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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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 occurrence of the Coanda effect in pulsatile flow through static models of the human vocal folds

Pulsatile flow through a one-sided diffuser and static divergent vocal-fold models is investigated to ascertain the relevance of viscous-driven flow asymmetries in the larynx. The models were 7.5 times real size, and the flow was scaled to match Reynolds and Strouhal numbers, as well as the translaryngeal pressure drop. The Reynolds number varied from 0-2000, for flow oscillation frequencies corresponding to 100 and 150 Hz life-size. Of particular interest was the development of glottal flow skewing by attachment to the bounding walls, or Coanda effect, in a pulsatile flow field, and its impact on speech. The vocal folds form a divergent passage during phases of the phonation cycle when viscous effects such as flow separation are important. It was found that for divergence angles of less than 20 degrees, the attachment of the flow to the vocal-fold walls occurred when the acceleration of the forcing function was zero, and the flow had reached maximum velocity. For a divergence angle of 40 degrees, the fully separated central jet never attached to the vocal-fold walls. Inferences are made regarding the impact of the Coanda effect on the sound source contribution in speech.     

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.     

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.     

The intermediate layer: A morphologic study of the elastin and hyaluronic acid constituents of normal human vocal folds

The lamina propria of vocal folds are important in voice production. We evaluated the morphologic features of elastin and hyaluronic acid, two important constituents of the lamina propria. Thirty normal human vocal folds were obtained from patients dying of traumatic causes without vocal fold injury. These tissues were immediately prepared for histologic and ultrastructural examination by standard methods. For specific study of the ultrastructure of the layers of the lamina propria, six vocal folds were divided horizontally through the midplane of the lamina propria. We found that the elastin composition of the vocal folds is variable, the largest amount being seen in the midportion on elastin-van Gieson (EVG) staining and ultrastructural evaluation. The superficial layer of the lamina propria contains fewer large elastin fibers. In this region, we found that elastin was predominantly composed of elaunin and oxytalan, which stain poorly with EVG. Using computer-assisted image analysis, we quantified the differences in elastin composition between the layers. The amount of elastin varied between men and women, and these differences could not be accurately measured by the methods employed. Hyaluronic acid was abundant especially in the midportion of the lamina propria and was significantly more abundant in men than women on quantification. The significance of these observations in normal vocal folds is discussed.     

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.     

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.