Modelling and validation of the non-linear elastic stress-strain behaviour of multi-layer silicone composites.

Multi-layer silicone composites are commonly used to mold deformable silicone vocal folds replicas. Nevertheless, so far the stress-strain characterisation of such composite specimens is limited to their effective Young's modulus (up to 40 kPa) characterising the elastic low-strain range, i.e. up to about 0.3. Therefore, in this work, the characterisation is extended to account for the non-linear strain range. Stress-strain curves on 6 single-layer and 34 multi-layer silicone specimens, with different layer stacking (serial, parallel, combined or arbitrary), are measured at room temperature using uni-axial tensile tests for strains up to 1.36, which amounts to about 4.5 times the extent of the linear low-strain range. Cubic polynomial and exponential two-parameter relationships are shown to provide accurate continuous fits (coefficient of determination R2≥99%) of the measured stress-strain data. It is then shown that the parameters can be a priori modelled as a constant or as a linear function of the effective low-strain Young's modulus for strains up to 1.55, i.e. 5 times the low-strain range. These a priori modelled parameter are confirmed by approximations of the best fit parameters for all assessed specimens as a function of the low-strain Young's modulus. Thus, the continuous stress-strain behaviour up to 1.55 can be predicted analytically from the effective low-strain Young's modulus either using the modelled parameters (R2≥85%) or the approximations of the best fit parameter sets (R2≥94%). Accurate stress-strain predictions are particularly useful for the design of composites with different composition and stacking. In addition, analytical expressions of the linear high-strain Young's modulus and the linear high-strain onset, again as a function of the effective low-strain Young's modulus, are formulated as well.

Experimental study on the quasi-steady approximation of glottal flows.

To examine the quasi-steady approximation of the glottal flow, widely used in the modeling of vocal fold oscillations, intraglottal pressure distributions were measured in a scaled-up static vocal fold model under time-varying flow conditions. The left and right vocal folds were slightly open and set to a symmetric and oblique configuration with a divergence angle. To realize time-varying flow conditions, the flow rate was sinusoidally modulated with a frequency of 2 and 10 Hz, which correspond to 112.5 and 562.5 Hz, respectively, in real life. Measurements of the intraglottal pressures under both steady and time-varying flows revealed that the pressure profiles of the time-varying flow conditions are non-distinguishable from those of the steady flow conditions as far as they have the same subglottal pressure as an input pressure. The air-jet separation point was also non-distinguishable between the steady and the time-varying flow conditions. Our study therefore suggests that the time-varying glottal flow can be approximated as a series of steady flow states with a matching subglottal pressure in the range of normal vocalization frequencies. Since the glottal closure was not taken into account in the present experiment, our argument is valid except for such a critical situation.

Influence of level difference due to vocal folds angular asymmetry on auto-oscillating replicas.

Dysphonia is often caused by level difference between left and right vocal folds, which are positioned on different angles with respect to the transverse plane, resulting in angular asymmetry. Unilateral vocal fold paralysis may cause such angular asymmetry. In this case, the normal vocal fold is located on the transverse plane, whereas the paralyzed vocal fold is rotated in the sagittal plane as its posterior edge is moved up to the superior direction. The effect of such angular asymmetry (up to 25°) between the left and right vocal fold on the auto-oscillation is experimentally studied using mechanical replicas. For all replicas, it is observed that, as full contact between vocal folds is lost, increase of angular asymmetry results in a decrease of the signal-to-noise ratio, an increase of the total harmonic distortion rate, and an increase of the oscillation threshold pressure. These general tendencies are in agreement with clinical findings reported for vertical level difference during phonation. In analogy to the preceding experimental study in which vocal folds are spaced in parallel with a vertical trade-off, a formula is proposed to describe the oscillation threshold as a function of angular asymmetry.

Multimodal radiation impedance of a waveguide with arbitrary cross-sectional shape terminated in an infinite baffle.

Simulations of waveguide acoustics require a description of the boundary condition at the open end. For problems involving higher order transverse modes, it is often described by a multimodal radiation impedance matrix. Expressions for the computation of this matrix for an infinite flange condition are available only for circular and rectangular cross-sectional shapes. Thus, a general expression valid for arbitrary cross-sectional shapes is of interest. Such an expression is proposed, validated against known cases, and applied to an arbitrary cross-section shape. The solution is shown to be computationally efficient.

Computational aeroacoustics to identify sound sources in the generation of sibilant /s/.

A sibilant fricative /s/ is generated when the turbulent jet in the narrow channel between the tongue blade and the hard palate is deflected downwards through the space between the upper and lower incisors and then impinges the space between the lower incisors and the lower lip. The flow eddies in that region become a source of direct aerodynamic sound, which is also diffracted by the speech articulators and radiated outwards. The numerical simulation of these phenomena is complex. The spectrum of an /s/ typically peaks between 4 and 10 kHz, which implies that very fine computational meshes are needed to capture the eddies producing such high frequencies. In this work, a large-scale computation of the aeroacoustics of /s/ has been performed for a realistic vocal tract geometry, resorting to two different acoustic analogies. A stabilized finite element method that acts as a large eddy simulation model has been adopted to solve the flow dynamics. Also, a numerical strategy has been implemented that allows the determination, in a single computational run, of the separate contribution of the sound diffracted by the upper incisors from the overall radiated sound. Results are presented for points located close to the lip opening showing the relative influence of the upper teeth depending on frequency.

Influence of vocal tract geometry simplifications on the numerical simulation of vowel sounds.

For many years, the vocal tract shape has been approximated by one-dimensional (1D) area functions to study the production of voice. More recently, 3D approaches allow one to deal with the complex 3D vocal tract, although area-based 3D geometries of circular cross-section are still in use. However, little is known about the influence of performing such a simplification, and some alternatives may exist between these two extreme options. To this aim, several vocal tract geometry simplifications for vowels [ɑ], [i], and [u] are investigated in this work. Six cases are considered, consisting of realistic, elliptical, and circular cross-sections interpolated through a bent or straight midline. For frequencies below 4-5 kHz, the influence of bending and cross-sectional shape has been found weak, while above these values simplified bent vocal tracts with realistic cross-sections are necessary to correctly emulate higher-order mode propagation. To perform this study, the finite element method (FEM) has been used. FEM results have also been compared to a 3D multimodal method and to a classical 1D frequency domain model.

Influence of lips on the production of vowels based on finite element simulations and experiments.

Three-dimensional (3-D) numerical approaches for voice production are currently being investigated and developed. Radiation losses produced when sound waves emanate from the mouth aperture are one of the key aspects to be modeled. When doing so, the lips are usually removed from the vocal tract geometry in order to impose a radiation impedance on a closed cross-section, which speeds up the numerical simulations compared to free-field radiation solutions. However, lips may play a significant role. In this work, the lips' effects on vowel sounds are investigated by using 3-D vocal tract geometries generated from magnetic resonance imaging. To this aim, two configurations for the vocal tract exit are considered: with lips and without lips. The acoustic behavior of each is analyzed and compared by means of time-domain finite element simulations that allow free-field wave propagation and experiments performed using 3-D-printed mechanical replicas. The results show that the lips should be included in order to correctly model vocal tract acoustics not only at high frequencies, as commonly accepted, but also in the low frequency range below 4 kHz, where plane wave propagation occurs.

Effects of higher order propagation modes in vocal tract like geometries.

In this paper, a multimodal theory accounting for higher order acoustical propagation modes is presented as an extension to the classical plane wave theory. This theoretical development is validated against experiments on vocal tract replicas, obtained using a 3D printer and finite element simulations. Simplified vocal tract geometries of increasing complexity are used to investigate the influence of some geometrical parameters on the acoustical properties of the vocal tract. It is shown that the higher order modes can produce additional resonances and anti-resonances and can also strongly affect the radiated sound. These effects appear to be dependent on the eccentricity and the cross-sectional shape of the geometries. Finally, the comparison between the simulations and the experiments points out the importance of taking visco-thermal losses into account to increase the accuracy of the resonance bandwidths prediction.

The role of initial flow conditions for sibilant fricative production.

Sibilant fricative sound production depends on the geometric and flow properties of the production system. Nevertheless, few studies deal with the potential impact of flow properties other than the inlet volume flow rate on the noise produced. In this work, an experimental study is presented using a replica based on a reconstructed oral cavity for the phoneme /s/. Initial flow conditions upstream from the sibilant groove are altered by varying the method of air supply. Statistical moments of the initial velocity distribution are characterized using hot-film anemometry and related to spectral features of the radiated acoustic pressure. Discrepancies in the dynamic amplitude (≤25%) and negative spectral slope (≤35%) observed at a constant Reynolds number but different initial upstream flow conditions are of the same order of magnitude as those previously reported in humans. This suggests that consideration of the upstream flow conditions is important in the study of sibilant fricative sound production.

Influence of glottal cross-section shape on phonation onset.

Phonation models commonly rely on the assumption of a two-dimensional glottal geometry to assess kinetic and viscous flow losses. In this paper, the glottal cross-section shape is taken into account in the flow model in order to capture its influence on vocal folds oscillation. For the assessed cross-section shapes (rectangular, elliptical, or circular segment) the minimum pressure threshold enabling to sustain vocal folds oscillation is altered for constriction degrees smaller than 75%. The discrepancy between cross-section shapes increases as the constriction degree decreases.

The influence of glottal cross-section shape on theoretical flow models.

Physical and mathematical phonation models commonly rely on a quasi-one-dimensional flow model. The assumption of quasi-one-dimensional flow through a glottis with fixed length is analyzed for different cross-section shapes: Circle, rectangle, ellipse, and circular segment. A simplified flow model is formulated which accounts for kinetic losses, viscosity, and cross-section shape. It is seen that the cross-section shape cannot be neglected since it alters boundary layer development and hence the viscous contribution to the pressure drop across the glottis. The commonly applied quasi-one-dimensional flow model is shown to be inaccurate, indicating the potential benefit of taking into account the cross-section shape.

Effect of source-tract acoustical coupling on the oscillation onset of the vocal folds.

This paper analyzes the interaction between the vocal folds and vocal tract at phonation onset due to the acoustical coupling between both systems. Data collected from a mechanical replica of the vocal folds show that changes in vocal tract length induce fluctuations in the oscillation threshold values of both subglottal pressure and frequency. Frequency jumps and maxima of the threshold pressure occur when the oscillation frequency is slightly above a vocal tract resonance. Both the downstream and upstream vocal tracts may produce those same effects. A simple mathematical model is next proposed, based on a lumped description of tissue mechanics, quasi-steady flow and one-dimensional acoustics. The model shows that the frequency jumps are produced by saddle-node bifurcations between limit cycles forming a classical pattern of a cusp catastrophe. The transition from a low frequency oscillation to a high frequency one may be achieved through two different paths: in case of a large acoustical coupling (narrow vocal tract) or high subglottal pressure, the bifurcations are crossed, which causes a frequency jump with a hysteresis loop. By reducing the acoustical coupling (wide vocal tract) or the subglottal pressure, a path around the bifurcations may be followed with a smooth frequency variation.

Experimental validation of flow models for a rigid vocal tract replica.

Flow through the vocal tract is studied through an in vitro rigid replica for different geometrical configurations and steady flow conditions with bulk Reynolds numbers Re<15,000. The vocal tract geometry is approximated by two consecutive obstacles, representing "tongue" and "tooth," in a rectangular channel of fixed length. For the upstream tongue obstacle with fixed constriction degree (81%) the streamwise position is varied and for the downstream obstacle the constriction degree is varied from 0% up to 96%. Different upstream pressures are considered for each geometrical configuration. Point pressure measurements at three fixed locations along the channel are experimentally assessed. In addition, the volume airflow rate is measured. The pressure distribution is estimated with a one-dimensional flow model, and the effects of different corrections to a laminar irrotational flow are assessed. The model outcome is validated against experimental data. Depending on the geometrical configuration, the best model accuracy is obtained by accounting for viscosity (needed for constriction degrees at the tooth that are small, i.e.,≤58%, or very large, i.e., ≥96%), a sudden constriction (large gap between both constrictions), or a bending geometry (narrow gap between both constrictions). Best overall model errors vary between 4% and 30% for all assessed geometrical configurations in cases where a tongue obstacle is present.

Experimental validation of quasi-one-dimensional and two-dimensional steady glottal flow models.

Physical modelling of phonation requires a mechanical description of the vocal fold coupled to a description of the flow within the glottis. In this study, an in-vitro set-up, allowing to reproduce flow conditions comparable to those of human glottal flow is used to systematically verify and discuss the relevance of the pressure and flow-rate predictions of several laminar flow models. The obtained results show that all the considered flow models underestimate the measured flow-rates and that flow-rates predicted with the one-dimensional model are most accurate. On the contrary, flow models based on boundary-layer theory and on the two-dimensional numerical resolution of Navier-Stokes equations yield most accurate pressure predictions. The influence of flow separation on the predictions is discussed since these two models can estimate relevant flow separation positions whereas this phenomenon is treated in a simplified ad-hoc way in the one-dimensional flow modelling. Laminar flow models appear to be unsuitable to describe the flow downstream of the glottal constriction. Therefore, the use of flow models taking into account three-dimensional effects as well as turbulence is motivated.

Validation of theoretical models of phonation threshold pressure with data from a vocal fold mechanical replica.

This paper analyzes the capability of a mucosal wave model of the vocal fold to predict values of phonation threshold lung pressure. Equations derived from the model are fitted to pressure data collected from a mechanical replica of the vocal folds. The results show that a recent extension of the model to include an arbitrary delay of the mucosal wave in its travel along the glottal channel provides a better approximation to the data than the original version of the model, which assumed a small delay. They also show that modeling the vocal tract as a simple inertive load, as has been proposed in recent analytical studies of phonation, fails to capture the effect of the vocal tract on the phonation threshold pressure with reasonable accuracy.

Modelling the human pharyngeal airway: validation of numerical simulations using in vitro experiments.

In the presented study, a numerical model which predicts the flow-induced collapse within the pharyngeal airway is validated using in vitro measurements. Theoretical simplifications were considered to limit the computation time. Systematic comparisons between simulations and measurements were performed on an in vitro replica, which reflects asymmetries of the geometry and of the tissue properties at the base of the tongue and in pathological conditions (strong initial obstruction). First, partial obstruction is observed and predicted. Moreover, the prediction accuracy of the numerical model is of 4.2% concerning the deformation (mean quadratic error on the constriction area). It shows the ability of the assumptions and method to predict accurately and quickly a fluid-structure interaction.

Theoretical simulation and experimental validation of inverse quasi-one-dimensional steady and unsteady glottal flow models.

In physical modeling of phonation, the pressure drop along the glottal constriction is classically assessed with the glottal geometry and the subglottal pressure as known input parameters. Application of physical modeling to study phonation abnormalities and pathologies requires input parameters related to in vivo measurable quantities commonly corresponding to the physical model output parameters. Therefore, the current research presents the inversion of some popular simplified flow models in order to estimate the subglottal pressure, the glottal constriction area, or the separation coefficient inherent to the simplified flow modeling for steady and unsteady flow conditions. The inverse models are firstly validated against direct simulations and secondly against in vitro measurements performed for different configurations of rigid vocal fold replicas mounted in a suitable experimental setup. The influence of the pressure corrections related to viscosity and flow unsteadiness on the flow modeling is quantified. The inversion of one-dimensional glottal flow models including the major viscous effects can predict the main flow quantities with respect to the in vitro measurements. However, the inverse model accuracy is strongly dependent on the pertinence of the direct flow modeling. The choice of the separation coefficient is preponderant to obtain pressure predictions relevant to the experimental data.

An in vitro setup to test the relevance and the accuracy of low-order vocal folds models.

An experimental setup and human vocal folds replica able to produce self-sustained oscillations are presented. The aim of the setup is to assess the relevance and the accuracy of theoretical vocal folds models. The applied reduced mechanical models are a variation of the classical two-mass model, and a simplification inspired on the delayed mass model for which the coupling between the masses is expressed as a fixed time delay. The airflow is described as a laminar flow with flow separation. The influence of a downstream resonator is taken into account. The oscillation pressure threshold and fundamental frequency are predicted by applying a stability analysis to the mechanical models. The measured frequency response of the mechanical replica together with the initial (rest) area allows us to determine the model parameters (spring stiffness, damping, geometry, masses). Validation of theoretical model predictions to experimental data shows the relevance of low-order models in gaining a qualitative understanding of phonation. However, quantitative discrepancies remain large due to an inaccurate estimation of the model parameters and the crudeness in either flow or mechanical model description. As an illustration it is shown that significant improvements can be made by accounting for viscous flow effects.

Automated recognition of spontaneous versus voluntary cough.

Cough or cough epochs may be an important and persistent symptom in many respiratory diseases requiring both a continuous and objective observation. The research presented in this paper is aimed at assessing a blind data-based classification between 'spontaneous' and 'voluntary' human cough on individual sound samples. Cough sounds were registered in the free acoustic field on 3 pathological and 9 healthy non-smoking subjects, all aged between 20 and 30. Each sound is represented by the normalized power spectral density (PSD). Different transformations of the cough PSD-vector are chosen as input features to the classification algorithm. An experimental error rate comparison between different neural and fuzzy classification networks is performed. All evaluated algorithms used the Euclidean metric. This resulted in a correct class-discrimination between 'spontaneous' and 'voluntary' cough for 96% of the cough database.