Bifurcations and chaos in register transitions of excised larynx experiments

Experimental data from an excised larynx are analyzed in the light of nonlinear dynamics. The excised larynx provides an experimental framework that enables artificial control and direct observation of the vocal fold vibrations. Of particular interest in this experiment is the coexistence of two distinct vibration patterns, which closely resemble chest and falsetto registers of the human voice. Abrupt transitions between the two registers are typically accompanied by irregular vibrations. Two approaches are presented for the modeling of the excised larynx experiment; one is the nonlinear predictive modeling of the experimental time series and the other is the biomechanical modeling (three-mass model) that takes into account basic mechanisms of the vocal fold vibrations. The two approaches show that the chest and falsetto vibrations correspond to two coexisting limit cycles, which jump to each other with a change in the bifurcation parameter. Irregular vibrations observed at the register jumps are due to chaos that exists near the two limit cycles. This provides an alternative mechanism to generate chaotic vibrations in excised larynx experiment, which is different from the conventionally known mechanisms such as strong asymmetry between the left and right vocal folds or excessively high subglottal pressure.     

Chaos in voice, from modeling to measurement.

Chaos has been observed in turbulence, chemical reactions, nonlinear circuits, the solar system, biological populations, and seems to be an essential aspect of most physical systems. Chaos may also be central to the interpretation of irregularity in voice disorders. This presentation will summarize the results from a series of our recent studies. These studies have demonstrated the prescence of chaos in computer models of vocal folds, experiments with excised larynges, and human voices. Methods based on nonlinear dynamics can be used to quantify chaos and irregularity in vocal fold vibration. Studies have suggested that disordered voices from laryngeal pathologies such as laryngeal paralysis, vocal polyps, and vocal nodules might exhibit chaotic behaviors. Conventional parameters, such as jitter and shimmer, may be unreliable for analysis of periodic and chaotic voice signals. Nonlinear dynamic methods, however, have differentiated between normal and pathological phonations and can describe the aperiodic or chaotic voice. Chaos theory and nonlinear dynamics can enchance our understanding and therefore our assessment of pathological phonation.     

Polyps and paralysis phonation classification with nonlinear dynamics model

In order to provide the basis for parameter selection of vocal diseases classification,a nonlinear dynamic modeling method is proposed.A biomechanical model of vocal cords with polyp or paralysis,which couples to glottal airflow to produce laryngeal sound source,is introduced.And then the fundamental frequency and its perturbation parameters are solved.Poincare section and bifurcation diagram are applied to nonlinear analysis of model vibration.By changing the pathological parameters or subglottal pressure,the changes of fundamental frequency and Lyapunov exponents are analyzed.The simulation results show that,vocal cord paralysis reduces the fundamental frequency,and the chaos occurs only within a certain pressure range;while vocal cord with a polyp don't reduce the fundamental frequency,chaos distributes throughout the entire range of pressure.Therefore this study is helpful for classification of polyp and paralysis by the acoustic diagnoses.     

Model-based classification of nonstationary vocal fold vibrations

Classification of vocal fold vibrations is an essential task of the objective assessment of voice disorders. For historical reasons, the conventional clinical examination of vocal fold vibrations is done during stationary, sustained phonation. However, the conclusions drawn from a stationary phonation are restricted to the observed steady-state vocal fold vibrations and cannot be generalized to voice mechanisms during running speech. This study addresses the approach of classifying real-time recordings of vocal fold oscillations during a nonstationary phonation paradigm in the form of a pitch raise. The classification is based on asymmetry measures derived from a time-dependent biomechanical two-mass model of the vocal folds which is adapted to observed vocal fold motion curves with an optimization procedure. After verification of the algorithm performance the method was applied to clinical problems. Recordings of ten subjects with normal voice and ten dysphonic subjects have been evaluated during stationary as well as nonstationary phonation. In the case of nonstationary phonation the model-based classification into "normal" and "dysphonic" succeeds in all cases, while it fails in the case of sustained phonation. The nonstationary vocal fold vibrations contain additional information about vocal fold irregularities, which are needed for an objective interpretation and classification of voice disorders.     

Quantifying the complexity of excised larynx vibrations from high-speed imaging using spatiotemporal and nonlinear dynamic analyses

In this paper, we investigate the biomechanical applications of spatiotemporal analysis and nonlinear dynamic analysis to quantitatively describe regular and irregular vibrations of twelve excised larynges from high-speed image recordings. Regular vibrations show simple spatial symmetry, temporal periodicity, and discrete frequency spectra, while irregular vibrations show complex spatiotemporal plots, aperiodic time series, and broadband spectra. Furthermore, the global entropy and correlation length from spatiotemporal analysis and the correlation dimension from nonlinear dynamic analysis reveal a statistical difference between regular and irregular vibrations. In comparison with regular vibrations, the global entropy and correlation dimension of irregular vibrations are statistically higher, while the correlation length is significantly lower. These findings show that spatiotemporal analysis and nonlinear dynamic analysis are capable of describing the complex dynamics of vocal fold vibrations from high-speed imaging and may potentially be helpful for understanding disordered behaviors in biomedical laryngeal systems.     

A model for vocal fold vibratory motion, contact area, and the electroglottogram

The electroglottogram (EGG) has been conjectured to be related to the area of contact between the vocal folds. This hypothesis has been substantiated only partially via direct and indirect observations. In this paper, a simple model of vocal fold vibratory motion is used to estimate the vocal fold contact area as a function of time. This model employs a limited number of vocal fold vibratory features extracted from ultra high-speed laryngeal films. These characteristics include the opening and closing vocal fold angles and the lag (phase difference) between the upper and lower vocal fold margins. The electroglottogram is simulated using the contact area, and the EGG waveforms are compared to measured EGGs for normal male voices producing both modal and pulse register tones. The model also predicts EGG waveforms for vocal fold vibration associated with a nodule or polyp.     

Nonlinear dynamics of the voice: Signal analysis and biomechanical modeling

Irregularities in voiced speech are often observed as a consequence of vocal fold lesions, paralyses, and other pathological conditions. Many of these instabilities are related to the intrinsic nonlinearities in the vibrations of the vocal folds. In this paper, bifurcations in voice signals are analyzed using narrow-band spectrograms. We study sustained phonation of patients with laryngeal paralysis and data from an excised larynx experiment. These spectrograms are compared with computer simulations of an asymmetric 2-mass model of the vocal folds. (c) 1995 American Institute of Physics.     

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.     

Resonance properties of the vocal folds: in vivo laryngoscopic investigation of the externally excited laryngeal vibrations

The study presents the first attempt to investigate resonance properties of the living vocal folds by means of laryngoscopy. Laryngeal vibrations were excited via a shaker placed on the neck of a male subject and observed by means of videostroboscopy and videokymography (VKG). When the vocal folds were tuned to the phonation frequency of 110 Hz and sinusoidal vibration with sweeping frequency (in the range 50-400 Hz) was delivered to the larynx, three clearly pronounced resonance peaks at frequencies around 110, 170, and 240 Hz were identified in the vocal fold tissues. Different modes of vibration of the vocal folds, observed as distinct lateral-medial oscillations with one, two, and three half-wavelengths along the glottal length, respectively, were associated with these resonance frequencies. At the external excitation frequencies below 100 Hz, vibrations of the ventricular folds, aryepiglottic folds and arytenoid cartilages were dominant in the larynx.     

Studying vocal fold vibrations in Parkinson's disease with a nonlinear model

A nonlinear model is applied to study pathologic vocal vibratory characteristics and voice treatments of Parkinson's disease. We find that a number of pathologic vocal characteristics commonly observed in Parkinson's disease, including reduced vibratory intensity, incomplete vocal closure, increased phonation threshold pressure, glottal tremor, subharmonics, and chaotic vocal fold vibrations, can be studied with this nonlinear model. We also find that two kinds of clinical voice treatments for Parkinson's disease, including respiratory effort treatment and Lee Silverman voice treatment can be studied with this computer model. Results suggest that respiratory effort treatment, in which subglottal pressure is increased, might aid in enhancing vibratory intensity, improving glottal closure, and avoiding vibratory irregularity. However, the Lee Silverman voice treatment, in which both subglottal pressure and vocal fold adduction are increased, might be better than respiratory effort treatment. Increasing vocal fold thickness would be further helpful to improve these pathologic characteristics. The model studies show consistencies with clinical observations. Computer models may be of value in understanding the dynamic mechanism of disordered voices and studying voice treatment effects in Parkinson's disease.     

Vibration in a self-oscillating vocal fold model with left-right asymmetry in body-layer stiffness

This study compares the phonatory behavior of an asymmetric vocal fold model to that of each individual vocal fold model in a hemi-configuration. Although phonation frequencies of the two folds in hemi-configurations had a ratio close to 1:3, a subharmonic synchronization between the two folds was not observed in the asymmetric model. Instead, the vibratory behavior was dominated by the dynamics of one fold only, and the other fold was enslaved to vibrate at the same frequency. Increasing subglottal pressure induced a shift in relative dominance between the two folds, leading to abrupt changes in both vibratory pattern and frequency.     

Comparison of biomechanical modeling of register transitions and voice instabilities with excised larynx experiments

Voice instabilities were studied using excised human larynx experiments and biomechanical modeling. With a controlled elongation of the vocal folds, the experiments showed registers with chest-like and falsetto-like vibrations. Observed instabilities included abrupt jumps between the two registers exhibiting hysteresis, aphonic episodes, subharmonics, and chaos near the register transitions. In order to model these phenomena, a three-mass model was constructed by adding a third mass on top of the simplified two-mass model. Simulation studies showed that the three-mass model can vibrate in both chest-like and falsetto-like patterns. Variation of tension parameters which mimic activities of laryngeal muscles could induce transitions between both registers. For reduced prephonatory areas and damping constants, extended coexistence of chest and falsetto registers was found, in agreement with experimental data. Subharmonics and deterministic chaos were observed close to transitions between the registers. It is concluded that the abrupt changes between chest and falsetto registers can be understood as shifts in dominance of eigenmodes of the vocal folds.     

Material parameter computation for multi-layered vocal fold models

Today, the prevention and treatment of voice disorders is an ever-increasing health concern. Since many occupations rely on verbal communication, vocal health is necessary just to maintain one's livelihood. Commonly applied models to study vocal fold vibrations and air flow distributions are self sustained physical models of the larynx composed of artificial silicone vocal folds. Choosing appropriate mechanical parameters for these vocal fold models while considering simplifications due to manufacturing restrictions is difficult but crucial for achieving realistic behavior. In the present work, a combination of experimental and numerical approaches to compute material parameters for synthetic vocal fold models is presented. The material parameters are derived from deformation behaviors of excised human larynges. The resulting deformations are used as reference displacements for a tracking functional to be optimized. Material optimization was applied to three-dimensional vocal fold models based on isotropic and transverse-isotropic material laws, considering both a layered model with homogeneous material properties on each layer and an inhomogeneous model. The best results exhibited a transversal-isotropic inhomogeneous (i.e., not producible) model. For the homogeneous model (three layers), the transversal-isotropic material parameters were also computed for each layer yielding deformations similar to the measured human vocal fold deformations.     

Nonlinear behavior of vocal fold vibration: The role of coupling between the vocal folds

Coupling between the vocal folds is one of the nonlinear mechanisms allowing regulation and synchronization of mucosal vibration. The purpose of this study was to establish that modulations such as diplophonia and abnormalities observed in vocal signals that may be observed in some cases of laryngeal pathology can be considered as nonlinear behavior due to the persistence of some physical interaction (coupling). An experimental model using excised porcine larynx was designed to create tension asymmetry between the vocal folds and to obtain vocal signals with modulations. Signals were analyzed by spectral analysis and the phase portrait method. Results were compared with computer-generated synthetic signals corresponding to nonlinear combinations of sinusoid signals. Under these conditions, evidence of nonlinear behavior was detected in 85% of experimental signals. These findings were interpreted as a demonstration of vocal fold interaction. Based on these findings, the authors conclude that (1) coupling must be taken into account in physical models of laryngeal physiology, and that (2) methods of nonlinear dynamics may be used for objective voice analysis.     

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.     

Phonation thresholds as a function of laryngeal size in a two-mass model of the vocal folds

This letter analyzes the oscillation onset-offset conditions of the vocal folds as a function of laryngeal size. A version of the two-mass model of the vocal folds is used, coupled to a two-tube approximation of the vocal tract in configuration for the vowel /a/. The standard male configurations of the laryngeal and vocal tract models are used as reference, and their dimensions are scaled using a single factor. Simulations of the vocal fold oscillation and oral output are produced for varying values of the scaling factor. The results show that the oscillation threshold conditions become more restricted for smaller laryngeal sizes, such as those appropriate for females and children.