Phonation thresholds as a function of laryngeal size in a two-mass model of the vocal folds

This letter analyzes the oscillation onset-offset conditions of the vocal folds as a function of laryngeal size. A version of the two-mass model of the vocal folds is used, coupled to a two-tube approximation of the vocal tract in configuration for the vowel /a/. The standard male configurations of the laryngeal and vocal tract models are used as reference, and their dimensions are scaled using a single factor. Simulations of the vocal fold oscillation and oral output are produced for varying values of the scaling factor. The results show that the oscillation threshold conditions become more restricted for smaller laryngeal sizes, such as those appropriate for females and children.     

Phonation threshold pressure and onset frequency in a two-layer physical model of the vocal folds

The influence of vocal fold geometry and stiffness on phonation onset was experimentally investigated using a body-cover physical model of the vocal folds. Results showed that a lower phonation threshold pressure and phonation onset frequency can be achieved by reducing body-layer or cover-layer stiffness, reducing medial surface thickness, or increasing cover-layer depth. Increasing body-layer stiffness also restricted vocal fold motion to the cover layer and reduced prephonatory glottal opening. Excitation of anterior-posterior modes was also observed, particularly for large values of the body-cover stiffness ratio. The results of this study were also discussed in relation to previous theoretical and experimental studies.     

Coherent structures of the near field flow in a self-oscillating physical model of the vocal folds

Current theories of voice production depend critically upon knowledge of the near field flow which emanates from the glottis. While most modern theories predict complex, three-dimensional structures in the near field flow, few investigations have attempted to quantify such structures. Using methods of flow visualization and digital particle image velocimetry, this study measured the near field flow structures immediately downstream of a self-oscillating, physical model of the vocal folds, with a vocal tract attached. A spatio-temporal analysis of the structures was performed using the method of empirical orthogonal eigenfunctions. Some of the observed flow structures included vortex generation, vortex convection, and jet flapping. The utility of such data in the future development of more accurate, low-dimensional models of voice production is discussed.     

Unsteady behavior of flow in a scaled-up vocal folds model

Measurements of the fluid flow through a scaled-up model of the human glottis are presented to determine whether glottal flow may be approximated as unsteady. Time- and space-resolved velocity vector fields from digital particle image velocimetry (DPIV) measurements of the flow through the gap between two moving, rigid walls are presented in four cases, over a range of Strouhal numbers: 0.010, 0.018, 0.035, 0.040, corresponding to life-scale f(0) of 30, 58, 109, and 126 Hz, respectively, at a Reynolds number of 8000. It is observed that (1) glottal flow onset is delayed after glottal opening and (2) glottal flow shutoff occurs prior to closure. A comparison between flow through a fully open, nonmoving glottis and that through the moving vocal folds shows a marked difference in spatial structure of the glottal jet. The following features of the flow are seen to exhibit strong dependence on cycle frequency: (a) glottal exit plane velocity, (b) volume flow, (c) vortex shedding rates, and (d) vortex amplitude. Vortex shedding appears to be a factor both in controlling flow resistance and in cycle-to-cycle volume flow variations. All these observations strongly suggest that glottal flow is inherently unsteady.     

Mechanisms of irregular vibration in a physical model of the vocal folds

Previous investigations have shown that one mechanism of irregular vocal fold vibration may be a desynchronization of two or more vibratory modes of the vocal fold tissues. In the current investigation, mechanisms of irregular vibration were further examined using a self-oscillating, physical model of vocal fold vibration, a hemi-model methodology, and high-speed, stereoscopic, digital imaging. Using the method of empirical eigen-functions, a spatiotemporal analysis revealed mechanisms of irregular vibration in subharmonic phonation and biphonation, which were not disclosed in a standard acoustic spectrum.     

Two-mass model of the vocal folds: negative differential resistance oscillation

The vocal folds and glottis are analyzed as a single system rather than as two separate but interacting systems, i.e., an aerodynamic one (the glottis) and a mechanical one (the vocal folds). Simplified steady flow calculations based on the two-mass model, and similar to those of Ishizaka and Matsudaira [SCRL Monograph No. 8, Santa Barbara, CA (1972)], are made except that flexible walls are assumed for both dc and ac flows. A negative differential resistance is found for steady flow when the coupling spring is weak compared to that of the lower mass. Dynamic transverse motion of the masses is represented by two transverse series resonant circuits in parallel within the glottis. The vocal tract is represented by a lumped resistance and inertance in series. Sustained, self-excited, small-amplitude oscillations can be obtained when the magnitude of the negative differential resistance is equal to the real part of the impedance of the rest of the circuit. The oscillation frequency depends only on the elasticity and mass of the vocal folds. The present analysis differs from Ishizaka and Matsudaira's analysis because their oscillation frequency decreases as dc volume velocity increases.     

Observation of perturbations in a lumped-element model of the vocal folds with application to some pathological cases

In this paper a mass-spring model is developed that is a hybrid of the two-mass and the longitudinal string models, proposed by Ishizaka and Flanagan [Bell Sys. Tech. J. 51, 1233-1268 (1972)] and Titze [Phonetica 28, 129-170 (1973)], respectively. The model is used to simulate the vibratory motion of both the normal and asymmetric vocal folds. Mouth-output pressure, lateral tissue displacement, phase plots, and energy diagrams are presented to demonstrate the interaction between vocal fold tissue and the aerodynamic flow between the folds. The results of the study suggest that this interaction is necessary for sustained large amplitude oscillation because the flow supplies the energy lost by the tissue damping. Tissue mass and stiffness were varied locally or uniformly. Decreased stress in the longitudinal string tension produced subharmonic and chaotic vibrations in the displacement, velocity and acceleration phase diagrams. Similar vibratory characteristics also appeared in pathological speech data analyzed using time domain jitter and shimmer measures and a harmonics-to-noise ratio metric. The subharmonics create an effect that has been perceptually described as diplophonia.     

A lumped mucosal wave model of the vocal folds revisited: recent extensions and oscillation hysteresis

This paper examines an updated version of a lumped mucosal wave model of the vocal fold oscillation during phonation. Threshold values of the subglottal pressure and the mean (DC) glottal airflow for the oscillation onset are determined. Depending on the nonlinear characteristics of the model, an oscillation hysteresis phenomenon may occur, with different values for the oscillation onset and offset threshold. The threshold values depend on the oscillation frequency, but the occurrence of the hysteresis is independent of it. The results are tested against pressure data collected from a mechanical replica of the vocal folds, and oral airflow data collected from speakers producing intervocalic /h/. In the human speech data, observed differences between voice onset and offset may be attributed to variations in voice pitch, with a very small or inexistent hysteresis phenomenon.     

Response of an open curved thin shell to a random pressure field arising from a turbulent boundary layer

A method is presented to predict the root mean square displacement response of an open curved thin shell structure subjected to a turbulent boundary-layer-induced random pressure field. The basic formulation of the dynamic problem is an efficient approach combining classic thin shell theory and the finite element method, in which the finite elements are flat rectangular shell elements with five degrees of freedom per node. The displacement functions are derived from Sanders’ thin shell theory. A numerical approach is proposed to obtain the total root mean square displacements of an open curved thin structure in terms of the cross spectral density of random pressure fields. The cross spectral density of pressure fluctuations in the turbulent pressure field is described using the Corcos formulation. Exact integrations over surface and frequency lead to an expression for the total root mean square displacement response in terms of the characteristics of the structure and flow. An in-house program based on the presented method was developed. The total root mean square displacements of a curved thin blade subjected to turbulent boundary layers were calculated and illustrated as a function of free stream velocity and damping ratio. A numerical implementation for the vibration of a cylinder excited by fully developed turbulent boundary layer flow was presented. The results compared favorably with those obtained using software developed by Lakis and Païdoussis (J. Sound Vib. 25 (1972) 1–27) using cylindrical elements and a hybrid finite element method.     

Analysis of the electric field propagation method: theoretical model applied to perfluorinated graded-index polymer optical fiber links

We evaluate a theoretical model based on the electric field propagation method but applied for the first time to amorphous perfluorinated graded-index polymer optical fibers (PF GIPOFs). The belief is that a better understanding of the factors that affect the fiber frequency response will prove very useful in increasing the performance of PF-GIPOF-based optical links in real situations. The influence of some parameters involved in the frequency response is addressed, and results show experimental data that validate, with tolerable discrepancy, the model described applied to this kind of optical fibers.     

Influence of acoustic loading on an effective single mass model of the vocal folds

Three-way interactions between sound waves in the subglottal and supraglottal tracts, the vibrations of the vocal folds, and laryngeal flow were investigated. Sound wave propagation was modeled using a wave reflection analog method. An effective single-degree-of-freedom model was designed to model vocal-fold vibrations. The effects of orifice geometry changes on the flow were considered by enforcing a time-varying discharge coefficient within a Bernoulli flow model. The resulting single-degree-of-freedom model allowed for energy transfer from flow to structural vibrations, an essential feature usually incorporated through the use of higher order models. The relative importance of acoustic loading and the time-varying flow resistance for fluid-structure energy transfer was established for various configurations. The results showed that acoustic loading contributed more significantly to the net energy transfer than the time-varying flow resistance, especially for less inertive supraglottal loads. The contribution of supraglottal loading was found to be more significant than that of subglottal loading. Subglottal loading was found to reduce the net energy transfer to the vocal-fold oscillation during phonation, balancing the effects of the supraglottal load.     

Three-dimensional biomechanical properties of human vocal folds: parameter optimization of a numerical model to match in vitro dynamics

The human voice signal originates from the vibrations of the two vocal folds within the larynx. The interactions of several intrinsic laryngeal muscles adduct and shape the vocal folds to facilitate vibration in response to airflow. Three-dimensional vocal fold dynamics are extracted from in vitro hemilarynx experiments and fitted by a numerical three-dimensional-multi-mass-model (3DM) using an optimization procedure. In this work, the 3DM dynamics are optimized over 24 experimental data sets to estimate biomechanical vocal fold properties during phonation. Accuracy of the optimization is verified by low normalized error (0.13 ± 0.02), high correlation (83% ± 2%), and reproducible subglottal pressure values. The optimized, 3DM parameters yielded biomechanical variations in tissue properties along the vocal fold surface, including variations in both the local mass and stiffness of vocal folds. That is, both mass and stiffness increased along the superior-to-inferior direction. These variations were statistically analyzed under different experimental conditions (e.g., an increase in tension as a function of vocal fold elongation and an increase in stiffness and a decrease in mass as a function of glottal airflow). The study showed that physiologically relevant vocal fold tissue properties, which cannot be directly measured during in vivo human phonation, can be captured using this 3D-modeling technique.     

On the relation between the phonation threshold lung pressure and the oscillation frequency of the vocal folds

This Letter presents an extension of a previous equation for the phonation threshold pressure by Titze [I. R. Titze, J. Acoust. Soc. Am. 83, 1536-1552 (1988)]. The extended equation contains the vocal-fold oscillation frequency as an explicit factor. It is derived from the mucosal wave model of the vocal folds by considering the general case of an arbitrary time delay for the mucosal wave to travel the glottal height. The results are illustrated with a numerical example, which shows good qualitative agreement with experimental measures.     

Botox for hyperadduction of the false vocal folds: A case report

We present a patient with severe hyperadduction of the false vocal folds (FVF) treated with Botulinum Toxin injections to each FVF. This patient presented with severe dysphonia and was found to demonstrate severe hyperadduction of the FVF's with all phonatory tasks. The patient was treated with extensive speech therapy without improvement in voice quality nor FVF motion pattern. He was then injected with Botox A bilaterally using a peroral approach to the FVFs. Shortly after treatment the patient experienced dramatic improvement in voice quality. Videolaryngoscopy revealed no adduction of the FVFs with phonation and essentially normal true vocal fold motion. He remained with normal voice quality one year after treatment without any further treatment. Possible mechanism of action of this type of treatment are discussed.     

Spinor-unit field representation of electromagnetism applied to a model inflationary cosmology

The new spinor-unit field representation of the electromagnetism (Nash in J Math Phys 51:042501-1–042501-27, 2010) (with quark and lepton sources) is integrated via minimal coupling with standard Einstein gravitation, to formulate a Lagrangian model of the very early universe. A completely new solution to the coupled Einstein–Maxwell equations, with sources, is derived. These equations are generalized somewhat, but not in a way that violates any physical principles. The solution of the coupled Euler–Lagrange field equations yields a scale factor a(t) (comoving coordinates) that initially exponentially increases N e-folds from a(0) ≈ 0 to a ₁ =? a(0) e ^N (N = 60 is illustrated), then exponentially decreases, then exponentially increases to a ₁, and so on almost periodically. (Oscillatory cosmological models are not knew, and have been derived from string theory and loop quantum gravity.) It is not known if the scale factor escapes this periodic trap. This model is noteworthy in several respects: 1. All fundamental fields other than gravity are realized by spinor fields. 2. A plausible connection between the unit field u and the generalization of the photon wave function with a form of Dark Energy is described, and a simple natural scenario is outlined that allocates a fraction of the total energy of the Universe to this form of Dark Energy. 3. A solution of an analog of the pure Einstein–Maxwell equations is found using an approach that is in marked contrast with the method followed to obtain a solution of the well known Friedmann model of a radiation-dominated universe.