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

The quality and timbre of disordered voices heavily rely on the vibration properties of the vocal folds. We discuss the representation of sagittal phase differences in vocal fold oscillations through a numerical biomechanical model involving lumped elements as well as distributed elements, i.e., delay lines. A dynamic glottal source model is proposed in which the fold displacement along the vertical and the sagittal dimensions is modelled using delay lines. In contrast to other models, with which the reproduction of sagittal phase differences is 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, i.e., the sagittal axis, and at the superior and inferior part of the glottis, i.e., the vertical axis, 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 sagittal phase differences are observed. Also, timing asymmetry parameters observed in hemi glottal area waveforms (GAWs) are used for fitting.