Experimental study on nonlinear source-filter interaction using synthetic vocal fold models

On the Alignment of Acoustic and Coupled Mechanic-Acoustic Eigenmodes in Phonation by Supraglottal Duct Variations

Sound generation in human phonation and the underlying fluid-structure-acoustic interaction that describes the sound production mechanism are not fully understood. A previous experimental study, with a silicone made vocal fold model connected to a straight vocal tract pipe of fixed length, showed that vibroacoustic coupling can cause a deviation in the vocal fold vibration frequency. This occurred when the fundamental frequency of the vocal fold motion was close to the lowest acoustic resonance frequency of the pipe. What is not fully understood is how the vibroacoustic coupling is influenced by a varying vocal tract length. Presuming that this effect is a pure coupling of the acoustical effects, a numerical simulation model is established based on the computation of the mechanical-acoustic eigenvalue. With varying pipe lengths, the lowest acoustic resonance frequency was adjusted in the experiments and so in the simulation setup. In doing so, the evolution of the vocal folds' coupled eigenvalues and eigenmodes is investigated, which confirms the experimental findings. Finally, it was shown that for normal phonation conditions, the mechanical mode is the most efficient vibration pattern whenever the acoustic resonance of the pipe (lowest formant) is far away from the vocal folds' vibration frequency. Whenever the lowest formant is slightly lower than the mechanical vocal fold eigenfrequency, the coupled vocal fold motion pattern at the formant frequency dominates.

An Investigation of Acoustic Back-Coupling in Human Phonation on a Synthetic Larynx Model

In the human phonation process, acoustic standing waves in the vocal tract can influence the fluid flow through the glottis as well as vocal fold oscillation. To investigate the amount of acoustic back-coupling, the supraglottal flow field has been recorded via high-speed particle image velocimetry (PIV) in a synthetic larynx model for several configurations with different vocal tract lengths. Based on the obtained velocity fields, acoustic source terms were computed. Additionally, the sound radiation into the far field was recorded via microphone measurements and the vocal fold oscillation via high-speed camera recordings. The PIV measurements revealed that near a vocal tract resonance frequency fR, the vocal fold oscillation frequency fo (and therefore also the flow field's fundamental frequency) jumps onto fR. This is accompanied by a substantial relative increase in aeroacoustic sound generation efficiency. Furthermore, the measurements show that fo-fR-coupling increases vocal efficiency, signal-to-noise ratio, harmonics-to-noise ratio and cepstral peak prominence. At the same time, the glottal volume flow needed for stable vocal fold oscillation decreases strongly. All of this results in an improved voice quality and phonation efficiency so that a person phonating with fo-fR-coupling can phonate longer and with better voice quality.

The effects of vocal tract constrictions on aerodynamic measures in a synthetic vocal fold model

According to nonlinear source-filter theory, as the strength of the coupling between the source and filter increases, typically by a decrease in the vocal tract cross-sectional area, the resultant increase in the inertance of the vocal tract yields an increase in the interactions between acoustic pressures within the vocal tract and the changing glottal airflow and/or the vibratory pattern of the vocal folds as noted in Titze [(2008). J. Acoust. Soc. Am. 123(4), 1902-1915]. The purpose of the current research was to examine the effects of parametric vocal tract constrictions mimicking epilaryngeal tube and lip narrowing on aerodynamic measures in a dynamic self-oscillating physical model of the vocal folds and vocal tract. Multilayered silicone vocal fold models were created based on Murray and Thomson [(2011). J. Visualized Exp. 58, e3498] and Murray and Thomson [(2012). J. Acoust. Soc. Am. 132(5), 3428-3438] and mounted to a simple synthetic trachea and supraglottal vocal tract model. Four constriction cross-sectional areas were examined at two locations (i.e., at the epilarynx and lip regions). Phonation threshold pressure and flow were measured at phonation onset and offset using four M5-CONV vocal fold models. Results indicated that both constriction magnitude and location are relevant factors in determining glottal aerodynamics. In general, a narrow epilarynx tube or lip constriction resulted in the lowest onset pressures and airflows while the no vocal tract condition resulted in the highest onset pressures and airflows.

Effect of Ligament Fibers on Dynamics of Synthetic, Self-Oscillating Vocal Folds in a Biomimetic Larynx Model

Synthetic silicone larynx models are essential for understanding the biomechanics of physiological and pathological vocal fold vibrations. The aim of this study is to investigate the effects of artificial ligament fibers on vocal fold vibrations in a synthetic larynx model, which is capable of replicating physiological laryngeal functions such as elongation, abduction, and adduction. A multi-layer silicone model with different mechanical properties for the musculus vocalis and the lamina propria consisting of ligament and mucosa was used. Ligament fibers of various diameters and break resistances were cast into the vocal folds and tested at different tension levels. An electromechanical setup was developed to mimic laryngeal physiology. The measurements included high-speed video recordings of vocal fold vibrations, subglottal pressure and acoustic. For the evaluation of the vibration characteristics, all measured values were evaluated and compared with parameters from ex and in vivo studies. The fundamental frequency of the synthetic larynx model was found to be approximately 200-520 Hz depending on integrated fiber types and tension levels. This range of the fundamental frequency corresponds to the reproduction of a female normal and singing voice range. The investigated voice parameters from vocal fold vibration, acoustics, and subglottal pressure were within normal value ranges from ex and in vivo studies. The integration of ligament fibers leads to an increase in the fundamental frequency with increasing airflow, while the tensioning of the ligament fibers remains constant. In addition, a tension increase in the fibers also generates a rise in the fundamental frequency delivering the physiological expectation of the dynamic behavior of vocal folds.

The Influence of Fiber Orientation of the Conus Elasticus in Vocal Fold Modeling

While the conus elasticus is generally considered a part of continuation of the vocal ligament, histological studies have revealed different fiber orientations that fibers are primarily aligned in the superior-inferior direction in the conus elasticus and in the anterior-posterior direction in the vocal ligament. In this work, two continuum vocal fold models are constructed with two different fiber orientations in the conus elasticus: the superior-inferior direction and the anterior-posterior direction. Flow-structure interaction simulations are conducted at different subglottal pressures to investigate the effects of fiber orientation in the conus elasticus on vocal fold vibrations, aerodynamic and acoustic measures of voice production. The results reveal that including the realistic fiber orientation (superior-inferior) in the conus elasticus yields smaller stiffness and larger deflection in the coronal plane at the junction of the conus elasticus and ligament and subsequently leads to a greater vibration amplitude and larger mucosal wave amplitude of the vocal fold. The smaller coronal-plane stiffness also causes a larger peak flow rate and higher skewing quotient. Furthermore, the voice generated by the vocal fold model with a realistic conus elasticus has a lower fundamental frequency, smaller first harmonic amplitude, and smaller spectral slope.

Dynamic System Coupling in Voice Production

Voice is a major means of communication for humans, non-human mammals and many other vertebrates like birds and anurans. The physical and physiological principles of voice production are described by two theories: the MyoElastic-AeroDynamic (MEAD) theory and the Source-Filter Theory (SFT). While MEAD employs a multiphysics approach to understand the motor control and dynamics of self-sustained vibration of vocal folds or analogous tissues, SFT predominantly uses acoustics to understand spectral changes of the source via linear propagation through the vocal tract. Because the two theories focus on different aspects of voice production, they are often applied distinctly in specific areas of science and engineering. Here, we argue that the MEAD and the SFT are linked integral aspects of a holistic theory of voice production, describing a dynamically coupled system. The aim of this manuscript is to provide a comprehensive review of both the MEAD and the source-filter theory with its nonlinear extension, the latter of which suggests a number of conceptual similarities to sound production in brass instruments. We discuss the application of both theories to voice production of humans as well as of animals. An appraisal of voice production in the light of non-linear dynamics supports the notion that voice production can best be described with a systems view, considering coupled systems rather than isolated contributions of individual sub-systems.

Detecting the dynamical instability of complex time series via partitioned entropy

A method is proposed to detect the dynamical instability of complex time series. We focus on how the partitioned entropy of an initially localized region of the attractor evolves in time and show that its growth rate corresponds to the first Lyapunov exponent. To avoid spurious detection of the dynamical instability, a criterion is further introduced to distinguish chaos from limit cycles or tori. Numerical experiments using prototypical models of chaotic systems demonstrate that the growth rate of the partitioned entropy indeed provides a good estimate of the first Lyapunov exponent. The method is also shown to be robust against observational noise and dynamical noise. Analysis of experimental data measured from a physical model of the vocal folds highlights the practical applicability of the present method to real-world data. Advantages of the present method over conventional methods are also discussed.

Comparison of one-dimensional and three-dimensional glottal flow models in left-right asymmetric vocal fold conditions

While the glottal flow is often simplified as one-dimensional (1D) in computational models of phonation to reduce computational costs, the 1D flow model has not been validated in left-right asymmetric vocal fold conditions, as often occur in both normal and pathological voice production. In this study, we performed three-dimensional (3D) and 1D flow simulations coupled to a two-mass model of adult male vocal folds and compared voice production at different degrees of left-right stiffness asymmetry. The flow and acoustic fields in 3D were obtained by solving the compressible Navier-Stokes equations using the volume penalization method with the moving vocal fold wall as an immersed boundary. Despite differences in the predicted flow pressure on vocal fold surface between the 1D and 3D flow models, the results showed reasonable agreement in vocal fold vibration patterns and selected voice outcome measures between the 1D and 3D models for the range of left-right asymmetric conditions investigated. This indicates that vocal fold properties play a larger role than the glottal flow in determining the overall pattern of vocal fold vibration and the produced voice, and the 1D flow simplification is sufficient in modeling phonation, at least for the simplified glottal geometry of this study.

Collision Pressure and Dissipated Power Dose in a Self-Oscillating Silicone Vocal Fold Model With a Posterior Glottal Opening

PURPOSE

The goal of this study was to experimentally evaluate how compensating for the adverse acoustic effects of a posterior glottal opening (PGO) by increasing subglottal pressure and changing supraglottal compression, as have been associated with vocal hyperfunction, influences the risk of vocal fold (VF) trauma.

METHOD

A self-oscillating synthetic silicone model of the VFs with an airflow bypass that modeled a PGO was investigated in a hemilaryngeal flow facility. The influence of compensatory mechanisms on collision pressure and dissipated collision power was investigated for different PGO areas and supraglottal compression. Compensatory behaviors were mimicked by increasing the subglottal pressure to achieve a target sound pressure level (SPL).

RESULTS

Increasing the subglottal pressure to compensate for decreased SPL due to a PGO produced higher values for both collision pressure and dissipated collision power. Whereas a 10-mm² PGO area produced a 12% increase in the peak collision pressure, the dissipated collision power increased by 122%, mainly due to an increase in the magnitude of the collision velocity. This suggests that the value of peak collision pressure may not fully capture the mechanisms by which phonotrauma occurs. It was also found that an optimal value of supraglottal compression exists that maximizes the radiated SPL, indicating the potential utility of supraglottal compression as a compensatory mechanism.

CONCLUSIONS

Larger PGO areas are expected to increase the risk of phonotrauma due to the concomitant increase in dissipated collision power associated with maintaining SPL. Furthermore, the risk of VF damage may not be fully characterized by only the peak collision pressure.

Embedded 3D printing of multi-layer, self-oscillating vocal fold models

The biomechanics of human voice production are commonly studied using benchtop silicone vocal fold models that mimic the vibration of their in vivo counterparts. These models often have multiple layers of differing stiffness that represent human vocal fold tissue layers and are fabricated using a multi-step casting process. The purpose of the present study is to introduce and demonstrate a process for fabricating functional multi-layer vocal fold models using an alternative approach, termed embedded 3D printing, that is a hybrid of casting and 3D printing. In this paper the fabrication process is described. Analysis of the resulting geometric and stiffness characteristics of the layers, including layer elastic modulus values ranging from less than 1 kPa to approximately 40 kPa, is presented. The results of tests demonstrating that the models are capable of sustained phonomimetic vibration are given. Capabilities and limitations of the embedded 3D printing process are discussed. It is concluded that the process has the potential to contribute to voice biomechanics research by facilitating prospective improvements in the fabrication, design, and functionality of multi-layer vocal fold models.

Effect of wavy trachea walls on the oscillation onset pressure of silicone vocal folds

The influence of non-smooth trachea walls on phonation onset and offset pressures and the fundamental frequency of oscillation were experimentally investigated for three different synthetic vocal fold models. Three models of the trachea were compared: a cylindrical tube (smooth walls) and wavy-walled tubes with ripple depths of 1 and 2 mm. Threshold pressures for the onset and offset of phonation were measured at the lower and upper ends of each trachea tube. All measurements were performed both with and without a supraglottal resonator. While the fundamental frequency was not affected by non-smooth trachea walls, the phonation onset and offset pressures measured right below the glottis decreased with an increasing ripple depth of the trachea walls (up to 20% for 2 mm ripples). This effect was independent from the type of glottis model and the presence of a supraglottal resonator. The pressures at the lower end of the trachea and the average volume velocities showed a tendency to decrease with an increasing ripple depth of the trachea walls but to a much smaller extent. These results indicate that the subglottal geometry and the flow conditions in the trachea can substantially affect the oscillation of synthetic vocal folds.

Experimental study of vocal-ventricular fold oscillations in voice production

Ventricular folds are located in the supraglottal region above the vocal folds. Although the ventricular folds do not vibrate under normal vocalizations, they vibrate under certain conditions, e.g., throat singing or ventricular fold dysphonia. In throat singing, the ventricular folds vibrate at the same frequency as (or at integer ratios of) the vocal fold vibration frequency. In ventricular fold dysphonia, on the other hand, the ventricular folds interfere with the vocal folds, giving rise to a hoarse voice. In the present study, the synthetic larynx model was utilized to examine the vocal-ventricular fold oscillations. Our experiments revealed that the vocal and ventricular folds can co-oscillate at the same frequency with an out-of-phase relation. Compared to the control condition, under which no ventricular folds exist, the phonation threshold pressure was increased in the presence of the ventricular folds. Acoustic analysis indicated that jitter was reduced and vocal efficiency was increased by the ventricular folds. Distance between the vocal and ventricular folds did not alter these oscillation properties. A computational model was further simulated to elucidate the mechanism underlying the observed vocal-ventricular fold oscillations. It has been suggested that out-of-phase oscillations of the vocal and ventricular folds are important for sustaining periodic laryngeal vibrations.