Two-mass Model Of Vocal Folds Research Articles

Effects of horizontal-to-vertical stiffness ratio on the vibration characteristics of a two-mass vocal fold model

In order to evaluate the effects of stiffness ratio of vocal fold on three-dimensional behavior of vocal fold vibration, numerical simulations were performed by using a two-mass vocal fold model with different stiffness ratio of the horizontal and vertical direction. A ratio of the spring constants for the same direction were fixed, while it for the orthogonal directions was changed. To simulate the airflow through the glottis, the one-dimensional Bernoulli’s equation was solved with an equivalent circuit for the compressible flow propagation. The vocal fold shape was represented by a smooth shape with cylindrical masses and tangential faces. The flow separation point was estimated using the boundary layer theory. The results showed that overall fundamental frequency of the vocal folds increased with increasing horizontal stiffness, whereas the vertical stiffness changes had few effects on it. We also found that there were topical conditions in which fundamental frequency rapidly changed with a few changes in stiffness ratio. The stiffness ratio at that time was from 0.80 to 1.08. Before and after the change, there was difference whether the motion trajectory of mass was circular or linear. These results indicate that the vertical stiffness largely affects the oscillation modes of vocal folds.

Comparison of one-dimensional and three-dimensional glottal flow models in left-right asymmetric vocal fold conditions

While the glottal flow is often simplified as one-dimensional (1D) in computational models of phonation to reduce computational costs, the 1D flow model has not been validated in left-right asymmetric vocal fold conditions, as often occur in both normal and pathological voice production. It is unclear to what extent the 1D model approximates the effect of three-dimensional (3D) flow phenomena and fluid-structure interaction. In this study, we performed 1D and 3D flow simulations coupled with the two-mass vocal fold model and compared vocal fold vibration patterns at different degrees of left-right stiffness asymmetry. The flow and acoustic fields in 3D were predicted by solving the compressible Navier-Stokes equations using the volume penalization method and considering the moving vocal fold wall as an immersed boundary. The results showed that vocal fold vibration amplitudes and left-right phase differences in the 3D flow were predicted by the 1D flow model under conditions of small left-right asymmetry, while vocal fold vibration amplitudes were underestimated at conditions of large left-right asymmetry. This indicates that 1D flow models may be sufficient in modeling phonation under left-right asymmetric conditions, although the performance can be further improved by more accurately predicting air pressure on vocal fold surface.

An acoustic source model for asymmetric intraglottal flow with application to reduced-order models of the vocal folds.

The complex three-way interaction between airflow, tissue, and sound, for asymmetric vocal fold vibration, is not well understood. Current modeling efforts are not able to explain clinical observations where drastic differences in sound production are often observed, with no noticeable differences in the vocal fold kinematics. To advance this understanding, an acoustical model for voiced sound generation in the presence of asymmetric intraglottal flows is developed. The source model operates in conjunction with a wave reflection analog propagation scheme and an asymmetric flow description within the glottis. To enable comparison with prior work, the source model is evaluated using a well-studied two-mass vocal fold model. The proposed source model is evaluated through acoustic measures of interest, including radiated sound pressure level, maximum flow declination rate, and spectral tilt, and also via its effects on the vocal fold dynamics. The influence of the model, in comparison to the standard symmetric Bernoulli flow description, results in an increased transfer of energy from the fluid to the vocal folds, increased radiated sound pressure level and maximum flow declination rate, and decreased spectral tilt. These differences are most pronounced for asymmetric vocal fold configurations that mimic unilateral paresis and paralysis, where minor kinematic changes can result in significant acoustic and aerodynamic differences. The results illustrate that fluid effects arising from asymmetric glottal flow can play an important role in the acoustics of pathological voiced speech.

Towards real-time two-dimensional wave propagation for articulatory speech synthesis

The precise simulation of voice production is a challenging task, especially when real-time performances are sought. To fulfill real-time constraints, most articulatory vocal synthesizers have to rely on highly simplified acoustic and anatomical models, based on 1D wave propagation and on the usage of vocal tract area functions. In this work, we present a 2D propagation model, designed to simulate the air flow traveling through the midsagittal contour of the vocal tract. Building on the work by Allen et al. [Andrew Allen and Nikunj Raghuvanshi, “Aerophones in flatland: Interactive wave simulation of wind instruments,” ACM Trans. Graph. 34, Article 134 (2015)], we leverage OpenGL and GPU parallelism for a real-time precise 2D airwave simulation. The domain is divided into cells according to a Finite-Difference Time-Domain scheme and coupled with a self-oscillating two-mass vocal fold model. To investigate the system’s ability to simulate the physiology of the vocal tract and its aerodynamics, two studies are presented. First, we compare the performances in vowel production of our 2D approach with other 1D wave propagation systems in literature, using area functions. Subsequently, this case is extended by replacing area functions with 2D vocal tract contours derived from 3D MRI data.

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

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

Functional morphology of the Alligator mississippiensis larynx with implications for vocal production.

Sauropsid vocalization is mediated by the syrinx in birds and the larynx in extant reptiles; but whereas avian vocal production has received much attention, the vocal mechanism of basal reptilians is poorly understood. The American alligator (Alligator mississippiensis) displays a large vocal repertoire during mating and in parent-offspring interactions. Although vocal outputs of these behaviors have received some attention, the underlying mechanism of sound production remains speculative. Here, we investigate the laryngeal anatomy of juvenile and adult animals by macroscopic and histological methods. Observations of the cartilaginous framework and associated muscles largely corroborate earlier findings, but one muscle, the cricoarytenoideus, exhibits a heretofore unknown extrinsic insertion that has important implications for effective regulation of vocal fold length and tension. Histological investigation of the larynx revealed a layered vocal fold morphology. The thick lamina propria consists of non-homogenous extracellular matrix containing collagen fibers that are tightly packed below the epithelium but loosely organized deep inside the vocal fold. We found few elastic fibers but comparatively high proportions of hyaluronan. Similar organizational complexity is also seen in mammalian vocal folds and the labia of the avian syrinx: convergent morphologies that suggest analogous mechanisms for sound production. In tensile tests, alligator vocal folds demonstrated a linear stress-strain behavior in the low strain region and nonlinear stress responses at strains larger than 15%, which is similar to mammalian vocal fold tissue. We have integrated morphological and physiological data in a two-mass vocal fold model, providing a systematic description of the possible acoustic space that could be available to an alligator larynx. Mapping actual call production onto possible acoustic space validates the model's predictions.

Corrected contact dynamics for the Steinecke and Herzel asymmetric two-mass model of the vocal folds

The simplified two-mass model of human vocal folds, proposed by Steinecke and Herzel [J. Acoust. Soc. Am. 97(3), 1874-1884 (1995)], has seen widespread use throughout the speech community. Herein, an error is corrected in the contact loadings on colliding vocal folds with asymmetric tissue properties, as arises clinically in cases of unilateral paralysis. A revised contact model is proposed that remediates the erroneous asymmetric contact forces. The vibration regime map presented in Steinecke and Herzel illustrating the dynamical behavior of the system is revised using the corrected collision model.

Subglottal pressure and fundamental frequency control in contact calls of juvenile Alligator mississippiensis

SUMMARYVocalization is rare among non-avian reptiles, with the exception of the crocodilians, the sister taxon of birds. Crocodilians have a complex vocal repertoire. Their vocal and respiratory system is not well understood but appears to consist of a combination of features that are also found in the extremely vocal avian and mammalian taxa. Anatomical studies suggest that the alligator larynx is able to abduct and adduct the vocal folds, but not to elongate or shorten them, and is therefore lacking a key regulator of frequency, yet alligators can modulate fundamental frequency remarkably well. We investigated the morphological and physiological features of sound production in alligators. Vocal fold length scales isometrically across a wide range of alligator body sizes. The relationship between fundamental frequency and subglottal pressure is significant in some individuals at some isolated points, such as call onset and position of maximum fundamental frequency. The relationship is not consistent over large segments of the call. Fundamental frequency can change faster than expected by pressure changes alone, suggesting an active motor pattern controls frequency and is intrinsic to the larynx. We utilized a two-mass vocal fold model to test whether abduction and adduction could generate this motor pattern. The fine-tuned interplay between subglottal pressure and glottal adduction can achieve frequency modulations much larger than those resulting from subglottal pressure variations alone and of similar magnitude, as observed in alligator calls. We conclude that the alligator larynx represents a sound source with only two control parameters (subglottal pressure and vocal fold adduction) in contrast to the mammalian larynx in which three parameters can be altered to modulate frequency (subglottal pressure, vocal fold adduction and length/tension).

An anatomically based, time-domain acoustic model of the subglottal system for speech production

A time-domain model of sound wave propagation in the branching airways of the subglottal system is presented. The model is formulated as an extension to an acoustic transmission-line modeling scheme originally developed for simulating the supraglottal system in the time-domain during speech production [Maeda (1982). Speech Commun. 1, 199-229; Mokhtari et al. (2008). Speech Commun. 50, 179-190]. The approach allows for predictions of time-varying acoustic pressure and volume velocity at any point along the various generations of subglottal airways from trachea to alveoli. In addition, the model can be configured so that its overall structure simulates different geometric forms, including airways that branch in a symmetric or asymmetric pattern. Three subglottal configurations, two symmetric and one asymmetric, were represented based on reported anatomical dimensions of the subglottal airways. Estimates of the acoustic input impedances of these subglottal configurations revealed resonant characteristics similar to those found in the previous studies. Simulations of voiced sound propagation into the subglottal airways, achieved by coupling the subglottal model to a two-mass vocal fold model and a supraglottal tract configured for different vowels, yielded predictions of time-domain sound pressure waveforms below the vocal folds that compare favorably to previous measurements in human subjects.

Chaotic vibration induced by turbulent noise in a two-mass model of vocal folds.

The contribution of turbulent noise was modeled in symmetric vocal folds. A two-mass model was used to simulate irregular vocal fold vibrations. The threshold values of system parameters to produce irregular vibrations were decreased as a result of turbulent airflow. Periodic vibrations were then driven into the regions of irregular vibrations. Using nonlinear dynamics including Poincaré map and Lyapunov exponents, irregular vibrations were demonstrated as chaos. For the deterministic vocal-fold model with noise free and steady airflow, a fine period-doubling bifurcation cascade was shown in a bifurcation diagram. However, turbulent noise added to the vocal-fold model would induce chaotic vibrations, broaden the regions of irregular vocal fold vibrations, and inhibit the fine period-doubling bifurcations in the bifurcation diagrams. The perturbations from neurological and biomechanical effects were simulated as a random variation of the vocal fold stiffness. Turbulent noise as an external random source, as well as random stiffness perturbation as an internal random source, played important roles in the presence of irregular vocal fold vibrations.