Modelling longitudinal phase differences in a lumped and distributed elements vocal fold model

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 modeled using numerical waveguide components. In contrast to other models, in which the reproduction of longitudinal phase differences are impossible (e.g., in two-mass models) or not easy to control (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 part of the glottis, while keeping the dynamic model simple and computationally efficient. The model is assessed by addressing the reproduction of oscillatory patterns observed in high-speed videoendoscopic data, in which A-P phase differences are observed, and of parameters related to the glottal area waveform.