Assessment of local vocal fold deformation characteristics in an in vitro static tensile test

Voice quality is strongly dependent on vocal fold dynamics, which in turn are dependent on lung pressure and vocal fold biomechanics. Numerical and physical models are often used to investigate the interactions of these different subsystems. However, the utility of numerical and physical models is limited unless appropriately validated with data from physiological models. Hence a method that enables analysis of local vocal fold deformations along the entire surface is presented. In static tensile tests, forces are applied to distinctive working points being located in cover and muscle, respectively, so that specific layer properties can be investigated. The forces are directed vertically upward and are applied along or above the vocal fold edge. The resulting deformations are analyzed using multiple perspectives and three-dimensional reconstruction. Deformation characteristics of four human vocal folds were investigated. Preliminary results showed two phases of deformation: a range with a small slope for small deformations fading into a significant nonlinear deformation trend with a high slope. An increase of tissue stiffness from posterior to anterior was detected. This trend is more significant for muscle and in the mid-anterior half of the vocal fold.     

Characterization of continuously inhomogeneous media with arbitrary thermophysical profiles using photothermal technique

A numerical method of determining depth profile of thermo-physical parameters of an inhomogeneous sample is presented. By dividing the inhomogeneous material into number of sublayers in which each single layer can be treated as homogeneous, the thermal-wave field of the material is obtained based on recurrence relations of thermophysical parameters of each divided layer. A numerical algorithm of determining the depth profile of thermophysical parameters in the continuously inhomogeneous material under excitation of arbitrary beam size has been demonstrated by a polynomial fitting process for three arbitrary generated thermophysical profiles.     

Sensitivity of vocal fold vibratory modes to their three-layer structure: implications for computational modeling of phonation

The sensitivity of the eigenmodes and eigenfrequencies of the human vocal fold to its three-layer structure is studied using finite-element modeling. The study covers a variety of three-dimensional vocal fold models ranging from an idealized, longitudinally uniform structure to a physiologically more realistic, longitudinally varying structure. Geometric parameters including the thickness of the ligament and cover layers as well as the ligament length are varied systematically. The results indicate that vocal fold vibratory modes are quite insensitive to the longitudinal variation in the thickness of the three layers as well as the variation in ligament length. However, significant overall changes in thickness of each layer can produce noticeable changes in these modes. The implications of these findings on computational modeling of phonation are discussed.     

Spatiotemporal classification of vocal fold dynamics by a multimass model comprising time-dependent parameters

A model-based approach is proposed to objectively measure and classify vocal fold vibrations by left-right asymmetries along the anterior-posterior direction, especially in the case of nonstationary phonation. For this purpose, vocal fold dynamics are recorded in real time with a digital high-speed camera during phonation of sustained vowels as well as pitch raises. The dynamics of a multimass model with time-dependent parameters are matched to vocal fold vibrations extracted at dorsal, medial, and ventral positions by an automatic optimization procedure. The block-based optimization accounts for nonstationary vibrations and compares the vocal fold and model dynamics by wavelet coefficients. The optimization is verified with synthetically generated data sets and is applied to 40 clinical high-speed recordings comprising normal and pathological voice subjects. The resulting model parameters allow an intuitive visual assessment of vocal fold instabilities within an asymmetry diagram and are applicable to an objective quantification of asymmetries.     

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

Simplified models have been used to simulate and study the flow-induced vibrations of the human vocal folds. While it is clear that the models' responses are sensitive to geometry, it is not clear how and to what extent specific geometric features influence model motion. In this study geometric features that played significant roles in governing the motion of a two-layer (body-cover), two-dimensional, finite element vocal fold model were identified. The model was defined using a flow solver based on the viscous, unsteady, Navier-Stokes equations and a solid solver that allowed for large strain and deformation. A screening-type design-of-experiments approach was used to identify the relative importance of 13 geometric parameters. Five output measures were analyzed to assess the magnitude of each geometric parameter's effect on the model's motion. The measures related to frequency, glottal width, flow rate, intraglottal angle, and intraglottal phase delay. The most significant geometric parameters were those associated with the cover--primarily the pre-phonatory intraglottal angle--as well as the body inferior angle. Some models exhibited evidence of improved model motion, including mucosal wave-like motion and alternating convergent-divergent glottal profiles, although further improvements are still needed to more closely mimic human vocal fold motion.     

Computation of physiological human vocal fold parameters by mathematical optimization of a biomechanical model

With the use of an endoscopic, high-speed camera, vocal fold dynamics may be observed clinically during phonation. However, observation and subjective judgment alone may be insufficient for clinical diagnosis and documentation of improved vocal function, especially when the laryngeal disease lacks any clear morphological presentation. In this study, biomechanical parameters of the vocal folds are computed by adjusting the corresponding parameters of a three-dimensional model until the dynamics of both systems are similar. First, a mathematical optimization method is presented. Next, model parameters (such as pressure, tension and masses) are adjusted to reproduce vocal fold dynamics, and the deduced parameters are physiologically interpreted. Various combinations of global and local optimization techniques are attempted. Evaluation of the optimization procedure is performed using 50 synthetically generated data sets. The results show sufficient reliability, including 0.07 normalized error, 96% correlation, and 91% accuracy. The technique is also demonstrated on data from human hemilarynx experiments, in which a low normalized error (0.16) and high correlation (84%) values were achieved. In the future, this technique may be applied to clinical high-speed images, yielding objective measures with which to document improved vocal function of patients with voice disorders.     

A constitutive model of the human vocal fold cover for fundamental frequency regulation

The elastic as well as time-dependent mechanical response of the vocal fold cover (epithelium and superficial layer of the lamina propria) under tension is one key variable in regulating the fundamental frequency. This study examines the hyperelastic and time-dependent tensile deformation behavior of a group of human vocal fold cover specimens (six male and five female). The primary goal is to formulate a constitutive model that could describe empirical trends in speaking fundamental frequency with reasonable confidence. The constitutive model for the tissue mechanical behavior consists of a hyperelastic equilibrium network in parallel with an inelastic, time-dependent network and is combined with the ideal string model for phonation. Results showed that hyperelastic and time-dependent parameters of the constitutive model can be related to observed age-related and gender-related differences in speaking fundamental frequency. The implications of these findings on fundamental frequency regulation are described. Limitations of the current constitutive model are discussed.     

The shear modulus of the human vocal fold in a transverse direction

The aim of this study was to measure the shear modulus of the vocal fold in a human hemilarynx, such that the data can be related to direction of applied stress and anatomical context. Dynamic spring rate data were collected using a modified linear skin rheometer using human hemilarynges, and converted to estimated shear modulus via application of a simple shear model. The measurement probe was attached to the epithelial layer of the vocal fold cover using suction. A sinusoidal force of 3g was applied to the epithelium, and the resultant displacement logged at a rate of 1kHz. Force measurement accuracy was 20microg and position measurement accuracy was 4microm. The force was applied in a transverse direction at the midmembranous point between the vocal process and the anterior commissure. The shear modulus of the three female vocal folds ranged from 814 to 1232Pa. The shear modulus of the three male vocal folds ranged from 1021 to 1796Pa. These data demonstrate that it is possible to obtain estimates for the shear modulus of the vocal fold while preserving anatomical context. The modulus values reported here are higher than those reported using parallel plate rheometry. This is to be expected as the tissue is attached to surrounding structures, and is under natural tension.     

A finite-element model of vocal-fold vibration

A finite-element model of the vocal fold is developed from basic laws of continuum mechanics to obtain the oscillatory characteristics of the vocal folds. The model is capable of accommodating inhomogeneous, anisotropic material properties and irregular geometry of the boundaries. It has provisions for asymmetry across the midplane, both from the geometric and tension point of view, which enables one to simulate certain kinds of voice disorders due to vocal-fold paralysis. It employs the measured viscoelastic properties of the vocal-fold tissues. The detailed construction of the matrix differential equations of motion is presented followed by the solution scheme. Finally, typical results are presented and validated using an eigenvalue method and a commercial finite-element package (ABAQUS).     

Preliminary Results of a New Temporary Vocal Fold Injection Material

Temporary vocal fold injection is a valuable procedure for vocal fold paralysis or paresis of uncertain permanency and as a trial augmentation to decide the value of vocal fold augmentation. A new material made from glycerin, carboxymethylcellulose, and water has recently been developed for temporary vocal fold augmentation. Eleven patients underwent vocal fold injection for the treatment of glottal incompetence with this material. The duration of effectiveness of this injection material was 2 to 3 months depending on the injection amount. This new material satisfies several requirements for an ideal temporary vocal fold injection material in terms of injectability, convenience, duration of effectiveness, and safety. The authors conclude that this new material is a good option for temporary vocal fold augmentation.     

Spatial arrangement of the structural elements ofvocal fold layers: An adjustment to the vibration process

It is well established that the multilayered structure of the vocal fold is highly adjusted to the requirements of the vibration process during phonation. There is also some partial data indicating that the spatial arrangement of each vocal fold layer corresponds to the functional requirements, and thus facilitate the phonation process. Nevertheless, all reports on the spatial arrangement of the vocal fold structures deal only with an individual element of the vocal fold histologic structure. The present study encompasses the spatial histologic analysis of all major elements of the vocal fold layers. It was demonstrated that the vocal fold epithelial cells, the connective and muscle fibers, and even the blood vessels run parallel to the vocal fold free edge, which indicates a high adjustment to the phonation requirements and the vibration process.     

Computational Simulations of Vocal Fold Vibration: Bernoulli Versus Navier–Stokes

The use of the mechanical energy (ME) equation for fluid flow, an extension of the Bernoulli equation, to predict the aerodynamic loading on a two-dimensional finite element vocal fold model is examined. Three steady, one-dimensional ME flow models, incorporating different methods of flow separation point prediction, were compared. For two models, determination of the flow separation point was based on fixed ratios of the glottal area at separation to the minimum glottal area; for the third model, the separation point determination was based on fluid mechanics boundary layer theory. Results of flow rate, separation point, and intraglottal pressure distribution were compared with those of an unsteady, two-dimensional, finite element Navier-Stokes model. Cases were considered with a rigid glottal profile as well as with a vibrating vocal fold. For small glottal widths, the three ME flow models yielded good predictions of flow rate and intraglottal pressure distribution, but poor predictions of separation location. For larger orifice widths, the ME models were poor predictors of flow rate and intraglottal pressure, but they satisfactorily predicted separation location. For the vibrating vocal fold case, all models resulted in similar predictions of mean intraglottal pressure, maximum orifice area, and vibration frequency, but vastly different predictions of separation location and maximum flow rate.     

Effect of inferior surface angle on the self-oscillation of a computational vocal fold model

Geometry of the human vocal folds strongly influences their oscillatory motion. While the effect of intraglottal geometry on phonation has been widely investigated, the study of the geometry of the inferior surface of the vocal folds has been limited. In this study the way in which the inferior vocal fold surface angle affects vocal fold vibration was explored using a two-dimensional, self-oscillating finite element vocal fold model. The geometry was parameterized to create models with five different inferior surface angles. Four of the five models exhibited self-sustained oscillations. Comparisons of model motion showed increased vertical displacement and decreased glottal width amplitude with decreasing inferior surface angle. In addition, glottal width and air flow rate waveforms changed as the inferior surface angle was varied. Structural, rather than aerodynamic, effects are shown to be the cause of the changes in model response as the inferior surface angle was varied. Supporting data including glottal pressure distribution, average intraglottal pressure, energy transfer, and flow separation point locations are discussed, and suggestions for future research are given.     

Voice production model integrating boundary-layer analysis of glottal flow and source-filter coupling

A voice production model is created in this work by considering essential aerodynamic and acoustic phenomena in human voice production. A precise flow analysis is performed based on a boundary-layer approximation and the viscous-inviscid interaction between the boundary layer and the core flow. This flow analysis can supply information on the separation point of the glottal flow and the thickness of the boundary layer, both of which strongly depend on the glottal configuration and yield an effective prediction of the flow behavior. When the flow analysis is combined with the modified two-mass model of the vocal fold [Pelorson et al. (1994). J. Acoust. Soc. Am. 96, 3416-3431], the resulting acoustic wave travels through the vocal tract and a pressure change develops in the vicinity of the glottis. This change can affect the glottal flow and the motion of the vocal folds, causing source-filter coupling. The property of the acoustic feedback is explicitly expressed in the frequency domain by using an acoustic tube model, allowing a clear interpretation of the coupling. Numerical experiments show that the vocal-tract input impedance and frequency responses representing the source-filter coupling have dominant peaks corresponding to the fourth and fifth formants. Results of time-domain simulations also suggest the importance of these high-frequency peaks in voice production.     

A theoretical study of the effects of various laryngeal configurations on the acoustics of phonation.

Simulation of glottal volume flow and vocal fold tissue movement was accomplished by numerical solution of a time-dependent boundary value problem, in which nonuniform, orthotropic, linear, incompressible vocal fold tissue media were surrounded by irregularly shaped boundaries, which were either fixed or subject to aerodynamic stresses. Spatial nonuniformity of the tissues was of the layered type, including a mucosal layer, a ligamental layer, and muscular layers. Orthotropy was required to stabilized the vocal folds longitudinally and to accomodate large variations in muscular stress. Incompressibility and vertical motions at the golttis played an important role in producing and sustaining phonation. A nominal configuration for male fundamental speaking pitches was selected, and the regulation of fundamental frequency, intensity, average volume flow, and vocal efficiency was investigated in terms of variations around this nominal configuration. Parameters which were varied consisted of geometrical factors such as length, thickness, and depth, factors for shaping the glottis, as well as tissue elasticities, tissue viscosities, and subglottal pressure. Since nonlinear stress-strain properties were not included, subglottal pressure did not produce a pronounced effect upon fundamental frequency under these somewhat edealized conditions F0 rasing correlated strongly with increased tension in the ligament, and somewhat with increasing tension in the vocalis. F0 lowering correlated with increase in vocal fold length when the tensions were held constant, but not with increase in vocal fold thickness. Vocal intensity and efficiency are shown to have local maxima as the configurational parameters are varied one at a time. It appears that oral acoustic power output and vocal efficiency can be maximized by proper adjustments of longitudinal tension of nonmuscular (mucosal and ligamental) tissue layers in relation to muscular layers. Quantitative verification of the "body-cover" theory is therefore suggested, and several further implications with regard to control of the human larynx are considered.     

Analysis of Vocal-fold Vibrations from High-Speed Laryngeal Images Using a Hilbert Transform-Based Methodology

This paper presents a Hilbert transform-based approach to analyze vocal fold vibrations in human subjects exhibiting normal and abnormal voice productions. This new approach is applied to the analysis of glottal area waveform (GAW) and is capable of providing useful information on the vocal fold vibration. The GAW is extracted from high-speed laryngeal images by delineating the glottal edge for each image frame. An analytic signal is generated through the Hilbert transform of the GAW, which yields a recognizable pattern of the vocal fold vibration in the analytic phase plane. The vibratory pattern is comprehensive and can be correlated with specific voice conditions. Quantitative measures of the glottal perturbation are introduced using the analytic amplitude and instantaneous frequency obtained from the analysis. Examples of clinical voice recordings are used to evaluate and test the effectiveness of this approach in providing qualitative representation and quantitative characteristics of vocal fold vibratory behavior. The results demonstrate the potential of using this new analytical tool incorporated with the high-speed laryngeal imaging modality for clinical voice assessment.     

Three-dimensional biomechanical properties of human vocal folds: parameter optimization of a numerical model to match in vitro dynamics

The human voice signal originates from the vibrations of the two vocal folds within the larynx. The interactions of several intrinsic laryngeal muscles adduct and shape the vocal folds to facilitate vibration in response to airflow. Three-dimensional vocal fold dynamics are extracted from in vitro hemilarynx experiments and fitted by a numerical three-dimensional-multi-mass-model (3DM) using an optimization procedure. In this work, the 3DM dynamics are optimized over 24 experimental data sets to estimate biomechanical vocal fold properties during phonation. Accuracy of the optimization is verified by low normalized error (0.13 ± 0.02), high correlation (83% ± 2%), and reproducible subglottal pressure values. The optimized, 3DM parameters yielded biomechanical variations in tissue properties along the vocal fold surface, including variations in both the local mass and stiffness of vocal folds. That is, both mass and stiffness increased along the superior-to-inferior direction. These variations were statistically analyzed under different experimental conditions (e.g., an increase in tension as a function of vocal fold elongation and an increase in stiffness and a decrease in mass as a function of glottal airflow). The study showed that physiologically relevant vocal fold tissue properties, which cannot be directly measured during in vivo human phonation, can be captured using this 3D-modeling technique.     

An Investigation of Cricoarytenoid Joint Mechanics Using Simulated Muscle Forces

Rotational and translational stiffnesses were calculated for arytenoid motion about the cricoarytenoid joint. These calculations were obtained from measurements on five excised human larynxes. For each larynx, known forces were applied to the arytenoid cartilage, and three markers were tracked as a function of applied forces. Assuming rigid body motion, arytenoid translations and rotations were computed for each applied force. Translational stiffnesses were obtained by plotting force versus displacement, and rotational stiffnesses were calculated by plotting torque versus angular rotation. A major finding was that the translational stiffness along the anterior-posterior direction was three times as great as the translational stiffnesses in the other two directions. This nonisotropic nature of the stiffnesses may be an important consideration for phonosurgeons who wish to avoid subluxation of the cricoarytenoid joint in patients. The computed rotational and translational stiffnesses currently are being implemented in 2D and 3D models. These stiffness parameters play a vital role in prephonatory glottal shaping, which in turn exerts a majorinfluence on all aspects of vocal fold vibration, including fundamental frequency, voice quality, voice register, and phonation threshold pressure.