Models Of Vocal Fold Vibration Research Articles

Muscular and neuronal control of voice production – forgotten findings, current concepts, and new developments

Voice production has been an area of interest in science since ancient times, and although advancing research has improved our understanding of the anatomy and function of the larynx, there is still little general consensus on these two topics. This review aims to outline the main developments in this field and highlight the areas where further research is needed. The most important hypotheses are presented and discussed highlighting the four main lines of research in the anatomy of the human larynx and their most important findings: (1) the arrangement of the muscle fibers of the thyroarytenoid muscle is not parallel to the vocal folds in the internal part (vocalis muscle), leading to altered properties during contraction; (2) the histological structure of the human vocal cords differs from other striated muscles; (3) there is a specialized type of heavy myosin chains in the larynx; and (4) the neuromuscular system of the larynx has specific structures that form the basis of an intrinsic laryngeal nervous system. These approaches are discussed in the context of current physiological models of vocal fold vibration, and new avenues of investigation are proposed.

On the significance of three-dimensional imaging for interpreting vocal fold dynamics

Physical mechanisms of regular and irregular vocal fold vibration were first studied in a finite element model of vocal fold vibration using the method of empirical eigenfunctions. Later the same method was used to successfully study physical mechanisms of vocal fold vibration in laboratory hemilarynx experiments (in which the medial surface of vocal fold was imaged). In subsequent clinical studies, however, the method exhibited significantly less interpretive power, presumably because of the limitations imposed by imaging from a 2D superior view. Our hypothesis is that the interpretive power of the method of empirical eigenfunctions will be significantly enhanced in clinical settings if 3D imaging is used instead of 2D imaging. To test this hypothesis, the method of empirical eigenfunctions was employed on the same finite element model implemented previously, as dynamical information was systematically removed from the analysis (interior tissue dynamics, medial surface dynamics, vertical dynamics of the superior surface, etc.). The natural modes of vibration were re-computed at each stage, and the deformations from the original natural modes were observed. The results suggest that in clinical settings, the method of empirical eigenfunctions retains significant interpretive power regarding physical mechanisms of irregular vibration when 3D imaging is used.

Analysis of glottal inverse filtering in the presence of source-filter interaction

The validity of glottal inverse filtering (GIF) to obtain a glottal flow waveform from radiated pressure signal in the presence and absence of source-filter interaction was studied systematically. A driven vocal fold surface model of vocal fold vibration was used to generate source signals. A one-dimensional wave reflection algorithm was used to solve for acoustic pressures in the vocal tract. Several test signals were generated with and without source-filter interaction at various fundamental frequencies and vowels. Linear Predictive Coding (LPC), Quasi Closed Phase (QCP), and Quadratic Programming (QPR) based algorithms, along with supraglottal impulse response, were used to inverse filter the radiated pressure signals to obtain the glottal flow pulses. The accuracy of each algorithm was tested for its recovery of maximum flow declination rate (MFDR), peak glottal flow, open phase ripple factor, closed phase ripple factor, and mean squared error. The algorithms were also tested for their absolute relative errors of the Normalized Amplitude Quotient, the Quasi-Open Quotient, and the Harmonic Richness Factor. The results indicated that the mean squared error decreased with increase in source-filter interaction level suggesting that the inverse filtering algorithms perform better in the presence of source-filter interaction. All glottal inverse filtering algorithms predicted the open phase ripple factor better than the closed phase ripple factor of a glottal flow waveform, irrespective of the source-filter interaction level. Major prediction errors occurred in the estimation of the closed phase ripple factor, MFDR, peak glottal flow, normalized amplitude quotient, and Quasi-Open Quotient. Feedback-related nonlinearity (source-filter interaction) affected the recovered signal primarily when fo was well below the first formant frequency of a vowel. The prediction error increased when fo was close to the first formant frequency due to the difficulty of estimating the precise value of resonance frequencies, which was exacerbated by nonlinear kinetic losses in the vocal tract.

On the necessity of using 3D imaging of vocal fold vibration

Physical mechanisms of regular and irregular vocal fold vibration were first studied using a computational model of vocal fold vibration. Later physical mechanisms of vocal fold vibration were studied in laboratory hemilarynx studies, where the medial surface of the vocal folds were imaged. While the method was also extended to clinical studies of vocal vibration, the method exhibited significantly less interpretive power in the clinical applications in which the superior surface of the vocal folds was imaged in 2D. Our hypothesis is that the interpretive power of the method of empirical eigenfunctions in studying the superior surface dynamics of the vocal folds will be significantly increased if one performs 3D imaging of the dynamics versus the standard 2D imaging. To test this hypothesis, the method of empirical eigenfunctions was employed on the same finite element model used in previous computational experiments. Our results confirm the hypothesis that the interpretive power of the method of empirical eigenfunctions was significantly increased in studying the superior surface dynamics of the vocal folds when 3D imaging was employed.

Subject-Specific Computational Modeling of Evoked Rabbit Phonation.

When developing high-fidelity computational model of vocal fold vibration for voice production of individuals, one would run into typical issues of unknown model parameters and model validation of individual-specific characteristics of phonation. In the current study, the evoked rabbit phonation is adopted to explore some of these issues. In particular, the mechanical properties of the rabbit's vocal fold tissue are unknown for individual subjects. In the model, we couple a 3D vocal fold model that is based on the magnetic resonance (MR) scan of the rabbit larynx and a simple one-dimensional (1D) model for the glottal airflow to perform fast simulations of the vocal fold dynamics. This hybrid three-dimensional (3D)/1D model is then used along with the experimental measurement of each individual subject for determination of the vocal fold properties. The vibration frequency and deformation amplitude from the final model are matched reasonably well for individual subjects. The modeling and validation approaches adopted here could be useful for future development of subject-specific computational models of vocal fold vibration.

Simulation on Vibration Characteristics of Throat and its Timbre

This article from the vocal cords vocal mechanism, this paper presents a new model of vocal fold vibration and found the theoretical basis of the model is analyzed in detail on the proposed model, the establishment of research and analysis. The main vocal organs acoustic and acoustic characteristics of speech analyzed in the process. Study on the characteristics of the excitation source, the acoustic properties of the vocal organs and research work status channel. Lastly we analyzed the relationship between the vibration characteristics of the vocal cords and larynx between pronunciation tones.

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 two-dimensional/three-dimensional hybrid structural model of the 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 provides acceptable accurate with the lowest possible computational expense. Inclusion of full three-dimensional (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 two-dimensional (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.

Comments on single-mass models of vocal fold vibration

Proposed mechanisms for single-mass oscillation in the vocal tract are examined critically. There are two areas that distinguish single-mass models: in the sophistication of the air flow modeling near the oscillator and whether or not oscillation depends on acoustic feedback. Two recent models that do not depend on acoustic feedback are examined in detail. One model that depends on changing flow separation points is extended with approximate calculations.

Mucosal wave analysis of a human vocal fold in the hemilarynx experiment

The mucosal wave propagation was investigated in laboratory experiments across a variety of phonatory conditions. The focus was on the medial and superior surface dynamics of the vocal fold, which quantify mucosal wave propagation, but have been relatively little studied. High‐speed, digital imaging of the entire surface of the vocal fold was performed using an excised human hemilarynx setup. Surface dynamics were characterized and differentiated across a variety of phonatory conditions. During sustained, flow‐induced oscillation, the local maxima of vocal fold mucosal displacements, velocities and acceleration and their particular phase delays in the glottal cycle were investigated. Statistical analysis was performed, examining the influence of applied stimulations. Increasing the airflow yielded higher values for lateral displacements as well as higher velocity/acceleration values. Elongating the vocal fold resulted in decreased lateral displacements. The mucosal wave propagation apparently increased for higher flow, elongated folds, and higher adduction forces. While an understanding of the correlation between vocal fold dynamics and phonatory physiology/pathology is still in its infancy, the data presented here help to establish such connections. The data are also useful for the development and evaluation of physical and numerical models of vocal fold vibration.

Anterior-posterior biphonation in a finite element model of vocal fold vibration

In this paper, a finite-element model is used to simulate anterior-posterior biphonation [Neubauer et al., J. Acoust. Soc. Am. 110(6), 3179-3192 (2001)]. The anterior-posterior stiffness asymmetric factor and the anterior-posterior shape asymmetric factor describe the asymmetry properties of vocal folds. Spatiotemporal plot, spectral analysis, anterior-posterior fundamental frequency ratio, cross covariation function, and correlation length quantitatively estimate the spatial asymmetry of vocal fold oscillations. Calculation results show that the anterior-posterior stiffness asymmetry decreases the spatial coherence of vocal fold vibration. When the stiffness asymmetry reaches a certain level, the drop in spatial coherence desynchronizes the vibration modes. The anterior and posterior sides of the vocal fold oscillate with two independent fundamental frequencies (f(a) and f(p)). The complex spectral characteristics of vocal fold vibration under biphonation conditions can be explained by the linear combination of f(a) and f(p). Empirical orthogonal eigenfunctions prove the existence of higher-order anterior-posterior modes when anterior-posterior biphonation occurs. Then, it is found that the anterior-posterior shape asymmetry also decreases the spatial coherence of vocal fold vibration, and shape asymmetry is a possible reason for anterior-posterior biphonation.

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.

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.

Influence of Vocal Fold Scarring on Phonation: Predictions from a Finite Element Model

A systematic study of the influence of vocal fold scarring on phonation was conducted. In particular, phonatory variables such as fundamental frequency, oral acoustic intensity, and phonation threshold pressure (PTP) were investigated as a function of the size and position of the laryngeal scar. By means of a finite element model of vocal fold vibration, the viscoelastic properties of both normal and scarred vocal fold mucosae were simulated on the basis of recent rheological data obtained from rabbit and canine models. The study showed that an increase in the viscoelasticity of the scarred mucosa resulted in an increase in fundamental frequency, an increase in PTP, and a decrease in oral acoustic intensity. With regard to positioning of the scar, the PTP increased most significantly when the scar was within +/-2 mm of the superior-medial junction of the vocal folds. The systematic data obtained in this investigation agree with the general clinical experience. In the future, these findings may be further validated on human subjects as newly emerging technologies such as linear skin rheometry and optical coherence tomography allow the histologic and viscoelastic properties of the normal and scarred vocal fold mucosae to be measured in the clinic.

Two-dimensional model of vocal fold vibration for sound synthesis of voice and soprano singing

Voiced sounds were simulated with a computer model of the vocal fold composed of a single mass vibrating both parallel and perpendicular to the airflow. Similarities with the two-mass model are found in the amplitudes of the glottal area and the glottal volume flow velocity, the variation in the volume flow waveform with the vocal tract shape, and the dependence of the oscillation amplitude upon the average opening area of the glottis, among other similar features. A few dissimilarities are also found in the more symmetric glottal and volume flow waveforms in the rising and falling phases. The major improvement of the present model over the two-mass model is that it yields a smooth transition between oscillations with an inductive load and a capacitive load of the vocal tract with no sudden jumps in the vibration frequency. Self-excitation is possible both below and above the first formant frequency of the vocal tract. By taking advantage of the wider continuous frequency range, the two-dimensional model can successfully be applied to the sound synthesis of a high-pitched soprano singing, where the fundamental frequency sometimes exceeds the first formant frequency.

Empirical Eigenfunctions and Medial Surface Dynamics of a Human Vocal Fold

The purpose of this investigation was to use an excised human larynx to substantiate physical mechanisms of sustained vocal fold oscillation over a variety of phonatory conditions. During sustained, flow-induced oscillation, dynamical data was collected from the medial surface of the vocal fold. The method of Empirical Eigenfunctions was used to analyze the data and to probe physical mechanisms of sustained oscillation. Thirty microsutures were mounted on the medial margin of a human vocal fold. Across five distinct phonatory conditions, the vocal fold was set into oscillation and imaged with a high-speed digital imaging system. The position coordinates of the sutures were extracted from the images and converted into physical coordinates. Empirical Eigenfunctions were computed from the time-varying physical coordinates, and mechanisms of sustained oscillation were explored. Using the method of Empirical Eigenfunctions, physical mechanisms of sustained vocal fold oscillation were substantiated. In particular, the essential dynamics of vocal fold vibration were captured by two dominant Empirical Eigenfunctions. The largest Eigenfunction primarily captured the alternating convergent/divergent shape of the medial surface of the vocal fold, while the second largest Eigenfunction primarily captured the lateral vibrations of the vocal fold. The hemi-larynx setup yielded a view of the medial surface of the vocal folds, revealing the tissue vibrations which produced sound. Through the use of Empirical Eigenfunctions, the underlying modes of vibration were computed, disclosing physical mechanisms of sustained vocal fold oscillation. The investigation substantiated previous theoretical analyses and yielded significant data to help evaluate and refine computational models of vocal fold vibration.

Geometric characterization of the laryngeal cartilage framework for the purpose of biomechanical modeling.

Some new anatomic data on the laryngeal cartilage framework have been obtained for the biomechanical modeling of the larynx. This study attempted to define and measure some biomechanically important morphometric features of the laryngeal framework, including both the human and the canine laryngeal frameworks, because the canine larynx has been frequently used as an animal model in gross morphology and in physiological experiments. The larynges of 9 men, 7 women, and 9 dogs were harvested and dissected after death. Linear and angular geometric measurements on the thyroid cartilage, the cricoid cartilage, and the arytenoid cartilage were made with a digital caliper and a protractor, respectively. The results are useful for constructing quantitative biomechanical models of vocal fold vibration and posturing (abduction and adduction), eg, continuum mechanical models and finite-element models of the vocal folds.

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.

Quantitative study of mucosal wave via videokymography in canine larynges.

Vocal fold mucosal wave movements are thought to be important in determining voice characteristics and quality. To see these movements, high-speed cinematography and videostroboscopy have been used clinically; however, these techniques have disadvantages that make them impractical for quantitative measurement of mucosal wave movements. This study explored the feasibility of using line-scan cameras for mucosal wave analysis. An excised larynx bench model was used to examine the effects of elongation and changes in subglottal pressure on the amplitude, frequency, and phase difference of vocal fold mucosal movements as calculated from line-scan images. The data showed a positive and linear relationship between an increase in subglottal pressure and amplitude of the mucosal wave; elongation of the vocal folds appeared to decrease the amplitude of mucosal wave upheaval at each level of subglottal pressure. Similarly, increase in subglottal pressure had a positive and linear relationship with increase in frequency of vibration; elongation of the vocal folds further increased the frequency at any given subglottal pressure. Phase difference between the movements of the upper and lower margins of the mucosal lips was estimated and did not appear to be significantly affected by changes in subglottal pressure and elongation. The data presented in this study are consistent with relationships that we would expect to be true from currently accepted models of vocal fold vibration.

Effects of dehydration on phonation in excised canine larynges.

The effects of exposure to dry air on phonation were measured in an ex vivo model of vocal fold vibration. Excised canine larynges were mounted on an apparatus and made to phonate at a constant subglottal pressure by means of unhumidified airflow. The phonation threshold pressure (PTP), glottal airflow, sound intensity of the acoustic output, and effects on vocal efficiency were also assessed. Student's t-test was performed on the results. In 17 larynges, the average PTP increased from 10.0 cm H2O to 15.0 cm H2O after exposure to dry airflow (p < .001). In addition, the average flow increased from 585 mL/s to 801 mL/s at a constant suprathreshold subglottal pressure (p < .001), and from 323 mL/s to 610 mL/s at the PTP (p < .001). The average acoustic output levels, measured during stable phonation segments, markedly decreased with exposure to the dry airflow, from 91.5 dB to 88.5 dB (p < .001). The average vocal efficiency decreased from 3.63 x 10(-4) to 7.00 x 10(-5) (p < .001). No such changes were seen in control larynges phonated with 100% humidified air used for driving the airflow. The results support previously reported modeling and experimental findings that dehydration of the vocal fold generally degrades laryngeal performance.