David A. Berry

A finite-element model of vocal-fold vibration

A finite-element model of the vocal fold is developed from basic laws of continuum mechanics to obtain the oscillatory characteristics of the vocal folds. The model is capable of accommodating inhomogeneous, anisotropic material properties and irregular geometry of the boundaries. It has provisions for asymmetry across the midplane, both from the geometric and tension point of view, which enables one to simulate certain kinds of voice disorders due to vocal-fold paralysis. It employs the measured viscoelastic properties of the vocal-fold tissues. The detailed construction of the matrix differential equations of motion is presented followed by the solution scheme. Finally, typical results are presented and validated using an eigenvalue method and a commercial finite-element package (ABAQUS).

INTERPRETATION OF BIOMECHANICAL SIMULATIONS OF NORMAL AND CHAOTIC VOCAL FOLD OSCILLATIONS WITH EMPIRICAL EIGENFUNCTIONS

Empirical orthogonal eigenfunctions are extracted from biomechanical simulations of normal and chaotic vocal fold oscillations. For normal phonation, two dominant empirical eigenfunctions capture the vibration patterns of the folds and exhibit a 1:1 entrainment. The eigenfunctions show some correspondence to theoretical low-order normal modes of a simplified, three-dimensional elastic continuum, and to the normal modes of a linearized two-mass model. The eigenfunctions also facilitate a physical interpretation of energy transfer mechanisms in vocal fold dynamics. Subharmonic regimes and chaotic oscillations are observed during simulations of a lax cover, in which case at least three empirical eigenfunctions are necessary to capture the resulting vocal fold oscillations. These chaotic oscillations might be understood in terms of a desynchronization of a few of the low-order modes, and may be related to mechanisms of creaky voice or vocal fry. Furthermore, some of the empirical eigenfunctions captured during complex oscillations correspond to higher-order normal modes described in earlier theoretical work. The empirical eigenfunctions may also be useful in the design of lower-order models (valid over the range for which the empirical eigenfunctions remain more or less constant), and may help facilitate bifurcation analyses of the biomechanical simulation.

Nonlinear dynamics of the voice: Signal analysis and biomechanical modeling.

Irregularities in voiced speech are often observed as a consequence of vocal fold lesions, paralyses, and other pathological conditions. Many of these instabilities are related to the intrinsic nonlinearities in the vibrations of the vocal folds. In this paper, bifurcations in voice signals are analyzed using narrow-band spectrograms. We study sustained phonation of patients with laryngeal paralysis and data from an excised larynx experiment. These spectrograms are compared with computer simulations of an asymmetric 2-mass model of the vocal folds. (c) 1995 American Institute of Physics.

Normal modes in a continuum model of vocal fold tissues

The Ritz method is used to calculate eigenmodes and eigenfrequencies in a continuum model of the vocal folds. The investigation represents a rectification and extension of previous studies, emphasizing the indispensability of utilizing natural boundary conditions when computing the characteristic modes of a system. Concurring with previous assertions, two of the lower-order eigenmodes are theorized to play a major role in facilitating self-oscillation of the folds during phonation. One mode, related to vertical phasing, is shown to have a more direct control over glottal convergence/divergence than indicated in previous calculations. Unlike lumped element models, the continuum model predicts that the eigenfrequencies of the two modes are closely spaced over an extensive range of tissue sizes and stiffnesses. This finding may help explain why the two modes entrain so naturally over a wide range of phonatory adjustments in human phonation.

High-speed digital imaging of the medial surface of the vocal folds

High-speed digital imaging of the medial surface of the vocal folds was performed in excised canine larynx experiments. Building on the excised larynx investigations of Baer [Ph.D. dissertation, MIT, Boston, MA (1975)] and hemilarynx investigations of Jiang and Titze [Laryngoscope 103, 872-882 (1993)], nine vocal fold fleshpoints were tracked simultaneously along the medial surface of one coronal plane of the left vocal fold using a Kodak EktaPro 4540 high-speed digital imaging system. By imaging from two distinct views, 3D reconstructions of fleshpoint trajectories were performed with a sampling frequency of 4.5 kHz and a spatial resolution of approximately 0.08 mm. Quantitative results were derived from a typical example of periodic chestlike vibrations. Furthermore, these data were decomposed into empirical eigenfunctions, the building blocks of vocal fold vibration, illuminating basic mechanisms of self-sustained oscillation. Previously, such mechanisms have only been explored theoretically using computer models of vocal fold vibration [Berry et al., J. Acoust. Soc. Am. 95, 3595-3604 (1994)]. Similar to the theoretical studies, two eigenfunctions captured 98% of the variance of the data. Because this investigation utilized high-speed technology, the methodology may also be used to examine complex, aperiodic vibrations. Thus, this technique allows mechanisms of regular and irregular vocal fold vibration to be explored using direct observations of vibrating tissues in the laboratory.

The influence of subglottal acoustics on laboratory models of phonation

Many previous laboratory investigations of phonation involving physical models, excised larynges, and in vivo canine larynges have failed to fully specify the subglottal system. Many of these same studies have reported a variety of nonlinear phenomena, including bifurcations (e.g., various classes of phonation onset and offset, register changes, frequency jumps), subharmonics, and chaos, and attributed such phenomena to the biomechanical properties of the larynx. However, such nonlinear phenomena may also be indicative of strong coupling between the voice source and the subglottal tract. Consequently, in such studies, it has not been clear whether the underlying mechanisms of such nonlinear phenomena were acoustical, biomechanical, or a coupling of the acoustical and biomechanical systems. Using a physical model of vocal fold vibration, and tracheal tube lengths which have been commonly reported in the literature, it is hypothesized and subsequently shown that such nonlinear phenomena may be replicated solely on the basis of laryngeal interactions with the acoustical resonances of the subglottal system. Recommendations are given for ruling out acoustical resonances as the source of nonlinear phenomena in future laboratory studies of phonation.

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.

Medial surface dynamics of an in vivo canine vocal fold during phonation

Quantitative measurement of the medial surface dynamics of the vocal folds is important for understanding how sound is generated within the larynx. Building upon previous excised hemilarynx studies, the present study extended the hemilarynx methodology to the in vivo canine larynx. Through use of an in vivo model, the medial surface dynamics of the vocal fold were examined as a function of active thyroarytenoid muscle contraction. Data were collected using high-speed digital imaging at a sampling frequency of 2000 Hz, and a spatial resolution of 1024 x 1024 pixels. Chest-like and fry-like vibrations were observed, but could not be distinguished based on the input stimulation current to the recurrent laryngeal nerve. The subglottal pressure did distinguish the registers, as did an estimate of the thyroarytenoid muscle activity. Upon quantification of the three-dimensional motion, the method of Empirical Eigenfunctions was used to extract the underlying modes of vibration, and to investigate mechanisms of sustained oscillation. Results were compared with previous findings from excised larynx experiments and theoretical models.

Aerodynamically and acoustically driven modes of vibration in a physical model of the vocal folds

In a single-layered, isotropic, physical model of the vocal folds, distinct phonation types were identified based on the medial surface dynamics of the vocal fold. For acoustically driven phonation, a single, in-phase, x-10 like eigenmode captured the essential dynamics, and coupled with one of the acoustic resonances of the subglottal tract. Thus, the fundamental frequency appeared to be determined primarily by a subglottal acoustic resonance. In contrast, aerodynamically driven phonation did not naturally appear in the single-layered model, but was facilitated by the introduction of a vertical constraint. For this phonation type, fundamental frequency was relatively independent of the acoustic resonances, and two eigenmodes were required to capture the essential dynamics of the vocal fold, including an out-of-phase x-11 like eigenmode and an in-phase x-10 like eigenmode, as described in earlier theoretical work. The two eigenmodes entrained to the same frequency, and were decoupled from subglottal acoustic resonances. With this independence from the acoustic resonances, vocal fold dynamics appeared to be determined primarily by near-field, fluid-structure interactions.

Physical mechanisms of phonation onset: A linear stability analysis of an aeroelastic continuum model of phonation

In an investigation of phonation onset, a linear stability analysis was performed on a two-dimensional, aeroelastic, continuum model of phonation. The model consisted of a vocal fold-shaped constriction situated in a rigid pipe coupled to a potential flow which separated at the superior edge of the vocal fold. The vocal fold constriction was modeled as a plane-strain linear elastic layer. The dominant eigenvalues and eigenmodes of the fluid-structure-interaction system were investigated as a function of glottal airflow. To investigate specific aerodynamic mechanisms of phonation onset, individual components of the glottal airflow (e.g., flow-induced stiffness, inertia, and damping) were systematically added to the driving force. The investigations suggested that flow-induced stiffness was the primary mechanism of phonation onset, involving the synchronization of two structural eigenmodes. Only under conditions of negligible structural damping and a restricted set of vocal fold geometries did flow-induced damping become the primary mechanism of phonation onset. However, for moderate to high structural damping and a more generalized set of vocal fold geometries, flow-induced stiffness remained the primary mechanism of phonation onset.