Interpretation of biomechanical simulations of normal and chaotic vocal fold oscillations with empirical eigenfunctions

An Improved Glottal Flow Model Based on Seq2Seq LSTM for Simulation of Vocal Fold Vibration

OBJECTIVES

An improved data-driven glottal flow model for fluid-structure interaction (FSI) simulation of the vocal fold vibration is proposed in this paper. This model aims to improve the prediction performance of the previously developed deep neural network (DNN) based empirical flow model (EFM)1 on accuracy and efficiency.

METHODS

A Seq2Seq long short-term memory (LSTM) network is employed in the present model to infer the flow rate and pressure distribution from the subglottal pressure and cross-section area distribution of the glottis. The training data is collected from the generalized glottal shape library generated in Zhang et al.1 RESULTS AND CONCLUSIONS: Compared to the EFM, the present model not only discards the time-consuming optimization process, but also drastically reduces the errors, therefore the prediction performance can be greatly improved. The present model is evaluated by coupling with a solid dynamics solver for FSI simulation, and the results demonstrate a great improvement on accuracy and efficiency.

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.

Subject-Specific Computational Fluid-Structure Interaction Modeling of Rabbit Vocal Fold Vibration

A full three-dimensional (3D) fluid-structure interaction (FSI) study of subject-specific vocal fold vibration is carried out based on the previously reconstructed vocal fold models of rabbit larynges. Our primary focuses are the vibration characteristics of the vocal fold, the unsteady 3D flow field, and comparison with a recently developed 1D glottal flow model that incorporates machine learning. The 3D FSI model applies strong coupling between the finite-element model for the vocal fold tissue and the incompressible Navier-Stokes equation for the flow. Five different samples of the rabbit larynx, reconstructed from the magnetic resonance imaging (MRI) scans after the in vivo phonation experiments, are used in the FSI simulation. These samples have distinct geometries and a different inlet pressure measured in the experiment. Furthermore, the material properties of the vocal fold tissue were determined previously for each individual sample. The results demonstrate that the vibration and the intraglottal pressure from the 3D flow simulation agree well with those from the 1D flow model based simulation. Further 3D analyses show that the inferior and supraglottal geometries play significant roles in the FSI process. Similarity of the flow pattern with the human vocal fold is discussed. This study supports the effective usage of rabbit larynges to understand human phonation and will help guide our future computational studies that address vocal fold disorders.

Acoustic structure and information content of trumpets in female Asian elephants (Elephas maximus)

Most studies on elephant vocal communication have focused on the low-frequency rumble, with less effort on other vocalization types such as the most characteristic elephant call, the trumpet. Yet, a better and more complete understanding of the elephant vocal system requires investigating other vocalization types and their functioning in more detail as well. We recorded adult female Asian elephants (Elephas maximus) at a private facility in Nepal and analyzed 206 trumpets from six individuals regarding their frequency, temporal and contour shape, and related acoustic parameters of the fundamental frequency. We also tested for information content regarding individuality and context. Finally, we recorded the occurrence of non-linear phenomena such as bifurcation, biphonation, subharmonics and deterministic chaos. We documented a mean fundamental frequency ± SD of 474 ± 70 Hz and a mean duration ± SD of 1.38 ± 1.46 s (Nindiv. = 6, Ncalls = 206). Our study reveals that the contour of the fundamental frequency of trumpets encodes information about individuality, but we found no evidence for trumpet subtypes in greeting versus disturbance contexts. Non-linear phenomena prevailed and varied in abundance among individuals, suggesting that irregularities in trumpets might enhance the potential for individual recognition. We propose that trumpets in adult female Asian elephants serve to convey an individual's identity as well as to signal arousal and excitement to conspecifics.

Vocal fold vibration mode changes due to cricothyroid and thyroarytenoid muscle interaction in a three-dimensional model of the canine larynx

Using a continuum model based on magnetic resonance imaging of a canine larynx, parametric simulations of the vocal fold vibration during phonation were conducted with the cricothyroid muscle (CT) and the thyroarytenoid muscle (TA) independently activated from zero to full activation. The fundamental frequency (f₀) first increased and then experienced a downward jump as TA activity gradually increased under moderate to high CT activation. Proper orthogonal decomposition analysis revealed that the vocal fold vibrations were dominated by two modes representing a lateral motion and rotational motion, respectively, and the f₀ drop was associated with a switch on the order of the two modes. In another parametric set where only the vocalis was active, f₀ increased monotonically with both TA and CT activity and the mode switch did not occur. The results suggested that the active stress in the TA, which causes large stress differences between the body and cover, is essential for the occurrence of the rotational mode and mode switch. Relatively greater TA activity tends to promote the rotational mode, while relatively greater CT activity tends to promote the lateral mode. The results also suggested that the vibration modes affected f₀ by affecting the contribution of the TA stress to the effective stiffness. The switch in the dominant mode caused the non-monotonic change of f₀.

Phase-averaged and cycle-to-cycle analysis of jet dynamics in a scaled up vocal-fold model

Phase-averaged and cycle-to-cycle analysis of key contributors to sound production in phonation is examined in a scaled-up vocal-fold model. Simultaneous temporally and spatially resolved pressure and velocity measurements permitted examination of each term in the streamwise integral momentum equation. The relative sizes of these terms were used to address the issue of whether transglottal pressure is a surrogate for vocal-fold drag, a quantity directly related to sound production. Further, time traces of transglottal pressure and volume flow rate provided insight into the role of cycle-to-cycle variations in voiced sound production which affect voice quality. Experiments were conducted using a 10× scaled-up model in a free-surface water tunnel. Two-dimensional vocal-fold models with semi-circular ends inside a square duct were driven with constant opening and closing speeds. The time from opening to closed, T_o , was half the oscillation period. Time-resolved digital particle image velocimetry (DPIV) and pressure measurements along the duct centreline were made for 3650 ≤ Re ≤ 8100 and equivalent life frequencies from 52.5 to 97.5 Hz. Results showed that transglottal pressure does serve as a surrogate for the vocal-fold drag. However, smaller but non-negligible momentum flux and inertia terms, caused by the jet and vocal-fold motions, may also contribute to vocal-fold drag. Further, cycle-to-cycle variations including jet switching and modulation are inherent in flows of this type despite their high degrees of symmetry and repeatability. The origins of these variations and their potential role in sound production and voice quality are discussed.

Computational simulations of respiratory-laryngeal interactions and their effects on lung volume termination during phonation: Considerations for hyperfunctional voice disorders

Glottal resistance plays an important role in airflow conservation, especially in the context of high vocal demands. However, it remains unclear if laryngeal strategies most effective in controlling airflow during phonation are consistent with clinical manifestations of vocal hyperfunction. This study used a previously validated three-dimensional computational model of the vocal folds coupled with a respiratory model to investigate which laryngeal strategies were the best predictors of lung volume termination (LVT) and how these strategies' effects were modulated by respiratory parameters. Results indicated that the initial glottal angle and vertical thickness of the vocal folds were the best predictors of LVT regardless of subglottal pressure, lung volume initiation, and breath group duration. The effect of vertical thickness on LVT increased with the subglottal pressure-highlighting the importance of monitoring loudness during voice therapy to avoid laryngeal compensation-and decreased with increasing vocal fold stiffness. A positive initial glottal angle required an increase in vertical thickness to complete a target utterance, especially when the respiratory system was taxed. Overall, findings support the hypothesis that laryngeal strategies consistent with hyperfunctional voice disorders are effective in increasing LVT, and that conservation of airflow and respiratory effort may represent underlying mechanisms in those disorders.

Biomechanical Models to Represent Vocal Physiology: A Systematic Review

Biomechanical modeling allows obtaining information on physical phenomena that cannot be directly observed. This study aims to review models that represent voice production. A systematic review of the literature was conducted using PubMed/Medline, SCOPUS, and IEEE Xplore databases. To select the papers, we used the protocol PRISMA Statement. A total of 53 publications were included in this review. This article considers a taxonomic classification of models found in the literature. We propose four categories in the taxonomy: (1) Models representing the Source (Vocal folds); (2) Models representing the Filter (Vocal Tract); (3) Models representing the Source - Filter Interaction; and (4) Models representing the Airflow - Source Interaction. We include a bibliographic analysis with the evolution of the publications per category. We provide an analysis of the number as well of publications in journals per year. Moreover, we present an analysis of the term occurrence and its frequency of usage, as found in the literature. In each category, different types of vocal production models are mentioned and analyzed. The models account for the analysis of evidence about aerodynamic, biomechanical, and acoustic phenomena and their correlation with the physiological processes involved in the production of the human voice. This review gives an insight into the state of the art related to the mathematical modeling of voice production, analyzed from the viewpoint of vocal physiology.

Occurrences of non-linear phenomena and vocal harshness in dog whines as indicators of stress and ageing

During social interactions, acoustic parameters of tetrapods' vocalisations reflect the emotional state of the caller. Higher levels of spectral noise and the occurrence of irregularities (non-linear phenomena NLP) might be negative arousal indicators in alarm calls, although less is known about other distress vocalisations. Family dogs experience different levels of stress during separation from their owner and may vocalise extensively. Analysing their whines can provide evidence for the relationship between arousal and NLP. We recorded 167 family dogs' separation behaviour including vocalisations, assessed their stress level based on behaviour and tested how these, their individual features, and owner reported separation-related problems (SRP) relate to their whines' (N = 4086) spectral noise and NLP. Dogs with SRP produced NLP whines more likely. More active dogs and dogs that tried to escape produced noisier whines. Older dogs' whines were more harmonic than younger ones', but they also showed a higher NLP ratio. Our results show that vocal harshness and NLP are associated with arousal in contact calls, and thus might function as stress indicators. The higher occurrence of NLP in older dogs irrespective to separation stress suggests loss in precise neural control of the larynx, and hence can be a potential ageing indicator.

Study of spatiotemporal liquid dynamics in a vibrating vocal fold by using a self-oscillating poroelastic model

The main purpose of this study is to investigate the spatiotemporal interstitial fluid dynamics in a vibrating vocal fold. A self-oscillating poroelastic model is proposed to study the liquid dynamics in the vibrating vocal folds by treating the vocal fold tissue as a transversally isotropic, fluid-saturated, porous material. Rich spatiotemporal liquid dynamics have been found. Specifically, in the vertical direction, the liquid is transported from the inferior side to the superior side due to the propagation of the mucosal wave. In the longitudinal direction, the liquid accumulates at the anterior-posterior midpoint. However, the contact between the two vocal folds forces the accumulated liquid out laterally in a very short time span. These findings could be helpful for exploring etiology of some laryngeal pathologies, optimizing laryngeal disease treatment, and understanding hemodynamics in the vocal folds.

Cycle-to-cycle flow variations in a square duct with a symmetrically oscillating constriction

Spatially and temporally resolved Digital Particle Image Velocimetry (DPIV) measurements are presented of flow complexities in a nominally two-dimensional, symmetric, duct with an oscillating constriction. The motivation for this research lies in advancing the state-of-the-art in applying integral control volume analysis to modeling unsteady internal flows. The specific target is acoustic modeling of human phonation. The integral mass and momentum equations are directly coupled to the acoustic equations and provide quantitative insight into acoustic source strengths in addition to the dynamics of the fluid-structure interactions in the glottis. In this study, a square cross-section duct was constructed with symmetric, computer controlled, oscillating constrictions that incorporate both rocking as well as oscillatory open/close motions. Experiments were run in a free-surface water tunnel over a Strouhal number range, based on maximum jet speed and model length, of 0.012 - 0.048, for a fixed Reynolds number, based on maximum gap opening and maximum jet speed, of 8000. In this study, the constriction motions were continuous with one open-close cycle immediately following another. While the model and its motions were nominally two-dimensional and symmetric, flow asymmetries and oscillation frequency dependent cycle-to-cycle variations were observed. These are examined in the context of terms in the integral conservation equations.

A Deep Neural Network Based Glottal Flow Model for Predicting Fluid-Structure Interactions during Voice Production

This paper proposes a machine-learning based reduced-order model that can provide fast and accurate prediction of the glottal flow during voice production. The model is based on the Bernoulli equation with a viscous loss term predicted by a deep neural network (DNN) model. The training data of the DNN model is a Navier-Stokes (N-S) equation-based three-dimensional simulation of glottal flows in various glottal shapes generated by a synthetic shape function, which can be obtained by superimposing the instantaneous modal displacements during vibration on the prephonatory geometry of the glottal shape. The input parameters of the DNN model are the geometric and flow parameters extracted from discretized cross sections of the glottal shapes and the output target is the corresponding flow resistance coefficient. With this trained DNN-Bernoulli model, the flow resistance coefficient as well as the flow rate and pressure distribution in any given glottal shape generated by the synthetic shape function can be predicted. The model is further coupled with a finite-element method based solid dynamics solver for simulating fluid-structure interactions (FSI). The prediction performance of the model for both static shape and FSI simulations is evaluated by comparing the solutions to those obtained by the Bernoulli and N-S model. The model shows a good prediction performance in accuracy and efficiency, suggesting a promise for future clinical use.

A computational study of the effects of vocal fold stiffness parameters on voice production

A three-dimensional flow-structure interaction model of voice production is used to investigate the effect of the stiffness parameters of vocal fold layers on voice production. The vocal fold is modeled as a three-layer structure consisting of the cover, ligament, and body layers. All the three layers are modeled as transversely isotropic materials for which the stiffness parameters include the transverse elastic modulus and longitudinal elastic modulus. The results show that, in addition to the obvious monotonic effects on the fundamental frequency, flow rate and glottis opening, the stiffness parameters also have significant and nonmonotonic effects on the divergent angle, open quotient, and closing velocity. It is further found that the longitudinal stiffness parameters generally have more significant impacts on glottal flows and vocal fold vibrations than the transverse stiffness parameters. The sensitivity analysis shows that, among all the stiffness parameters, the transverse and longitudinal stiffness of the ligament layer have the most dominant effect on most output measures.

Effect of Longitudinal Variation of Vocal Fold Inner Layer Thickness on Fluid-Structure Interaction During Voice Production

A three-dimensional fluid-structure interaction computational model was used to investigate the effect of the longitudinal variation of vocal fold inner layer thickness on voice production. The computational model coupled a finite element method based continuum vocal fold model and a Navier-Stokes equation based incompressible flow model. Four vocal fold models, one with constant layer thickness and the others with different degrees of layer thickness variation in the longitudinal direction, were studied. It was found that the varied thickness resulted in up to 24% stiffness reduction at the middle and up to 47% stiffness increase near the anterior and posterior ends of the vocal fold; however, the average stiffness was not affected. The fluid-structure interaction simulations on the four models showed that the thickness variation did not affect vibration amplitude, glottal flow rate, and the waveform related parameters. However, it increased glottal angles at the middle of the vocal fold, suggesting that vocal fold vibration amplitude was determined by the average stiffness of the vocal fold, while the glottal angle was determined by the local stiffness. The models with longitudinal variation of layer thickness consumed less energy during the vibrations compared with the constant layer thickness one.

Coherency of circadian rhythms in the SCN is governed by the interplay of two coupling factors

Circadian clocks are autonomous oscillators driving daily rhythms in physiology and behavior. In mammals, a network of coupled neurons in the suprachiasmatic nucleus (SCN) is entrained to environmental light-dark cycles and orchestrates the timing of peripheral organs. In each neuron, transcriptional feedbacks generate noisy oscillations. Coupling mediated by neuropeptides such as VIP and AVP lends precision and robustness to circadian rhythms. The detailed coupling mechanisms between SCN neurons are debated. We analyze organotypic SCN slices from neonatal and adult mice in wild-type and multiple knockout conditions. Different degrees of rhythmicity are quantified by pixel-level analysis of bioluminescence data. We use empirical orthogonal functions (EOFs) to characterize spatio-temporal patterns. Simulations of coupled stochastic single cell oscillators can reproduce the diversity of observed patterns. Our combination of data analysis and modeling provides deeper insight into the enormous complexity of the data: (1) Neonatal slices are typically stronger oscillators than adult slices pointing to developmental changes of coupling. (2) Wild-type slices are completely synchronized and exhibit specific spatio-temporal patterns of phases. (3) Some slices of Cry double knockouts obey impaired synchrony that can lead to co–existing rhythms (“splitting”). (4) The loss of VIP-coupling leads to desynchronized rhythms with few residual local clusters. Additional information was extracted from co–culturing slices with rhythmic neonatal wild-type SCNs. These co–culturing experiments were simulated using external forcing terms representing VIP and AVP signaling. The rescue of rhythmicity via co–culturing lead to surprising results, since a cocktail of AVP-antagonists improved synchrony. Our modeling suggests that these counter-intuitive observations are pointing to an antagonistic action of VIP and AVP coupling. Our systematic theoretical and experimental study shows that dual coupling mechanisms can explain the astonishing complexity of spatio-temporal patterns in SCN slices.

The mammalian circadian clock is orchestrated by a network of coupled neurons. Brain slice preparations allow the analysis of coupling mechanisms mediated by neuropeptides. From bioluminescence recordings, we extract single cell characteristics such as period, amplitude and damping rate. Our data-based stochastic network model involves local coupling between cells and additional external forcing. Available experimental data guide our simulations with two distinct coupling and forcing mechanisms representing the neuropeptides VIP and AVP. We compare our simulations with experiments from neonatal and adult wild-type brain slices and multiple knockouts. Furthermore, we study co–culturing of slices with synchronized neonatal wild-type slices. The extreme complexity of the spatio-temporal patterns is quantified using empirical orthogonal functions (EOFs). The experimental reduction of AVP coupling leads to surprising observations. In double knockouts, inhibition of AVP signaling can improve synchrony, whereas, in triple knockouts, coherency is reduced. Our network modeling shows that these counter-intuitive observations can be explained by an antagonistic action of VIP and AVP signaling. The agreement of experiments and simulations suggests that quite complex spatio-temporal patterns can appear as emergent properties of oscillator networks with dual coupling mechanisms.

Sensitivity analysis of muscle mechanics-based voice simulator to determine gender-specific speech characteristics

The purpose of this study was to investigate the gender differences in voice simulation using a sensitivity analysis approach. A global, Monte Carlo-based approach was employed, and the relationships between biomechanical inputs (lung pressure and muscle activation levels) and acoustic outputs (fundamental frequency, f₀, and sound pressure level, SPL) were investigated for male and female versions of a voice simulator model. The gender distinction in the model was based on an anatomical scaling of the laryngeal structures. Results showed strong relationships for f₀ and SPL as functions of lung pressure, as well as for f₀ as a function of cricothyroid and thyroarytenoid muscle activity, in agreement with previous literature. Also expected was a systematic shift in f₀ range between the genders. It was found that the female model exhibited greater pitch strength (saliency) than the male model, which might equate to a perceptually more periodic or higher-quality voice for females. In addition, the female model required slightly higher lung pressures than the male model to achieve the same SPL, suggesting a possibly greater phonatory effort and predisposition for fatigue in the female voice. The methods and results of this study lay the groundwork for a complete mapping of simulator sound signal characteristics as a function of simulator input parameters and a better understanding of gender-specific voice production and vocal health.

Vocal instabilities in a three-dimensional body-cover phonation model

The goal of this study is to identify vocal fold conditions that produce irregular vocal fold vibration and the underlying physical mechanisms. Using a three-dimensional computational model of phonation, parametric simulations are performed with co-variations in vocal fold geometry, stiffness, and vocal tract shape. For each simulation, the cycle-to-cycle variations in the amplitude and period of the glottal area function are calculated, based on which the voice is classified into three types corresponding to regular, quasi-steady or subharmonic, and chaotic phonation. The results show that vocal folds with a large medial surface vertical thickness and low transverse stiffness are more likely to exhibit irregular vocal fold vibration when tightly approximated and subject to high subglottal pressure. Transition from regular vocal fold vibration to vocal instabilities is often accompanied by energy redistribution among the first few vocal fold eigenmodes, presumably due to nonlinear interaction between eigenmodes during vocal fold contact. The presence of a vocal tract may suppress such contact-related vocal instabilities, but also induce new instabilities, particularly for less constricted vocal fold conditions, almost doubling the number of vocal fold conditions producing irregular vibration.

Vocal fold contact patterns based on normal modes of vibration

The fluid-structure interaction and energy transfer from respiratory airflow to self-sustained vocal fold oscillation continues to be a topic of interest in vocal fold research. Vocal fold vibration is driven by pressures on the vocal fold surface, which are determined by the shape of the glottis and the contact between vocal folds. Characterization of three-dimensional glottal shapes and contact patterns can lead to increased understanding of normal and abnormal physiology of the voice, as well as to development of improved vocal fold models, but a large inventory of shapes has not been directly studied previously. This study aimed to take an initial step toward characterizing vocal fold contact patterns systematically. Vocal fold motion and contact was modeled based on normal mode vibration, as it has been shown that vocal fold vibration can be almost entirely described by only the few lowest order vibrational modes. Symmetric and asymmetric combinations of the four lowest normal modes of vibration were superimposed on left and right vocal fold medial surfaces, for each of three prephonatory glottal configurations, according to a surface wave approach. Contact patterns were generated from the interaction of modal shapes at 16 normalized phases during the vibratory cycle. Eight major contact patterns were identified and characterized by the shape of the flow channel, with the following descriptors assigned: convergent, divergent, convergent-divergent, uniform, split, merged, island, and multichannel. Each of the contact patterns and its variation are described, and future work and applications are discussed.

Effect of vocal fold stiffness on voice production in a three-dimensional body-cover phonation model

Although stiffness conditions in the multi-layered vocal folds are generally considered to have a large impact on voice production, their specific role in controlling vocal fold vibration and voice acoustics is unclear. Using a three-dimensional body-cover continuum model of phonation, this study shows that changes in vocal fold stiffness have a large effect on F0 and the means and amplitudes of the glottal area and flow rate. However, varying vocal fold stiffness, particularly along the anterior-posterior direction, has a much smaller effect on the closed quotient, vertical phase difference, and the spectral shape of the output acoustics, which are more effectively controlled by changes in the vertical thickness of the medial surface. These results suggest that although changes in vocal fold stiffness are often correlated with production of different voice types, there is no direct cause-effect relation between vocal fold stiffness and voice types, and the correlation may simply result from the fact that both vocal fold stiffness and geometry are regulated by the same set of laryngeal muscles. These results also suggest the possibility of developing reduced-order models of phonation in which the vocal fold is simplified to a one-layer structure.

Modeling the Pathophysiology of Phonotraumatic Vocal Hyperfunction With a Triangular Glottal Model of the Vocal Folds

PURPOSE

Our goal was to test prevailing assumptions about the underlying biomechanical and aeroacoustic mechanisms associated with phonotraumatic lesions of the vocal folds using a numerical lumped-element model of voice production.

METHOD

A numerical model with a triangular glottis, posterior glottal opening, and arytenoid posturing is proposed. Normal voice is altered by introducing various prephonatory configurations. Potential compensatory mechanisms (increased subglottal pressure, muscle activation, and supraglottal constriction) are adjusted to restore an acoustic target output through a control loop that mimics a simplified version of auditory feedback.

RESULTS

The degree of incomplete glottal closure in both the membranous and posterior portions of the folds consistently leads to a reduction in sound pressure level, fundamental frequency, harmonic richness, and harmonics-to-noise ratio. The compensatory mechanisms lead to significantly increased vocal-fold collision forces, maximum flow-declination rate, and amplitude of unsteady flow, without significantly altering the acoustic output.

CONCLUSION

Modeling provided potentially important insights into the pathophysiology of phonotraumatic vocal hyperfunction by demonstrating that compensatory mechanisms can counteract deterioration in the voice acoustic signal due to incomplete glottal closure, but this also leads to high vocal-fold collision forces (reflected in aerodynamic measures), which significantly increases the risk of developing phonotrauma.

Comparison of a fiber-gel finite element model of vocal fold vibration to a transversely isotropic stiffness model

A fiber-gel vocal fold model is compared to a transversely isotropic stiffness model in terms of normal mode vibration. The fiber-gel finite element model (FG-FEM) consists of a series of gel slices, each with a two-dimensional finite element mesh, in a plane transverse to the tissue fibers. The gel slices are coupled with fibers under tension in the anterior-posterior dimension. No vibrational displacement in the fiber-length direction is allowed, resulting in a plane strain state. This is consistent with the assumption of transverse displacement of a simple string, offering a wide range of natural frequencies (well into the kHz region) with variable tension. For low frequencies, the results compare favorably with the natural frequencies of a transversely isotropic elastic stiffness model (TISM) in which the shear modulus in the longitudinal plane is used to approximate the effect of fiber tension. For high frequencies, however, the natural frequencies do not approach the string mode frequencies unless plane strain is imposed on the TISM model. The simplifying assumption of plane strain, as well as the use of analytical closed-form shape functions, allow for substantial savings in computational time, which is important in clinical and exploratory applications of the FG-FEM model.

Computational Modeling of Fluid-Structure-Acoustics Interaction during Voice Production

The paper presented a three-dimensional, first-principle based fluid-structure-acoustics interaction computer model of voice production, which employed a more realistic human laryngeal and vocal tract geometries. Self-sustained vibrations, important convergent-divergent vibration pattern of the vocal folds, and entrainment of the two dominant vibratory modes were captured. Voice quality-associated parameters including the frequency, open quotient, skewness quotient, and flow rate of the glottal flow waveform were found to be well within the normal physiological ranges. The analogy between the vocal tract and a quarter-wave resonator was demonstrated. The acoustic perturbed flux and pressure inside the glottis were found to be at the same order with their incompressible counterparts, suggesting strong source-filter interactions during voice production. Such high fidelity computational model will be useful for investigating a variety of pathological conditions that involve complex vibrations, such as vocal fold paralysis, vocal nodules, and vocal polyps. The model is also an important step toward a patient-specific surgical planning tool that can serve as a no-risk trial and error platform for different procedures, such as injection of biomaterials and thyroplastic medialization.

Evaluation of an asymmetric anterior glottic web in an excised canine larynx model

The main objective of the study is to model asymmetry within anterior glottic webs in excised larynges using sutures and apply aerodynamic and acoustic analyses. Anterior glottic webs (AGW) were modeled in eight excised larynges using sutures secured at the level of the glottis to mimic the scar tissue of the web. Each of the eight larynges were tested under three different pressure increments for each of the three models of AGW: symmetric, vertically asymmetric, and laterally asymmetric. Phonation threshold pressure (PTP) and flow (PTF) differed significantly across AGW conditions (p = 0.006 and p = 0.005, respectively). Additionally, vocal efficiency was significantly different among conditions (p = 0.005) as well as significantly lower in the asymmetric groups (p = 0.015 and p = 0.007). Perturbation measures were not significantly different across conditions. Correlation dimension (D2) was significantly different at PTP, 1.25 × PTP, and 1.5 × PTP (p = 0.003, p = 0.010, and p < 0.001, respectively) as well as significantly higher in the asymmetric groups at each pressure increment. The increased PTP, PTF, and D2 values as well as decreased vocal efficiency among the asymmetric conditions indicates a significant decrease in vocal function, and thus represents that asymmetries could be a contributing factor to the pathological symptoms associated with glottic webs.

Mechanics of human voice production and control

As the primary means of communication, voice plays an important role in daily life. Voice also conveys personal information such as social status, personal traits, and the emotional state of the speaker. Mechanically, voice production involves complex fluid-structure interaction within the glottis and its control by laryngeal muscle activation. An important goal of voice research is to establish a causal theory linking voice physiology and biomechanics to how speakers use and control voice to communicate meaning and personal information. Establishing such a causal theory has important implications for clinical voice management, voice training, and many speech technology applications. This paper provides a review of voice physiology and biomechanics, the physics of vocal fold vibration and sound production, and laryngeal muscular control of the fundamental frequency of voice, vocal intensity, and voice quality. Current efforts to develop mechanical and computational models of voice production are also critically reviewed. Finally, issues and future challenges in developing a causal theory of voice production and perception are discussed.

Characterization of the Medial Surface of the Vocal Folds

A method is developed for the quantification of the medial surface of the vocal folds in excised larynges. Lead molds were constructed from the glottal airway of a canine larynx for 3 distinct glottal configurations corresponding to “pressed” folds, just barely adducted folds, and 1-mm-abducted folds as measured between the vocal processes. With a high-resolution laser striping system, the 3-dimensional molds were digitally scanned. Low-order polynomials were fitted to the data, and goodness-of-fit statistics were reported. For all glottal configurations, a linear variation (flat surface) approximated the data with a coefficient of determination of 90%. This coefficient increased to roughly 95% when a quadratic variation (curvature) was included along the vertical dimension. If more than the top 5 mm or so of the folds was included (the portion usually corresponding to vibration), a cubic variation along the vertical dimension was necessary to explain a change in concavity at the conus elasticus. These findings suggest the utility of a model based on a convergence coefficient and a bulging coefficient. For all glottal configurations, the convergence coefficients and bulging coefficients can be computed. Because pre-phonatory conditions have a profound influence on vocal fold vibration and on the quality of phonation, such shaping parameters are highly significant. With the viability of this method substantiated, it is envisioned that future studies will characterize greater quantities of glottal shapes, including those of human vocal folds.

Influence of Vocal Fold Scarring on Phonation: Predictions from a Finite Element Model

Objectives:

A systematic study of the influence of vocal fold scarring on phonation was conducted. In particular, phonatory variables such as fundamental frequency, oral acoustic intensity, and phonation threshold pressure (PTP) were investigated as a function of the size and position of the laryngeal scar.

Methods:

By means of a finite element model of vocal fold vibration, the viscoelastic properties of both normal and scarred vocal fold mucosae were simulated on the basis of recent rheological data obtained from rabbit and canine models.

Results:

The study showed that an increase in the viscoelasticity of the scarred mucosa resulted in an increase in fundamental frequency, an increase in PTP, and a decrease in oral acoustic intensity. With regard to positioning of the scar, the PTP increased most significantly when the scar was within ±2 mm of the superior-medial junction of the vocal folds.

Conclusions:

The systematic data obtained in this investigation agree with the general clinical experience. In the future, these findings may be further validated on human subjects as newly emerging technologies such as linear skin rheometry and optical coherence tomography allow the histologic and viscoelastic properties of the normal and scarred vocal fold mucosae to be measured in the clinic.

The mechanisms of subharmonic tone generation in a synthetic larynx model

The sound spectra obtained in a synthetic larynx exhibited subharmonic tones that are characteristic for diplophonia. Although the generation of subharmonics is commonly associated with asymmetrically oscillating vocal folds, the synthetic elastic vocal folds showed symmetrical oscillations. The amplitudes of the subharmonics decreased with an increasing lateral diameter of the supraglottal channel, which indicates a strong dependence of the supraglottal boundary conditions. Investigations of the supraglottal flow field revealed small cycle-to-cycle variations of the static pressure in the region of the pulsatile glottal jet as the origin of the first subharmonic tone. It is located at half the fundamental frequency of the vocal fold oscillation. A principle component analysis of the supraglottal flow field with the fully developed glottal jet revealed a large recirculation area in the second spatial eigenvector which deflected the glottal jet slightly in a perpendicular direction of the jet axis. The rotation direction of the recirculation area changed with different oscillation cycles between clockwise and counterclockwise. As both directions were uniformly distributed across all acquired oscillation cycles, a cycle-wise change can be assumed. It is concluded that acoustic subharmonics are generated by small fluctuations of the glottal jet location favored by small lateral diameters of the supraglottal channel.

Non-stationary Bayesian estimation of parameters from a body cover model of the vocal folds

The evolution of reduced-order vocal fold models into clinically useful tools for subject-specific diagnosis and treatment hinges upon successfully and accurately representing an individual patient in the modeling framework. This, in turn, requires inference of model parameters from clinical measurements in order to tune a model to the given individual. Bayesian analysis is a powerful tool for estimating model parameter probabilities based upon a set of observed data. In this work, a Bayesian particle filter sampling technique capable of estimating time-varying model parameters, as occur in complex vocal gestures, is introduced. The technique is compared with time-invariant Bayesian estimation and least squares methods for determining both stationary and non-stationary parameters. The current technique accurately estimates the time-varying unknown model parameter and maintains tight credibility bounds. The credibility bounds are particularly relevant from a clinical perspective, as they provide insight into the confidence a clinician should have in the model predictions.

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.

The postnatal ontogeny of the sexually dimorphic vocal apparatus in goitred gazelles (Gazella subgutturosa)

This study quantitatively documents the progressive development of sexual dimorphism of the vocal organs along the ontogeny of the goitred gazelle (Gazella subgutturosa). The major, male-specific secondary sexual features, of vocal anatomy in goitred gazelle are an enlarged larynx and a marked laryngeal descent. These features appear to have evolved by sexual selection and may serve as a model for similar events in male humans. Sexual dimorphism of larynx size and larynx position in adult goitred gazelles is more pronounced than in humans, whereas the vocal anatomy of neonate goitred gazelles does not differ between sexes. This study examines the vocal anatomy of 19 (11 male, 8 female) goitred gazelle specimens across three age-classes, that is, neonates, subadults and mature adults. The postnatal ontogenetic development of the vocal organs up to their respective end states takes considerably longer in males than in females. Both sexes share the same features of vocal morphology but differences emerge in the course of ontogeny, ultimately resulting in the pronounced sexual dimorphism of the vocal apparatus in adults. The main differences comprise larynx size, vocal fold length, vocal tract length, and mobility of the larynx. The resilience of the thyrohyoid ligament and the pharynx, including the soft palate, and the length changes during contraction and relaxation of the extrinsic laryngeal muscles play a decisive role in the mobility of the larynx in both sexes but to substantially different degrees in adult females and males. Goitred gazelles are born with an undescended larynx and, therefore, larynx descent has to develop in the course of ontogeny. This might result from a trade-off between natural selection and sexual selection requiring a temporal separation of different laryngeal functions at birth and shortly after from those later in life. J. Morphol. 277:826-844, 2016. © 2016 Wiley Periodicals, Inc.

Regulation of glottal closure and airflow in a three-dimensional phonation model: implications for vocal intensity control

Maintaining a small glottal opening across a large range of voice conditions is critical to normal voice production. This study investigated the effectiveness of vocal fold approximation and stiffening in regulating glottal opening and airflow during phonation, using a three-dimensional numerical model of phonation. The results showed that with increasing subglottal pressure the vocal folds were gradually pushed open, leading to increased mean glottal opening and flow rate. A small glottal opening and a mean glottal flow rate typical of human phonation can be maintained against increasing subglottal pressure by proportionally increasing the degree of vocal fold approximation for low to medium subglottal pressures and vocal fold stiffening at high subglottal pressures. Although sound intensity was primarily determined by the subglottal pressure, the results suggest that, to maintain small glottal opening as the sound intensity increases, one has to simultaneously tighten vocal fold approximation and/or stiffen the vocal folds, resulting in increased glottal resistance, vocal efficiency, and fundamental frequency.

Validation of a flow-structure-interaction computation model of phonation

Computational models of vocal fold (VF) vibration are becoming increasingly sophisticated, their utility currently transiting from exploratory research to predictive research. However, validation of such models has remained largely qualitative, raising questions over their applicability to interpret clinical situations. In this paper, a computational model with a segregated implementation is detailed. The model is used to predict the fluid-structure interaction (FSI) observed in a physical replica of the VFs when it is excited by airflow. Detailed quantitative comparisons are provided between the computational model and the corresponding experiment. First, the flow model is separately validated in the absence of VF motion. Then, in the presence of flow-induced VF motion, comparisons are made of the flow pressure on the VF walls and of the resulting VF displacements. Self-similarity of spatial distributions of flow pressure and VF displacements is highlighted. The self-similarity leads to normalized pressure and displacement profiles. It is shown that by using linear superposition of average and fluctuation components of normalized computed displacements, it is possible to determine displacements in the physical VF replica over a range of VF vibration conditions. Mechanical stresses in the VF interior are related to the VF displacements, thereby the computational model can also determine VF stresses over a range of phonation conditions.

Complex vibratory patterns in an elephant larynx

Elephants' low-frequency vocalizations are produced by flow-induced self-sustaining oscillations of laryngeal tissue. To date, little is known in detail about the vibratory phenomena in the elephant larynx. Here, we provide a first descriptive report of the complex oscillatory features found in the excised larynx of a 25 year old female African elephant (Loxodonta africana), the largest animal sound generator ever studied experimentally. Sound production was documented with high-speed video, acoustic measurements, air flow and sound pressure level recordings. The anatomy of the larynx was studied with computed tomography (CT) and dissections. Elephant CT vocal anatomy data were further compared with the anatomy of an adult human male. We observed numerous unusual phenomena, not typically reported in human vocal fold vibrations. Phase delays along both the inferior-superior and anterior-posterior (A-P) dimension were commonly observed, as well as transverse travelling wave patterns along the A-P dimension, previously not documented in the literature. Acoustic energy was mainly created during the instant of glottal opening. The vestibular folds, when adducted, participated in tissue vibration, effectively increasing the generated sound pressure level by 12 dB. The complexity of the observed phenomena is partly attributed to the distinct laryngeal anatomy of the elephant larynx, which is not simply a large-scale version of its human counterpart. Travelling waves may be facilitated by low fundamental frequencies and increased vocal fold tension. A travelling wave model is proposed, to account for three types of phenomena: A-P travelling waves, 'conventional' standing wave patterns, and irregular vocal fold vibration.

Quantifying spatiotemporal properties of vocal fold dynamics based on a multiscale analysis of phonovibrograms

In order to objectively assess the laryngeal vibratory behavior, endoscopic high-speed cameras capture several thousand frames per second of the vocal folds during phonation. However, judging all inherent clinically relevant features is a challenging task and requires well-founded expert knowledge. In this study, an automated wavelet-based analysis of laryngeal high-speed videos based on phonovibrograms is presented. The phonovibrogram is an image representation of the spatiotemporal pattern of vocal fold vibration and constitutes the basis for a computer-based analysis of laryngeal dynamics. The features extracted from the wavelet transform are shown to be closely related to a basic set of video-based measurements categorized by the European Laryngological Society for a subjective assessment of pathologic voices. The wavelet-based analysis further offers information about irregularity and lateral asymmetry and asynchrony. It is demonstrated in healthy and pathologic subjects as well as for a surgical group that was examined before and after the removal of a vocal fold polyp. The features were found to not only classify glottal closure characteristics but also quantify the impact of pathologies on the vibratory behavior. The interpretability and the discriminative power of the proposed feature set show promising relevance for a computer-assisted diagnosis and classification of voice disorders.

Glottal opening and closing events investigated by electroglottography and super-high-speed video recordings

Previous research has suggested that the peaks in the first derivative (dEGG) of the electroglottographic (EGG) signal are good approximate indicators of the events of glottal opening and closing. These findings were based on high-speed video (HSV) recordings with frame rates 10 times lower than the sampling frequencies of the corresponding EGG data. The present study attempts to corroborate these previous findings, utilizing super-HSV recordings. The HSV and EGG recordings (sampled at 27 and 44 kHz, respectively) of an excised canine larynx phonation were synchronized by an external TTL signal to within 0.037 ms. Data were analyzed by means of glottovibrograms, digital kymograms, the glottal area waveform and the vocal fold contact length (VFCL), a new parameter representing the time-varying degree of ‘zippering’ closure along the anterior–posterior (A–P) glottal axis. The temporal offsets between glottal events (depicted in the HSV recordings) and dEGG peaks in the opening and closing phase of glottal vibration ranged from 0.02 to 0.61 ms, amounting to 0.24–10.88% of the respective glottal cycle durations. All dEGG double peaks coincided with vibratory A–P phase differences. In two out of the three analyzed video sequences, peaks in the first derivative of the VFCL coincided with dEGG peaks, again co-occurring with A–P phase differences. The findings suggest that dEGG peaks do not always coincide with the events of glottal closure and initial opening. Vocal fold contacting and de-contacting do not occur at infinitesimally small instants of time, but extend over a certain interval, particularly under the influence of A–P phase differences.

Subject-specific computational modeling of human phonation

A direct numerical simulation of flow-structure interaction is carried out in a subject-specific larynx model to study human phonation under physiological conditions. The simulation results compare well to the established human data. The resulting glottal flow and waveform are found to be within the normal physiological ranges. The effects of realistic geometry on the vocal fold dynamics and the glottal flow are extensively examined. It is found that the asymmetric anterior-posterior laryngeal configuration produces strong anterior-posterior asymmetries in both vocal fold vibration and glottal flow which has not been captured in the simplified models. It needs to be pointed out that the observations from the current numerical simulation are only valid for the flow conditions investigated. The limitations of the study are also discussed.

The influence of material anisotropy on vibration at onset in a three-dimensional vocal fold model

Although vocal folds are known to be anisotropic, the influence of material anisotropy on vocal fold vibration remains largely unknown. Using a linear stability analysis, phonation onset characteristics were investigated in a three-dimensional anisotropic vocal fold model. The results showed that isotropic models had a tendency to vibrate in a swing-like motion, with vibration primarily along the superior-inferior direction. Anterior-posterior (AP) out-of-phase motion was also observed and large vocal fold vibration was confined to the middle third region along the AP length. In contrast, increasing anisotropy or increasing AP-transverse stiffness ratio suppressed this swing-like motion and allowed the vocal fold to vibrate in a more wave-like motion with strong medial-lateral motion over the entire medial surface. Increasing anisotropy also suppressed the AP out-of-phase motion, allowing the vocal fold to vibrate in phase along the entire AP length. Results also showed that such improvement in vibration pattern was the most effective with large anisotropy in the cover layer alone. These numerical predictions were consistent with previous experimental observations using self-oscillating physical models. It was further hypothesized that these differences may facilitate complete glottal closure in finite-amplitude vibration of anisotropic models as observed in recent experiments.