Aerodynamics and Lumped-Masses Combined with Delay Lines for Modeling Vertical and Anterior-Posterior Phase Differences in Pathological Vocal Fold Vibration

We discuss the representation of anterior-posterior (A-P) phase differences in vocal cord oscillations through a numerical biomechanical model involving lumped elements as well as distributed elements, i.e., delay lines. A dynamic glottal source model is illustrated in which the fold displacement along the vertical and the longitudinal dimensions is explicitly modeled by numerical waveguide components representing the propagation on the fold cover tissue. In contrast to other models of the same class, in which the reproduction of longitudinal phase differences are intrinsically impossible (e.g., in two-mass models) or not easy to control explicitely (e.g., in 3D 16-mass and multi-mass models in general), the one proposed here provides direct control over the amount of phase delay between folds oscillations at the posterior and anterior side of the glottis, while keeping the dynamic model simple and computationally efficient. The model is assessed by addressing the reproduction of typical oscillatory patterns observed in high-speed videoendoscopic data, in which A-P phase differences are observed. Experimental results are provided which demonstrate the ability of the approach to effectively reproduce different oscillatory patterns of the vocal folds.