Finite element modeling of vocal fold bulging with thyroarytenoid activation

Experimental data suggested that the change between chest and falsetto is determined by the muscles of the larynx, specifically the thyroarytenoid muscle, and the resultant bulging of the vocal fold. However, a finite element model has not been developed to demonstrate that the physiological and acoustic changes associated with a shift between chest and falsetto voice can be achieved solely by muscle activations. Because finite element models of the vocal fold to date have not explicitly calculated the change in the shape of the medial surface, or bulging, as a result of muscle contraction, this project sought to advance the state of vocal fold modeling by explicitly calculating medial surface bulging resulting from the activation of the thyroarytenoid muscle and implicitly accounting for the effects of the other intrinsic laryngeal muscles and then applied that model to the question of medial bulging inducing a change between chest voice and falsetto.

Initial modeling was compared to data from a live canine. These data pointed to the importance of muscle fiber orientation for allowing the muscularis and vocalis, two parts of the thyroarytenoid, to function differently. The most important finding was that the surface of the vocal fold touching the thyroid cartilage needed to be able to slide along the thyroid to allow the cases with large amounts of lengthening or shortening to solve.

The learning from the canine model was transferred to a human model that was used to calculate the medial surface for a variety of muscle activations. The most important change to the human model was the change from the Blemker model to the transverse-isotropic Mooney-Rivlin model to accommodate the large motions in the model. Also important was the reduction and relocation of the ligament to the medial superior region of the vocal fold, which allowed the inferior medial surface to abduct sufficiently to differentiate between chest and falsetto.

The human model was solved for the expected range of muscle activations and the resulting medial surface bulging regressed as a function of position on the medial surface and muscle activation. Significant observations from those solutions included the importance of the model constraints allowing thinning in the vertical direction. Also significant was the observation that at high strains, TA activation tended to provide resistance to inferior abduction rather than bulging, which bore a strong resemblance to stress stiffening.

The regression of the medial surface bulging resulted in a fit that had more bowing than was predicted by VoxInSilico, a voice simulation program. The additional bowing altered the spectral slope of the chest solution but did not affect the spectral slope of the falsetto solution. Despite the additional bowing in the regression, the difference in spectral slope between chest voice and falsetto remained.