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.     

A numerical analysis of phonation using a two-dimensional flexible channel model of the vocal folds.

A two-dimensional flexible channel model of the vocal folds coupled with an unsteady one-dimensional flow model is presented for an analysis of the mechanism of phonation. The vocal fold is approximated by springs and dampers distributed in the main flow direction that are enveloped with an elastic cover. In order to approximate three-dimensional collision of the vocal folds using the two-dimensional model, threshold values for the glottal width are introduced. The numerical results show that the collision plays an important role in speech sound, especially for higher resonant frequency components, because it causes the source sound to include high-frequency components.     

The expiration reflex from the vocal folds.

The authors present their 30 years' experience with expiration reflex. The reflex can be elicited from vocal folds by mechanical, chemical or electrical stimulation of the superior laryngeal nerve of man and laboratory animals, except mice and rats. It manifests itself by a short, forcible expiratory effort without a preceding inspiration which is indispensable for cough effort. The role of expiration reflex is to prevent penetration of foreign bodies into airways, expelling phlegm and detritus from subglottal area. The initial inspiration before expiration is undesired and could lead to inspiration pneumonia. The reflex is well known to laryngologists as '"laryngeal cough." Its receptors are small in number, localised mainly in medial margin of vocal folds deep in mucosa which can explain their stability in pathological conditions of the larygx. Afferentiation of the reflex is via laryngeal nerve similarly to sneezing and cough. Expiration reflex is not co-ordinated by a single "centre" but rather by a network system in the brain stem. Its motor pattern is supposedly produced by "multifunctional" population of medullar neurones in Botzinger complex and the rostral ventral respiratory group involved also in the genesis of breathing and cough. However, in cats also other neurones may play a vital role in production, shaping and mediation of the motor pattern of respiratory reflex, localised in rostral pons, lateral tegmental field or in the raphe medullar midline.     

TFF peptides in the human false vocal folds of the larynx

TFF peptides (formerly P domain peptides, trefoil factors) are typical secretory products of mucin-producing cells and are thought to influence the rheological properties of mucous gels. We investigated the localization of these peptides in the human false vocal folds of the larynx, also known as the ventricular folds or vestibular folds. An analysis of TFF peptide mRNA by RT-PCR and TFF protein by Western blot detected TFF1 and TFF3, but not TFF2. Immunohistochemistry revealed TFF1 to be associated with the secretory product of goblet cells and mucous parts of subepithelial seromucous glands. TFF3 occurred in columnar epithelial cells of the mucosa and in serous cells and excretory duct cells of seromucous glands. These peptides may play a role in the rheological function of mucus secreted onto the true vocal folds and are thus important constituents of vocal production.     

A fully coupled poroelastic reactive-transport model of cartilage

Cartilage maintains its integrity in a hostile mechanical environment. This task is made more difficult because cartilage has no blood supply, and so nutrients and growth factors need to be transported greater distances than normal to reach cells several millimetres from the cartilage surface. The chondrocytes embedded within the extracellular matrix (ECM) are essential for maintaining the mechanical integrity of the ECM, through a balance of degradation and synthesis of collagen and proteoglycans. A chondrocyte senses various chemical and mechanical signals in its local microenvironment, responding by appropriate adaption of the local ECM. Clearly a 'systems understanding' of cartilage behaviour is of critical importance in developing an integrated understanding of both normal and abnormal physiology of cartilage. In a series of papers, we have developed a reactive-transport porous-media model to investigate the coupled processes of growth factor transport, mechanical deformation and fluid flow, and in this paper, we extend the model to include biosynthesis and degradation of matrix molecules. The model is validated using three independent experimental data sets, it being found that a single set of parameters described the experimental results remarkably well. The model is then employed to make predictions about changes in proteoglycan content under a variety of conditions. This model may prove useful in predicting the behaviour of tissue engineering constructs, or predicting the outcome of repair processes in cartilage.     

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.     

Informing phenomenological structural bone remodelling with a mechanistic poroelastic model

Studies suggest that fluid motion in the extracellular space may be involved in the cellular mechanosensitivity at play in the bone tissue adaptation process. Previously, the authors developed a mesoscale predictive structural model of the femur using truss elements to represent trabecular bone, relying on a phenomenological strain-based bone adaptation algorithm. In order to introduce a response to bending and shear, the authors considered the use of beam elements, requiring a new formulation of the bone adaptation drivers. The primary goal of the study presented here was to isolate phenomenological drivers based on the results of a mechanistic approach to be used with a beam element representation of trabecular bone in mesoscale structural modelling. A single-beam model and a microscale poroelastic model of a single trabecula were developed. A mechanistic iterative adaptation algorithm was implemented based on fluid motion velocity through the bone matrix pores to predict the remodelled geometries of the poroelastic trabecula under 42 different loading scenarios. Regression analyses were used to correlate the changes in poroelastic trabecula thickness and orientation to the initial strain outputs of the beam model. Linear (\(R^2>0.998\)) and third-order polynomial (\(R^2 >0.98\)) relationships were found between change in cross section and axial strain at the central axis, and between beam reorientation and ratio of bending strain to axial strain, respectively. Implementing these relationships into the phenomenological predictive algorithm for the mesoscale structural femur has the potential to produce a model combining biofidelic structure and mechanical behaviour with computational efficiency.     

Geometrical model for the native-state folds of proteins

We recently introduced a physical model [T.X. Hoang, A. Trovato, F. Seno, J.R. Banavar, A. Maritan, Geometry and symmetry pre-sculpt the free energy landscape of proteins. Proc. Natl. Acad. Sci. U. S. A. 101 (2004) 7960-7964, J.R. Banavar, T.X. Hoang, A. Maritan, F. Seno, A. Trovato, A unified perspective on proteins-a physics approach. Phys. Rev., E 70 (2004) 041905] for proteins which incorporates, in an approximate manner, several key features such as the inherent anisotropy of a chain molecule, the geometrical and energetic constraints placed by the hydrogen bonds and sterics, and the role played by hydrophobicity. Within this framework, marginally compact conformations resembling the native state folds of proteins emerge as broad competing minima in the free energy landscape even for a homopolymer. Here we show how the introduction of sequence heterogeneity using a simple scheme of just two types of amino acids, hydrophobic (H) and polar (P), and sequence design allows a selected putative native fold to become the free energy minimum at low temperature. The folding transition exhibits thermodynamic cooperativity, if one neglects the degeneracy between two different low energy conformations sharing the same fold topology.     

Perfusion studies of steady flow in poroelastic myocardium tissue

The behaviour of the heart has always elicited interest and particularly the study of its myocardium, as 5-10% of the blood pumped by the heart is passed through the coronary arteries to the myocardium itself. An in-depth investigation of the myocardium behaviour is useful. The present work aims to investigate how myocardium perfusion is influenced by myocardial stress and diseased states, and in general by LV pumping abnormalities. LV myocardial perfusion can then serve as a possible index of the capacity of the LV to respond to its work demand, and thus of the risk of heart failure. The poroelastic analysis of the myocardium based on finite element method (FEM) for regional perfusion through a rectangular element with various physiological ranges of loading conditions was studied.     

A poroelastic continuum model of the cupula partition and the response dynamics of the vestibular semicircular canal.

Using mixture theory, an axisymmetric continuum model is presented describing the response dynamics of the vestibular semicircular canals to canal-centered head rotation in which the cupula partition is modeled as a poroelastic mixture of interpenetrating solid and fluid constituents. The solid matrix of the cupula is assumed to behave as a linear elastic material, whereas the fluid constituent is assumed to be Newtonian. A regular perturbation analysis of the fluid dynamics in the canal provides a dynamic boundary condition, which acts across the cupula partition. Numerical solution of the coupled system of momentum equations provides the spatio-temporal displacement fields for both the fluid and solid constituents of the cupula. Results indicate that at frequencies above 1 Hz, the fluid constituent is dynamically entrained by the solid matrix such that their motions are bound as if to exist as a single component. The resulting high-frequency response is consistent with the macromechanical response predicted by single-component viscoelastic models of the cupula. Below 1 Hz, the dynamic coupling between the fluid and solid constituents weakens and the transcupular differential pressure is sufficient to force fluid through the mixture with little deformation of the solid matrix. Results are sensitive to the precise value of the cupular permeability. One of the most important distinctions between the present analysis and previous impermeable models of the cupula arises at the micromechanical level in terms of the local fluid flow that is predicted to occur within the cupula and around the ciliary bundles and sensory hair cells. Another important result reveals that the permeation dynamics predicted below 1 Hz gives rise to the same low-frequency macromechanical response as would occur with an impermeable viscoelastic structure having a much greater stiffness. Current estimates of the mechanical stiffness of the cupula, based solely on afferent nerve data, may therefore overestimate the true value intrinsic to the solid matrix by as much as an order of magnitude.     

Geometry of human vocal folds and glottal channel for mathematical and biomechanical modeling of voice production

Current models of the vocal folds derive their shape from approximate information rather than from exactly measured data. The objective of this study was to obtain detailed measurements on the geometry of human vocal folds and the glottal channel in phonatory position. A non-destructive casting methodology was developed to capture the vocal fold shape from excised human larynges on both medial and superior surfaces. Two female larynges, each in two different phonatory configurations corresponding to low and high fundamental frequency of the vocal fold vibrations, were measured. A coordinate measuring machine was used to digitize the casts yielding 3D computer models of the vocal fold shape. The coronal sections were located in the models, extracted and fitted by piecewise-defined cubic functions allowing a mathematical expression of the 2D shape of the glottal channel. Left-right differences between the cross-sectional shapes of the vocal folds were found in both the larynges.     

A model of tissue thromboplastin

The molecular structure of the human brain tissue thromboplastin was studied by the method of NMR-31P and 1H using the shifting reagent. Molecular model of the tissue thromboplastin is suggested. According to the model only 10-20% of polar phosphate-containing heads are exposed outside. Phospholipids located deeper form hexagonal (HII) cylinders which may consist only of lipids or of complexes with proteins.     

Phase relationship between dynamics of the subglottic pressure and oscillatory movement of the vocal folds. I. Sustained phonation

The phase relationship between subglottic pressure and vocal fold length has been studied during sustained phonation in five subjects with normal larynx. Pressure was measured by tracheal puncture and vocal fold length was deduced from simultaneous measurement of translaryngeal impedance in the horizontal plane and transglottal light flux in the vertical plane. The pressure sine wave shows a phase lead of slightly less than 90 degrees relative to the length sine wave. Thus during sustained phonation the vocal apparatus behaves like a harmonic oscillator; the frequency of oscillation is determined by the mechanical parameters of the vibrating system; the source of periodic energy supply is the subglottal pressure wave.     

A challenge to the undefeated nasolabial folds

Previous attempts to improve the nasolabial folds have been disappointing. By extending the face lift skin dissection to the nasolabial fold and up onto the malar prominence, reducing the fat of this fold by excision, and applying direct posterior retraction to the freed facial skin, rather dramatic improvement in the nasolabial folds have been achieved. This is a preliminary report with a follow-up of 8 months or less.     

A fibril reinforced nonhomogeneous poroelastic model for articular cartilage: inhomogeneous response in unconfined compression

The depth dependence of material properties of articular cartilage, known as the zonal differences, is incorporated into a nonlinear fibril-reinforced poroelastic model developed previously in order to explore the significance of material heterogeneity in the mechanical behavior of cartilage. The material variations proposed are based on extensive observations. The collagen fibrils are modeled as a distinct constituent which reinforces the other two constituents representing proteoglycans and water. The Young's modulus and Poisson's ratio of the drained nonfibrillar matrix are so determined that the aggregate compressive modulus for confined geometry fits the experimental data. Three nonlinear factors are considered, i.e. the effect of finite deformation, the dependence of permeability on dilatation and the fibril stiffening with its tensile strain. Solutions are extracted using a finite element procedure to simulate unconfined compression tests. The features of the model are then demonstrated with an emphasis on the results obtainable only with a nonhomogeneous model, showing reasonable agreement with experiments. The model suggests mechanical behaviors significantly different from those revealed by homogeneous models: not only the depth variations of the strains which are expected by qualitative analyses, but also, for instance, the relaxation-time dependence of the axial strain which is normally not expected in a relaxation test. Therefore, such a nonhomogeneous model is necessary for better understanding of the mechanical behavior of cartilage.     

An extended biphasic model for charged hydrated tissues with application to the intervertebral disc

Finite element models for hydrated soft biological tissue are numerous but often exhibit certain essential deficiencies concerning the reproduction of relevant mechanical and electro-chemical responses. As a matter of fact, singlephasic models can never predict the interstitial fluid flow or related effects like osmosis. Quite a few models have more than one constituent, but are often restricted to the small-strain domain, are not capable of capturing the intrinsic viscoelasticity of the solid skeleton, or do not account for a collagen fibre reinforcement. It is the goal of this contribution to overcome these drawbacks and to present a thermodynamically consistent model, which is formulated in a very general way in order to reproduce the behaviour of almost any charged hydrated tissue. Herein, the Theory of Porous Media (TPM) is applied in combination with polyconvex Ogden-type material laws describing the anisotropic and intrinsically viscoelastic behaviour of the solid matrix on the basis of a generalised Maxwell model. Moreover, other features like the deformation-dependent permeability, the possibility to include inhomogeneities like varying fibre alignment and behaviour, or osmotic effects based on the simplifying assumption of Lanir are also included. Finally, the human intervertebral disc is chosen as a representative for complex soft biological tissue behaviour. In this regard, two numerical examples will be presented with focus on the viscoelastic and osmotic capacity of the model.