid osmotic pressure and allowing more effective osmosis of fluid directly from the interstitial spaces back into the capillaries.     

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.     

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.     

Mechanics of interstitial-lymphatic fluid transport: theoretical foundation and experimental validation

Interstitial fluid movement is intrinsically linked to lymphatic drainage. However, their relationship is poorly understood, and associated pathologies are mostly untreatable. In this work we test the hypothesis that bulk tissue fluid movement can be evaluated in situ and described by a linear biphasic theory which integrates the regulatory function of the lymphatics with the mechanical stresses of the tissue. To accomplish this, we develop a novel experimental and theoretical model using the skin of the mouse tail. We then use the model to demonstrate how interstitial–lymphatic fluid movement depends on a balance between the elasticity, hydraulic conductivity, and lymphatic conductance as well as to demonstrate how chronic swelling (edema) alters the equipoise between tissue fluid balance parameters. Specifically, tissue fluid equilibrium is perturbed with a continuous interstitial infusion of saline into the tip of the tail. The resulting gradients in tissue stress are measured in terms of interstitial fluid pressure using a servo-null system. These measurements are then fit to the theory to provide in vivo estimates of the tissue hydraulic conductivity, elastic modulus, and overall resistance to lymphatic drainage. Additional experiments are performed on edematous tails to show that although chronic swelling causes an increase in the hydraulic conductivity, its greatly increased distensibility (due to matrix remodeling) dampens the driving forces for fluid movement and leads to fluid stagnation. This model is useful for examining potential treatments for edema and lymphatic disorders as well as substances which may alter tissue fluid balance and/or lymphatic drainage.     

Some effects of global joint morphology on local stress aberrations near imprecisely reduced intra-articular fractures

Cadaver models of contact pressure aberration near displaced intra-articular fractures complement clinical experience, but inter-specimen variability often complicates interpretation of in vitro data. A contact finite element formulation is here used to study juxta-articular stress distributions in a plane strain model of tibial plateau step-off incongruity. Attention is focused on the influence of global morphologic parameters: intact joint surface curvatures, cartilage thickness, and cartilage stiffness. The computed stress distributions agreed well with experimental recordings for a typical 3 mm incongruity in an otherwise normal joint. Both decreased cartilage thickness and increased cartilage modulus led to elevations in the peak local contact stress, and to concentration of contact stress near the edge of the step-off incongruity. Similar effects were seen when reduction of global joint congruency was modelled by decreasing the concavity of the tibial plateau. While the observed degree of coupling between global morphology and local stress aberration was by no means negligible, the sensitivity of the stresses to variations in individual parameters was relatively mild. This suggests that the finite element results will be useful for experimental data interpretation.     

Influence of interstitial fluid dynamics on growth and therapy of angiogenic tumor. Analysis by mathematical model

We have developed a spatially distributed mathematical model of angiogenic tumor growth in tissue with account of interstitial fluid dynamics and bevacizumab monotherapy. In this model the process of neovascularization is initiated by tumor cells in a state of metabolic stress, vascular endothelial growth factor (VEGF) being its main mediator. The model takes into consideration the convection flows arising in dense tissue due to active proliferation and migration of tumor cells as well as interstitial fluid inflow from blood vascular system, its outflow through lymphatic system and redistribution in the area of tumor growth. The work considers the diffusive approximation of interstitial fluid dynamics in tumor and normal tissue. Numerical study of the model showed that in absence of therapy a peritumoral edema is formed due to the increase of interstitial fluid inflow from angiogenic capillaries. In the case of rapid interstitial fluid outflow through lymphatic system and its fast transport from necrotic zone to normal tissue the regimes of full growth stop are observed in case of low-invasive tumor. Under bevacizumab monotherapy the peritumoral edema vanishes and low-invasive tumor may not only decelerate its growth, but also start shrinking for a large range of parameters.     

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. J. Morphol., 2010. © 2009 Wiley‐Liss, Inc.     

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.     

Hydrodynamic thickening of lubricating fluid layer beneath sliding mesothelial tissues

The delicate mesothelial surfaces of the pleural space and other serosal cavities slide relative to each, lubricated by pleural fluid. In the absence of breathing motion, differences between lung and chest wall shape could eventually cause the lungs and chest wall to come into contact. Whether sliding motion keeps lungs and chest wall separated by a continuous liquid layer is not known. To explore the effects of hydrodynamic pressures generated by mesothelial sliding, we measured the thickness of the liquid layer beneath the peritoneal surface of a 3-cm disk of rat abdominal wall under a normal stress of 2 cm H2O sliding against a glass plate rotating at 0-1 rev/s. Thickness of the lubricating layer was determined microscopically from the appearance of fluorescent microspheres adherent to the tissue and glass. Usually, fluid thickness near the center of the tissue disk increased with the onset of glass rotation, increasing to 50-200 microm at higher rotation rates, suggesting hydrodynamic pumping. However, thickness changes often differed substantially among tissue samples and between clockwise and counter-clockwise rotation, and sometimes thickness decreased with rotation, suggesting that topographic features of the tissue are important in determining global hydrodynamic effects. We conclude that mesothelial sliding induces local hydrodynamic pressure gradients and global hydrodynamic pumping that typically increases the thickness of the lubricating fluid layer, moving fluid against the global pressure gradient. A similar phenomenon could maintain fluid continuity in the pleural space, reducing frictional force and shear stress during breathing.