Material parameter computation for multi-layered vocal fold models

Abstract

Today, the prevention and treatment of voice disorders is an ever-increasing health concern. Since many occupations rely on verbal communication, vocal health is necessary just to maintain one's livelihood. Commonly applied models to study vocal fold vibrations and air flow distributions are self sustained physical models of the larynx composed of artificial silicone vocal folds. Choosing appropriate mechanical parameters for these vocal fold models while considering simplifications due to manufacturing restrictions is difficult but crucial for achieving realistic behavior. In the present work, a combination of experimental and numerical approaches to compute material parameters for synthetic vocal fold models is presented. The material parameters are derived from deformation behaviors of excised human larynges. The resulting deformations are used as reference displacements for a tracking functional to be optimized. Material optimization was applied to three-dimensional vocal fold models based on isotropic and transverse-isotropic material laws, considering both a layered model with homogeneous material properties on each layer and an inhomogeneous model. The best results exhibited a transversal-isotropic inhomogeneous (i.e., not producible) model. For the homogeneous model (three layers), the transversal-isotropic material parameters were also computed for each layer yielding deformations similar to the measured human vocal fold deformations.

Figure 1

An endoscopic view onto the vocal folds.

Figure 2

On the left, the view through the prism on the vocal fold is depicted. The two induced views enable the 3D computation of the suture positions. Here from the 3D coordinates of the sutures are computed. On the right, the reconstructed 3D vocal fold can be seen. Here, on suture S2 it was pulled applying 10 g.

Figure 3

Magnitude of displacement of sutures S2, S3, and S4 and the corresponding weights were applied.

Figure 4

Flowchart of the optimization process. Actions from CFS++ and SCPIP (shaded) are shown.

Figure 5

Geometry and boundary conditions used to validate the method.

Figure 6

3D model of the vocal fold showing the boundary conditions. Black: pressure, light gray: free boundaries, and dark gray: fixed boundaries.

Figure 7

3D model with mid-plane (left) that was used for generating a reference displacement using a forward simulation and corresponding 2D vocal fold model (right) used for the optimization process.

Figure 8

Comparison of optimal boundary displacement achieved with different material laws. The transversally isotropic optimization solution is clearly superior to the isotropic solution as can be seen in the close up.

Figure 9

Comparison of optimization results for different material laws to the reference displacement. The optimization was done in 3D combining five different load cases. The visualized curves show the deformation corresponding to one of these load cases at a cut in the vertical–lateral plane at the middle (left picture) and 3.4 mm left of the middle (right picture). The transversal-isotropic optimization is much more close to the reference displacement. Free transversal-isotropic material optimization, where a completely inhomogeneous material with transversal-isotropic material parameters varying from point to point is optimized, is just shown as a benchmark.

Figure 10

The surface displacement (solid vectors) at the sutures as extracted from the hemilarynx-experiments used as reference deformation for one load case with applied force (dashed vector). The load case corresponds to the experiment shown in Fig. 2.