A numerical study of dehydration induced fracture toughness degradation in human cortical bone.

A 2D plane strain extended finite element method (XFEM) model was developed to simulate three-point bending fracture toughness tests for human bone conducted in hydrated and dehydrated conditions. Bone microstructures and crack paths observed by micro-CT imaging were simulated using an XFEM damage model. Critical damage strains for the osteons, matrix, and cement lines were deduced for both hydrated and dehydrated conditions and it was found that dehydration decreases the critical damage strains by about 50%. Subsequent parametric studies using the various microstructural models were performed to understand the impact of individual critical damage strain variations on the fracture behavior. The study revealed the significant impact of the cement line critical damage strains on the crack paths and fracture toughness during the early stages of crack growth. Furthermore, a significant sensitivity of crack growth resistance and crack paths on critical strain values of the cement lines was found to exist for the hydrated environments where a small change in critical strain values of the cement lines can alter the crack path to give a significant reduction in fracture resistance. In contrast, in the dehydrated state where toughness is low, the sensitivity to changes in critical strain values of the cement lines is low. Overall, our XFEM model was able to provide new insights into how dehydration affects the micromechanisms of fracture in bone and this approach could be further extended to study the effects of aging, disease, and medical therapies on bone fracture.

A comprehensive set of ultrashort echo time magnetic resonance imaging biomarkers to assess cortical bone health: A feasibility study at clinical field strength.

INTRODUCTION: Conventional bone imaging methods primarily use X-ray techniques to assess bone mineral density (BMD), focusing exclusively on the mineral phase. This approach lacks information about the organic phase and bone water content, resulting in an incomplete evaluation of bone health. Recent research highlights the potential of ultrashort echo time magnetic resonance imaging (UTE MRI) to measure cortical porosity and estimate BMD based on signal intensity. UTE MRI also provides insights into bone water distribution and matrix organization, enabling a comprehensive bone assessment with a single imaging technique. Our study aimed to establish quantifiable UTE MRI-based biomarkers at clinical field strength to estimate BMD and microarchitecture while quantifying bound water content and matrix organization. METHODS: Femoral bones from 11 cadaveric specimens (n = 4 males 67-92 yrs of age, n = 7 females 70-95 yrs of age) underwent dual-echo UTE MRI (3.0 T, 0.45 mm resolution) with different echo times and high resolution peripheral quantitative computed tomography (HR-pQCT) imaging (60.7 µm voxel size). Following registration, a 4.5 mm HR-pQCT region of interest was divided into four quadrants and used across the multi-modal images. Statistical analysis involved Pearson correlation between UTE MRI porosity index and a signal-intensity technique used to estimate BMD with corresponding HR-pQCT measures. UTE MRI was used to calculate T1 relaxation time and a novel bound water index (BWI), compared across subregions using repeated measures ANOVA. RESULTS: The UTE MRI-derived porosity index and signal-intensity-based estimated BMD correlated with the HR-pQCT variables (porosity: r = 0.73, p = 0.006; BMD: r = 0.79, p = 0.002). However, these correlations varied in strength when we examined each of the four quadrants (subregions, r = 0.11-0.71). T1 relaxometry and the BWI exhibited variations across the four subregions, though these differences were not statistically significant. Notably, we observed a strong negative correlation between T1 relaxation time and the BWI (r = -0.87, p = 0.0006). CONCLUSION: UTE MRI shows promise for being an innocuous method for estimating cortical porosity and BMD parameters while also giving insight into bone hydration and matrix organization. This method offers the potential to equip clinicians with a more comprehensive array of imaging biomarkers to assess bone health without the need for invasive or ionizing procedures.

Mechanics of linear microcracking in trabecular bone.

Microcracking in trabecular bone is responsible both for the mechanical degradation and remodeling of the trabecular bone tissue. Recent results on trabecular bone mechanics have demonstrated that bone tissue microarchitecture, tissue elastic heterogeneity and tissue-level mechanical anisotropy all should be considered to obtain detailed information on the mechanical stress state. The present study investigated the influence of tissue microarchitecture, tissue heterogeneity in elasticity and material separation properties and tissue-level anisotropy on the microcrack formation process. Microscale bone models were executed with the extended finite element method. It was demonstrated that anisotropy and heterogeneity of the bone tissue contribute significantly to bone tissue toughness and the resistance of trabecular bone to microcrack formation. The compressive strain to microcrack initiation was computed to increase by a factor of four from an assumed homogeneous isotropic tissue to an assumed anisotropic heterogenous tissue.

Incorporating tissue anisotropy and heterogeneity in finite element models of trabecular bone altered predicted local stress distributions.

Trabecular bone is composed of organized mineralized collagen fibrils, which results in heterogeneous and anisotropic mechanical properties at the tissue level. Recently, biomechanical models computing stresses and strains in trabecular bone have indicated a significant effect of tissue heterogeneity on predicted stresses and strains. However, the effect of the tissue-level mechanical anisotropy on the trabecular bone biomechanical response is unknown. Here, a computational method was established to automatically impose physiologically relevant orientation inherent in trabecular bone tissue on a trabecular bone microscale finite element model. Spatially varying tissue-level anisotropic elastic properties were then applied according to the bone mineral density and the local tissue orientation. The model was used to test the hypothesis that anisotropy in both homogeneous and heterogeneous models alters the predicted distribution of stress invariants. Linear elastic finite element computations were performed on a 3 mm cube model isolated from a microcomputed tomography scan of human trabecular bone from the distal femur. Hydrostatic stress and von Mises equivalent stress were recorded at every element, and the distributions of these values were analyzed. Anisotropy reduced the range of hydrostatic stress in both tension and compression more strongly than the associated increase in von Mises equivalent stress. The effect of anisotropy was independent of the spatial redistribution high compressive stresses due to tissue elastic heterogeneity. Tissue anisotropy and heterogeneity are likely important mechanisms to protect bone from failure and should be included for stress analyses in trabecular bone.

Experiments on the low frequency barrier characteristics of cellular metamaterial panels in a diffuse sound field.

The metamaterial under investigation here consists of a periodic arrangement of unit plates in a grid-like frame such that there is a contrast in the local areal mass between cell interior and cell wall. In the low frequency range and under normal incidence this metamaterial panel exhibits a sound transmission loss significantly larger than the transmission loss of an unstructured panel with the same homogeneous mass per unit area. However, when the incident sound field is diffuse, the relative advantage of the metamaterial barrier is reduced or eliminated. A sequence of experiments is documented to demonstrate that the relative advantage of the metamaterial barrier can be realized even in a diffuse sound field by creating a hybrid barrier system which embeds the metamaterial layer between a normalizing waveguide layer on the incident side and an absorbing layer on the transmitted side. The sound normalizing waveguide layer is a lattice structure, and the absorbing layer is high performance glass fiber mat. By using measurements of the transmission loss of a 1.2 m square panel system the role of each of these components is demonstrated.

Role of gradients in vocal fold elastic modulus on phonation.

New studies show that the elastic properties of the vocal folds (VFs) vary locally. In particular strong gradients exist in the distribution of elastic modulus along the length of the VF ligament, which is an important load-bearing constituent of the VF tissue. There is further evidence that changes in VF health are associated with alterations in modulus gradients. The role of VF modulus gradation on VF vibration and phonation remains unexplored. In this study the magnitude of the gradient in VF elastic modulus is varied, and sophisticated computational simulations are performed of the self-oscillation of three-dimensional VFs with realistic modeling of airflow physical properties. Results highlight that phonation frequency, characteristic modes of deformation and phase differences, glottal airflow rate, spectral-width of vocal output, and glottal jet dynamics are dependent on the magnitude of VF elastic modulus gradation. The results advance the understanding of how VF functional gradation can lead to perceptible changes in speech quality.

The role of glottal surface adhesion on vocal folds biomechanics.

The airway surface liquid (ASL) is a very thin mucus layer and covers the vocal fold (VF) surface. Adhesion mediated by the ASL occurs during phonation as the VFs separate after collision. Such adhesion is hypothesized to determine voice quality and health. However, biomechanical insights into the adhesive processes during VF oscillation are lacking. Here, a computational study is reported on self-sustained VF vibration involving contact and adhesion. The VF structural model and the glottal airflow are considered fully three-dimensional. The mechanical behavior of the ASL is described through a constitutive traction-separation law where mucosal cohesive strength, cohesive energy, and rupture length enter. Cohesive energy values considered are bound below by the cohesive energy of water at standard temperature and pressure. Cohesive strength values considered are bound above by prior reported data on the adhesive strength of mucosal surface of rat small intestine. This model introduces a mechanical length scale into the analysis. The sensitivity of various aspects of VF dynamics such as flow-declination rate, VF separation under adhesive condition, and formation of multiple local fluid bridges is determined in relation to specific ASL adhesive properties. It is found that for the ASL considered here, the characteristics of the VF separation process are of debond type. Instabilities lead to the breakup of the bond area into several smaller bond patches. Such finding is consistent with in vivo observations.

Validation of a flow-structure-interaction computation model of phonation.

Computational models of vocal fold (VF) vibration are becoming increasingly sophisticated, their utility currently transiting from exploratory research to predictive research. However, validation of such models has remained largely qualitative, raising questions over their applicability to interpret clinical situations. In this paper, a computational model with a segregated implementation is detailed. The model is used to predict the fluid-structure interaction (FSI) observed in a physical replica of the VFs when it is excited by airflow. Detailed quantitative comparisons are provided between the computational model and the corresponding experiment. First, the flow model is separately validated in the absence of VF motion. Then, in the presence of flow-induced VF motion, comparisons are made of the flow pressure on the VF walls and of the resulting VF displacements. Self-similarity of spatial distributions of flow pressure and VF displacements is highlighted. The self-similarity leads to normalized pressure and displacement profiles. It is shown that by using linear superposition of average and fluctuation components of normalized computed displacements, it is possible to determine displacements in the physical VF replica over a range of VF vibration conditions. Mechanical stresses in the VF interior are related to the VF displacements, thereby the computational model can also determine VF stresses over a range of phonation conditions.

Computational modeling of vibration-induced systemic hydration of vocal folds over a range of phonation conditions.

Predicting phonation conditions that are benign to voice health remains a biomechanically relevant problem. Our objective is to provide insight into vocal fold (VF) hydration based on continuum-based VF models that are able to compute VF stresses during phonation and a scheme for the extraction and generalization of such computational data based on the principle of linear superposition. Because VF tissue is poroelastic, spatial gradients of VF hydrostatic stresses computed for a given phonation condition determine VF interstitial fluid flow. The present approach transforms, based on linear superposition principles, the computed interstitial fluid velocities at the particular phonation to those at an arbitrary phonation condition. Intersititial fluid flow characteristics for a range of phonation conditions are compared. For phonation conditions with no or moderate collision, no dehydration per vibration cycle is predicted throughout the VF. For more severe collision conditions, tissue dehydration is restricted to a region close to the glottal surface. Interstitial fluid displacement in the VF is found to be heterogeneous and strongly dependent on the phonation condition. A phonation condition is found to exist for which dehydration peaks. The proposed method significantly expands the scope and relevance of conducting isolated numerical simulations of VF vibration.

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.

Collagen microstructure in the vocal ligament: initial results on the potential effects of smoking.

OBJECTIVES/HYPOTHESIS: This investigation quantitatively characterizes the collagenous microstructure of human vocal ligament specimens excised postmortem from nonsmokers and smokers. STUDY DESIGN: Retrospective cohort study. METHODS: Second harmonic generation (SHG) imaging was performed at three anatomical locations of vocal ligament specimens: anterior, mid-membranous, and posterior regions. Two microstructural parameters were extracted from the SHG images: (1) normalized fiber density, and (2) fiber dispersion coefficient, quantifying the degree of collagen fiber dispersion about a preferred direction. RESULTS: For both the nonsmoker and smoker subjects, the fiber dispersion coefficient was heterogeneous. Differences in the collagenous structure of nonsmokers and smoker subjects were pronounced at the mid-membranous location. However, the directionality of the heterogeneity in the smoker subjects was opposite to that in the nonsmoker subjects. Specifically, the fiber dispersion coefficient in the nonsmoker subjects was lower in the mid-membranous region (indicating more fiber alignment) than at the anterior/posterior regions, but for the smoker subjects the fiber dispersion coefficient was higher at the mid-membranous region. The normalized fiber density was near constant in the nonsmoker subjects, but the smoker subjects had fewer fibers in the mid-membranous region than at the anterior/posterior regions. CONCLUSION: Spatial microstructural variations may exist in the vocal fold ligament both in nonsmokers and smokers. Smoking appears to influence the degree and direction of microstructure heterogeneity in the vocal fold ligament.

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.

The anisotropic hyperelastic biomechanical response of the vocal ligament and implications for frequency regulation: a case study.

One of the primary mechanisms to vary one's vocal frequency is through vocal fold length changes. As stress and deformation are linked to each other, it is hypothesized that the anisotropy in the biomechanical properties of the vocal fold tissue would affect the phonation characteristics. A biomechanical model of vibrational frequency rise during vocal fold elongation is developed which combines an advanced biomechanical characterization protocol of the vocal fold tissue with continuum beam models. Biomechanical response of the tissue is related to a microstructurally informed, anisotropic, nonlinear hyperelastic constitutive model. A microstructural characteristic (the dispersion of collagen) was represented through a statistical orientation function acquired from a second harmonic generation image of the vocal ligament. Continuum models of vibration were constructed based upon Euler-Bernoulli and Timoshenko beam theories, and applied to the study of the vibration of a vocal ligament specimen. From the natural frequency predictions in dependence of elongation, two competing processes in frequency control emerged, i.e., the applied tension raises the frequency while simultaneously shear deformation lowers the frequency. Shear becomes much more substantial at higher modes of vibration and for highly anisotropic tissues. The analysis was developed as a case study based on a human vocal ligament specimen.

Empirical measurements of biomechanical anisotropy of the human vocal fold lamina propria.

The vocal folds are known to be mechanically anisotropic due to the microstructural arrangement of fibrous proteins such as collagen and elastin in the lamina propria. Even though this has been known for many years, the biomechanical anisotropic properties have rarely been experimentally studied. We propose that an indentation procedure can be used with uniaxial tension in order to obtain an estimate of the biomechanical anisotropy within a single specimen. Experiments were performed on the lamina propria of three male and three female human vocal folds dissected from excised larynges. Two experiments were conducted: each specimen was subjected to cyclic uniaxial tensile loading in the longitudinal (i.e., anterior-posterior) direction, and then to cyclic indentation loading in the transverse (i.e., medial-lateral) direction. The indentation experiment was modeled as contact on a transversely isotropic half-space using the Barnett-Lothe tensors. The longitudinal elastic modulus E(L) was computed from the tensile test, and the transverse elastic modulus E(T) and longitudinal shear modulus G(L) were obtained by inverse analysis of the indentation force-displacement response. It was discovered that the average of E(L) /E(T) was 14 for the vocal ligament and 39 for the vocal fold cover specimens. Also, the average of E(L)/G(L), a parameter important for models of phonation, was 28 for the vocal ligament and 54 for the vocal fold cover specimens. These measurements of anisotropy could contribute to more accurate models of fundamental frequency regulation and provide potentially better insights into the mechanics of vocal fold vibration.

Could spatial heterogeneity in human vocal fold elastic properties improve the quality of phonation?

The physical mechanisms leading to the acoustic and perceptual qualities of voice are not well understood. This study examines the spatial distribution of biomechanical properties in human vocal folds and explores the consequences of these properties on phonation. Vocal fold lamina propria specimens isolated from nine excised human male larynges were tested in uniaxial tension (six from non-smokers, three from smokers). An optical method was employed to determine the local stretch, from which the elastic modulus of three segments in the anterior-posterior direction was calculated. Several specimens exhibited a significant heterogeneity in the modulus with the middle segment stiffer than the other segments. It was concluded that such modulus gradients are stronger in specimens from non-smokers than smokers. To understand the functional implications of a modulus gradient, the first eigenmode of vibration was calculated with a finite element model. With a modulus gradient, the vocal fold's eigenmode deflection was spread along the anterior-posterior length, whereas for a homogeneous modulus distribution, the deflection was more focused around the mid-coronal plane. Consequently, the strong modulus gradient may enable more complete glottal closure, which is important for normal phonation, while a more homogeneous modulus may be responsible for poor glottal closure and a perceived "breathy" voice.

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.

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.

Can deterministic mechanical size effects contribute to fracture and microdamage accumulation in trabecular bone?

Failure of bone under monotonic and cyclic loading is related to the bone mineral density, the quality of the bone matrix, and the evolution of microcracks. The theory of linear elastic fracture mechanics has commonly been applied to describe fracture in bone. Evidence is presented that bone failure can be described through a non-linear theory of fracture. Thereby, deterministic size effects are introduced. Concepts of a non-linear theory are applied to discern how the interaction among bone matrix constituents (collagen and mineral), microcrack characteristics, and trabecular architecture can create distinctively differences in the fracture resistance at the bone tissue level. The non-linear model is applied to interpret pre-clinical data concerning the effects of anti-osteoporotic agents on bone properties. The results show that bisphosphonate (BP) treatments that suppress bone remodeling will change trabecular bone in ways such that the size of the failure process zone relative to the trabecular thickness is reduced. Selective estrogen receptor modulators (SERMs) that suppress bone remodeling will change trabecular bone in ways such that the size of the failure process zone relative to the trabecular thickness is increased. The consequences of these changes are reflected in bone mechanical response and predictions are consistent with experimental observations in the animal model which show that BP treatment is associated with more brittle fracture and microcracks without altering the average length of the cracks, whereas SERM treatments lead to a more ductile fracture and mainly increase crack length with a smaller increase in microcrack density. The model suggests that BPs may be more effective in cases in which bone mass is very low, whereas SERMS may be more effective when milder osteoporotic symptoms are present.

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.

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.