Parameter estimation of an asymmetric vocal-fold system from glottal area time series using chaos synchronization

Modeling the Pathophysiology of Phonotraumatic Vocal Hyperfunction With a Triangular Glottal Model of the Vocal Folds

PURPOSE

Our goal was to test prevailing assumptions about the underlying biomechanical and aeroacoustic mechanisms associated with phonotraumatic lesions of the vocal folds using a numerical lumped-element model of voice production.

METHOD

A numerical model with a triangular glottis, posterior glottal opening, and arytenoid posturing is proposed. Normal voice is altered by introducing various prephonatory configurations. Potential compensatory mechanisms (increased subglottal pressure, muscle activation, and supraglottal constriction) are adjusted to restore an acoustic target output through a control loop that mimics a simplified version of auditory feedback.

RESULTS

The degree of incomplete glottal closure in both the membranous and posterior portions of the folds consistently leads to a reduction in sound pressure level, fundamental frequency, harmonic richness, and harmonics-to-noise ratio. The compensatory mechanisms lead to significantly increased vocal-fold collision forces, maximum flow-declination rate, and amplitude of unsteady flow, without significantly altering the acoustic output.

CONCLUSION

Modeling provided potentially important insights into the pathophysiology of phonotraumatic vocal hyperfunction by demonstrating that compensatory mechanisms can counteract deterioration in the voice acoustic signal due to incomplete glottal closure, but this also leads to high vocal-fold collision forces (reflected in aerodynamic measures), which significantly increases the risk of developing phonotrauma.

An extended Kalman filter approach to non-stationary Bayesian estimation of reduced-order vocal fold model parameters

The Bayesian framework for parameter inference provides a basis from which subject-specific reduced-order vocal fold models can be generated. Previously, it has been shown that a particle filter technique is capable of producing estimates and associated credibility intervals of time-varying reduced-order vocal fold model parameters. However, the particle filter approach is difficult to implement and has a high computational cost, which can be barriers to clinical adoption. This work presents an alternative estimation strategy based upon Kalman filtering aimed at reducing the computational cost of subject-specific model development. The robustness of this approach to Gaussian and non-Gaussian noise is discussed. The extended Kalman filter (EKF) approach is found to perform very well in comparison with the particle filter technique at dramatically lower computational cost. Based upon the test cases explored, the EKF is comparable in terms of accuracy to the particle filter technique when greater than 6000 particles are employed; if less particles are employed, the EKF actually performs better. For comparable levels of accuracy, the solution time is reduced by 2 orders of magnitude when employing the EKF. By virtue of the approximations used in the EKF, however, the credibility intervals tend to be slightly underpredicted.

Non-stationary Bayesian estimation of parameters from a body cover model of the vocal folds

The evolution of reduced-order vocal fold models into clinically useful tools for subject-specific diagnosis and treatment hinges upon successfully and accurately representing an individual patient in the modeling framework. This, in turn, requires inference of model parameters from clinical measurements in order to tune a model to the given individual. Bayesian analysis is a powerful tool for estimating model parameter probabilities based upon a set of observed data. In this work, a Bayesian particle filter sampling technique capable of estimating time-varying model parameters, as occur in complex vocal gestures, is introduced. The technique is compared with time-invariant Bayesian estimation and least squares methods for determining both stationary and non-stationary parameters. The current technique accurately estimates the time-varying unknown model parameter and maintains tight credibility bounds. The credibility bounds are particularly relevant from a clinical perspective, as they provide insight into the confidence a clinician should have in the model predictions.

Aerodynamic and nonlinear dynamic acoustic analysis of tension asymmetry in excised canine larynges

PURPOSE

To model tension asymmetry caused by superior laryngeal nerve paralysis (SLNP) in excised larynges and apply perturbation, nonlinear dynamic, and aerodynamic analyses.

METHOD

SLNP was modeled in 8 excised larynges using sutures and weights to mimic cricothyroid (CT) muscle function. Weights were removed from one side to create tension asymmetry, mimicking unilateral SLNP. Two sets of weights were used, 1 light and 1 heavy. Five conditions were evaluated: (a) no tension, (b) symmetrical light tension, (c) asymmetrical light tension, (d) symmetrical heavy tension, and (e) asymmetrical heavy tension.

RESULTS

Perturbation parameters were not significantly different across conditions: percent jitter, χ(2)(4) = 3.70, p = .451; percent shimmer, F(4) = 0.95, p = .321. In addition, many measurements were invalid (error values >10). Second-order entropy was significantly different across conditions, F(4) = 5.432, p = .002, whereas correlation dimension was not, F(4) = 0.99, p = .428. Validity of these nonlinear dynamic parameters was demonstrated by low standard deviations. Phonation threshold pressure, χ (2)(4) = 22.50, p < .001, and power, χ (2)(4) = 9.50, p = .05, differed significantly across conditions, whereas phonation threshold flow did not, χ (2)(4) = 4.08, p = .396.

CONCLUSIONS

Nonlinear dynamic analysis differentiated between symmetrical and asymmetrical tension conditions, whereas traditional perturbation analysis was less useful in characterizing type 2 or 3 vocal signals. Supplementing acoustic with aerodynamic parameters may help distinguish among laryngeal disorders of neuromuscular origin.

Investigating acoustic correlates of human vocal fold vibratory phase asymmetry through modeling and laryngeal high-speed videoendoscopy

Vocal fold vibratory asymmetry is often associated with inefficient sound production through its impact on source spectral tilt. This association is investigated in both a computational voice production model and a group of 47 human subjects. The model provides indirect control over the degree of left-right phase asymmetry within a nonlinear source-filter framework, and high-speed videoendoscopy provides in vivo measures of vocal fold vibratory asymmetry. Source spectral tilt measures are estimated from the inverse-filtered spectrum of the simulated and recorded radiated acoustic pressure. As expected, model simulations indicate that increasing left-right phase asymmetry induces steeper spectral tilt. Subject data, however, reveal that none of the vibratory asymmetry measures correlates with spectral tilt measures. Probing further into physiological correlates of spectral tilt that might be affected by asymmetry, the glottal area waveform is parameterized to obtain measures of the open phase (open/plateau quotient) and closing phase (speed/closing quotient). Subjects' left-right phase asymmetry exhibits low, but statistically significant, correlations with speed quotient (r=0.45) and closing quotient (r=-0.39). Results call for future studies into the effect of asymmetric vocal fold vibration on glottal airflow and the associated impact on voice source spectral properties and vocal efficiency.

Nonlinear vocal fold dynamics resulting from asymmetric fluid loading on a two-mass model of speech

Nonlinear vocal fold dynamics arising from asymmetric flow formations within the glottis are investigated using a two-mass model of speech with asymmetric vocal fold tensioning, representative of unilateral vocal fold paralysis. A refined theoretical boundary-layer flow solver is implemented to compute the intraglottal pressures, providing a more realistic description of the flow than the standard one-dimensional, inviscid Bernoulli flow solution. Vocal fold dynamics are investigated for subglottal pressures of 0.6 < p(s) < 1.5 kPa and tension asymmetries of 0.5 < Q < 0.8. As tension asymmetries become pronounced the asymmetric flow incites nonlinear behavior in the vocal fold dynamics at subglottal pressures that are associated with normal speech, behavior that is not captured with standard Bernoulli flow solvers. Regions of bifurcation, coexistence of solutions, and chaos are identified.

Automatic diagnosis of vocal fold paresis by employing phonovibrogram features and machine learning methods

The clinical diagnosis of voice disorders is based on examination of the rapidly moving vocal folds during phonation (f0: 80-300Hz) with state-of-the-art endoscopic high-speed cameras. Commonly, analysis is performed in a subjective and time-consuming manner via slow-motion video playback and exhibits low inter- and intra-rater reliability. In this study an objective method to overcome this drawback is presented being based on Phonovibrography, a novel image analysis technique. For a collective of 45 normophonic and paralytic voices the laryngeal dynamics were captured by specialized Phonovibrogram features and analyzed with different machine learning algorithms. Classification accuracies reached 93% for 2-class and 73% for 3-class discrimination. The results were validated by subjective expert ratings given the same diagnostic criteria. The automatic Phonovibrogram analysis approach exceeded the experienced raters' classifications by 9%. The presented method holds a lot of potential for providing reliable vocal fold diagnosis support in the future.

Multiparameter estimation using only a chaotic time series and its applications

An important extension to the techniques of synchronization-based parameter estimation is presented. Based on adaptive chaos synchronization, several methods are proposed to dynamically estimate multiple parameters using only a scalar chaotic time series. In comparison with previous schemes, the presented methods decrease the cost of parameter estimation and are more applicable in practice. Numerical examples are used to demonstrate the effectiveness and robustness of the presented methods. As an example application, an implementation of multichannel digital communication is proposed, where multiparameter modulation is used to simultaneously transmit more than one digital message. From a theoretical perspective, such an encoding increases the difficulty to directly read out the message from the transmitted signal and decreases the implementation cost.

Extracting Physiologically Relevant Parameters of Vocal Folds From High-Speed Video Image Series

In this paper, a new method is proposed to extract the physiologically relevant parameters of the vocal fold mathematic model including masses, spring constants and damper constants from high-speed video (HSV) image series. This method uses a genetic algorithm to optimize the model parameters until the model and the realistic vocal folds have similar dynamic behavior. Numerical experiments theoretically test the validity of the proposed parameter estimation method. Then the validated method is applied to extract the physiologically relevant parameters from the glottal area series measured by HSV in an excised larynx model. With the estimated parameters, the vocal fold model accurately describes the vibration of the observed vocal folds. Further studies show that the proposed parameter estimation method can successfully detect the increase of longitudinal tension due to the vocal fold elongation from the glottal area signal. These results imply the potential clinical application of this method in inspecting the tissue properties of vocal fold.

Theoretical and experimental studies of parameter estimation based on chaos feedback synchronization

In this paper, we perform theoretical and experimental studies of parameter estimation based on chaos feedback synchronization. The Chua chaotic system is applied as the original system, and its time series of a single variable is applied as a feedback variable to drive a simulative system. The simplex method is employed to minimize the synchronization error in the simulative system to iteratively approach the original system parameters. Furthermore, the effects of feedback function, feedback weight, and noise are investigated. The parameter estimation method based on feedback synchronization shows its robustness to noise perturbation. Finally, the circuit experiment of parameter estimation is implemented in order to examine its practical applicability. The original Chua circuit parameters can be well approached from its recorded time series of a single variable. The results show the parameter estimation method based on feedback synchronization may be capable of estimating real system parameters from a chaotic time series.