Patrick Mergell

Irregular vocal-fold vibration—High-speed observation and modeling

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.

Modelling biphonation—the role of the vocal tract

Abstract Instabilities of the human voice source appear in normal voices under certain conditions (newborn cries, vocal fry, creaky voice) and are symptomatic of voice pathologies. Vocal instabilities are intimately related to bifurcations of the underlying nonlinear dynamical system. We analyse in this paper bifurcations in 2-mass models of the vocal folds and study, in particular, how the incorporation of the vocal tract affects bifurcation diagrams. A comparison of a simplified model (Steinecke and Herzel, 1995) with an extended version including vocal tract resonances reveals that essential features of the bifurcation diagrams (as e.g. frequency locking of both folds and toroidal oscillations) are found in both model versions. However, vocal instabilities appear in the extended model at lower subglottal pressures and even for weak asymmetries.

Phonation onset: Vocal fold modeling and high-speed glottography

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.

Quantitative characterization of functional voice disorders using motion analysis of high-speed video and modeling

A semi-automatic motion analysis software is used to extract elongation-time diagrams (trajectories) of vocal fold vibrations from digital high-speed video sequences. By combining digital image processing with biomechanical modeling we extract characteristic parameters such as phonation onset time and pitch. A modified two-mass model of the vocal folds is employed in order to fit the main features of the simulated time series to those of the extracted trajectories. Due to the variation of the model parameters, general conclusions can be made about laryngeal dysfunctions such as functional dysphonia. We show the first results of semi-automatic motion analysis in combination with model simulations as a step towards a computer aided diagnosis 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.