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

Examining the influence of epithelium layer modeling approaches on vocal fold kinematics and kinetics

Grouping the thin epithelium and thicker superficial lamina propria layers into a single cover layer has been widely adopted in finite element vocal fold models. Recent silicone vocal fold studies have suggested, however, that inclusion of a distinct epithelial layer leads to more physiologically representative motion. This study systematically explores the ramifications of incorporating an epithelial layer into a cover grouping for finite element vocal fold modeling. A membrane model for the epithelium is introduced to facilitate parametric investigation by reducing the mesh density requirement of the epithelium into a single infinitesimally thin layer. Excluding the epithelium entirely leads to increased energy in higher order modes and larger inferior-superior excursion of the folds. Integrating the epithelium into a cover layer with volume-weighted average stiffness results in similar kinematics to that of a model treating the epithelium as a distinct layer. However, the internal stress/strain and contact pressure during collision are higher, and viscous dissipation is lower, when the epithelium is integrated into the cover. Thus, careful treatment of the epithelium is recommended for finite element studies, particularly when employing the models for estimating measures dependent upon internal stress/strain and/or collision pressure, such as vocal dose.

Voice production in a MRI-based subject-specific vocal fold model with parametrically controlled medial surface shape

The goal of this study was to investigate how realistic changes in medial surface shape, as occur in human phonation, affect voice production. In a parametric magnetic resonance imaging-based three-dimensional vocal fold model, the superior and inferior portions of the medial surface were systematically manipulated to produce different medial surface contours similar to those observed in previous excised larynx and in vivo canine larynx experiments. Voice simulations were performed to investigate the differences in the resulting voice production. The results showed that both superior-medial bulging and inferior-medial bulging of the medial surface, which led to an increased vertical thickness and a more rectangular glottal configuration, increased the closed quotient of vocal fold vibration. Changes in medial surface shape also had significant effects on the phonation threshold pressure. The degree of these effects of changes in medial surface shape was larynx specific, and varied significantly depending on the vocal fold cross-sectional geometry and its variation along the anterior-posterior direction. The results suggest that, in addition to vocal fold approximation, surgical interventions of voice disorders should also aim at restoring a rectangular and sufficiently thick medial surface.

Aeroacoustic source characterization in a physical model of phonation

This paper presents measurements conducted in a physical model of the adult human airway. The goals of this work are to (1) benchmark the physical model to excised larynx models in the literature and (2) empirically demonstrate the relationship between vocal fold drag and sound production. Results from the airway model are first benchmarked to published time-averaged behavior of excised larynx models. The airway model in this work exhibited higher glottal volume flow, lower glottal resistance, and less fundamental frequency variation than excised larynx models. Next, concurrent measurements of source behavior and radiated sound were compared. Unsteady transglottal pressure (a surrogate measure for vocal fold drag) and radiated sound, measured at the mouth, showed good correlation. In particular, the standard deviation and the ratio of the power of the first and second harmonics of the transglottal and mouth pressures were strongly correlated. This empirical result supports the assertion that vocal fold drag is the principal source of sound in phonation.

Computational Models of Laryngeal Aerodynamics: Potentials and Numerical Costs

Human phonation is based on the interaction between tracheal airflow and laryngeal dynamics. This fluid-structure interaction is based on the energy exchange between airflow and vocal folds. Major challenges in analyzing the phonatory process in-vivo are the small dimensions and the poor accessibility of the region of interest. For improved analysis of the phonatory process, numerical simulations of the airflow and the vocal fold dynamics have been suggested. Even though most of the models reproduced the phonatory process fairly well, development of comprehensive larynx models is still a subject of research. In the context of clinical application, physiological accuracy and computational model efficiency are of great interest. In this study, a simple numerical larynx model is introduced that incorporates the laryngeal fluid flow. It is based on a synthetic experimental model with silicone vocal folds. The degree of realism was successively increased in separate computational models and each model was simulated for 10 oscillation cycles. Results show that relevant features of the laryngeal flow field, such as glottal jet deflection, develop even when applying rather simple static models with oscillating flow rates. Including further phonatory components such as vocal fold motion, mucosal wave propagation, and ventricular folds, the simulations show phonatory key features like intraglottal flow separation and increased flow rate in presence of ventricular folds. The simulation time on 100 CPU cores ranged between 25 and 290 hours, currently restricting clinical application of these models. Nevertheless, results show high potential of numerical simulations for better understanding of phonatory process.

Effect of level difference between left and right vocal folds on phonation: Physical experiment and theoretical study

As an alternative factor to produce asymmetry between left and right vocal folds, the present study focuses on level difference, which is defined as the distance between the upper surfaces of the bilateral vocal folds in the inferior-superior direction. Physical models of the vocal folds were utilized to study the effect of the level difference on the phonation threshold pressure. A vocal tract model was also attached to the vocal fold model. For two types of different models, experiments revealed that the phonation threshold pressure tended to increase as the level difference was extended. Based upon a small amplitude approximation of the vocal fold oscillations, a theoretical formula was derived for the phonation threshold pressure. This theory agrees with the experiments, especially when the phase difference between the left and right vocal folds is not extensive. Furthermore, an asymmetric two-mass model was simulated with a level difference to validate the experiments as well as the theory. The primary conclusion is that the level difference has a potential effect on voice production especially for patients with an extended level of vertical difference in the vocal folds, which might be taken into account for the diagnosis of voice disorders.

A parametric vocal fold model based on magnetic resonance imaging

This paper introduces a parametric three-dimensional body-cover vocal fold model based on magnetic resonance imaging (MRI) of the human larynx. Major geometric features that are observed in the MRI images but missing in current vocal fold models are discussed, and their influence on vocal fold vibration is evaluated using eigenmode analysis. Proper boundary conditions for the model are also discussed. Based on control parameters corresponding to anatomic landmarks that can be easily measured, this model can be adapted toward a subject-specific vocal fold model for voice production research and clinical applications.

Dynamic vocal fold parameters with changing adduction in ex-vivo hemilarynx experiments

Ex-vivo hemilarynx experiments allow the visualization and quantification of three-dimensional dynamics of the medial vocal fold surface. For three excised human male larynges, the vibrational output, the glottal flow resistance, and the sound pressure during sustained phonation were analyzed as a function of vocal fold adduction for varying subglottal pressure. Empirical eigenfunctions, displacements, and velocities were investigated along the vocal fold surface. For two larynges, an increase of adduction level resulted in an increase of the glottal flow resistance at equal subglottal pressures. This caused an increase of lateral and vertical oscillation amplitudes and velocity indicating an improved energy transfer from the airflow to the vocal folds. In contrast, the third larynx exhibited an amplitude decrease for rising adduction accompanying reduction of the flow resistance. By evaluating the empirical eigenfunctions, this reduced flow resistance was assigned to an unbalanced oscillation pattern with predominantly lateral amplitudes. The results suggest that adduction facilitates the phonatory process by increasing the glottal flow resistance and enhancing the vibrational amplitudes. However, this interrelation only holds for a maintained balanced ratio between vertical and lateral displacements. Indeed, a balanced vertical-lateral oscillation pattern may be more beneficial to phonation than strong periodicity with predominantly lateral vibrations.

Cause-effect relationship between vocal fold physiology and voice production in a three-dimensional phonation model

The goal of this study is to better understand the cause-effect relation between vocal fold physiology and the resulting vibration pattern and voice acoustics. Using a three-dimensional continuum model of phonation, the effects of changes in vocal fold stiffness, medial surface thickness in the vertical direction, resting glottal opening, and subglottal pressure on vocal fold vibration and different acoustic measures are investigated. The results show that the medial surface thickness has dominant effects on the vertical phase difference between the upper and lower margins of the medial surface, closed quotient, H1-H2, and higher-order harmonics excitation. The main effects of vocal fold approximation or decreasing resting glottal opening are to lower the phonation threshold pressure, reduce noise production, and increase the fundamental frequency. Increasing subglottal pressure is primarily responsible for vocal intensity increase but also leads to significant increase in noise production and an increased fundamental frequency. Increasing AP stiffness significantly increases the fundamental frequency and slightly reduces noise production. The interaction among vocal fold thickness, stiffness, approximation, and subglottal pressure in the control of F0, vocal intensity, and voice quality is discussed.

Comprehensive, Population-Based Sensitivity Analysis of a Two-Mass Vocal Fold Model

Previous vocal fold modeling studies have generally focused on generating detailed data regarding a narrow subset of possible model configurations. These studies can be interpreted to be the investigation of a single subject under one or more vocal conditions. In this study, a broad population-based sensitivity analysis is employed to examine the behavior of a virtual population of subjects and to identify trends between virtual individuals as opposed to investigating a single subject or model instance. Four different sensitivity analysis techniques were used in accomplishing this task. Influential relationships between model input parameters and model outputs were identified, and an exploration of the model’s parameter space was conducted. Results indicate that the behavior of the selected two-mass model is largely dominated by complex interactions, and that few input-output pairs have a consistent effect on the model. Results from the analysis can be used to increase the efficiency of optimization routines of reduced-order models used to investigate voice abnormalities. Results also demonstrate the types of challenges and difficulties to be expected when applying sensitivity analyses to more complex vocal fold models. Such challenges are discussed and recommendations are made for future studies.

The role of glottal surface adhesion on vocal folds biomechanics

The airway surface liquid (ASL) is a very thin mucus layer and covers the vocal fold (VF) surface. Adhesion mediated by the ASL occurs during phonation as the VFs separate after collision. Such adhesion is hypothesized to determine voice quality and health. However, biomechanical insights into the adhesive processes during VF oscillation are lacking. Here, a computational study is reported on self-sustained VF vibration involving contact and adhesion. The VF structural model and the glottal airflow are considered fully three-dimensional. The mechanical behavior of the ASL is described through a constitutive traction-separation law where mucosal cohesive strength, cohesive energy, and rupture length enter. Cohesive energy values considered are bound below by the cohesive energy of water at standard temperature and pressure. Cohesive strength values considered are bound above by prior reported data on the adhesive strength of mucosal surface of rat small intestine. This model introduces a mechanical length scale into the analysis. The sensitivity of various aspects of VF dynamics such as flow-declination rate, VF separation under adhesive condition, and formation of multiple local fluid bridges is determined in relation to specific ASL adhesive properties. It is found that for the ASL considered here, the characteristics of the VF separation process are of debond type. Instabilities lead to the breakup of the bond area into several smaller bond patches. Such finding is consistent with in vivo observations.

Bi-stable vocal fold adduction: a mechanism of modal-falsetto register shifts and mixed registration

The origin of vocal registers has generally been attributed to differential activation of cricothyroid and thyroarytenoid muscles in the larynx. Register shifts, however, have also been shown to be affected by glottal pressures exerted on vocal fold surfaces, which can change with loudness, pitch, and vowel. Here it is shown computationally and with empirical data that intraglottal pressures can change abruptly when glottal adductory geometry is changed relatively smoothly from convergent to divergent. An intermediate shape between large convergence and large divergence, namely, a nearly rectangular glottal shape with almost parallel vocal fold surfaces, is associated with mixed registration. It can be less stable than either of the highly angular shapes unless transglottal pressure is reduced and upper stiffness of vocal fold tissues is balanced with lower stiffness. This intermediate state of adduction is desirable because it leads to a low phonation threshold pressure with moderate vocal fold collision. Achieving mixed registration consistently across wide ranges of F0, lung pressure, and vocal tract shapes appears to be a balancing act of coordinating laryngeal muscle activation with vocal tract pressures. Surprisingly, a large transglottal pressure is not facilitative in this process, exacerbating the bi-stable condition and the associated register contrast.

Characterization of the vocal fold vertical stiffness in a canine model

OBJECTIVES/HYPOTHESIS

Characterizing the vertical stiffness gradient that exists between the superior and inferior aspects of the medial surface of the vocal fold. Characterization of this stiffness gradient could elucidate the mechanism behind the divergent glottal shape observed during closing.

STUDY DESIGN

Basic science.

METHODS

Indentation testing of the folds was done in a canine model. Stress-strain curves are generated using a customized load-cell and the differential Young's modulus is calculated as a function of strain.

RESULTS

Results from 11 larynges show that stress increases as a function of strain more rapidly in the inferior aspect of the fold. The calculations for local Young's modulus show that at high strain values, a stiffness gradient is formed between the superior and inferior aspects of the fold.

CONCLUSIONS

For small strain values, which are observed at low subglottal pressures, the stiffness of the tissue is similar in both the superior and inferior aspects of the vocal fold. Consequently, the lateral force that is applied by the glottal flow at both aspects results in almost identical displacements, yielding no divergence angle. Conversely, at higher strain values, which are measured in high subglottal pressure, the inferior aspect of the vocal fold is much stiffer than the superior edge; thus, any lateral force that is applied at both aspects will result in a much greater displacement of the superior edge, yielding a large divergence angle. The increased stiffness observed at the inferior edge could be due to the proximity of the conus elasticus.

A synthetic, self-oscillating vocal fold model platform for studying augmentation injection

OBJECTIVE

To design and evaluate a platform for studying the mechanical effects of augmentation injections using synthetic, self-oscillating vocal fold models.

STUDY DESIGN

Basic science.

METHODS

Life-sized, synthetic, multilayer, self-oscillating vocal fold models were created that simulated bowing via volumetric reduction of the body layer relative to that of a normal, unbowed model. Material properties of the layers were unchanged. Models with varying degrees of bowing were created and paired with normal models. Following initial acquisition of data (onset pressure, vibration frequency, flow rate, and high-speed image sequences), bowed models were injected with silicone that had material properties similar to those used in augmentation procedures. Three different silicone injection quantities were tested: sufficient to close the glottal gap, insufficient to close the glottal gap, and excess silicone to create convex bowing of the bowed model. The above-mentioned metrics were again taken and compared. Pre- and post-injection high-speed image sequences were acquired using a hemilarynx setup, from which medial surface dynamics were quantified.

RESULTS

The models vibrated with mucosal wave-like motion and at onset pressures and frequencies typical of human phonation. The models successfully exhibited various degrees of bowing which were then mitigated by injecting filler material. The models showed general pre- to post-injection decreases in onset pressure, flow rate, and open quotient and a corresponding increase in vibration frequency.

CONCLUSION

The model may be useful in further explorations of the mechanical consequences of augmentation injections.

The role of finite displacements in vocal fold modeling

Human vocal folds experience flow-induced vibrations during phonation. In previous computational models, the vocal fold dynamics has been treated with linear elasticity theory in which both the strain and the displacement of the tissue are assumed to be infinitesimal (referred to as model I). The effect of the nonlinear strain, or geometric nonlinearity, caused by finite displacements is yet not clear. In this work, a two-dimensional model is used to study the effect of geometric nonlinearity (referred to as model II) on the vocal fold and the airflow. The result shows that even though the deformation is under 1 mm, i.e., less than 10% of the size of the vocal fold, the geometric nonlinear effect is still significant. Specifically, model I underpredicts the gap width, the flow rate, and the impact stress on the medial surfaces as compared to model II. The study further shows that the differences are caused by the contact mechanics and, more importantly, the fluid-structure interaction that magnifies the error from the small-displacement assumption. The results suggest that using the large-displacement formulation in a computational model would be more appropriate for accurate simulations of the vocal fold dynamics.

AERODYNAMIC SOUND OF A BODY IN ARBITRARY, DEFORMABLE MOTION, WITH APPLICATION TO PHONATION

The method of tailored Green's functions advocated by Doak (Proceedings of the Royal Society A254 (1960) 129 - 145.) for the solution of aeroacoustic problems is used to analyse the contribution of the mucosal wave to self-sustained modulation of air flow through the glottis during the production of voiced speech. The amplitude and phase of the aerodynamic surface force that maintains vocal fold vibration are governed by flow separation from the region of minimum cross-sectional area of the glottis, which moves back and forth along its effective length accompanying the mucosal wave peak. The correct phasing is achieved by asymmetric motion of this peak during the opening and closing phases of the glottis. Limit cycle calculations using experimental data of Berry et al. (Journal of the Acoustical Society of America 110 (2001) 2539 - 2547.) obtained using an excised canine hemilarynx indicate that the mechanism is robust enough to sustain oscillations over a wide range of voicing conditions.

Influence of numerical model decisions on the flow-induced vibration of a computational vocal fold model

Computational vocal fold models are often used to study the physics of voice production. In this paper the sensitivity of predicted vocal fold flow-induced vibration and resulting airflow patterns to several modeling selections is explored. The location of contact lines used to prevent mesh collapse and assumptions of symmetry were found to influence airflow patterns. However, these variables had relatively little effect on the vibratory response of the vocal fold model itself. Model motion was very sensitive to Poisson's ratio. The importance of these parameter sensitivities in the context of vocal fold modeling is discussed.

Influence of subglottic stenosis on the flow-induced vibration of a computational vocal fold model

The effect of subglottic stenosis on vocal fold vibration is investigated. An idealized stenosis is defined, parameterized, and incorporated into a two-dimensional, fully-coupled finite element model of the vocal folds and laryngeal airway. Flow-induced responses of the vocal fold model to varying severities of stenosis are compared. The model vibration was not appreciably affected by stenosis severities of up to 60% occlusion. Model vibration was altered by stenosis severities of 90% or greater, evidenced by decreased superior model displacement, glottal width amplitude, and flow rate amplitude. Predictions of vibration frequency and maximum flow declination rate were also altered by high stenosis severities. The observed changes became more pronounced with increasing stenosis severity and inlet pressure, and the trends correlated well with flow resistance calculations. Flow visualization was used to characterize subglottal flow patterns in the space between the stenosis and the vocal folds. Underlying mechanisms for the observed changes, possible implications for human voice production, and suggestions for future work are discussed.

Vibratory responses of synthetic, self-oscillating vocal fold models

The flow-induced responses of four self-oscillating synthetic vocal fold models are compared. All models were life-sized and fabricated using flexible silicone compounds with material properties comparable to those of human vocal fold tissue. Three of the models had two layers of different stiffness to represent the body-cover grouping of vocal fold tissue. Two of the two-layer models were based on the "M5" geometry [Scherer et al., J. Acoust. Soc. Am. 109, 1616-1630 (2001)], while the third was based on magnetic resonance imaging data. The fourth model included several layers, including a thin epithelial layer, an exceedingly flexible superficial lamina propria layer, a ligament layer that included an anteriorly-posteriorly oriented fiber to restrict vertical motion, and a body layer. Measurements were performed with these models in full larynx and hemilarynx configurations. Data included onset pressure, vibration frequency, glottal flow rate, maximum glottal width, and medial surface motion, the latter two of which were acquired using high-speed imaging techniques. The fourth, multi-layer model exhibited onset pressure, frequency, and medial surface motion traits that are comparable to published human vocal fold data. Importantly, the model featured an alternating convergent-divergent glottal profile and mucosal wave-like motion, characteristics which are important markers of human vocal fold vibration.

Frequency response of synthetic vocal fold models with linear and nonlinear material properties

PURPOSE

The purpose of this study was to create synthetic vocal fold models with nonlinear stress-strain properties and to investigate the effect of linear versus nonlinear material properties on fundamental frequency (F0) during anterior-posterior stretching.

METHOD

Three materially linear and 3 materially nonlinear models were created and stretched up to 10 mm in 1-mm increments. Phonation onset pressure (Pon) and F0 at Pon were recorded for each length. Measurements were repeated as the models were relaxed in 1-mm increments back to their resting lengths, and tensile tests were conducted to determine the stress-strain responses of linear versus nonlinear models.

RESULTS

Nonlinear models demonstrated a more substantial frequency response than did linear models and a more predictable pattern of F0 increase with respect to increasing length (although range was inconsistent across models). Pon generally increased with increasing vocal fold length for nonlinear models, whereas for linear models, Pon decreased with increasing length.

CONCLUSION

Nonlinear synthetic models appear to more accurately represent the human vocal folds than do linear models, especially with respect to F0 response.