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Introduction: In a recent publication, the phasegram, a bifurcation diagram over time, has been introduced as an intuitive visualization tool for assessing the vibratory states of oscillating systems. Here, this nonlinear dynamics approach is augmented with quantitative analysis parameters, and it is applied to clinical laryngeal high-speed video (HSV) endoscopic recordings of healthy and pathological phonations., Methods: HSV data from a total of 73 females diagnosed as healthy (n = 42), or with functional dysphonia (n = 15) or with unilateral vocal fold paralysis (n = 16), were quantitatively analyzed. Glottal area waveforms (GAW) and left and right hemi-GAWs (hGAW) were extracted from the HSV recordings. Based on Poincaré sections through phase space-embedded signals, two novel quantitative parameters were computed: the phasegram entropy (PE) and the phasegram complexity estimate (PCE), inspired by signal entropy and correlation dimension computation, respectively., Results: Both PE and PCE assumed higher average values (suggesting more irregular vibrations) for the pathological as compared with the healthy participants, thus significantly discriminating healthy group from the paralysis group (P = 0.02 for both PE and PCE). Comparisons of individual PE or PCE data for the left and the right hGAW within each subject resulted in asymmetry measures for the regularity of vocal fold vibration. The PCE-based asymmetry measure revealed significant differences between the healthy group and the paralysis group (P = 0.03)., Conclusions: Quantitative phasegram analysis of GAW and hGAW data is a promising tool for the automated processing of HSV data in research and in clinical practice., (Copyright © 2016 The Voice Foundation. Published by Elsevier Inc. All rights reserved.)

Biomechanical modeling and bifurcation theory are applied to study phonation onset and register transition. A four-mass body-cover model with a smooth geometry is introduced to reproduce characteristic features of chest and falsetto registers. Sub- and supraglottal resonances are modeled using a wave-reflection model. Simulations for increasing and decreasing subglottal pressure reveal that the phonation onset exhibits amplitude jumps and hysteresis referring to a subcritical Hopf bifurcation. The onset pressure is reduced due to vocal tract resonances. Hysteresis is observed also for the voice breaks at the chest-falsetto transition. Varying the length of the subglottal resonator has only minor effects on this register transition. Contrarily, supraglottal resonances have a strong effect on the pitch, at which the chest-falsetto transition is found. Experiment of glissando singing shows that the supraglottis has indeed an influence on the register transition.

A nonlinear modeling approach is presented for the reconstruction of the synchronization structure in an asymmetric two-mass model from time series data. The asymmetric two-mass model describes a variety of normal and pathological human voices associated with synchronous and desynchronous oscillations of the two asymmetric vocal folds. Our technique recovers the synchronization diagram, which yields the regimes of synchronization as well as desynchronization, which are dependent upon the asymmetry parameter and the subglottal pressure. This allows the prediction of the regime of pathological phonation associated with desynchronization of the vocal folds from a few sets of recorded time series. It is shown that the modeling is quite effective when the time series data are chaotic and if they are taken from a regime of desynchronization. We discuss the applicability of the present approach as a diagnostic tool for voice pathologies.

This report is on direct observation and modal analysis of irregular spatio-temporal vibration patterns of vocal fold pathologies in vivo. The observed oscillation patterns are described quantitatively with multiline kymograms, spectral analysis, and spatio-temporal plots. The complex spatio-temporal vibration patterns are decomposed by empirical orthogonal functions into independent vibratory modes. It is shown quantitatively that biphonation can be induced either by left-right asymmetry or by desynchronized anterior-posterior vibratory modes, and the term "AP (anterior-posterior) biphonation" is introduced. The presented phonation examples show that for normal phonation the first two modes sufficiently explain the glottal dynamics. The spatio-temporal oscillation pattern associated with biphonation due to left-right asymmetry can be explained by the first three modes. Higher-order modes are required to describe the pattern for biphonation induced by anterior-posterior vibrations. Spatial irregularity is quantified by an entropy measure, which is significantly higher for irregular phonation than for normal phonation. Two asymmetry measures are introduced: the left-right asymmetry and the anterior-posterior asymmetry, as the ratios of the fundamental frequencies of left and right vocal fold and of anterior-posterior modes, respectively. These quantities clearly differentiate between left-right biphonation and anterior-posterior biphonation. This paper proposes methods to analyze quantitatively irregular vocal fold contour patterns in vivo and complements previous findings of desynchronization of vibration modes in computer modes and in in vitro experiments.

Direct observations of nonstationary asymmetric vocal-fold oscillations are reported. Complex time series of the left and the right vocal-fold vibrations are extracted from digital high-speed image sequences separately. The dynamics of the corresponding high-speed glottograms reveals transitions between low-dimensional attractors such as subharmonic and quasiperiodic oscillations. The spectral components of either oscillation are given by positive linear combinations of two fundamental frequencies. Their ratio is determined from the high-speed sequences and is used as a parameter of laryngeal asymmetry in model calculations. The parameters of a simplified asymmetric two-mass model of the larynx are preset by using experimental data. Its bifurcation structure is explored in order to fit simulations to the observed time series. Appropriate parameter settings allow the reproduction of time series and differentiated amplitude contours with quantitative agreement. In particular, several phase-locked episodes ranging from 4:5 to 2:3 rhythms are generated realistically with the model.

Although the mammalian larynx exhibits little structural variation compared to sound-producing organs in other taxa (birds or insects), there are some morphological features which could lead to significant differences in acoustic functioning, such as air sacs and vocal membranes. The vocal membrane (or "vocal lip") is a thin upward extension of the vocal fold that is present in many bat and primate species. The vocal membrane was modeled as an additional geometrical element in a two-mass model of the larynx. It was found that vocal membranes of an optimal angle and length can substantially lower the subglottal pressure at which phonation is supported, thus increasing vocal efficiency, and that this effect is most pronounced at high frequencies. The implications of this finding are discussed for animals such as bats and primates which are able to produce loud, high-pitched calls. Modeling efforts such as this provide guidance for future empirical investigations of vocal membrane structure and function, can provide insight into the mechanisms of animal communication, and could potentially lead to better understanding of human clinical disorders such as sulcus vocalis.

Phonation onset is discussed in the framework of dynamical systems as a Hopf bifurcation, i.e., as a transition from damped to sustained vocal fold oscillations due to changes of parameters defining the underlying laryngeal configuration (e.g., adduction, subglottal pressure, muscular activity). An analytic envelope curve of the oscillation onset is deduced by analyzing the Hopf bifurcation in mathematical models of the vocal folds. It is governed by a single time constant which can be identified with the physiological parameter phonation onset time. This parameter reflects the laryngeal state prior to phonation and can be used as a quantitative classification criterion in order to assess the phonation onset in clinical diagnosis. The extraction of the phonation onset time from simulated time series using a simplified two-mass model and from digital high-speed videos is described in detail. It shows a good agreement between theory and measurement.

Vocal fold vibration patterns during phonation are presented with different digital imaging systems. With newly developed technical equipment color images up to 1000 digital images/s were obtained without light intensifying enhancement techniques via rigid and flexible endoscopy. With this color high-speed system, morphologic structures, such as small blood vessels, were visualized in high-resolution quality as a result of additional color information. In another system, zooming of endoscopic pictures via pixel interpolation algorithms provided full-monitor presentation of vocal fold vibratory patterns. This system allows PC-based synchronization with microphone and electroglottographic signals in a frame-by-frame technique. Although only processing gray scale images, analyses of dynamic changes in modes of vibration were facilitated by the higher frame rate recording of up to 2000 frames/s and, in addition, they display corresponding analog signals. Both methods provide clinically important information. Furthermore, we demonstrated irregular vocal fold vibration patterns in a healthy adult volunteer. In this experiment, the irregular vibratory modes were induced by voluntarily applying asymmetric vocal fold tension. The asymmetric vocal fold vibration pattern resulted in (functionally induced) roughness of the voice as predicted by computer models of asymmetric vocal fold vibration. Digital high-speed cinematography proved to be a highly promising technique in the analysis of dysphonia and provided physiological examples that could be compared with models of coupled nonlinear oscillators.

Several authors have recently demonstrated the intimate relationship between nonlinear dynamics and observations in vocal fold vibration (Herzel, 1993; Mende, Herzel, & Wermke, 1990; Titze, Baken, & Herzel, 1993). The aim of this paper is to analyze vocal disorders from a nonlinear dynamics point of view. Basic concepts and analysis techniques from nonlinear dynamics are reviewed and related to voice. The voices of several patients with vocal disorders are analyzed using traditional voice analysis techniques and methods from nonlinear dynamics. The two methods are shown to complement each other in many ways. Likely physiological mechanisms of the observed nonlinear phenomena are presented, and it is shown how much of the terminology in the literature describing rough voice can be unified within the framework of nonlinear dynamics.

Empirical orthogonal eigenfunctions are extracted from biomechanical simulations of normal and chaotic vocal fold oscillations. For normal phonation, two dominant empirical eigenfunctions capture the vibration patterns of the folds and exhibit a 1:1 entrainment. The eigenfunctions show some correspondence to theoretical low-order normal modes of a simplified, three-dimensional elastic continuum, and to the normal modes of a linearized two-mass model. The eigenfunctions also facilitate a physical interpretation of energy transfer mechanisms in vocal fold dynamics. Subharmonic regimes and chaotic oscillations are observed during simulations of a lax cover, in which case at least three empirical eigenfunctions are necessary to capture the resulting vocal fold oscillations. These chaotic oscillations might be understood in terms of a desynchronization of a few of the low-order modes, and may be related to mechanisms of creaky voice or vocal fry. Furthermore, some of the empirical eigenfunctions captured during complex oscillations correspond to higher-order normal modes described in earlier theoretical work. The empirical eigenfunctions may also be useful in the design of lower-order models (valid over the range for which the empirical eigenfunctions remain more or less constant), and may help facilitate bifurcation analyses of the biomechanical simulation.