Modeling of chaotic vibrations in symmetric vocal folds

Normal Voice in Children Between 6 and 12 Years of Age: Database and Nonlinear Analysis

This study was carried out using a transversal design. It aimed to investigate possible changes of the normal voice in children before mutation, to create a database for the parameters used in the study, and to examine the use of fractal dimension and the largest Lyapunov exponent (LLE) in the assessment of nonpathological phenomena. Two hundred twelve children were enrolled: 111 females and 101 males; and 9 six-year-olds, 24 seven-year-olds, 18 eight-year-olds, 25 nine-year-olds, 27 ten-year-olds, 55 eleven-year-olds, and 54 twelve-year-olds. Fundamental frequency (Fo) decreased with age and was lower in boys than in girls. Jitter and shimmer did not significantly differ with age or gender. Fractal dimension and LLE were significantly lower in boys; LLE decreased with age. The present series confirmed the established findings that Fo is lower in boys than in girls, even before mutation, and decreases with age; two other classical voice analysis parameters, jitter and shimmer, also showed the same behavior as described in the literature. The study of nonlinear parameters (fractal dimension and LLE) showed that laryngeal dynamics is more stable in boys than in girls, and that stability is correlated with age.

Nonlinear dynamic mechanism of vocal tremor from voice analysis and model simulations

Nonlinear dynamic analysis and model simulations are used to study the nonlinear dynamic characteristics of vocal folds with vocal tremor, which can typically be characterized by low frequency modulation and aperiodicity. Tremor voices from patients with disorders such as paresis, Parkinson's disease, hyperfunction, and adductor spasmodic dysphonia show low-dimensional characteristics, differing from random noise. Correlation dimension analysis statistically distinguishes tremor voices from normal voices. Furthermore, a nonlinear tremor model is proposed to study the vibrations of the vocal folds with vocal tremor. Fractal dimensions and positive Lyapunov exponents demonstrate the evidence of chaos in the tremor model, where amplitude and frequency play important roles in governing vocal fold dynamics. Nonlinear dynamic voice analysis and vocal fold modeling may provide a useful set of tools for understanding the dynamic mechanism of vocal tremor in patients with laryngeal diseases.

Chaotic component obscured by strong periodicity in voice production system

The effect of glottal aerodynamics in producing the nonlinear characteristics of voice is investigated by comparing the outputs of the asymmetric composite model and the two-mass model. The two-mass model assumes the glottal airflow to be laminar, nonviscous, and incompressible. In this model, when the asymmetric factor is decreased from 0.65 to 0.35, only 1:1 and 1:2 modes are detectable. However, with the same parameters, four vibratory modes (1:1, 1:2, 2:4, 2:6) are found in the asymmetric composite model using the Navier-Stokes equations to describe the complex aerodynamics in the glottis. Moreover, the amplitude of the waveform is modulated by a small-amplitude noiselike series. The nonlinear detection method reveals that this noiselike modulation is not random, but rather it is deterministic chaos. This result agrees with the phenomenon often seen in voice, in which the voice signal is strongly periodic but modulated by a small-amplitude chaotic component. The only difference between the two-mass model and the composite model is in their descriptions of glottal airflow. Therefore, the complex aerodynamic characteristics of glottal airflow could be important in generating the nonlinear dynamic behavior of voice production, including bifurcation and a small-amplitude chaotic component obscured by strong periodicity.

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.

A biphasic theory for the viscoelastic behaviors of vocal fold lamina propria in stress relaxation

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.

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.

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.

Asymmetric airflow and vibration induced by the Coanda effect in a symmetric model of the vocal folds

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.

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.

Exploiting nonlinear recurrence and fractal scaling properties for voice disorder detection

BACKGROUND

Voice disorders affect patients profoundly, and acoustic tools can potentially measure voice function objectively. Disordered sustained vowels exhibit wide-ranging phenomena, from nearly periodic to highly complex, aperiodic vibrations, and increased "breathiness". Modelling and surrogate data studies have shown significant nonlinear and non-Gaussian random properties in these sounds. Nonetheless, existing tools are limited to analysing voices displaying near periodicity, and do not account for this inherent biophysical nonlinearity and non-Gaussian randomness, often using linear signal processing methods insensitive to these properties. They do not directly measure the two main biophysical symptoms of disorder: complex nonlinear aperiodicity, and turbulent, aeroacoustic, non-Gaussian randomness. Often these tools cannot be applied to more severe disordered voices, limiting their clinical usefulness.

METHODS

This paper introduces two new tools to speech analysis: recurrence and fractal scaling, which overcome the range limitations of existing tools by addressing directly these two symptoms of disorder, together reproducing a "hoarseness" diagram. A simple bootstrapped classifier then uses these two features to distinguish normal from disordered voices.

RESULTS

On a large database of subjects with a wide variety of voice disorders, these new techniques can distinguish normal from disordered cases, using quadratic discriminant analysis, to overall correct classification performance of 91.8 +/- 2.0%. The true positive classification performance is 95.4 +/- 3.2%, and the true negative performance is 91.5 +/- 2.3% (95% confidence). This is shown to outperform all combinations of the most popular classical tools.

CONCLUSION

Given the very large number of arbitrary parameters and computational complexity of existing techniques, these new techniques are far simpler and yet achieve clinically useful classification performance using only a basic classification technique. They do so by exploiting the inherent nonlinearity and turbulent randomness in disordered voice signals. They are widely applicable to the whole range of disordered voice phenomena by design. These new measures could therefore be used for a variety of practical clinical purposes.

Determination of phonation instability pressure and phonation pressure range in excised larynges

PURPOSE

The present study was a methodological study designed to reveal the dynamic mechanisms of phonation instability pressure (PIP) using bifurcation analysis. Phonation pressure range (PPR) was also proposed for assessing the pressure range of normal vocal fold vibrations.

METHOD

The authors first introduced the concept of bifurcation on the basis of a symmetric vocal fold model and then applied the bifurcation analysis to data from excised larynges. By recording acoustic signals from 10 excised larynges, the authors measured phonation threshold pressure (PTP), PIP, and PPR at the bifurcation pressure points from the spectrograms as subglottal pressure was progressively increased. Furthermore, to investigate the effects of vocal fold elongation on PTP, PIP, and PPR, the authors manipulated the elongation of the vocal folds at 0%, 5%, 10%, and 15% of the resting vocal fold length.

RESULTS

The authors found that PTP, PIP, and PPR were effectively determined using the bifurcation analysis. When vocal fold elongation was increased from 0% to 15%, PTP was significantly increased (p < .001), PIP was not significantly changed (p = .54), and PPR was significantly decreased (p = .003).

CONCLUSION

PIP and PPR represent important parameters to assess phonation instability. Bifurcation analysis represents a valuable procedure for revealing the mechanisms behind PTP, PIP, and PPR and for investigating the effects of vocal fold biomechanical parameters on these 3 pressure parameters.

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.

Phonatory Impairment in Parkinson's Disease: Evidence from Nonlinear Dynamic Analysis and Perturbation Analysis

Many persons with Parkinson's disease (PD) will eventually experience vocal impairment as their condition advances. Using standard perturbation analyses (parameters like jitter and shimmer) to measure fluctuations in phonatory signal may inhibit researchers from recognizing severely disordered patterns that seem to be present in the voices of some PD patients. Nonlinear dynamic analysis can quantify these aperiodic patterns, which indicate severe pathology that is usually characterized perceptually by hoarseness. Here, sustained vowel phonations of a heterogeneous group of PD subjects (20 women and 21 men) were compared with those of a control group (22 women and 18 men) based on results of nonlinear dynamic analyses (D(2)) and perturbation analyses. Results showed PD subjects as a whole to have significantly higher D(2) values than control subjects (P = 0.016), which indicates increased signal complexity in PD vocal pathology. Differences in the comparison of these two groups were significant in jitter (P = 0.014) but nonsignificant in shimmer (P = 0.695). Furthermore, the performance on these three measures was affected by subject sex. Nonlinear dynamic analysis showed significantly higher D(2) in the female PD group than in the female control group (P = 0.001), but jitter and shimmer did not show such a difference. The male PD group had statistically higher jitter than the male control group (P = 0.036), but these groups did not differ in D(2) or shimmer. Overall, nonlinear dynamic analysis may be a valuable method for the diagnosis of Parkinsonian laryngeal pathology.

The influence of epilarynx area on vocal fold dynamics

OBJECTIVE

This study investigated the influence of epilarynx area on an excised human vocal fold during phonation.

STUDY DESIGN

A hemilarynx set-up using an excised human larynx was used. An artificial vocal tract with an epilarynx tube of variable cross-sectional area was attached. High-speed imaging was performed and standard phonatory variables were measured.

RESULTS

Glottal airflow, fundamental frequency, and sound level increased as a function of subglottal pressure. A decrease in epilarynx area decreased phonation threshold pressure, glottal airflow, and vocal fold displacements and velocities.

CONCLUSIONS

Preliminary experimental results confirm that narrowing the epilarynx area facilitates phonation by decreasing phonation threshold pressure, presumably through impedance matching of the glottal source and vocal tract.

SIGNIFICANCE

As this phenomenon associated with epilarynx narrowing is further quantified and generalized, eventually new surgical alterations of the epilaryngeal structure may be suggested to facilitate phonation, in addition to standard phonosurgical procedures.

Anterior-posterior biphonation in a finite element model of vocal fold vibration

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.

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.

An asymmetric smooth contour two-mass model for recurrent laryngeal nerve paralysis

Irregular vocal fold vibrations are assumed to be a major cause of hoarseness. A common clinical condition presenting with hoarseness is a unilateral recurrent laryngeal nerve paralysis (RLNP). In order to explain high-speed video recordings of clinical RLNP, RLNP-type vocal fold vibrations are simulated by extending the well known two-mass model (2MM) to an asymmetric smooth-contour two-mass model (SC2MM). Polynomial interpolations form a smooth surface over the lumped elements of the 2MM. Laryngeal asymmetry is accounted for by introduction of an asymmetry coefficient and an anterior commissure angle which models a variable glottal closure insufficiency. Compared to the 2MM, the SC2MM yields a smaller glottal volume flow and is more stable in critical parameter constellations of RLNP-like conditions. It is able to model the vocal fold dynamics during a glottal closure insufficiency.

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

In this paper, we apply an iterative parameter adaption scheme based on chaos synchronization to estimate system parameters of the asymmetric vocal folds from glottal area time series. The original asymmetric vocal-fold system associated with recurrent laryngeal paralysis shows chaotic vibrations with positive Lyapunov exponents. Aperiodic glottal area time series from the original system will be applied as the feedback variable coupling the simulative and the original vocal-fold systems. The parameter adaption technique based on chaos synchronization is employed to manipulate the simulative system parameters. The chaotic vibrations, system parameters, and the bifurcation diagram of the original vocal-fold system can be exactly reproduced in the simulative system, and the two chaotic systems can be synchronized. Furthermore, the effects of noise, sampling rate, and equation difference due to nonlinear spring terms on vocal-fold parameter estimations are investigated. Despite large noise perturbations, large equation differences, and low sampling rate, the parameter adaption scheme can effectively estimate the original vocal-fold system parameters. This study provides a theoretical base to apply chaos synchronization to estimate the vocal-fold system parameters from the glottal area data and show its potential application in laryngeal physiology.

Some Physiological Correlates to Regular and Irregular Phonation at the End of an Utterance

This article examines respiratory and acoustic events at the ends of utterances that coincide with the end of a breath. All utterances end with a vowel. Between the start of the final fall in signal amplitude and the end of phonation, the alveolar pressure falls by 1.2-2.6 cm H2O, on average, and glottal area increases by a factor of 4.0 (median). The mean glottal area at the end of phonation ranges from 9.6 to 13.5 mm2 across subjects. Physiological correlates are examined for utterances that end with regular and with irregular phonation. Irregular phonation is usually produced with brief intervals of adduction followed by longer intervals of abduction and/or with incomplete closure of the folds. This physiological correlate to irregular phonation is not consistent with descriptions of vocal fry or creaky voice in which the vocal folds are tightly adducted over most of the cycle. The rise in average glottal area and drop in alveolar pressure were similar for utterances that ended with regular phonation and those that ended with irregular phonation. These data suggest that a similar phonation-ending gesture underlies both groups of utterances. This gesture includes abduction of the vocal folds and a drop in alveolar pressure.

Simulation of vocal fold impact pressures with a self-oscillating finite-element model

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.

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.

Perturbation and Nonlinear Dynamic Analyses of Voices from Patients with Unilateral Laryngeal Paralysis

This study used perturbation methods (eg, jitter and shimmer) and nonlinear dynamic methods (eg, phase space reconstruction and correlation dimension) to analyze sustained voices generated by normal subjects and patients with unilateral laryngeal paralysis. We found that normal and pathological voices had low-dimensional dynamic characteristics. For nearly periodic voices, jitter and shimmer values of pathological voices from patients with unilateral laryngeal paralysis were significantly different from normal voices. For nearly periodic and aperiodic voices, the correlation dimensions of pathological voices were statistically higher than normal voices. Receiver operating characteristic analysis was used to evaluate the diagnostic performances of jitter, shimmer, and correlation dimension. High sensitivity and specificity of these three acoustic analyses in distinguishing unilateral laryngeal paralysis patients from normal subjects were found. We concluded that combining traditional perturbation analysis and nonlinear dynamic analysis might provide efficient descriptions of pathological voices and represent a valuable tool for clinical diagnosis of laryngeal paralysis.

Comparison of nonlinear dynamic methods and perturbation methods for voice analysis

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.

Spatiotemporal chaos in excised larynx vibrations

Spatiotemporal chaos in excised larynx vibrations is reported using high-speed digital imaging. Spatiotemporal correlation and eigenmode analyses are applied to describe the spatiotemporal dynamics of the vocal fold vibrations and to investigate the effects of subglottal pressure. High subglottal pressures cause spatiotemporal chaos with decreased spatiotemporal correlation and increased entropy in the vocal fold vibrations. Spatiotemporal analysis shows a valuable biomedical application in investigating the spatiotemporal chaotic dynamics of the vocal fold system.

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.

Recurrence plot analysis of nonstationary data: the understanding of curved patterns

Recurrence plots of the calls of the Nomascus concolor (Western black crested gibbon) and Hylobates lar (White-handed gibbon) show characteristic circular, curved, and hyperbolic patterns superimposed to the main temporal scale of the signal. It is shown that these patterns are related to particular nonstationarities in the signal. Some of them can be reproduced by artificial signals like frequency modulated sinusoids and sinusoids with time divergent frequency. These modulations are too faint to be resolved by conventional time-frequency analysis with similar precision. Therefore, recurrence plots act as a magnifying glass for the detection of multiple temporal scales in slightly modulated signals. The detected phenomena in these acoustic signals can be explained in the biomechanical context by taking in account the role of the muscles controlling the vocal folds.

Measurement of vocal fold collision forces during phonation: methods and preliminary data

Forces applied to vocal fold tissue as the vocal folds collide may cause tissue injury that manifests as benign organic lesions. A novel method for measuring this quantity in humans in vivo uses a low-profile force sensor that extends along the length and depth of the glottis. Sensor design facilitates its placement and stabilization so that phonation can be initiated and maintained while it is in place, with minimal interference in vocal fold vibration. In 2 individuals with 1 vibrating vocal fold and 1 nonvibrating vocal fold, peak collision force correlates more strongly with voice intensity than pitch. Vocal fold collision forces in 1 individual with 2 vibrating vocal folds are of the same order of magnitude as in previous studies. Correlations among peak collision force, voice intensity, and pitch were indeterminate in this participant because of the small number of data points. Sensor modifications are proposed so that it can be used to reliably estimate collision force in individuals with 2 vibrating vocal folds and with changing vocal tract conformations.

Nonlinear phenomena in contemporary vocal music

Complex and multiphonic voice signals of vocal improvisors are analyzed within the framework of nonlinear dynamics. Evidence is given that nonlinear phenomena are extensively used by performers associated with contemporary music. Narrow-band spectrograms of complex vocalizations are used to visualize the appearance of nonlinear phenomena (spectral bifurcation diagrams). Possible production mechanisms are discussed in connection with previous research, personal performance and pedagogical experience. Examples for period doubling, biphonation and irregular aperiodic phonation in vocal sonorities of contemporary vocal improvisors are given, and glottal whistle production encompassed with biphonation and triphonation is shown. Furthermore, coincidences of harmonics-formant matching associated with abrupt transitions to subharmonics and biphonation in the vocal output are provided. This also shows the recurrent use of nonlinear phenomena by performers. It is argued that mechanisms such as source-tract coupling or vocal fold desynchronization due to asymmetry are used in a reproducible way for musical tasks.

Chaotic vibrations of a vocal fold model with a unilateral polyp

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.

Estimating model parameters by chaos synchronization

Using chaos synchronization and a proposed iterative method of parameter adaptation, we precisely estimate the model parameters of chaotic systems and synchronize two chaotic systems with originally mismatching model parameters. This parameter adaptation method can be applied to a spatiotemporal chaotic system with a one-way-coupled map lattice. As a biomedical application, this method is capable of estimating the asymmetric tension parameter of a vocal fold model.

Nonlinear dynamics of phonations in excised larynx experiments

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.

Bifurcations and chaos in the cries of full-term and preterm infants

Pain-induced crying episodes were collected from groups of full-term and preterm infants and analyzed acoustically for the relative occurrence of various dysphonation segments. The crying episodes of full-term infants were found to contain a greater number of bifurcation and aperiodic segments compared to preterm infants. The results suggest that bifurcation and aperiodic segments are normally occurring phonatory events during infant crying. The differences observed between infant groups are discussed in regard to neuromaturational differences in infants' expression to a painful stimulus.

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.

Vibration parameter extraction from endoscopic image series of the vocal folds

An approach is given to extract parameters affecting phonation based upon digital high-speed recordings of vocal fold vibrations and a biomechanical model. The main parameters which affect oscillation are vibrating masses, vocal fold tension, and subglottal air pressure. By combining digital high-speed observations with the two-mass-model by Ishizaka and Flanagan (1972) as modified by Steinecke and Herzel (1995), an inversion procedure has been developed which allows the identification and quantization of laryngeal asymmetries. The problem is regarded as an optimization procedure with a nonconvex objective function. For this kind of problem, the choice of appropriate initial values is important. This optimization procedure is based on spectral features of vocal fold movements. The applicability of the inversion procedure is first demonstrated in simulated vocal fold curves. Then, inversion results are presented for a healthy voice and a hoarse voice as a case of functional dysphonia caused by laryngeal asymmetry.