A computational study of depth of vibration into vocal fold tissues.

The effective depth of vocal fold vibration is self-regulated and generally not known a priori in vocalization. In this study, the effective depth was quantified systematically under various phonatory conditions using a fiber-gel finite element vocal fold model. The horizontal and vertical excursions of each finite element nodal point trajectory were recorded to compute trajectory areas. The extent of vibration was then studied based on the variation of trajectory radii as a function of depth in several coronal sections along the anterior-posterior direction. The results suggested that the vocal fold nodal trajectory excursions decrease systematically as a function of depth but are affected by the layered structure of the vocal folds. The effective depth of vibration was found to range between 15 and 55% of the total anatomical depth across all phonatory conditions. The nodal trajectories from the current study were compared qualitatively with the results from excised human hemi-larynx experiments published in Döllinger and Berry [(2006). J. Voice. 20(3), 401-413]. An estimate of the effective mass of a one-mass vocal fold model was also computed based on the effective depth of vibration observed in this study under various phonatory conditions.