Resonance properties of the vocal folds: in vivo laryngoscopic investigation of the externally excited laryngeal vibrations

The study presents the first attempt to investigate resonance properties of the living vocal folds by means of laryngoscopy. Laryngeal vibrations were excited via a shaker placed on the neck of a male subject and observed by means of videostroboscopy and videokymography (VKG). When the vocal folds were tuned to the phonation frequency of 110 Hz and sinusoidal vibration with sweeping frequency (in the range 50-400 Hz) was delivered to the larynx, three clearly pronounced resonance peaks at frequencies around 110, 170, and 240 Hz were identified in the vocal fold tissues. Different modes of vibration of the vocal folds, observed as distinct lateral-medial oscillations with one, two, and three half-wavelengths along the glottal length, respectively, were associated with these resonance frequencies. At the external excitation frequencies below 100 Hz, vibrations of the ventricular folds, aryepiglottic folds and arytenoid cartilages were dominant in the larynx.     

The dynamics of length change in canine vocal folds

The time courses of vocal fold elongation and contraction have beenmeasured as a function of intrinsic laryngeal muscle activity. The superior and recurrent laryngeal nerves of anesthetized canines were stimulated supramaximally (on-off in all combinations) while the vocal folds were surgically exposed and illuminated for conventional and higher speed (300 frames per second) video recording. Microsutures were placed on various points on the vocal folds to measure elongation and contraction. Vocal fold strain, defined as elongation divided by rest length, ranged from −17% to +45%. The typical time constant for exponential increase or decrease in strain was about 30 ms. This reflects primarily the intrinsic muscle activation times rather than a passive (inertial or viscoelastic) response of cricothyroid joint rotation or translation.     

Nonlinear oscillation of pathological vocal folds during vocalization

The extended two-mass model is adopted to analyze the nonlinear oscillation of pathological vocal folds during vocalization. Redundant tissue or area in laryngeal patients is modeled as a massless rigid connected to the upper mass of the vocal folds, and a parameter Q is introduced to represent the change of glottal configurations and tension imbalance between the left and right sides of vocal folds. Numerical simulations demonstrate that the pathological vocal-fold decreases the threshold of Q to generate nonlinear vocal oscillation, indicating the improvement of the sensitivity of vocal folds to asymmetries and enhancing the coupling between two sides. Furthermore, the pathological vocal-fold can lower the fundamental frequency and eliminate high-order harmonics, For example, the fundamental frequency decreases from 119.94 Hz to 84.95 Hz when Q=0.58 and the sub-glottal pressure 1450 Pa. However, there are no prominent effects on the amplitudes of sub-harmonic and low-order harmonics.     

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.     

The physics of small-amplitude oscillation of the vocal folds

A theory of vocal fold oscillation is developed on the basis of the body-cover hypothesis. The cover is represented by a distributed surface layer that can propagate a mucosal surface wave. Linearization of the surface-wave displacement and velocity, and further small-amplitude approximations, yields closed-form expressions for conditions of oscillation. The theory predicts that the lung pressure required to sustain oscillation, i.e., the oscillation threshold pressure, is reduced by reducing the mucosal wave velocity, by bringing the vocal folds closer together and by reducing the convergence angle in the glottis. The effect of vocal tract acoustic loading is included. It is shown that vocal tract inertance reduces the oscillation threshold pressure, whereas vocal tract resistance increases it. The treatment, which is applicable to falsetto and breathy voice, as well as onset or release of phonation in the absence of vocal fold collision, is harmonized with former treatments based on two-mass models and collapsible tubes.     

Model-based classification of nonstationary vocal fold vibrations

Classification of vocal fold vibrations is an essential task of the objective assessment of voice disorders. For historical reasons, the conventional clinical examination of vocal fold vibrations is done during stationary, sustained phonation. However, the conclusions drawn from a stationary phonation are restricted to the observed steady-state vocal fold vibrations and cannot be generalized to voice mechanisms during running speech. This study addresses the approach of classifying real-time recordings of vocal fold oscillations during a nonstationary phonation paradigm in the form of a pitch raise. The classification is based on asymmetry measures derived from a time-dependent biomechanical two-mass model of the vocal folds which is adapted to observed vocal fold motion curves with an optimization procedure. After verification of the algorithm performance the method was applied to clinical problems. Recordings of ten subjects with normal voice and ten dysphonic subjects have been evaluated during stationary as well as nonstationary phonation. In the case of nonstationary phonation the model-based classification into "normal" and "dysphonic" succeeds in all cases, while it fails in the case of sustained phonation. The nonstationary vocal fold vibrations contain additional information about vocal fold irregularities, which are needed for an objective interpretation and classification of voice disorders.     

Nonlinear behavior of vocal fold vibration: The role of coupling between the vocal folds

Coupling between the vocal folds is one of the nonlinear mechanisms allowing regulation and synchronization of mucosal vibration. The purpose of this study was to establish that modulations such as diplophonia and abnormalities observed in vocal signals that may be observed in some cases of laryngeal pathology can be considered as nonlinear behavior due to the persistence of some physical interaction (coupling). An experimental model using excised porcine larynx was designed to create tension asymmetry between the vocal folds and to obtain vocal signals with modulations. Signals were analyzed by spectral analysis and the phase portrait method. Results were compared with computer-generated synthetic signals corresponding to nonlinear combinations of sinusoid signals. Under these conditions, evidence of nonlinear behavior was detected in 85% of experimental signals. These findings were interpreted as a demonstration of vocal fold interaction. Based on these findings, the authors conclude that (1) coupling must be taken into account in physical models of laryngeal physiology, and that (2) methods of nonlinear dynamics may be used for objective voice analysis.     

Stroboscopic signs associated with benign lesions of the vocal folds

Stroboscopic signs were systematically rated for a group of 80 patients with benign vocal fold lesions, most of whom had either a nodule or a polyp. Each group revealed a characteristic pattern of ranking of signs and exhibited differences of most predominant signs. The results of the ratings were submitted to a multiple discriminant analysis to determine if post hoc stroboscopic ratings could be used to correctly classify patients into one of four diagnostic groups and into one of two treatment groups. All patients except one were correctly classified into the diagnostic groups, and all were correctly classified into the treatment groups. The important signs for classifying patients into the diagnostic groups were roughness of the edge of the affected vocal fold, phase closure pattern, and phase symmetry. The important signs for classifying patients into the treatment groups were roughness of the edge of the affected vocal fold, glottal closure configuration, and vibration characteristics of the affected (or more affected) vocal fold. The results suggest that objective evaluation of stroboscopic examinations can be valuable in correctly diagnosing patients and in selecting the proper treatment regimen for the patient.     

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.     

Rotationally symmetric vibrations of orthotropic layered cylindrical shells

The derivation of the general equations of motion for the analysis of laminated cylindrical shells consisting of layers of orthotropic laminae, and the equations of motion for rotationally symmetric deformation made previously by the authors are used in this study. The three coupled differential equations governing the rotationally symmetric motion of each layer of a cylindrical shell with rotary inertia neglected are replaced by another set of three differential equations where the solutions can be obtained systematically. General solutions for laminated cylindrical shells of finite length are presented. Coupled frequencies and several mode shapes for a fixed-end cylindrical shell with one and two orthotropic layers of various geometric dimensions are calculated for illustrative purposes. The results based on the present analysis for a single layered shell are compared to the results obtained according to the classical analysis.     

Modal interaction in chaotic vibrations of a shallow double-curved shell-panel

Experimental results and analytical results are presented on chaotic vibrations of a shallow double-curved shell-panel subjected to gravity and periodic excitation. Modal interactions in the chaotic responses are discussed. The shell-panel with square boundary is simply supported for deflection. In-plane displacement at the boundary is elastically constrained. In the experiment, time histories of the chaotic responses at the spatial multiple positions of the shell-panel are measured for the inspection of modal interaction. In the analysis, the shallow shell-panel is assumed to have constant curvatures along to orthogonal directions and geometric initial imperfection. The Donnell-Mushtari-Vlasov type equation is used as governing equation with lateral inertia force. Assuming deflection with multiple modes of vibration, the governing equation is reduced to a set of nonlinear ordinary differential equations by the Bubnov-Galerkin procedure. Chaotic responses are integrated numerically. The chaotic responses, which are obtained by the experiment and the analysis, are inspected with the Fourier spectra, the Poincaré projections, the maximum Lyapunov exponents and the Lyapunov dimension. Contribution of modes of vibration to the chaotic responses is analyzed by the principal component analysis, i.e., Karhunen-Loève transformation.     

对称混沌系统的非线性动力学行为及控制

基于线性反馈控制思想，提出了一种对称动力学系统及其控制混沌的方法，给出了预期各周期轨道反馈系数的选择原则，适当选择反馈系数，即可得到不同的周期轨道.将此方法应用 到Logistic映射中，取得了良好的控制效果. 关键词： 反馈控制 周期转道 对称系统     

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.     

The effect of viscosity changes in the vocal folds on the range of oscillation

Changes in vocal fold oscillation threshold pressure were induced in excised canine larynges by experimentally causing fluid movement into and out of the vocal folds. The transport was facilitated by exposing the vocal folds to various osmotic solutions, and it was assumed that changes in hydration caused changes in the internal tissue viscosity. A range of oscillation threshold pressures was measured for each condition of hydration by varying length and glottal width. The oscillation threshold pressure shifted as predicted. Decreased hydration (increased viscosity) raised the threshold of oscillation, and increased hydration (decreased viscosity) lowered the threshold of oscillation. This apparently represents the first in vitro model for the study of the effect of viscosity changes of the internal environment of the vocal folds on phonation.     

Axially symmetric vibrations of fluid-filled poroelastic circular cylindrical shells

Employing Biot's theory of wave propagation in liquid saturated porous media, axially symmetric vibrations of fluid-filled and empty poroelastic circular cylindrical shells of infinite extent are investigated for different wall-thicknesses. Let the poroelastic cylindrical shells are homogeneous and isotropic. The frequency equation of axially symmetric vibrations each for a pervious and an impervious surface is derived. Particular cases when the fluid is absent are considered both for pervious and impervious surfaces. The frequency equation of axially symmetric vibrations propagating in a fluid-filled and an empty poroelastic bore, each for a pervious and an impervious surface is derived as a limiting case when ratio of thickness to inner radius tends to infinity as the outer radius tends to infinity. Cut-off frequencies when the wavenumber is zero are obtained for fluid-filled and empty poroelastic cylindrical shells both for pervious and impervious surfaces. When the wavenumber is zero, the frequency equation of axially symmetric shear vibrations is independent of nature of surface, i.e., pervious or impervious and also it is independent of presence of fluid in the poroelastic cylindrical shell. Non-dimensional phase velocity for propagating modes is computed as a function of ratio of thickness to wavelength in absence of dissipation. These results are presented graphically for two types of poroelastic materials and then discussed. In general, the phase velocity of an empty poroelastic cylindrical shell is higher than that of a fluid-filled poroelastic cylindrical shell.The phase velocity of a fluid-filled bore is higher than that of an empty poroelastic bore. Previous results are shown as a special case of present investigation. Results of purely elastic solid are obtained.     

Studying vocal fold vibrations in Parkinson's disease with a nonlinear model

A nonlinear model is applied to study pathologic vocal vibratory characteristics and voice treatments of Parkinson's disease. We find that a number of pathologic vocal characteristics commonly observed in Parkinson's disease, including reduced vibratory intensity, incomplete vocal closure, increased phonation threshold pressure, glottal tremor, subharmonics, and chaotic vocal fold vibrations, can be studied with this nonlinear model. We also find that two kinds of clinical voice treatments for Parkinson's disease, including respiratory effort treatment and Lee Silverman voice treatment can be studied with this computer model. Results suggest that respiratory effort treatment, in which subglottal pressure is increased, might aid in enhancing vibratory intensity, improving glottal closure, and avoiding vibratory irregularity. However, the Lee Silverman voice treatment, in which both subglottal pressure and vocal fold adduction are increased, might be better than respiratory effort treatment. Increasing vocal fold thickness would be further helpful to improve these pathologic characteristics. The model studies show consistencies with clinical observations. Computer models may be of value in understanding the dynamic mechanism of disordered voices and studying voice treatment effects in Parkinson's disease.     

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.