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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. [ABSTRACT FROM AUTHOR]

The addition of a fourth type of voice to Titze’s voice classification scheme is proposed. This fourth voice type is characterized by primarily stochastic noise behavior and is therefore unsuitable for both perturbation and correlation dimension analysis. Forty voice samples were classified into the proposed four types using narrowband spectrograms. Acoustic, perceptual, and correlation dimension analyses were completed for all voice samples. Perturbation measures tended to increase with voice type. Based on reliability cutoffs, the type 1 and type 2 voices were considered suitable for perturbation analysis. Measures of unreliability were higher for type 3 and 4 voices. Correlation dimension analyses increased significantly with signal type as indicated by a one-way analysis of variance. Notably, correlation dimension analysis could not quantify the type 4 voices. The proposed fourth voice type represents a subset of voices dominated by noise behavior. Current measures capable of evaluating type 4 voices provide only qualitative data (spectrograms, perceptual analysis, and an infinite correlation dimension). Type 4 voices are highly complex and the development of objective measures capable of analyzing these voices remains a topic of future investigation. [ABSTRACT FROM AUTHOR]

This study aimed to measure solid and liquid component parameters for canine vocal fold lamina propria tissue, as is consistent with the solid and liquid fraction parameters in the context of the biphasic theory. A liquid-displacement apparatus was developed and utilized to estimate volumes of small samples of tissue. Accuracy was determined by calibrations with an object of known mass and density (copper). The experimental apparatus was then used to determine the volume of eight tissue samples, followed by an apparently complete dehydration of the samples, yielding the dry or solid tissue. The mass and volume fractions of the liquid component were sufficiently higher than those of the solid component. These results represent preliminary experimental evidence for the biphasic composition (solid-liquid) of canine lamina propria tissue as predicted in the biphasic theory. This study presents an effective experimental method to estimate some of the biphasic model parameters, and may provide a valuable application in exploring the viscoelastic behaviors of vocal fold lamina propria tissue. [ABSTRACT FROM AUTHOR]

The effect of the pressure recovery at glottal exit is introduced to modify the one-mass model. Using the modified one-mass model, the phonation critical condition, including phonation threshold pressure and phonation threshold flow, is analyzed by using the small-amplitude oscillation theory. It is found that the phonation threshold pressure is not sensitive to the change of the prephonatory glottal width at a wide glottal gap. This result agrees with previous experimental observations and suggests that the low slope of dependence of phonation threshold pressure on prephonatory gap found by Chan and Titze [J. Acoust. Soc. Am. 119, 2351–2362 (2006)] could be a consequence of the pressure recovery effect at the glottal exit. In addition, it is predicted that the phonation threshold flow is always significantly increased with the prephonatory gap even at a wide prephonatory glottal gap. Therefore, the phonation threshold flow has an advantage in assessing the phonatory system at a wide prephonatory gap in comparison with the phonation threshold pressure. The phonation threshold flow can be a useful aerodynamic parameter for pathological conditions in which the incomplete glottal gap is often seen. [ABSTRACT FROM AUTHOR]

In this study, a biphasic theory is applied to investigate the viscoelastic behaviors of vocal fold lamina propria during stress relaxation. The vocal fold lamina propria tissue is described as a biphasic material composed of a solid phase and an interstitial fluid phase. The biphasic theory reveals the interaction between the solid and the fluid. For the one-dimensional case, the analytical solutions of solid displacement, fluid velocity, and stress are derived. The biphasic theory predicts the stress relaxation of the vocal fold lamina propria. The quasilinear viscoelastic model as well as its higher-order elastic parameters can be derived from this biphasic theory. Furthermore, the fluid is found to support the majority of the stress at the early stage of stress relaxation; however, when the time becomes sufficiently large, the solid eventually bears all the stress. The early fluid stress support is much higher than the eventual solid support and may be important for understanding the effects of dehydration on tissue damage. By considering the solid-fluid structure of the vocal fold lamina propria, the biphasic theory allows for a more physical theory of tissue viscoelasticity than a single phase solid description and may provide a valuable physical mechanism for the observed vocal fold rheologic behaviors. [ABSTRACT FROM AUTHOR]

A model constructed from Navier-Stokes equations and a two-mass vocal fold description is proposed in this study. The composite model not only has the capability to describe the aerodynamics in a vibratory glottis but also can be used to study the vocal fold vibration under the driving of the complex airflow in the glottis. Numerical simulations show that this model can predict self-oscillations of the coupled glottal aerodynamics and vocal fold system. The Coanda effect could occur in the vibratory glottis even though the vocal folds have left-right symmetric prephonatory shape and tissue properties. The Coanda effect causes the asymmetric flow in the glottis and the difference in the driving force on the left and right vocal folds. The different pressures applied to the left and right vocal folds induce their displacement asymmetry. By using various lung pressures (0.6–2.0 kPa) to drive the composite model, it was found that the asymmetry of the vocal fold displacement is increased from 1.87% to 11.2%. These simulation results provide numerical evidence for the presence of asymmetric flow in the vibratory glottis; moreover, they indicate that glottal aerodynamics is an important factor in inducing the asymmetric vibration of the vocal folds. [ABSTRACT FROM AUTHOR]

Phonation threshold flow (PTF) is proposed as a new aerodynamic parameter of the speech production system in this study. PTF is defined as the minimum airflow that can initiate stable vocal fold vibration. Because the glottal airflow can be noninvasively measured, it is suggested that the aerodynamic parameter PTF may be more practical for clinical vocal disease assessment. In order to investigate the relationship between PTF and phonatory system properties, the stability of the body-cover vocal fold model was analyzed. The study has theoretically shown that PTF is a sensitive aerodynamic parameter dependent on tissue properties, glottal configuration, and vocal tract loading. It was predicted that PTF can be reduced by decreasing tissue viscosity, decreasing mucosal wave velocity, increasing vocal fold thickness, or decreasing prephonatory glottal area. Furthermore, it was predicted that a divergent glottis or low vocal tract resistance lead to a reduced PTF. Also discussed is the potential significance of PTF in investigating the energy distribution in a vocal fold vibration system and related clinical applications. [ABSTRACT FROM AUTHOR]

In this paper, a finite-element model is used to simulate anterior-posterior biphonation [Neubauer et al., J. Acoust. Soc. Am. 110(6), 3179–3192 (2001)]. The anterior-posterior stiffness asymmetric factor and the anterior-posterior shape asymmetric factor describe the asymmetry properties of vocal folds. Spatiotemporal plot, spectral analysis, anterior-posterior fundamental frequency ratio, cross covariation function, and correlation length quantitatively estimate the spatial asymmetry of vocal fold oscillations. Calculation results show that the anterior-posterior stiffness asymmetry decreases the spatial coherence of vocal fold vibration. When the stiffness asymmetry reaches a certain level, the drop in spatial coherence desynchronizes the vibration modes. The anterior and posterior sides of the vocal fold oscillate with two independent fundamental frequencies (fa and fp). The complex spectral characteristics of vocal fold vibration under biphonation conditions can be explained by the linear combination of fa and fp. Empirical orthogonal eigenfunctions prove the existence of higher-order anterior-posterior modes when anterior-posterior biphonation occurs. Then, it is found that the anterior-posterior shape asymmetry also decreases the spatial coherence of vocal fold vibration, and shape asymmetry is a possible reason for anterior-posterior biphonation. [ABSTRACT FROM AUTHOR]

Vocal fold impact pressures were studied using a self-oscillating finite-element model capable of simulating vocal fold vibration and airflow. The calculated airflow pressure is applied on the vocal fold as the driving force. The airflow region is then adjusted according to the calculated vocal fold displacement. The interaction between airflow and the vocal folds produces a self-oscillating solution. Lung pressures between 0.2 and 2.5 kPa were used to drive this self-oscillating model. The spatial distribution of the impact pressure was studied. Studies revealed that the tissue collision during phonation produces a very large impact pressure which correlates with the lung pressure and glottal width. Larger lung pressure and a narrower glottal width increase the impact pressure. The impact pressure was found to be roughly the square root of lung pressure. In the inferior-superior direction, the maximum impact pressure is related to the narrowest glottis. In the anterior-posteriorfirection, the greatest impact pressure appears at the midpoint of the vocal fold. The match between our numerical simulations and clinical observations suggests that this self-oscillating finite-element model might be valuable for predicting mechanical trauma of the vocal folds. [ABSTRACT FROM AUTHOR]

Nonlinear dynamic methods and perturbation methods are compared in terms of the effects of signal length, sampling rate, and noise. Results of theoretical and experimental studies quantitatively show that measurements representing frequency and amplitude perturbations are not applicable to chaotic signals because of difficulties in pitch tracking and sensitivity to initial state differences. Perturbation analyses are only reliable when applied to nearly periodic voice samples of sufficiently long signal lengths that were obtained at high sampling rates and low noise levels. In contrast, nonlinear dynamic methods, such as correlation dimension, allow the quantification of chaotic time series. Additionally, the correlation dimension method presents a more stable analysis of nearly periodic voice samples for shorter signal lengths, lower sampling rates, and higher noise levels. The correlation dimension method avoids some of the methodological issues associated with perturbation methods, and may potentially improve the ability for real time analysis as well as reduce costs in experimental designs for objectively assessing voice disorders. [ABSTRACT FROM AUTHOR]

Phase space reconstruction, correlation dimension, and second-order entropy, methods from nonlinear dynamics, are used to analyze sustained vowels generated by patients before and after surgical excision of vocal polyps. Two conventional acoustic perturbation parameters, jitter and shimmer, are also employed to analyze voices before and after surgery. Presurgical and postsurgical analyses of jitter, shimmer, correlation dimension, and second-order entropy are statistically compared. Correlation dimension and second-order entropy show a statistically significant decrease after surgery, indicating reduced complexity and higher predictability of postsurgical voice dynamics. There is not a significant postsurgical difference in shimmer, although jitter shows a significant postsurgical decrease. The results suggest that jitter and shimmer should be applied to analyze disordered voices with caution; however, nonlinear dynamic methods may be useful for analyzing abnormal vocal function and quantitatively evaluating the effects of surgical excision of vocal polyps. [ABSTRACT FROM AUTHOR]

A nonlinear model was proposed to study chaotic vibrations of vocal folds with a unilateral vocal polyp. The model study found that the vocal polyp affected glottal closure and caused aperiodic vocal fold vibrations. Using nonlinear dynamic methods, aperiodic vibrations of the vocal fold model with a polyp were attributed to low-dimensional chaos. Bifurcation diagrams showed that vocal polyp size, stiffness, and damping had important effects on vocal fold vibrations. An increase in polyp size tended to induce subharmonic patterns and chaos. This study provides a theoretical basis to model aperiodic vibrations of vocal folds with a laryngeal mass. [ABSTRACT FROM AUTHOR]

Nonlinear dynamic methods including correlation dimension and Lyapunov exponents are applied to quantitatively analyze phonations in excised larynx experiments. Irregular phonations are typically characterized by aperiodic waveforms and broadband spectra. Finite correlation dimensions and positive Lyapunov exponents of irregular phonations demonstrate the existence of chaos in excised larynx phonations. Furthermore, the correlation dimension, maximal Lyapunov exponent, jitter, shimmer, and peak prominence ratio are used to statistically distinguish irregular phonations from normal phonations. The correlation dimension and maximal Lyapunov exponent indicate a significant difference between irregular and normal phonations; however, jitter, shimmer, and peak prominence ratio do not reveal such a significant difference and thus are unsuitable to differentiate between irregular phonations and normal phonations. These findings might potentially assist investigators in understanding rough phonations and developing clinically valuable methodologies for the diagnosis of voice disorders. [ABSTRACT FROM AUTHOR]

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. © 2002 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

The chaos mechanism of above-range phonation was examined in symmetrically modeled vocal folds by using the traditional two-mass model assumption. The Poincaré map technique was used to display chaotic attractors. This method provided an effective description of irregular vocal-fold movements. The power spectrum, Lyapunov exponent, and Kaplan-Yorke dimension were employed to describe chaotic vibrations in the vocal-fold model. These nonlinear dynamic analyses suggested that, for the positive Lyapunov exponent, chaotic attractors contribute to irregular vocal-fold vibrations. Descriptions of complicated irregular vibrations of the vocal fold yielded evidence of chaos. To investigate the effects of independent parameters such as subglottal pressure, coupling stiffness, and phonation neutral area, bifurcation diagrams based on the Poincaré map were discussed. The results confirmed that the dynamics of the two-mass model was strongly influenced by independent parameters. Nonlinear dynamic methods were expected to provide useful information for better understanding of irregular vocal-fold vibrations as well as of the dynamic mechanism of above-range phonation in excised larynx experimentation. © 2001 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

It has been widely recognized that the FFT-based spectrogram does not provide good simultaneous resolution in both time and frequency domains. A new method of spectral analysis has been developed based upon the Gabor expansion and the Wigner-Ville distribution. The resolution of the Gabor spectrogram is twice as high as that of a FFT-based spectrogram. In this report, FFT-based spectrograms and Gabor spectrograms are compared for 5 English vowels, 6 stops consonants, 4 fricatives, and vowels format transitions in a CVD contents on 6 normal subjects. Results demonstrate that the Gabor spectrogram is a promising alternative for FFT-based spectrogram in speech analysis because of its higher temporal and frequency resolution. [ABSTRACT FROM AUTHOR]

Examination of surface wave properties in the vocal fold mucosa is becoming an important part of assessment of vocal function. A key wave property is propagation velocity, which determines the phase delay between upper and lower margins of the vocal folds. Excised canine larynges were used in this study to measure this phase delay, and therewith propagation velocity. The motion of two fleshpoints was tracked stroboscopically. Differential displacements between the fleshpoints were matched to displacements of a model. A least-squared fit of the data to the model provided the numerical values of propagation velocity, which varied from 0.5 m/s to about 2.0 m/s, depending on fundamental frequency. The corresponding phase delay along the medial surface of the vocal folds varied from about 60°/mm to 30°/mm. [Work supported by NIDCD, Grant No. P60-DC0976.] [ABSTRACT FROM AUTHOR]

In this study, a biphasic theory is applied to investigate the viscoelastic behaviors of vocal fold lamina propria during stress relaxation. The vocal fold lamina propria tissue is described as a biphasic material composed of a solid phase and an interstitial fluid phase. The biphasic theory reveals the interaction between the solid and the fluid. For the one-dimensional case, the analytical solutions of solid displacement, fluid velocity, and stress are derived. The biphasic theory predicts the stress relaxation of the vocal fold lamina propria. The quasilinear viscoelastic model as well as its higher-order elastic parameters can be derived from this biphasic theory. Furthermore, the fluid is found to support the majority of the stress at the early stage of stress relaxation; however, when the time becomes sufficiently large, the solid eventually bears all the stress. The early fluid stress support is much higher than the eventual solid support and may be important for understanding the effects of dehydration on tissue damage. By considering the solid-fluid structure of the vocal fold lamina propria, the biphasic theory allows for a more physical theory of tissue viscoelasticity than a single phase solid description and may provide a valuable physical mechanism for the observed vocal fold rheologic behaviors.

The effect of the pressure recovery at glottal exit is introduced to modify the one-mass model. Using the modified one-mass model, the phonation critical condition, including phonation threshold pressure and phonation threshold flow, is analyzed by using the small-amplitude oscillation theory. It is found that the phonation threshold pressure is not sensitive to the change of the prephonatory glottal width at a wide glottal gap. This result agrees with previous experimental observations and suggests that the low slope of dependence of phonation threshold pressure on prephonatory gap found by Chan and Titze [J. Acoust. Soc. Am. 119, 2351-2362 (2006)] could be a consequence of the pressure recovery effect at the glottal exit. In addition, it is predicted that the phonation threshold flow is always significantly increased with the prephonatory gap even at a wide prephonatory glottal gap. Therefore, the phonation threshold flow has an advantage in assessing the phonatory system at a wide prephonatory gap in comparison with the phonation threshold pressure. The phonation threshold flow can be a useful aerodynamic parameter for pathological conditions in which the incomplete glottal gap is often seen.

A model constructed from Navier-Stokes equations and a two-mass vocal fold description is proposed in this study. The composite model not only has the capability to describe the aerodynamics in a vibratory glottis but also can be used to study the vocal fold vibration under the driving of the complex airflow in the glottis. Numerical simulations show that this model can predict self-oscillations of the coupled glottal aerodynamics and vocal fold system. The Coanda effect could occur in the vibratory glottis even though the vocal folds have left-right symmetric prephonatory shape and tissue properties. The Coanda effect causes the asymmetric flow in the glottis and the difference in the driving force on the left and right vocal folds. The different pressures applied to the left and right vocal folds induce their displacement asymmetry. By using various lung pressures (0.6-2.0 kPa) to drive the composite model, it was found that the asymmetry of the vocal fold displacement is increased from 1.87% to 11.2%. These simulation results provide numerical evidence for the presence of asymmetric flow in the vibratory glottis; moreover, they indicate that glottal aerodynamics is an important factor in inducing the asymmetric vibration of the vocal folds.

In this paper, a finite-element model is used to simulate anterior-posterior biphonation [Neubauer et al., J. Acoust. Soc. Am. 110(6), 3179-3192 (2001)]. The anterior-posterior stiffness asymmetric factor and the anterior-posterior shape asymmetric factor describe the asymmetry properties of vocal folds. Spatiotemporal plot, spectral analysis, anterior-posterior fundamental frequency ratio, cross covariation function, and correlation length quantitatively estimate the spatial asymmetry of vocal fold oscillations. Calculation results show that the anterior-posterior stiffness asymmetry decreases the spatial coherence of vocal fold vibration. When the stiffness asymmetry reaches a certain level, the drop in spatial coherence desynchronizes the vibration modes. The anterior and posterior sides of the vocal fold oscillate with two independent fundamental frequencies (f(a) and f(p)). The complex spectral characteristics of vocal fold vibration under biphonation conditions can be explained by the linear combination of f(a) and f(p). Empirical orthogonal eigenfunctions prove the existence of higher-order anterior-posterior modes when anterior-posterior biphonation occurs. Then, it is found that the anterior-posterior shape asymmetry also decreases the spatial coherence of vocal fold vibration, and shape asymmetry is a possible reason for anterior-posterior biphonation.

Vocal fold impact pressures were studied using a self-oscillating finite-element model capable of simulating vocal fold vibration and airflow. The calculated airflow pressure is applied on the vocal fold as the driving force. The airflow region is then adjusted according to the calculated vocal fold displacement. The interaction between airflow and the vocal folds produces a self-oscillating solution. Lung pressures between 0.2 and 2.5 kPa were used to drive this self-oscillating model. The spatial distribution of the impact pressure was studied. Studies revealed that the tissue collision during phonation produces a very large impact pressure which correlates with the lung pressure and glottal width. Larger lung pressure and a narrower glottal width increase the impact pressure. The impact pressure was found to be roughly the square root of lung pressure. In the inferior-superior direction, the maximum impact pressure is related to the narrowest glottis. In the anterior-posteriorfirection, the greatest impact pressure appears at the midpoint of the vocal fold. The match between our numerical simulations and clinical observations suggests that this self-oscillating finite-element model might be valuable for predicting mechanical trauma of the vocal folds.

Nonlinear dynamic methods and perturbation methods are compared in terms of the effects of signal length, sampling rate, and noise. Results of theoretical and experimental studies quantitatively show that measurements representing frequency and amplitude perturbations are not applicable to chaotic signals because of difficulties in pitch tracking and sensitivity to initial state differences. Perturbation analyses are only reliable when applied to nearly periodic voice samples of sufficiently long signal lengths that were obtained at high sampling rates and low noise levels. In contrast, nonlinear dynamic methods, such as correlation dimension, allow the quantification of chaotic time series. Additionally, the correlation dimension method presents a more stable analysis of nearly periodic voice samples for shorter signal lengths, lower sampling rates, and higher noise levels. The correlation dimension method avoids some of the methodological issues associated with perturbation methods, and may potentially improve the ability for real time analysis as well as reduce costs in experimental designs for objectively assessing voice disorders.

Phase space reconstruction, correlation dimension, and second-order entropy, methods from nonlinear dynamics, are used to analyze sustained vowels generated by patients before and after surgical excision of vocal polyps. Two conventional acoustic perturbation parameters, jitter and shimmer, are also employed to analyze voices before and after surgery. Presurgical and postsurgical analyses of jitter, shimmer, correlation dimension, and second-order entropy are statistically compared. Correlation dimension and second-order entropy show a statistically significant decrease after surgery, indicating reduced complexity and higher predictability of postsurgical voice dynamics. There is not a significant postsurgical difference in shimmer, although jitter shows a significant postsurgical decrease. The results suggest that jitter and shimmer should be applied to analyze disordered voices with caution; however, nonlinear dynamic methods may be useful for analyzing abnormal vocal function and quantitatively evaluating the effects of surgical excision of vocal polyps.

A nonlinear model was proposed to study chaotic vibrations of vocal folds with a unilateral vocal polyp. The model study found that the vocal polyp affected glottal closure and caused aperiodic vocal fold vibrations. Using nonlinear dynamic methods, aperiodic vibrations of the vocal fold model with a polyp were attributed to low-dimensional chaos. Bifurcation diagrams showed that vocal polyp size, stiffness, and damping had important effects on vocal fold vibrations. An increase in polyp size tended to induce subharmonic patterns and chaos. This study provides a theoretical basis to model aperiodic vibrations of vocal folds with a laryngeal mass.