A model for vocal fold vibratory motion, contact area, and the electroglottogram

The electroglottogram (EGG) has been conjectured to be related to the area of contact between the vocal folds. This hypothesis has been substantiated only partially via direct and indirect observations. In this paper, a simple model of vocal fold vibratory motion is used to estimate the vocal fold contact area as a function of time. This model employs a limited number of vocal fold vibratory features extracted from ultra high-speed laryngeal films. These characteristics include the opening and closing vocal fold angles and the lag (phase difference) between the upper and lower vocal fold margins. The electroglottogram is simulated using the contact area, and the EGG waveforms are compared to measured EGGs for normal male voices producing both modal and pulse register tones. The model also predicts EGG waveforms for vocal fold vibration associated with a nodule or polyp.     

Determination of superior surface strains and stresses, and vocal fold contact pressure in a synthetic larynx model using digital image correlation

Stresses and strains within the vocal fold tissue may play a critical role in voice fatigue, in tissue damage and resulting voice disorders, and in tissue healing. In this study, experiments were performed to determine mechanical fields on the superior surface of a self-oscillating physical model of the human vocal folds using a three-dimensional digital image correlation method. Digital images obtained using a high-speed camera together with a mirror system were used to measure displacement fields, from which strains, strain rates, and stresses on the superior surface of the model vocal folds were computed. The dependence of these variables on flow rate was established. A Hertzian impact model was used to estimate the contact pressure on the medial surface from superior surface strains. A tensile stress dominated state was observed on the superior surface, including during collision between the model folds. Collision between the model vocal folds limits the medial-lateral stress levels on the superior surface, in conjunction with compressive stress or contact pressure on the medial surface.     

The membranous contact quotient: A new phonatory measure of glottal competence

The membranous contact quotient (MCQ) is introduced as a measure of dynamic glottal competence. It is defined as the ratio of the membranous contact glottis (the anterior-posterior length of contact between the two membranous vocal folds) and the membranous vocal fold length. An elliptical approximation to the vocal fold contour during phonation was used to predict MCQ values as a function of vocal process gap (adduction), maximum glottal width, and membranous glottal length. MCQ is highly dependent on the vocal process gap and the maximum glottal width, but not on vocal fold length. Five excised larynges were used to obtain MCQ data for a wide range of vocal process gaps and maximum glottal widths. Predicted and measured MCQ values had a correlation of 0.93, with an average absolute difference of 9.6% (SD = 10.5%). The model is better at higher values of MCQ. The theory for MCQ is also expressed as a function of vocal process gap and subglottal pressure to suggest production control potential. The MCQ measure is obtainable with the use of stroboscopy and appears to be a potentially useful clinical measure.     

A theoretical model of the pressure field arising from asymmetric intraglottal flows applied to a two-mass model of the vocal folds

A theoretical flow solution is presented for predicting the pressure distribution along the vocal fold walls arising from asymmetric flow that forms during the closing phases of speech. The resultant wall jet was analyzed using boundary layer methods in a non-inertial reference frame attached to the moving wall. A solution for the near-wall velocity profiles on the flow wall was developed based on a Falkner-Skan similarity solution and it was demonstrated that the pressure distribution along the flow wall is imposed by the velocity in the inviscid core of the wall jet. The method was validated with experimental velocity data from 7.5 times life-size vocal fold models, acquired for varying flow rates and glottal divergence angles. The solution for the asymmetric pressures was incorporated into a widely used two-mass model of vocal fold oscillation with a coupled acoustical model of sound propagation. Asymmetric pressure loading was found to facilitate glottal closure, which yielded only slightly higher values of maximum flow declination rate and radiated sound, and a small decrease in the slope of the spectral tilt. While the impact on symmetrically tensioned vocal folds was small, results indicate the effect becomes more significant for asymmetrically tensioned vocal folds.     

Symptomatology of adductor spasmodic dysphonia: A physiologic model

Vocal symptomatology of adductor spasmodic dysphonia (SD) is reviewed critically from historical, epidemiologic, and clinical perspectives. A model of symptomatology of this disorder based on a large patient population, and clinical and physiologic observations is advanced. The model incorporates crucial symptomatic and asymptomatic phonatory and nonphonatory physiologic parameters of laryngeal behavior in these patients. These parameters include vocal fold contact area, vocal fold collision force, glottic compression, and subglottic air pressure. Inappropriate efferent discharges from brain-stem basal ganglia are hypothesized as causing overadduction of the vocal folds in phonation, generating the basic and fundamental vocal symptom of adductor SD—strained, strangled, overpressured voice quality. Cortical loops are implicated as accountable for compensatory vocal behavior, not as the primary site of the disorder. Symptom occurrence, variability, magnitude, effects, and failure of treatment approaches, as well as recurrence of symptoms after ablative or invasive procedures, are explained by this model. The model also predicts that symptomatology of adductor spasmodic dysphonia is unique to this disorder and that symptoms are phonotopically organized. The minimal diagnostic battery based on the model is presented, and it is shown how this battery aids in the differential diagnosis of adductor SD and other phonatory disorders that closely mimic the vocal symptoms of adductor spasmodic dysphonia, including tremor.     

Subjective evaluations of sound radiated by impacted plates, using the design of experiments method

This study combines physical and subjective approaches to evaluate the sound quality of impacted plates. A numerical model, based on the Hertz law of contact, has been used to determine the sound pressure level at any point in space resulting from an impact. Sounds synthesized using this model and those from experiments can then be exploited in a physical analysis and/or a subjective analysis of the effects associated with variations in parameters. Here the influence of certain physical parameters on the sound perception of impacted plates is evaluated through a design of experiments method and a subjective test of preference. The subjective test is based on an estimate of preference between two pairs of synthetic sounds by varying several structural parameters at the same time. This differs from other studies that vary only one parameter at a time and fix the other parameters.     

Simulation of vocal fold impact pressures with a self-oscillating finite-element model

Vocal fold impact pressures were studied using a self-oscillating finite-element model capable of simulating vocal fold vibration and airflow. The calculated airflow pressure is applied on the vocal fold as the driving force. The airflow region is then adjusted according to the calculated vocal fold displacement. The interaction between airflow and the vocal folds produces a self-oscillating solution. Lung pressures between 0.2 and 2.5 kPa were used to drive this self-oscillating model. The spatial distribution of the impact pressure was studied. Studies revealed that the tissue collision during phonation produces a very large impact pressure which correlates with the lung pressure and glottal width. Larger lung pressure and a narrower glottal width increase the impact pressure. The impact pressure was found to be roughly the square root of lung pressure. In the inferior-superior direction, the maximum impact pressure is related to the narrowest glottis. In the anterior-posteriorfirection, the greatest impact pressure appears at the midpoint of the vocal fold. The match between our numerical simulations and clinical observations suggests that this self-oscillating finite-element model might be valuable for predicting mechanical trauma of the vocal folds.     

Analytic Representation of Volume Flow as a Function of Geometry and Pressure in a Static Physical Model of the Glottis

A static physical model of the larynx (model M5) was used to obtain a large set of volume flows as a function of symmetric glottal geometry and transglottal pressure. The measurements cover ranges of these variables relevant to human phonation. A generalized equation was created to accurately estimate the glottal volume flow given specific glottal geometries and transglottal pressures. Both the data and the generalized formula give insights into the flow behavior for different glottal geometries, especially the contrast between convergent and divergent glottal angles at different glottal diameters. The generalized equation produced a fit to the entire M5 dataset (267 points) with an average accuracy of 3.4%. The accuracy was about seven times better than that of the Ishizaka-Flanagan approach to glottal flow and about four times better than that of a pressure coefficient approach. Thus, for synthesis purposes, the generalized equation presented here should provide more realistic glottal flows (based on steady flow conditions) as suitable inputs to the vocal tract, for given values of transglottal pressure and glottal geometry. Applications of the generalized formula to pulses generated by vocal fold motions typical of those produced by the Ishizaka-Flanagan coupled-oscillator model and the more recent body-cover model of Story and Titze are also included.     

Gender differences in vocal fold contact computed from electroglottographic signals: the influence of measurement criteria

EGGW is a phonatory parameter that can be derived from electroglottographic (EGG) signals and used to infer the relative degree of vocal fold contact. Vocal fold models predict that men will exhibit medial bulging of their vocal folds during phonation but women will not. These models lead us to expect gender differences in the magnitude of EGGW. Nevertheless, significant gender differences in EGGW for adults with normal voices have not been documented in previous studies when EGGW was computed from criterion lines placed at 25%-40% of the amplitude of the uninverted EGG wave form. We hypothesized that EGGW would better reflect gender differences in vocal fold adductory patterns if EGGW was computed from portions of the wave form that were associated with more vocal fold contact. EGGW was measured for seven men and seven women with normal voices. When EGGW was computed from segments of the wave form that were associated with relatively greater vocal fold contact (i.e., using criterion levels of > or = 55%), findings were consistent with the gender-specific adductory patterns that have been proposed from vocal fold models. Guidelines for appropriate placement of criterion lines when computing EGGW are discussed.     

A methodological and preliminary study on the acoustic effect of a trumpet player's vocal tract

A methodological study is presented to examine the acoustic role of the vocal tract in playing the trumpet. Preliminary results obtained for one professional player are also shown to demonstrate the effectiveness of the method. Images of the vocal tract with a resolution of 0.5 mm (2 mm in thickness) were recorded with magnetic resonance imaging to observe the tongue posture and estimate the vocal-tract area function during actual performance. The input impedance was then calculated for the player's air column including both the supra- and subglottal tracts using an acoustic tube model including the effect of wall losses. Finally, a time-domain blowing simulation by Adachi and Sato [J. Acoust. Soc. Am. 99, 1200-1209 (1996)] was performed with a model of the lips. In this simulation, the oscillating frequency of the lips was slightly affected by using different shapes of the vocal tract measured for the player. In particular, when the natural frequency of the lips was gradually increased, the transition to the higher mode occurred at different frequencies for different vocal-tract shapes. Furthermore, simulation results showed that the minimum blowing pressure required to attain the lip oscillation can be reduced by adjusting the vocal-tract shape properly.     

Pressure-flow relationships during phonation as afunction of adduction

Pressure-flow relationships were obtained for five excised caninelarynges. Simultaneous recordings were made of average subglottal pressure, average air flow, and the electroglottograph at various levels of adduction and vocal fold lengths. The level of adduction was controlled by positioning the arytenoid cartilages via laterally imbedded three-prong attachments and by the use of intra-arytenoid shims. Adduction was quantified by measuring the vocal process gap. Results indicated a linear pressure-flow relationship within the experimental range of phonation for each level of adduction. Differential glottal resistance increased as the vocal process gap was reduced. A model is presented for the differential resistance as a hyperbolic function of vocal process gap. The pressure-flow relationship and the model can be used in computer simulations of speech production and for clinical insight into the aerodynamic function of the human larynx.     

Effect of inferior surface angle on the self-oscillation of a computational vocal fold model

Geometry of the human vocal folds strongly influences their oscillatory motion. While the effect of intraglottal geometry on phonation has been widely investigated, the study of the geometry of the inferior surface of the vocal folds has been limited. In this study the way in which the inferior vocal fold surface angle affects vocal fold vibration was explored using a two-dimensional, self-oscillating finite element vocal fold model. The geometry was parameterized to create models with five different inferior surface angles. Four of the five models exhibited self-sustained oscillations. Comparisons of model motion showed increased vertical displacement and decreased glottal width amplitude with decreasing inferior surface angle. In addition, glottal width and air flow rate waveforms changed as the inferior surface angle was varied. Structural, rather than aerodynamic, effects are shown to be the cause of the changes in model response as the inferior surface angle was varied. Supporting data including glottal pressure distribution, average intraglottal pressure, energy transfer, and flow separation point locations are discussed, and suggestions for future research are given.     

马铁菊头蝠声道声学特性的数值分析

采用有限元数值计算得到了马铁菊头蝠声道内部的声场分布,给出了马铁菊头蝠声道内几种特殊的腔体结构在蝙蝠发声过程中的作用。通过微型CT扫描并经过三维重构得到了马铁菊头蝠声道的三维立体模型用于有限元数值计算,通过在声门处放置单位声源计算得到了整个声道内部以及鼻孔周围的声压分布。结果表明,马铁菊头蝠声道包含了鼻腔结构后声波在声门上方的声压幅度明显大于不含鼻腔结构的情况,从传输曲线来看,声门上方鼻腔的存在使得系统对声波传输在二次谐波频率处呈现低阻抗效果,同时鼻腔的改变还可影响二次谐波的位置。而声门下方的气管空腔主要影响声波的背向转播,声门下方的气管空腔的存在可明显降低蝙蝠发声时声场在声道声门下方的声压幅度,同时抑制声音背向传播时二次谐波成分的强度。      

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.     

Glottal flow through a two-mass model: comparison of Navier-Stokes solutions with simplified models

A new numerical model of the vocal folds is presented based on the well-known two-mass models of the vocal folds. The two-mass model is coupled to a model of glottal airflow based on the incompressible Navier-Stokes equations. Glottal waves are produced using different initial glottal gaps and different subglottal pressures. Fundamental frequency, glottal peak flow, and closed phase of the glottal waves have been compared with values known from the literature. The phonation threshold pressure was determined for different initial glottal gaps. The phonation threshold pressure obtained using the flow model with Navier-Stokes equations corresponds better to values determined in normal phonation than the phonation threshold pressure obtained using the flow model based on the Bernoulli equation. Using the Navier-Stokes equations, an increase of the subglottal pressure causes the fundamental frequency and the glottal peak flow to increase, whereas the fundamental frequency in the Bernoulli-based model does not change with increasing pressure.     

Material parameter computation for multi-layered vocal fold models

Today, the prevention and treatment of voice disorders is an ever-increasing health concern. Since many occupations rely on verbal communication, vocal health is necessary just to maintain one's livelihood. Commonly applied models to study vocal fold vibrations and air flow distributions are self sustained physical models of the larynx composed of artificial silicone vocal folds. Choosing appropriate mechanical parameters for these vocal fold models while considering simplifications due to manufacturing restrictions is difficult but crucial for achieving realistic behavior. In the present work, a combination of experimental and numerical approaches to compute material parameters for synthetic vocal fold models is presented. The material parameters are derived from deformation behaviors of excised human larynges. The resulting deformations are used as reference displacements for a tracking functional to be optimized. Material optimization was applied to three-dimensional vocal fold models based on isotropic and transverse-isotropic material laws, considering both a layered model with homogeneous material properties on each layer and an inhomogeneous model. The best results exhibited a transversal-isotropic inhomogeneous (i.e., not producible) model. For the homogeneous model (three layers), the transversal-isotropic material parameters were also computed for each layer yielding deformations similar to the measured human vocal fold deformations.     

The effect of cricothyroid muscle action on the relation between subglottal pressure and fundamental frequency in an in vivo canine model.

The relation between subglottal pressure (Ps) and fundamental frequency (F0) in phonation was investigated with an in vivo canine model. Direct muscle stimulation was used in addition to brain stimulation. This allowed the Ps-F0 slope to be quantified in terms of cricothyroid muscle activity. Results showed that, for ranges of 0-2 mA constant current stimulation of the cricothyroid muscle, the Ps-F0 slope ranged from 10 Hz/kPa to 60 Hz/kPa. These results were compared to similar slopes obtained in a previous study on excised larynges in which the vocal fold length was varied instead of cricothyroid activation. A physical interpretation of the Ps-F0 slope is that the amplitude-to-length ratio of the vocal folds decreases with CT activity, resulting in a smaller time-varying stiffness. In other words, there is less dependence of F0 on amplitude of vibration when the vocal folds are long instead of short.     

Correspondence of electroglottographic closed quotient to vocal fold impact stress in excised canine larynges

The purpose of this study was to explore the possible use of the electroglottographic closed quotient (EGG CQ) as a noninvasive estimate of vocal fold impact stress (SI). Two excised canine larynges were used. Each larynx was mounted and vocal fold oscillation was induced using a humidified air source. Twentyseven experimental trials were conducted for each larynx. Trials involved variations in vocal process gap, vocal fold elongation, and subglottic pressure. Simultaneous measures were made of vocal fold SI at the midpoint of the membranous vocal folds, and EGG CQ (dimensionless ratio). The results indicated that when threshold and saturation effects were excluded, the SI and the CQ were strongly related (linear correlation r = .83 and .96 for the two individual larynges, and .81 for the combined data). Within the region of linear relation, an increase of .15 in the CQ corresponded to about 1 kPa increase in SI for the combined data. Discussion focuses on possible clinical implications and the likely reasons for threshold and saturation phenomena.