The effect of vocal fold vertical stiffness variation on voice production

Sensitivity of Phonation Onset Pressure to Vocal Fold Stiffness Distribution

Phonation onset is characterized by the unstable growth of vocal fold (VF) vibrations that ultimately results in self-sustained oscillation and the production of modal voice. Motivated by histological studies, much research has focused on the role of the layered structure of the vocal folds in influencing phonation onset, wherein the outer "cover" layer is relatively soft and the inner "body" layer is relatively stiff. Recent research, however, suggests that the body-cover (BC) structure over-simplifies actual stiffness distributions by neglecting important spatial variations, such as inferior-superior (IS) and anterior-posterior gradients and smooth transitions in stiffness from one histological layer to another. Herein, we explore sensitivity of phonation onset to stiffness gradients and smoothness. By assuming no a priori stiffness distribution and considering a second-order Taylor series sensitivity analysis of phonation onset pressure with respect to stiffness, we find two general smooth stiffness distributions most strongly influence onset pressure: a smooth stiffness containing aspects of BC differences and IS gradients in the cover, which plays a role in minimizing onset pressure, and uniform increases in stiffness, which raise onset pressure and frequency. While the smooth stiffness change contains aspects qualitatively similar to layered BC distributions used in computational studies, smooth transitions in stiffness result in higher sensitivity of onset pressure than discrete layering. These two general stiffness distributions also provide a simple, low-dimensional, interpretation of how complex variations in VF stiffness affect onset pressure, enabling refined exploration of the effects of stiffness distributions on phonation onset.

Three-Dimensional Printing of Ultrasoft Silicone with a Functional Stiffness Gradient

A methodology for three-dimensionally printing ultrasoft silicone with a functional stiffness gradient is presented. Ultraviolet-cure silicone was deposited via two independently controlled extruders into a thixotropic, gel-like, silicone oil-based support matrix. Each extruder contained a different liquid silicone formulation. The extrusion rates were independently varied during printing such that the combined selectively deposited material contained different ratios of the two silicones, resulting in localized control of material stiffness. Tests to validate the process are reported, including tensile testing of homogeneous cubic specimens to quantify the range of material stiffness that could be printed, indentation testing of cuboid specimens to characterize printed stiffness gradients, and vibratory testing of synthetic multilayer vocal fold (VF) models to demonstrate that the method may be applied to the fabrication of biomechanical models for voice production research. The cubic specimens exhibited linear stress-strain data with tensile elasticity modulus values between 1.11 and 27.1 kPa, more than a factor of 20 in stiffness variation. The cuboid specimens exhibited material variations that were visually recognizable and quantifiable via indentation testing. The VF models withstood rigorous phonatory flow-induced vibration and exhibited vibratory characteristics comparable to those of previous models. Overall, while process refinements are needed, the results of these tests demonstrate the ability to print ultrasoft silicone with stiffness gradients.

Reconstruction of Vocal Fold Medial Surface 3D Trajectories: Effects of Neuromuscular Stimulation and Airflow

INTRODUCTION

Analysis of medial surface dynamics of the vocal folds (VF) is critical to understanding voice production and treatment of voice disorders. We analyzed VF medial surface vibratory dynamics, evaluating the effects of airflow and nerve stimulation using 3D reconstruction and empirical eigenfunctions (EEF).

STUDY DESIGN

In vivo canine hemilarynx phonation.

METHODS

An in vivo canine hemilarynx was phonated while graded stimulation of the recurrent and superior laryngeal nerves (RLN and SLN) was performed. For each phonatory condition, vibratory cycles were 3D reconstructed from tattooed landmarks on the VF medial surface at low, medium, and high airflows. Parameters describing medial surface trajectory shape were calculated, and underlying patterns were emphasized using EEFs. Fundamental frequency and smoothed cepstral peak prominence (CPPS) were calculated from acoustic data.

RESULTS

Convex-hull area of landmark trajectories increased with increasing flow and decreasing nerve activation level. Trajectory shapes observed included circular, ellipsoid, bent, and figure-eight. They were more circular on the superior and anterior VF, and more elliptical and line-like on the inferior and posterior VF. The EEFs capturing synchronal opening and closing (EEF1) and alternating convergent/divergent (EEF2) glottis shapes were mostly unaffected by flow and nerve stimulation levels. CPPS increased with higher airflow except for low RLN activation and very dominant SLN stimulation.

CONCLUSION

We analyzed VF vibration as a function of neuromuscular stimulation and airflow levels. Oscillation patterns such as figure-eight and bent trajectories were linked to high nerve activation and flow. Further studies investigating longer sections of 3D reconstructed oscillations are needed.

LEVEL OF EVIDENCE

N/A, Basic Science Laryngoscope, 134:1249-1257, 2024.

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.

Predicting 3D soft tissue dynamics from 2D imaging using physics informed neural networks

Tissue dynamics play critical roles in many physiological functions and provide important metrics for clinical diagnosis. Capturing real-time high-resolution 3D images of tissue dynamics, however, remains a challenge. This study presents a hybrid physics-informed neural network algorithm that infers 3D flow-induced tissue dynamics and other physical quantities from sparse 2D images. The algorithm combines a recurrent neural network model of soft tissue with a differentiable fluid solver, leveraging prior knowledge in solid mechanics to project the governing equation on a discrete eigen space. The algorithm uses a Long-short-term memory-based recurrent encoder-decoder connected with a fully connected neural network to capture the temporal dependence of flow-structure-interaction. The effectiveness and merit of the proposed algorithm is demonstrated on synthetic data from a canine vocal fold model and experimental data from excised pigeon syringes. The results showed that the algorithm accurately reconstructs 3D vocal dynamics, aerodynamics, and acoustics from sparse 2D vibration profiles.

A Deep Learning-Based Generalized Empirical Flow Model of Glottal Flow During Normal Phonation

This paper proposes a deep learning-based generalized empirical flow model (EFM) that can provide a fast and accurate prediction of the glottal flow during normal phonation. The approach is based on the assumption that the vibration of the vocal folds can be represented by a universal kinematics equation (UKE), which is used to generate a glottal shape library. For each shape in the library, the ground truth values of the flow rate and pressure distribution are obtained from the high-fidelity Navier-Stokes (N-S) solution. A fully connected deep neural network (DNN) is then trained to build the empirical mapping between the shapes and the flow rate and pressure distributions. The obtained DNN-based EFM is coupled with a finite element method (FEM)-based solid dynamics solver for fluid-structure-interaction (FSI) simulation of phonation. The EFM is evaluated by comparing the N-S solutions in both static glottal shapes and FSI simulations. The results demonstrate a good prediction performance in accuracy and efficiency.

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.

Computational Modeling of Voice Production Using Excised Canine Larynx

A combined experimental-numerical work was conducted to comprehensively validate a subject-specific continuum model of voice production in larynx using excised canine laryngeal experiments. The computational model is a coupling of the Navier-Stokes equations for glottal flow dynamics and a finite element model of vocal fold dynamics. The numerical simulations employed a cover-body vocal fold structure with the geometry reconstructed from magnetic resonance imaging scans and the material properties determined through an optimization-based inverse process of experimental indentation measurement. The results showed that the simulations predicted key features of the dynamics observed in the experiments, including the skewing of the glottal flow waveform, mucosal wave propagation, continuous increase of the divergent angle and intraglottal swirl strength during glottal closing, and flow recirculation between glottal jet and vocal fold. The simulations also predicted the increase of the divergent angle, glottal jet speed, and intraglottal flow swirl strength with the subglottal pressure, same as in the experiments. Quantitatively, the simulations over-predicted the frequency and jet speed and under-predicted the flow rate and divergent angle for the larynx under study. The limitations of the model and their implications were discussed.

Impact of Vertical Stiffness Gradient on the Maximum Divergence Angle

INTRODUCTION

During vocal fold vibration, the medial surface of both folds forms a convergent shape during opening and a divergent shape during closing. A greater maximum divergence angle is associated with greater closing forces which will increase the closing speed of the glottis. An increased closing speed results in a greater acoustic intensity and greater vocal efficiency. Indentation testing showed that as the strain increases, the inferior aspect of the folds becomes stiffer than the superior aspect, resulting in the vertical stiffness gradient (VSG). We hypothesize that a reduction of the vertical stiffness gradient will reduce the maximum divergence angle.

METHODS

Four excised canine larynges were tested. Stress-strain curves of the superior and inferior aspects of the fold in the mid membranous plane of the baseline larynges were taken using the indentation method. Calcium hydroxylapatite (CaHA) crystals were then injected into the superior aspect of the fold. The stress-strain tests were repeated. Particle imaging velocimetry (PIV) of the intraglottal velocity fields was performed in three larynges at different subglottal pressures in the mid coronal plane for the baseline and CaHA-injected larynges.

RESULTS

CaHA injection reduced the inferior-superior stiffness gradient in all larynges. The maximal divergence angle was markedly reduced. In some cases, there was not a divergent angle.

DISCUSSION

Marked reduction of the vertical stiffness gradient significantly reduces the maximum divergence angle. Clinical implications will be discussed.

LEVEL OF EVIDENCE

NA Laryngoscope, 131:E1934-E1940, 2021.

Investigating blunt force trauma to the larynx: The role of inferior-superior vocal fold displacement on phonation

Blunt force trauma to the larynx, which may result from motor vehicle collisions, sports activities, etc., can cause significant damage, often leading to displaced fractures of the laryngeal cartilages, thereby disrupting vocal function. Current surgical interventions primarily focus on airway restoration to stabilize the patient, with restoration of vocal function usually being a secondary consideration. Due to laryngeal fracture, asymmetric vertical misalignment of the left or right vocal fold (VF) in the inferior-superior direction often occurs. This affects VF closure and can lead to a weak, breathy voice requiring increased vocal effort. It is unclear, however, how much vertical VF misalignment can be tolerated before voice quality degrades significantly. To address this need, the influence of inferior-superior VF displacement on phonation is investigated in 1.0mm increments using synthetic, self-oscillating VF models in a physiologically-representative facility. Acoustic (SPL, frequency, H1-H2, jitter, and shimmer), kinematic (amplitude and phase differences), and aerodynamic parameters (flow rate and subglottal pressure) are investigated as a function of inferior-superior vertical displacement. Significant findings include that once the inferior-superior medial length of the VF is surpassed, sustained phonation degrades precipitously, becoming severely pathological. If laryngeal reconstruction approaches can ensure VF contact is maintained during phonation (i.e., vertical displacement doesn't surpass VF medial length), improved vocal outcomes are expected.

A three-dimensional vocal fold posturing model based on muscle mechanics and magnetic resonance imaging of a canine larynx

In this work, a high-fidelity three-dimensional continuum model of the canine laryngeal framework was developed for simulating laryngeal posturing. By building each muscle and cartilage from magnetic resonance imaging (MRI), the model is highly realistic in anatomy. The muscle mechanics is modeled using the finite-element method. The model was tested by simulating vocal fold postures under systematic activations of individual as well as groups of laryngeal muscles, and it accurately predicted vocal fold posturing parameters reported from in vivo canine larynges. As a demonstration of its application, the model was then used to investigate muscle controls of arytenoid movements, medial surface morphology, and vocal fold abduction. The results show that the traditionally categorized adductor and abductor muscles can have opposite effects on vocal fold posturing, making highly complex laryngeal adjustments in speech and singing possible. These results demonstrate that a realistic comprehensive larynx model is feasible, which is a critical step toward a causal physics-based model of voice production.

A finite element study on the cause of vocal fold vertical stiffness variation

A finite element method based numerical indentation technique was used to quantify the effect of the material stiffness variation and the subglottal convergence angle of the vocal fold on the vertical stiffness difference of the medial surface. It was found that the vertical stiffness difference increased with the increasing subglottal angle, and it tended to saturate beyond a subglottal angle of about 50°. The material stiffness variation could be as important as the subglottal angle depending on the actual material properties.