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.     

A theoretical study of f0-f1 interaction with application to resonant speaking and singing voice

An interactive source-filter system, consisting of a three-mass body-cover model of the vocal folds and a wave reflection model of the vocal tract, was used to test the dependence of vocal fold vibration on the vocal tract. The degree of interaction is governed by the epilarynx tube, which raises the vocal tract impedance to match the impedance of the glottis. The key component of the impedance is inertive reactance. Whenever there is inertive reactance, the vocal tract assists the vocal folds in vibration. The amplitude of vibration and the glottal flow can more than double, and the oral radiated power can increase up to 10 dB. As F0 approaches F1, the first formant frequency, the interactive source-filter system loses its advantage (because inertive reactance changes to compliant reactance) and the noninteractive system produces greater vocal output. Thus, from a voice training and control standpoint, there may be reasons to operate the system in either interactive and noninteractive modes. The harmonics 2F0 and 3F0 can also benefit from being positioned slightly below F1.     

Phonation threshold pressure: a missing link in glottal aerodynamics.

Phonation threshold pressure has previously been defined as the minimum lung pressure required to initiate phonation. By modeling the dependence of this pressure on fundamental frequency, it is shown that relatively simple aerodynamic relations for time-varying flow in the glottis are obtained. Lung pressure and peak glottal flow are nearly linearly related, but not proportional. For this reason, traditional power law relations between vocal power and lung pressure may not hold. Glottal impendance for time-varying flow should be defined differentially rather than as a simple ratio between lung pressure and peak flow. It is shown that the peak flow, the peak flow derivative, the open quotient, and the speed quotient of inverse-filtered glottal flow waveforms all depend explicitly on phonation threshold pressure. Data from singers are compared with those from nonsingers. The primary difference is that singers obtain two to three times greater peak flow for a given lung pressure, suggesting that they adjust their glottal or vocal tract impedance for optimal flow transfer between the source and the resonantor.     

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.     

On subglottal formant analysis

When subglottal pressure signals which are recorded during normal speech production are spectrally analyzed, the frequency of the first spectral maximum appears to deviate appreciably from the first resonance frequency which has been reported in the literature and which stems from measurements of the acoustic impedance of the subglottal system. It is postulated that this is caused by the spectrum of the excitation function. This hypothesis is corroborated by a modeling study. Using an extended version of the well-known two-mass model of the vocal folds that can account for a glottal leak, it is shown that under realistic physiological assumptions glottal flow waveforms are generated whose spectral properties cause a downward shift of the location of the first spectral maximum in the subglottal pressure signals. The order of magnitude of this effect is investigated for different glottal settings and with a subglottal system that is modeled according to the impedance measurements reported in the literature. The outcomes of this modeling study show that the location of the first spectral maximum of the subglottal pressure may deviate appreciably from the natural frequency of the subglottal system. As a consequence, however, the comfortable assumption that in normal speech the glottal excitation function is constant and zero during the "closed glottis interval" has to be called into question.     

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.     

Measures of phonation type in Hmong

This study examines measures of glottal flow for vowels of Hmong, a Southeast Asian language which uses breathy and normal phonation contrastively. A software inverse filter was used to recover glottal airflow from oral airflow recordings. Properties of glottal flow measured in the time domain were glottal pulse symmetry and relative closed-phase duration. In the frequency domain, measures of spectral tilt and the amplitude difference between F0 and H2 were applied to discrete Fourier transforms (DFTs) of the glottal flow waveforms. Spectral tilt could not be reliably measured for many tokens. For the other measures, values were available for all tokens and were compared across phonation types. Flow pulse symmetry is not significantly different for breathy and normal-voice vowels. On the other hand, prominence of the fundamental relative to the second harmonic is a very significant correlate of the breathy/normal distinction, as is the relative closed-phase duration. These results are considered in light of an existing model of the voice source.     

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.     

Voice production model integrating boundary-layer analysis of glottal flow and source-filter coupling

A voice production model is created in this work by considering essential aerodynamic and acoustic phenomena in human voice production. A precise flow analysis is performed based on a boundary-layer approximation and the viscous-inviscid interaction between the boundary layer and the core flow. This flow analysis can supply information on the separation point of the glottal flow and the thickness of the boundary layer, both of which strongly depend on the glottal configuration and yield an effective prediction of the flow behavior. When the flow analysis is combined with the modified two-mass model of the vocal fold [Pelorson et al. (1994). J. Acoust. Soc. Am. 96, 3416-3431], the resulting acoustic wave travels through the vocal tract and a pressure change develops in the vicinity of the glottis. This change can affect the glottal flow and the motion of the vocal folds, causing source-filter coupling. The property of the acoustic feedback is explicitly expressed in the frequency domain by using an acoustic tube model, allowing a clear interpretation of the coupling. Numerical experiments show that the vocal-tract input impedance and frequency responses representing the source-filter coupling have dominant peaks corresponding to the fourth and fifth formants. Results of time-domain simulations also suggest the importance of these high-frequency peaks in voice production.     

Magnetic permeability and microstructure of the Bi,Si oxides-doped NiZnCu ferrite composite material

Bi,Si oxides-doped NiZnCu ferrite composite material has been fabricated with different sintering times. The microstructure of the samples was investigated by X-ray diffraction (XRD) and scanning electron microscope (SEM). The complex permeability has been measured up to 1 GHz by the impedance analyzers. The complex permeability has been simulated based on the magnetic circuit model, and the result was compared with the experimental results. In the low-frequency region, the real part of the permeability of the composite material is lower than the one of non-doped NiZnCu ferrite, on the other hand it is higher than non-doped sample in the high-field region. The peak position of the imaginary part is shifted to higher frequency in the composite material.     

Source-tract interaction with prescribed vocal fold motion

An equation describing the time-evolution of glottal volume velocity with specified vocal fold motion is derived when the sub- and supra-glottal vocal tracts are present. The derivation of this Fant equation employs a property explicated in Howe and McGowan [(2011) J. Fluid Mech. 672, 428-450] that the Fant equation is the adjoint to the equation characterizing the matching conditions of sub- and supra-glottal Green's functions segments with the glottal segment. The present aeroacoustic development shows that measurable quantities such as input impedances at the glottis, provide the coefficients for the Fant equation when source-tract interaction is included in the development. Explicit expressions for the Green's function are not required. With the poles and zeros of the input impedance functions specified, the Fant equation can be solved. After the general derivation of the Fant equation, the specific cases where plane wave acoustic propagation is described either by a Sturm-Liouville problem or concatenated cylindrical tubes is considered. Simulations show the expected skewing of the glottal volume velocity pulses depending on whether the fundamental frequency is below or above a sub- or supra-glottal formant. More complex glottal wave forms result when both the first supra-glottal fundamental frequencies are high and close to the first sub-glottal formant.     

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.     

余弦-高斯光束的焦平面及其位置

在余弦_高斯光束通过薄透镜聚焦系统的光场分布函数的基础上,利用二阶矩定义导出了聚焦余弦_高斯光束的光斑函数的解析表达式,由此求得束腰宽度及位置,进而给出了余弦_高斯光束的相对焦移的解析表达式。分析了光学系统参数以及光束参数对实际焦平面位置的影响并作了数值计算。     

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.     

Acoustic impedance microscopy for biological tissue characterization

A new method for two-dimensional acoustic impedance imaging for biological tissue characterization with micro-scale resolution was proposed. A biological tissue was placed on a plastic substrate with a thickness of 0.5 mm. A focused acoustic pulse with a wide frequency band was irradiated from the “rear side” of the substrate. In order to generate the acoustic wave, an electric pulse with two nanoseconds in width was applied to a PVDF-TrFE type transducer. The component of echo intensity at an appropriate frequency was extracted from the signal received at the same transducer, by performing a time–frequency domain analysis. The spectrum intensity was interpreted into local acoustic impedance of the target tissue. The acoustic impedance of the substrate was carefully assessed prior to the measurement, since it strongly affects the echo intensity. In addition, a calibration was performed using a reference material of which acoustic impedance was known. The reference material was attached on the same substrate at different position in the field of view. An acoustic impedance microscopy with 200 × 200 pixels, its typical field of view being 2 × 2 mm, was obtained by scanning the transducer. The development of parallel fiber in cerebella cultures was clearly observed as the contrast in acoustic impedance, without staining the specimen. The technique is believed to be a powerful tool for biological tissue characterization, as no staining nor slicing is required.     

Vocal intensity in speakers and singers.

Vocal intensity is studied as a function of fundamental frequency and lung pressure. A combination of analytical and empirical models is used to predict sound pressure levels from glottal waveforms of five professional tenors and twenty five normal control subjects. The glottal waveforms were obtained by inverse filtering the mouth flow. Empirical models describe features of the glottal flow waveform (peak flow, peak flow derivative, open quotient, and speed quotient) in terms of lung pressure and phonation threshold pressure, a key variable that incorporates the Fo dependence of many of the features of the glottal flow. The analytical model describes the contributions to sound pressure levels SPL by the vocal tract. Results show that SPL increases with Fo at a rate of 8-9 dB/octave provided that lung pressure is raised proportional to phonation threshold pressure. The SPL also increases at a rate of 8-9 dB per doubling of excess pressure over threshold, a new quantity that assumes considerable importance in vocal intensity calculations. For the same excess pressure over threshold, the professional tenors produced 10-12 dB greater intensity than the male nonsingers, primarily because their peak airflow was much higher for the same pressure. A simple set of rules is devised for predicting SPL from source waveforms.     

The acoustical impedance of holes in the wall of flow ducts

The radiation impedance of circular and oblong holes in the wall of a flow duct has been measured as a function of the flow velocity. The boundary layer at the wall of the duct is thin compared to the dimensions of the orifices. At low Strouhal numbers (quasi-static case) and constant boundary layer thickness, the flow resistance of the orifice (real part of the impedance) increases in proportion to the flow velocity. The imaginary part of the impedance corresponds to a constant, negative attached mass above the orifice, i.e. the impedance is spring-like. In the transition range from air at rest to the quasi-static case (high Strouhal numbers) the impedance as a function of the flow velocity describes a spiral in the complex plane. The mechanism causing the flow dependence of the impedance is illustrated by a simple model of the flow above the orifice. As a practical example of the flow-dependent impedance of orifices, the flow-dependent sensitivity of a probe microphone used in flowing media is discussed.     

A flow waveform-matched low-dimensional glottal model based on physical knowledge

The purpose of this study is to explore the possibility for physically based mathematical models of the voice source to accurately reproduce inverse filtered glottal volume-velocity waveforms. A low-dimensional, self-oscillating model of the glottal source with waveform-matching properties is proposed. The model relies on a lumped mechano-aerodynamic scheme loosely inspired by the one- and multimass lumped models. The vocal folds are represented by a single mechanical resonator and a propagation line which takes into account the vertical phase differences. The vocal-fold displacement is coupled to the glottal flow by means of an aerodynamic driving block which includes a general parametric nonlinear component. The principal characteristics of the flow-induced oscillations are retained, and the overall model is able to match inverse-filtered glottal flow signals. The method offers in principle the possibility of performing transformations of the glottal flow by acting on the physiologically based parameters of the model. This is a desirable property, e.g., for speech synthesis applications. The model was tested on a data set which included inverse-filtered glottal flow waveforms of different characteristics. The results demonstrate the possibility of reproducing natural speech waveforms with high accuracy, and of controlling important characteristics of the synthesis such as pitch.     

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.     

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.