Computational Models of Laryngeal Aerodynamics: Potentials and Numerical Costs

Vocal Fold Kinematics and Convergent-Divergent Oscillatory Glottis: Basic Insights Using Mucosal Wave Modeling and Synthetic Kymograms

PURPOSE

Owing to mucosal waves, the oscillatory glottis is ideally expected to be convergent during opening and divergent during closing. However, this does not necessarily hold for voice disorders. Here, we pave the way for recognizing COnvergent-DIvergent (CODI) waveforms quantitatively and study the kinematic conditions in which they occur.

METHOD

We simulated 3,125 laryngoscopic glottal waveforms using a kinematic vocal fold (VF) model and synthetic kymograms. We independently varied the oscillatory amplitudes of the upper and lower VF margins, AU and AL (0.1 to 1.1 mm), vertical phase difference (VPD; 0° to 125°), glottal halfwidth HW (-0.05 to 1.2 mm), and prephonatory glottal convergence angle ψCVG (-15° to 35°) to simulate normal and disordered conditions. We introduced the upper and lower margin quotients, QU and QL, quantifying the proportion of time when the upper margin is at the glottal edge during the opening, and when the lower margin is at the glottal edge during the closing, respectively. A CODI waveform was defined as the case when QU = QL = 1.

RESULTS

The likelihood of obtaining the CODI waveform was highest when AU and AL were similar, ψCVG was close to 0, HW was below 0.45 mm, and VPD was larger than 50°. In 88% of the simulated cases, the waveforms did not fulfill the CODI conditions. In these cases, either the lower margin was hidden during some portion of the closing phase or the upper margin was not at the glottal edge during some portion of the opening phase.

CONCLUSION

The study provides the basis for a better understanding of the variability of glottal waveforms and the appearance of mucosal waves related to VF kinematics.

Pressure Distributions in Glottal Geometries With Multichannel Airflows

OBJECTIVES

Computer simulation of self-sustained oscillation of the vocal folds has been successful with application of simple Bernoulli-like driving pressures. As voice simulation is now applied to asymmetric vibration with complex mode structures that yield partial vocal fold contact, the driving pressures need refinement.

STUDY DESIGN AND METHODOLOGY

Two independent approaches were used to obtain pressure distributions. The first was a high-fidelity immersed-boundary method computation and the second was a series of pressure tap measurements on scaled-up physical models. Glottal geometries were based on normal surface modes of vibration. Samples are chosen from a large inventory of measured and calculated profiles.

RESULTS

Pressure distributions show the complexity that can exist in the driving forces on vocal fold surfaces. Qualitative similarity between computation and measurement was established for a variety of contact patterns, showing diverse pressure gradients in multiple directions.

CONCLUSIONS

Simplified Bernoulli approaches to glottal pressure distributions are defensible when a single flow channel is preserved in vocal fold oscillation. However, when there are contact islands that produce confluence or difluence of multiple airflow channels, the pressure gradients vary profoundly. Small quantitative differences were observed between measurement and calculation, primarily due to spatial sampling.

Using a vertical three-mass computational model of the vocal folds to match human phonation of three adult males

Computer models of phonation are used to study various parameters that are difficult to control, measure, and observe in human subjects. Imitating human phonation by varying the prephonatory conditions of computer models offers insight into the variations that occur across human phonatory production. In the present study, a vertical three-mass computer model of phonation [Perrine, Scherer, Fulcher, and Zhai (2020). J. Acoust. Soc. Am. 147, 1727-1737], driven by empirical pressures from a physical model of the vocal folds (model M5), with a vocal tract following the design of Ishizaka and Flanagan [(1972). Bell Sys. Tech. J. 51, 1233-1268] was used to match prolonged vowels produced by three male subjects using various pitch and loudness levels. The prephonatory conditions of tissue mass and tension, subglottal pressure, glottal diameter and angle, posterior glottal gap, false vocal fold gap, and vocal tract cross-sectional areas were varied in the model to match the model output with the fundamental frequency, alternating current airflow, direct current airflow, skewing quotient, open quotient, maximum flow negative derivative, and the first three formant frequencies from the human production. Parameters were matched between the model and human subjects with an average overall percent mismatch of 4.40% (standard deviation = 6.75%), suggesting a reasonable ability of the simple low dimensional model to mimic these variables.

Comparison of Aerosol Emissions during Specific Speech Tasks

OBJECTIVES/HYPOTHESIS

Recent investigations into the behavior of aerosolized emissions from the oral cavity have shown that particulate emissions do indeed occur during speech. To date, there is little information about the relative contribution of different speech sounds in producing particle emissions in a free field. This study compares airborne aerosol generation in participants producing isolated speech sounds: fricative consonants, plosive consonants, and vowel sounds.

STUDY DESIGN

Prospective, reversal experimental design, where each participant served as their own control and all participants were exposed to all stimuli.

METHODS

While participants produced isolated speech tasks, a planar beam of laser light, a high-speed camera, and image software calculated the number of particulates detected over time. This study compared airborne aerosols emitted by human participants at a distance of 2.54 cm between the laser sheet and the mouth.

RESULTS

Statistically significant increases in particulate count over ambient dust distribution for all speech sounds. When collapsed across loudness levels, emitted particles in vowel sounds were statistically greater than consonants, suggesting that mouth opening, as opposed to the place of vocal tract constriction or manner of sound production, might also be influential in the degree to which particulates become aerosolized during speech.

CONCLUSIONS

The results of this research will inform boundary conditions for computational models of aerosolized particulates during speech.

Error detection and filtering of incompressible flow simulations for aeroacoustic predictions of human voice

The presented filtering technique is proposed to detect errors and correct outliers inside the acoustic sources, respectively, the first time derivative of the incompressible pressure obtained from large eddy simulations with prescribed vocal fold motion using overlay mesh methods. Regarding the perturbed convective wave equation, the time derivative of the incompressible pressure is the primary sound source in the human phonation process. However, the incompressible pressure can be erroneous and have outliers when fulfilling the divergence-free constraint of the velocity field. This error is primarily occurring for non-conserving prescribed vocal fold motions. Therefore, the method based on a continuous stationary random process was designed to detect rare events in the time derivative of the pressure. The detected events are then localized and treated by a defined window function to increase their probability. As a consequence, the data quality of the non-linearly filtered data is enhanced significantly. Furthermore, the proposed method can also be used to assess convergence of the aeroacoustic source terms, and detect regions and time intervals, which show a non-converging behavior by an impulse-like structure.

Effects of Sulcus Vocalis Depth on Phonation in Three-Dimensional Fluid-Structure Interaction Laryngeal Models

Sulcus vocalis is an indentation parallel to the edge of vocal fold, which may extend into the cover and ligament layer of the vocal fold or deeper. The effects of sulcus vocalis depth d on phonation and the vocal cord vibrations are investigated in this study. The three-dimensional laryngeal models were established for healthy vocal folds (0 mm) and different types of sulcus vocalis with the typical depth of 1 mm, 2 mm, and 3 mm. These models with fluid-structure interaction (FSI) are computed numerically by sequential coupling method, which includes an immersed boundary method (IBM) for modelling the glottal airflow, a finite-element method (FEM) for modelling vocal fold tissue. The results show that a deeper sulcus vocalis in the cover layer decreases the vibrating frequency of vocal folds and expands the prephonatory glottal half-width which increases the phonation threshold pressure. The larger sulcus vocalis depth makes vocal folds difficult to vibrate and phonate. The effects of sulcus vocalis depth suggest that the feature such as phonation threshold pressure could assist in the detection of healthy vocal folds and different types of sulcus vocalis.

3D-FV-FE Aeroacoustic Larynx Model for Investigation of Functional Based Voice Disorders

For the clinical analysis of underlying mechanisms of voice disorders, we developed a numerical aeroacoustic larynx model, called simVoice, that mimics commonly observed functional laryngeal disorders as glottal insufficiency and vibrational left-right asymmetries. The model is a combination of the Finite Volume (FV) CFD solver Star-CCM+ and the Finite Element (FE) aeroacoustic solver CFS++. simVoice models turbulence using Large Eddy Simulations (LES) and the acoustic wave propagation with the perturbed convective wave equation (PCWE). Its geometry corresponds to a simplified larynx and a vocal tract model representing the vowel /a/. The oscillations of the vocal folds are externally driven. In total, 10 configurations with different degrees of functional-based disorders were simulated and analyzed. The energy transfer between the glottal airflow and the vocal folds decreases with an increasing glottal insufficiency and potentially reflects the higher effort during speech for patients being concerned. This loss of energy transfer may also have an essential influence on the quality of the sound signal as expressed by decreasing sound pressure level (SPL), Cepstral Peak Prominence (CPP), and Vocal Efficiency (VE). Asymmetry in the vocal fold oscillations also reduces the quality of the sound signal. However, simVoice confirmed previous clinical and experimental observations that a high level of glottal insufficiency worsens the acoustic signal quality more than oscillatory left-right asymmetry. Both symptoms in combination will further reduce the quality of the sound signal. In summary, simVoice allows for detailed analysis of the origins of disordered voice production and hence fosters the further understanding of laryngeal physiology, including occurring dependencies. A current walltime of 10 h/cycle is, with a prospective increase in computing power, auspicious for a future clinical use of simVoice.

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.

A one-dimensional flow model enhanced by machine learning for simulation of vocal fold vibration

A one-dimensional (1D) unsteady and viscous flow model that is derived from the momentum and mass conservation equations is described, and to enhance this physics-based model, a machine learning approach is used to determine the unknown modeling parameters. Specifically, an idealized larynx model is constructed and ten cases of three-dimensional (3D) fluid-structure interaction (FSI) simulations are performed. The flow data are then extracted to train the 1D flow model using a sparse identification approach for nonlinear dynamical systems. As a result of training, we obtain the analytical expressions for the entrance effect and pressure loss in the glottis, which are then incorporated in the flow model to conveniently handle different glottal shapes due to vocal fold vibration. We apply the enhanced 1D flow model in the FSI simulation of both idealized vocal fold geometries and subject-specific anatomical geometries reconstructed from the magnetic resonance imaging images of rabbits' larynges. The 1D flow model is evaluated in both of these setups and shown to have robust performance. Therefore, it provides a fast simulation tool that is superior to the previous 1D models.

Hybrid aeroacoustic approach for the efficient numerical simulation of human phonation

A hybrid aeroacoustic approach was developed for the efficient numerical computation of human phonation. In the first step, an incompressible flow simulation on a three-dimensional (3 D) computational grid, which is capable of resolving all relevant turbulent scales, is performed using STARCCM+ and finite volume method. In the second step, the acoustic source terms on the flow grid are computed and a conservative interpolation to the acoustic grid is performed. Finally, the perturbed convective wave equation is solved to obtain the acoustic field in 3 D with the finite element solver CFS++. Thereby, the conservative transformation of the acoustic sources from the flow grid to the acoustic grid is a key step to allow coarse acoustic grids without reducing accuracy. For this transformation, two different interpolation strategies are compared and grid convergence is assessed. Overall, 16 simulation setups are compared. The initial (267 000 degrees of freedom) and the optimized (21 265 degrees of freedom) simulation setup were validated by measurements of a synthetic larynx model. To conclude, the total computational time of the acoustic simulation is reduced by 95% compared to the initial simulation setup without a significant reduction of accuracy, being 7%, in the frequency range of interest.

Computational Fluid Dynamics Analysis of Surgical Approaches to Bilateral Vocal Fold Immobility

OBJECTIVES

Bilateral vocal fold immobility (BVFI) is a rare and life-threatening condition in which both vocal folds are fixed, resulting in airway obstruction associated with life-threatening respiratory compromise. Treatment of BVFI is largely surgical and remains an unsatisfactory compromise between voice, breathing, and swallowing. No comparisons between currently employed techniques currently exist. We sought to employ computational fluid dynamics (CFD) modeling to delineate the optimal surgical approach for BVFI.

METHODS

Utilizing clinical computed tomography of BVFI subjects, coupled with image analytics employing CFD models and subject pulmonary function data, we compared the airflow features in the baseline pathologic states and changes seen between endoscopic cordotomy, endoscopic suture lateralization, and posterior cricoid expansion.

RESULTS

CFD modeling demonstrated that the greatest airflow velocity occurs through the posterior glottis on inspiration and anterior glottis on expiration in both the normal condition and in BVFI. Glottic airflow velocity and resistance were significantly higher in the BVFI condition compared to normal. Geometric indices (cross-sectional area of airway) were lower in posterior cricoid expansion surgery when compared to alternate surgical approaches. CFD measures (airflow velocity and resistance) improved with all surgical approaches but were superior with posterior cricoid expansion.

CONCLUSION

CFD modeling can provide discrete, quantitative assessment of the airflow through the laryngeal inlet, and offers insights into the pathophysiology and changes that occur after surgery for BVFI.

LEVEL OF EVIDENCE

NA. Laryngoscope, 130:E57-E64, 2020.

Laryngeal Pressure Estimation With a Recurrent Neural Network

Quantifying the physical parameters of voice production is essential for understanding the process of phonation and can aid in voice research and diagnosis. As an alternative to invasive measurements, they can be estimated by formulating an inverse problem using a numerical forward model. However, high-fidelity numerical models are often computationally too expensive for this. This paper presents a novel approach to train a long short-term memory network to estimate the subglottal pressure in the larynx at massively reduced computational cost using solely synthetic training data. We train the network on synthetic data from a numerical two-mass model and validate it on experimental data from 288 high-speed ex vivo video recordings of porcine vocal folds from a previous study. The training requires significantly fewer model evaluations compared with the previous optimization approach. On the test set, we maintain a comparable performance of 21.2% versus previous 17.7% mean absolute percentage error in estimating the subglottal pressure. The evaluation of one sample requires a vanishingly small amount of computation time. The presented approach is able to maintain estimation accuracy of the subglottal pressure at significantly reduced computational cost. The methodology is likely transferable to estimate other parameters and training with other numerical models. This improvement should allow the adoption of more sophisticated, high-fidelity numerical models of the larynx. The vast speedup is a critical step to enable a future clinical application and knowledge of parameters such as the subglottal pressure will aid in diagnosis and treatment selection.