Ingo R Titze, Fariborz Alipour, Douglas Blake, Anil Palaparthi

A fiber-gel vocal fold model is compared to a transversely isotropic stiffness model in terms of normal mode vibration. The fiber-gel finite element model (FG-FEM) consists of a series of gel slices, each with a two-dimensional finite element mesh, in a plane transverse to the tissue fibers. The gel slices are coupled with fibers under tension in the anterior-posterior dimension. No vibrational displacement in the fiber-length direction is allowed, resulting in a plane strain state. This is consistent with the assumption of transverse displacement of a simple string, offering a wide range of natural frequencies (well into the kHz region) with variable tension. For low frequencies, the results compare favorably with the natural frequencies of a transversely isotropic elastic stiffness model (TISM) in which the shear modulus in the longitudinal plane is used to approximate the effect of fiber tension. For high frequencies, however, the natural frequencies do not approach the string mode frequencies unless plane strain is imposed on the TISM model. The simplifying assumption of plane strain, as well as the use of analytical closed-form shape functions, allow for substantial savings in computational time, which is important in clinical and exploratory applications of the FG-FEM model.