On the application of the lattice Boltzmann method to the investigation of glottal flow

The production of voice is directly related to the vibration of the vocal folds, which is generated by the interaction between the glottal flow and the tissue of the vocal folds. In the current study, the aerodynamics of the symmetric glottis is investigated numerically for a number of static configurations. The numerical investigation is based on the lattice Boltzmann method (LBM), which is an alternative approach within computational fluid dynamics. Compared to the traditional Navier-Stokes computational fluid dynamics methods, the LBM is relatively easy to implement and can deal with complex geometries without requiring a dedicated grid generator. The multiple relaxation time model was used to improve the numerical stability. The results obtained with LBM were compared to the results provided by a traditional Navier-Stokes solver and experimental data. It was shown that LBM results are satisfactory for all the investigated cases.     

Identification of geometric parameters influencing the flow-induced vibration of a two-layer self-oscillating computational vocal fold model

Simplified models have been used to simulate and study the flow-induced vibrations of the human vocal folds. While it is clear that the models' responses are sensitive to geometry, it is not clear how and to what extent specific geometric features influence model motion. In this study geometric features that played significant roles in governing the motion of a two-layer (body-cover), two-dimensional, finite element vocal fold model were identified. The model was defined using a flow solver based on the viscous, unsteady, Navier-Stokes equations and a solid solver that allowed for large strain and deformation. A screening-type design-of-experiments approach was used to identify the relative importance of 13 geometric parameters. Five output measures were analyzed to assess the magnitude of each geometric parameter's effect on the model's motion. The measures related to frequency, glottal width, flow rate, intraglottal angle, and intraglottal phase delay. The most significant geometric parameters were those associated with the cover--primarily the pre-phonatory intraglottal angle--as well as the body inferior angle. Some models exhibited evidence of improved model motion, including mucosal wave-like motion and alternating convergent-divergent glottal profiles, although further improvements are still needed to more closely mimic human vocal fold motion.     

Theoretical assessment of unsteady aerodynamic effects in phonation

This paper ranks the importance of unsteady aerodynamic mechanisms in glottal flow. Particular emphasis is given to separation point motion, acceleration of glottal airflow by vocal fold motion, and viscous blockage. How nondimensional parameters such as the Reynolds, Strouhal, and Womersley numbers help in this ranking is also addressed. An equation of motion is derived which includes terms explicitly describing the effects of interest, assuming (1) a symmetrical glottis, (2) zero pressure recovery downstream of the vocal folds, and (3) a quasisteady glottal jet. Estimating the order of magnitude of the terms in this equation, it is shown that the flow is characterized by two temporal regimes: (1) a flow initiation/shutoff regime where local unsteady acceleration and wall motion dominate, and (2) a "quasisteady" regime where the flow is dominated by convective acceleration. In the latter case, separation point motion and viscous blockage are shown to be out of phase with motion of the vocal folds, thereby impacting the shape of the glottal volume flow waveform. The analysis suggests that glottal flow may be considered quasisteady only insofar as traditional assumptions concerning glottal jet behavior can be confirmed.     

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.     

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.     

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.     

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.     

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.     

Vocal fold and ventricular fold vibration in period-doubling phonation: physiological description and aerodynamic modeling

Occurrences of period-doubling are found in human phonation, in particular for pathological and some singing phonations such as Sardinian A Tenore Bassu vocal performance. The combined vibration of the vocal folds and the ventricular folds has been observed during the production of such low pitch bass-type sound. The present study aims to characterize the physiological correlates of this acoustical production and to provide a better understanding of the physical interaction between ventricular fold vibration and vocal fold self-sustained oscillation. The vibratory properties of the vocal folds and the ventricular folds during phonation produced by a professional singer are analyzed by means of acoustical and electroglottographic signals and by synchronized glottal images obtained by high-speed cinematography. The periodic variation in glottal cycle duration and the effect of ventricular fold closing on glottal closing time are demonstrated. Using the detected glottal and ventricular areas, the aerodynamic behavior of the laryngeal system is simulated using a simplified physical modeling previously validated in vitro using a larynx replica. An estimate of the ventricular aperture extracted from the in vivo data allows a theoretical prediction of the glottal aperture. The in vivo measurements of the glottal aperture are then compared to the simulated estimations.     

A computational study of asymmetric glottal jet deflection during phonation

Two-dimensional numerical simulations are used to explore the mechanism for asymmetric deflection of the glottal jet during phonation. The model employs the full Navier-Stokes equations for the flow but a simple laryngeal geometry and vocal-fold motion. The study focuses on the effect of Reynolds number and glottal opening angle with a particular emphasis on examining the importance of the so-called "Coanda effect" in jet deflection. The study indicates that the glottal opening angle has no substantial effect on glottal jet deflection. Deflection in the glottal jet is always preceded by large-scale asymmetry in the downstream portion of the glottal jet. A detailed analysis of the velocity and vorticity fields shows that these downstream asymmetric vortex structures induce a flow at the glottal exit which is the primary driver for glottal jet deflection.     

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.     

On the use of the derivative of electroglottographic signals for characterization of nonpathological phonation

Electroglottography is a common method for providing noninvasive measurements of glottal activity. The derivative of the electroglottographic signal, however, has not attracted much attention, although it yields reliable indicators of glottal closing instants. The purpose of this paper is to provide a guide to the usefulness of this signal. The main features that are to be found in this signal are presented on the basis of an extensive analysis of a database of items sung by 18 trained singers. Glottal opening and closing instants are related to peaks in the signal; the latter can be used to measure glottal parameters such as fundamental frequency and open quotient. In some cases, peaks are doubled or imprecise, which points to special (but by no means uncommon) glottal configurations. A correlation-based algorithm for the automatic measurement of fundamental frequency and open quotient using the derivative of electroglottographic signals is proposed. It is compared to three other electroglottographic-based methods with regard to the measurement of open quotient in inverse-filtered derived glottal flow. It is shown that agreement with the glottal-flow measurements is much better than most threshold-based measurements in the case of sustained sounds.     

Flow separation in a computational oscillating vocal fold model

A finite-volume computational model that solves the time-dependent glottal airflow within a forced-oscillation model of the glottis was employed to study glottal flow separation. Tracheal input velocity was independently controlled with a sinusoidally varying parabolic velocity profile. Control parameters included flow rate (Reynolds number), oscillation frequency and amplitude of the vocal folds, and the phase difference between the superior and inferior glottal margins. Results for static divergent glottal shapes suggest that velocity increase caused glottal separation to move downstream, but reduction in velocity increase and velocity decrease moved the separation upstream. At the fixed frequency, an increase of amplitude of the glottal walls moved the separation further downstream during glottal closing. Increase of Reynolds number caused the flow separation to move upstream in the glottis. The flow separation cross-sectional ratio ranged from approximately 1.1 to 1.9 (average of 1.47) for the divergent shapes. Results suggest that there may be a strong interaction of rate of change of airflow, inertia, and wall movement. Flow separation appeared to be "delayed" during the vibratory cycle, leading to movement of the separation point upstream of the glottal end only after a significant divergent angle was reached, and to persist upstream into the convergent phase of the cycle.     

Visualization and Quantification of the Medial Surface Dynamics of an Excised Human Vocal Fold During Phonation

SUMMARY: The purpose of this investigation was to investigate physical mechanisms of vocal fold vibration during normal phonation through quantification of the medial surface dynamics of the fold. An excised hemilarynx setup was used. The dynamics of 30 microsutures mounted on the medial surface of a human vocal fold were analyzed across 18 phonatory conditions. The vibrations were recorded with a digital high-speed camera at a frequency of 4,000 Hz. The positions of the sutures were extracted and converted to three-dimensional coordinates using a linear approximation technique. The data were reduced to principal eigenfuctions, which captured over 90% of the variance of the data, and suggested mechanisms of sustained vocal fold oscillation. The vibrations were imaged as the following phonatory conditions were manipulated: glottal airflow, an adductory force applied to the muscular process, and an elongation force applied to the thyroid cartilage. Over the range of variables studied, only the variation in glottal airflow yielded significant changes in subglottal pressure and fundamental frequency. All recordings showed high correlation for the distribution of the dynamics across the medial surface of the vocal fold. The distribution of the different displacement directions and velocities showed the highest variations around the superior region of the medial surface. Although the computed vibration patterns of the two largest empirical eigenfunctions were consistent with previous experimental observations, the relative prominence of the two eigenfunctions changed as a function of glottal airflow, impacting theories of vocal efficiency and vocal economy.     

The phonation critical condition in rectangular glottis with wide prephonatory gaps

The effect of the pressure recovery at glottal exit is introduced to modify the one-mass model. Using the modified one-mass model, the phonation critical condition, including phonation threshold pressure and phonation threshold flow, is analyzed by using the small-amplitude oscillation theory. It is found that the phonation threshold pressure is not sensitive to the change of the prephonatory glottal width at a wide glottal gap. This result agrees with previous experimental observations and suggests that the low slope of dependence of phonation threshold pressure on prephonatory gap found by Chan and Titze [J. Acoust. Soc. Am. 119, 2351-2362 (2006)] could be a consequence of the pressure recovery effect at the glottal exit. In addition, it is predicted that the phonation threshold flow is always significantly increased with the prephonatory gap even at a wide prephonatory glottal gap. Therefore, the phonation threshold flow has an advantage in assessing the phonatory system at a wide prephonatory gap in comparison with the phonation threshold pressure. The phonation threshold flow can be a useful aerodynamic parameter for pathological conditions in which the incomplete glottal gap is often seen.     

SIM--simultaneous inverse filtering and matching of a glottal flow model for acoustic speech signals

A new method "simultaneous inverse filtering and model matching" (SIM) is proposed that allows one to calculate voice source measures without any user interaction. It is based on the discrete all-pole modeling (DAP) technique for inverse filtering (IF), which is modified to include a model of the glottal flow as integral part [LF model, Fant et al., STL-QPSR (Stockholm) 4/1985, 1-13 (1986)]. As the correct LF parameters are initially unknown, they are estimated in an iterative procedure using multi-dimensional optimization techniques that are initialized according to the results of an exhaustive search. The error criteria applied reflect how well the IF is performed after the spectral contribution of the glottal flow has been removed. The resulting optimal LF parameter constellation serves as the basis to calculate 11 voice source measures. The performance was evaluated using synthesized signals and recordings of natural utterances. For the synthesized signals, the accuracy to reproduce the original parameters was high (correlations exceeding 0.88) for measures where the starting point of the glottal cycle did not enter explicitly. Errors were smaller compared to conventional estimation methods where the measures were estimated from the IF signal. The analysis of natural utterances indicates that problems still exist with regard to robustness, but that under advantageous conditions the open quotient, the speed quotient, the closing quotient, the parabolic spectral parameter, and the negative peak amplitude of the glottal flow derivative can indeed be determined automatically by the SIM method.     

Laryngeal Mechanisms During Human 4-kHz Vocalization Studied With CT, Videostroboscopy, and Color Doppler Imaging

The objective of this study was to investigate the underlying laryngeal mechanisms during the specific human 4-kHz vocalization. The laryngeal configuration during this vocalization was measured using high-resolution computerized tomographic scan and videostrobolaryngoscopy. The color Doppler imaging (CDI) of medical ultrasound was used to detect the vibrations of glottal and supraglottal mucosa. During the 4-kHz vocalization, the ventricular folds were adducted in the shape of a bimodal chink and the vocal folds were shaped as a "V" with an opening at the posterior glottis. In the coronal view, the laryngeal ventricles had collapsed and a divergent shaped conduit was observed at the posterior portion of the larynx. The surface mucosa vibration detected by CDI was noted over the bilateral ventricular folds and aryepiglottic folds. The vibration displacement was estimated to be on the order of 0.1mm. This vibration amplitude was too small to be detected in videostrobolaryngoscopy. The laryngeal configuration and CDI data suggested a diffuser jet with periodic vorticity bursts in the larynx producing 4 kHz voice.     

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.     

Measurement of the glottal impedance with a mechanical model

An approximate but realistic model of the human larynx was constructed to gain better knowledge of the complex glottal impedance and its dependence on glottal width, flow, and frequency. The glottal width was adjustable from 0 to 3 mm, the flow from 0 to 500 cm3/s. The model was fitted into a system of tubes, through which compressed air could be conducted. Supraglottally, a broadband signal was fed into the tube, and, with a two-microphone directional coupler, the complex glottal impedance at a given reference plane was directly determined as a function of frequency. Since the calculated impedance is sensitively dependent on the definition of the position of the reference plane, it is difficult to obtain quantitative statements about the frequency dependence. Nevertheless, in the presence of flow, it is possible to achieve reliable results by analysis of the relative position of the measured curves. On the one hand, the glottal inductance decreases linearly with increasing flow velocity; on the other hand, it diminishes nonlinearly with decreasing frequency. Finally, some difficulties in the definition of glottal impedance are pointed out.