Petr Šidlof

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.

In vitro experimental investigation of voice production.

The process of human phonation involves a complex interaction between the physical domains of structural dynamics, fluid flow, and acoustic sound production and radiation. Given the high degree of nonlinearity of these processes, even small anatomical or physiological disturbances can significantly affect the voice signal. In the worst cases, patients can lose their voice and hence the normal mode of speech communication. To improve medical therapies and surgical techniques it is very important to understand better the physics of the human phonation process. Due to the limited experimental access to the human larynx, alternative strategies, including artificial vocal folds, have been developed. The following review gives an overview of experimental investigations of artificial vocal folds within the last 30 years. The models are sorted into three groups: static models, externally driven models, and self-oscillating models. The focus is on the different models of the human vocal folds and on the ways in which they have been applied.

Comparison of Acceleration and Impact Stress as Possible Loading Factors in Phonation: A Computer Modeling Study

Impact stress (the impact force divided by the contact area of the vocal folds) has been suspected to be the main traumatizing mechanism in voice production, and the main cause of vocal fold nodules. However, there are also other factors, such as the repetitive acceleration and deceleration, which may traumatize the vocal fold tissues. Using an aeroelastic model of voice production, the present study quantifies the acceleration and impact stress values in relation to lung pressure, fundamental frequency (F0) and prephonatory glottal half-width. Both impact stress and acceleration were found to increase with lung pressure. Compared to impact stress, acceleration was less dependent on prephonatory glottal width and, thus, on voice production type. Maximum acceleration values were about 5–10 times greater for high F0 (approx. 400 Hz) compared to low F0 (approx. 100 Hz), whereas maximum impact stress remained nearly unchanged. This suggests that acceleration, i.e. the inertia forces, may present at high F0 a greater load for the vocal folds, and in addition to the collision forces may contribute to the fact that females develop vocal fold nodules and other vocal fold traumas more frequently than males.

A hybrid approach to the computational aeroacoustics of human voice production

The aeroacoustic mechanisms in human voice production are complex coupled processes that are still not fully understood. In this article, a hybrid numerical approach to analyzing sound generation in human voice production is presented. First, the fluid flow problem is solved using a parallel finite-volume computational fluid dynamics (CFD) solver on a fine computational mesh covering the larynx. The CFD simulations are run for four geometrical configurations: both with and without false vocal folds, and with fixed convergent or convergent–divergent motion of the medial vocal fold surface. Then the aeroacoustic sources and propagation of sound waves are calculated using Lighthill’s analogy or acoustic perturbation equations on a coarse mesh covering the larynx, vocal tract, and radiation region near the mouth. Aeroacoustic sound sources are investigated in the time and frequency domains to determine their precise origin and correlation with the flow field. The problem of acoustic wave propagation from the larynx and vocal tract into the free field is solved using the finite-element method. Two different vocal-tract shapes are considered and modeled according to MRI vocal-tract data of the vowels /i/ and /u/. The spectra of the radiated sound evaluated from acoustic simulations show good agreement with formant frequencies known from human subjects.

Estimation of impact stress using an aeroelastic model of voice production.

The maximum impact stress at the contact of the vocal folds achieved during the oscillation cycle was estimated in phonation using an aeroelastic model of voice production. Relations of impact stress to the lung pressure, fundamental frequency of self-oscillations, prephonatory glottal width, sound pressure level generated at the end of the glottis and vibration amplitude of the vocal folds were studied. Using the fundamental frequency, prephonatory glottal width, lung pressure and airflow rate values found in normal speech, maximum impact stress values of 2–3 kPa were obtained. The results fall well within the limits reported for excised canine larynges and human subjects. Impact stress increased with lung pressure almost linearly after the phonation threshold but reached a plateau when the limit of maximum glottal opening was reached. When the fundamental frequency and lung pressure were kept constant, impact stress appears to fit closely with a parabolic function of prephonatory glottal half-width.

Acoustic perturbation equations and Lighthill's acoustic analogy for the human phonation

In speech, air is driven through the larynx by compression of the lungs. Thereby, air flows through the glottis which forces the vocal folds to oscillate which in turn results in a pulsating air flow. This air flow is the main source of the generated sound-the phonation. The acoustic wave then passes through the vocal tract, which acts as a filter modulating the propagated sound leaving the mouth. We model the fluid-structure-acoustic interaction with a so called hybrid approach. The air flow in the larynx, together with a prescribed vocal fold motion, is simulated with help of the open source solver OpenFOAM. Based on the resulting fluid field, acoustic source terms and the wave propagation is calculated within the finite element solver CFS++. Two methods are available to choose from, Lighthills acoustic analogy and an aeroacoustic analogy based on a perturbation ansatz. Additionally, the simulation domain is extended by a realistic but geometrical fixed vocal tract and connected to a propagation region. The different acoustic approaches are compared, by analysing the acoustic pressure in the glottis (source region) and outside the vocal tract. Moreover, to illustrate the effects of the vocal tract an alternative geometry is used for comparison.

Large-Eddy Simulation of Internal Flow through Human Vocal Folds

The phonatory process occurs when air is expelled from the lungs through the glottis and the pressure drop causes flow-induced oscillations of the vocal folds. The flow fields created in phonation are highly unsteady and the coherent vortex structures are also generated. For accuracy it is essential to compute on humanlike computational domain and appropriate mathematical model. The work deals with numerical simulation of air flow within the space between plicae vocales and plicae vestibulares. In addition to the dynamic width of the rima glottidis, where the sound is generated, there are lateral ventriculus laryngis and sacculus laryngis included in the computational domain as well. The paper presents the results from OpenFOAM which are obtained with a large-eddy simulation using second-order finite volume discretization of incompressible Navier-Stokes equations. Large-eddy simulations with different subgrid scale models are executed on structured mesh. In these cases are used only the subgrid scale models which model turbulence via turbulent viscosity and Boussinesq approximation in subglottal and supraglottal area in larynx.

Evaluation of Interferograms of Unsteady Subsonic Airflow Past a Fluttering Airfoil

The paper reports on time-resolved interferometric measurements of unsteady flow fields around a fluttering NACA0015 airfoil. A mechanical model with two degrees of freedom (pitch and plunge) has been designed and tested in a high-speed subsonic wind tunnel. Aeroelastic instability of the classical flutter and dynamic stall type has been observed in the Mach number range M = 0.2 0.5. The interferograms were recorded using a Mach-Zehnder interferometer and a high-speed camera. An in-house software IFGPro was developed for the postprocessing and evaluation of the interferogram sequences, yielding pressure distribution, lift and drag force on the airfoil.

Wind Tunnel Measurements of Flow-Induced Vibration of a NACA0015 Airfoil Model

The paper reports on interferometric measurements of flow over a NACA0015 airfoil model during flutter limit cycle oscillations. The airfoil model is fixed on an elastic support allowing motion with two degrees of freedom — pitch and plunge. The structural mass and stiffness matrices can be tuned to certain extent, so that the eigenfrequencies of the two modes approach as needed. The model is equipped with dynamic pressure probes and sensors measuring the airfoil vertical position. The flow field around the airfoil was measured by Mach-Zehnder interferometer and registered using a high-speed camera synchronously with the mechanical vibration and pressure measurements. The Mach number of the incident airflow was gradually increased and the response of the aeroelastic system to initial impulse measured, until the flutter instability onset occurred. Flutter boundaries were evaluated for various additional masses attached (i.e., for various plunging mode eigenfrequencies), and post-critical behavior of the system investigated. The interferograms recorded by the high-speed camera were postprocessed, yielding pressure distribution around the airfoil during its vibration and an estimate of the total aerodynamic force and energy transfer from the airflow to the structure.Copyright

Numerical Analysis of Airflow in Human Vocal Folds Using Finite Element and Finite Volume Method

The paper compares two approaches for solution of the unsteady airflow in human vocal folds: a 2D finite element model (with optional vocal fold oscillation) and a 3D finite volume computation (with optional turbulence model). The equations are solved using open-source libraries. The results show that the 3D flow effects are significant, particularly further downstream glottis.