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.
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