Direct-numerical simulation of the glottal jet and vocal-fold dynamics in a three-dimensional laryngeal model

An immersed-boundary method based flow solver coupled with a finite-element solid dynamics solver is employed in order to conduct direct-numerical simulations of phonatory dynamics in a three-dimensional model of the human larynx. The computed features of the glottal flow including mean and peak flow rates, and the open and skewness quotients are found to be within the normal physiological range. The flow-induced vibration pattern shows the classical "convergent-divergent" glottal shape, and the vibration amplitude is also found to be typical for human phonation. The vocal fold motion is analyzed through the method of empirical eigenfunctions and this analysis indicates a 1:1 modal entrainment between the "adduction-abduction" mode and the "mucosal wave" mode. The glottal jet is found to exhibit noticeable cycle-to-cycle asymmetric deflections and the mechanism underlying this phenomenon is examined.     

Physiologic and acoustic differences between male and female voices

Comparison is drawn between male and female larynges on the basis of overall size, vocal fold membranous length, elastic properties of tissue, and prephonatory glottal shape. Two scale factors are proposed that are useful for explaining differences in fundamental frequency, sound power, mean airflow, and glottal efficiency. Fundamental frequency is scaled primarily according to the membranous length of the vocal folds (scale factor of 1.6), whereas mean airflow, sound power, glottal efficiency, and amplitude of vibration include another scale factor (1.2) that relates to overall larynx size. Some explanations are given for observed sex differences in glottographic waveforms. In particular, the simulated (computer-modeled) vocal fold contact area is used to infer male-female differences in the shape of the glottis. The female glottis appears to converge more linearly (from bottom to top) than the male glottis, primarily because of medial surface bulging of the male vocal folds.     

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.     

Three-dimensional biomechanical properties of human vocal folds: parameter optimization of a numerical model to match in vitro dynamics

The human voice signal originates from the vibrations of the two vocal folds within the larynx. The interactions of several intrinsic laryngeal muscles adduct and shape the vocal folds to facilitate vibration in response to airflow. Three-dimensional vocal fold dynamics are extracted from in vitro hemilarynx experiments and fitted by a numerical three-dimensional-multi-mass-model (3DM) using an optimization procedure. In this work, the 3DM dynamics are optimized over 24 experimental data sets to estimate biomechanical vocal fold properties during phonation. Accuracy of the optimization is verified by low normalized error (0.13 ± 0.02), high correlation (83% ± 2%), and reproducible subglottal pressure values. The optimized, 3DM parameters yielded biomechanical variations in tissue properties along the vocal fold surface, including variations in both the local mass and stiffness of vocal folds. That is, both mass and stiffness increased along the superior-to-inferior direction. These variations were statistically analyzed under different experimental conditions (e.g., an increase in tension as a function of vocal fold elongation and an increase in stiffness and a decrease in mass as a function of glottal airflow). The study showed that physiologically relevant vocal fold tissue properties, which cannot be directly measured during in vivo human phonation, can be captured using this 3D-modeling technique.     

Analysis of spasmodic dysphonia by aerodynamic and laryngostroboscopic measurements

Sequential assessment of laryngeal function using laryngostroboscopy and phonatory air flow assessment was carried out in 18 patients with spasmodic dysphonia (SD). Comparison was made between findings in patients before treatment (n = 18), after unilateral recurrent nerve block by lidocaine (n = 6), after bilateral injections of botulinum toxin (Botox) (n = 13), and prior to Botox reinjection (n = 3). Unilateral nerve block resulted in higher mean phonatory airflows than after bilateral Botox injections. Both unilateral nerve block and Botox injections increased fluctuant or alternating flow source (AC); however, unilateral nerve block resulted in more unmodulated airflow leakage. Phonation time on a single breath was longer than with Botox injection. Bilateral Botox injections resulted in better glottal closure, fewer instances of vocal fold level differences, and, better vocal fold vibrations with phase symmetry, as determined by laryngostroboscopy. Partial bilateral denervation using Botox resulted in laryngeal function, which appeared to be intermediate between that of tightly squeezed pretreatment status and a breathy voice with incomplete adduction after unilateral nerve block. Of all treatments assessed, bilateral partial denervation by Botox appeared to be the most physiologic in restoring normal vocal fold vibratory function and airflow.     

Measures of spectral slope using an excised larynx model

Spectral measures of the glottal source were investigated using an excised canine larynx (CL) model for various aerodynamic and phonatory conditions. These measures included spectral harmonic difference H1-H2 and spectral slope that are highly correlated with voice quality but not reported in a systematic manner using an excised larynx model. It was hypothesized that the acoustic spectra of the glottal source were significantly influenced by the subglottal pressure, glottal adduction, and vocal fold elongation, as well as the resulting vibration pattern. CLs were prepared, mounted on the bench with and without false vocal folds, and made to oscillate with a flow of heated and humidified air. Major control parameters were subglottal pressure, adduction, and elongation. Electroglottograph, subglottal pressure, flow rate, and audio signals were analyzed using custom software. Results suggest that an increase in subglottal pressure and glottal adduction may change the energy balance between harmonics by increasing the spectral energy of the first few harmonics in an unpredictable manner. It is suggested that changes in the dynamics of vocal fold motion may be responsible for different spectral patterns. The finding that the spectral harmonics do not conform to previous findings was demonstrated through various cases. Results of this study may shed light on phonatory spectral control when the larynx is part of a complete vocal tract system.     

Analysis of Vocal-fold Vibrations from High-Speed Laryngeal Images Using a Hilbert Transform-Based Methodology

This paper presents a Hilbert transform-based approach to analyze vocal fold vibrations in human subjects exhibiting normal and abnormal voice productions. This new approach is applied to the analysis of glottal area waveform (GAW) and is capable of providing useful information on the vocal fold vibration. The GAW is extracted from high-speed laryngeal images by delineating the glottal edge for each image frame. An analytic signal is generated through the Hilbert transform of the GAW, which yields a recognizable pattern of the vocal fold vibration in the analytic phase plane. The vibratory pattern is comprehensive and can be correlated with specific voice conditions. Quantitative measures of the glottal perturbation are introduced using the analytic amplitude and instantaneous frequency obtained from the analysis. Examples of clinical voice recordings are used to evaluate and test the effectiveness of this approach in providing qualitative representation and quantitative characteristics of vocal fold vibratory behavior. The results demonstrate the potential of using this new analytical tool incorporated with the high-speed laryngeal imaging modality for clinical voice assessment.     

Vocal fold bulging effects on phonation using a biophysical computer model

Glottal adduction is a primary laryngeal variable that helps to determine glottal configuration and phonatory output. Greater adduction of the vocal folds can be produced by narrowing the gap between the vocal processes or by bulging the medial surface of the vocal folds. This study examined phonatory effects due to changing the degree of bulging using a computational model. Bulging was modeled as a quadratic surface and was related to active muscle stress. Results indicated that bulging had a significant effect on glottal flow resistance, maximum glottal width and area, and mean glottal volume velocity. The results are discussed relative to clinical issues of hyperfunction.     

Medial Surface Dynamics as a Function of Subglottal Pressure in a Canine Larynx Model

During vocal fold vibration, there may be a mucosal wave in the superior-inferior (vertical) direction, resulting in a convergent shape during opening and a divergent shape during closing. Most of our understanding of the converging/diverging shape of the glottis has come from studies in a hemilarynx model. Previous work has shown that vibratory patterns in the full excised larynx are different than the hemilarynx. This study characterized the dynamics of the medial glottal wall geometry during vibrations in the full excised canine larynx model. Using particle image velocimetry, the intraglottal geometry was measured at the midmembranous coronal plane in an excised canine larynx model. Measurements of the glottal area were taken simultaneously using high-speed imaging. The results show that skewing of the glottal area waveform occurs without the presence of a vocal tract and that the phase-lag of the superior edge relative to the inferior edge is smaller than reported and depends on the subglottal pressure. In addition, it shows that the glottal divergence angle during closing is proportional to the magnitude of the acoustic intensity and the intraglottal negative pressure. This preliminary data suggests that more studies are needed to determine the important mechanisms determining the relationship between intraglottal flow, intraglottal geometry, and acoustics.     

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.     

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 airflow and transglottal air pressure measurements for male and female speakers in low, normal, and high pitch

Measurements on the inverse filtered airflow waveform and of estimated average transglottal pressure and glottal airflow were made from syllable sequences in low, normal, and high pitch for 25 male and 20 female speakers. Correlation analyses indicated that several of the airflow measurements were more directly related to voice intensity than to fundamental frequency (F₀). Results suggested that pressure may have different influences in low and high pitch in this speech task. It is suggested that unexpected results of increased pressure in low pitch were related to maintaining voice quality, that is, avoiding vocal fry. In high pitch, the increased pressure may serve to maintain vocal fold vibration. The findings suggested different underlying laryngeal mechanisms and vocal adjustments for increasing and decreasing F₀ from normal pitch.     

Bifurcations in excised larynx experiments

Bifurcation analysis was applied to vocal fold vibration in excised larynx experiments. Phonation onset and vocal instabilities were studied in a parameter plane spanned by subglottal pressure and asymmetry of either vocal fold adduction or elongation. Various phonatory regimes were observed, including single vocal fold oscillations. Selected spectra demonstrated correspondence between these regimes and vocal registers noted in the literature. To illustrate the regions spanned by the various phonatory regimes, two-dimensional bifurcation diagrams were generated. Many instabilities or bifurcations were noted in the regions of coexistence, i.e., regions in which the phonatory regimes overlap. Bifurcations were illustrated with spectrograms and fundamental frequency contours. Where possible, results from these studies were related to clinical observations.     

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.     

高速摄影成像分析声带振动发声的前后不对称性

高速摄影成像直接观察到声带振动的前后不对称性。将11个离体狗喉声带进行发声实验,设置3组声门下压分别为10 cm H₂O,20 cm H₂O和30 cm H₂O,利用高速摄像仪和传声器,分别记录不同声门下压的声带振动图像和声信号.对高速摄影成像与同步采集的声信号基频进行定量分析和比较,基频均随声门下压的增大而增加。此外,对两种测量方法得到的基频进行相关分析比较,得到在同一声门下压下两种方法的基频相关系数均大于0.9,表明高速摄影成像得到的基频与声信号的基频具有高度相关性。高速摄影成像能直观地测量声带振动行为,对研究声带振动发声机理提供了有价值的测量手段。高速摄影获得的声带线性结构上25%,50%,75%位置处的振动幅度,显示了声带前后振动不对称且声门下压较低时振动不对称较明显。      

Approximations of open quotient and speed quotient from glottal airflow and egg waveforms : Effects of measurement criteria and sound pressure level

Noninvasive measures of vocal fold activity are useful for describingnormal and disordered voice production. Measures of open and speed quotient from glottal airflow and electroglottographic (EGG) waveforms have been used to describe timing events associated with vocal fold vibration. To date, there has been little consistency in the measurement criteria used to calculate quotient values. In this study, criteria of 20% and 50% were applied to the AC amplitude of glottal airflow and inverted EGG waveforms for measurement of open quotient. Criteria of 20%, 50%, and 80%, and a midslope criterion that segmented the waveform between 20% and 80% of the waveform amplitude, were used for the calculation of speed quotient. Subjects produced waveforms at sound pressure levels (SPL) of 70, 75, 80 and 85 dB. Results indicated that approximations of open quotient obtained from the glottal airflow waveform significantly decreased using both the 20% and 50% criteria as SPL increased from 80 to 85 dB. No significant changes were found in open quotient from the EGG waveform as a function of SPL. Results of speed quotient measures from the glottal airflow and EGG waveforms showed a generally increasing trend as SPL increased, although the differences were not statistically significant. The data suggest that the signal type, measurement criterion and SPL must be considered in interpreting quotient measures.     

Experimental study of the effects of surface mucus viscosity on the glottic cycle

Numerous clinical findings indicate that viscosity of laryngeal mucosa is a crucial factor in glottal perfomance. Experience using experimental test benches has shown the importance of humidifying air stream used to induce vibration in excised larynges. Nevertheless, there is a lack of knowledge particularly regarding the physicochemical properties of laryngeal mucus. The purpose of this study was to research vocal fold vibration in excised larynges using artificial mucus of precisely known viscosity. Eight freshly harvested porcine larynges were examined. Parameters measured were Fo and vocal fold contact time. Measurements were performed under three conditions: basal (no fluid application on vocal cord surface), after application of a fluid of 60cP viscosity (Visc60), and after application of a fluid of 100cP viscosity (Visc100). Electroglottographic measurements were performed at two different times for each condition: 1 s after airflow onset (T1) and 6 seconds after airflow onset (T2). Statistical analysis consisted of comparing data obtained under each condition at T1 and T2. The results showed a significant decrease in Fo after application of Visc60 and Visc100 fluids and a decrease in Fo at T2. Closure time was significantly higher under Visc60 conditions and under Visc100 conditions than under basal conditions. Application of artificial mucus to the mucosa of the vocal folds lowered vibratory frequency and prolonged the contact phase. Our interpretation of this data is that the presence of mucus on the surface of the vocal folds generated superficial tension and caused adhesion, which is a source of nonlinearity in vocal vibration.     

In Vivo Quantification of the Intraglottal Pressure: Modal Phonation and Voice Onset

Intraglottal pressure is the driving force of vocal fold vibration. Its time course during the open phase of the vibratory cycle is essential in the mechanics of phonation, but measuring it directly is difficult and may hinder spontaneous voicing. However, it can be computed from the in vivo measured transglottal flow and glottal area (hence the air particle velocity) on the basis of the Bernoulli energy law and the interaction with the inertance of the vocal tract. As to sustained modal phonation, calculations are presented for the two possible shapes of glottal duct: convergent and divergent, including absolute calibration in order to obtain quantitative physical values. Whatever the glottal duct configuration, the calculations based on measured values of glottal area and air flow show that the integrated intraglottal pressure during the opening phase systematically exceeds that during the closing phase, which is the basic condition for sustaining vocal fold oscillation. The key point is that the airflow curve is skewed to the right relative to the glottal area curve. The skewing results from air compressibility and vocal tract inertance. The intraglottal pressure becomes negative during the closing phase. As to the soft (or physiological) voice onset, a similar approach shows that the integrated pressure differences (opening phase − closing phase) actually increase as the onset progresses, and this applies to the results based on Bernoulli's energy law as well as to those based on the interaction with the inertance of the vocal tract. Furthermore and similarly, the phase lead of the pressure wave with respect to the glottal opening progressively increases. The underlying explanation lies in the progressively increasing skewing of the airflow curve to the right with respect to the glottal area curve.     

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.