The vocal ligament is known to have nonlinear variation in geometry, yet this is rarely considered in empirical or computational studies. This paper investigates the effects of a nonlinear variation of the anterior-to-posterior geometry and the corresponding spatial variation in elastic modulus on the fundamental frequency of vibration for the vocal ligament. Uniaxial tensile tests were performed on a vocal ligament specimen dissected from an excised 60-year-old male larynx. Digital image correlation (DIC) was used to obtain the spatial deformation field for the entire ligament specimen. DIC results revealed that the tensile deformation was very heterogeneous, with the least amount of deformation occurring in the region of smallest cross sectional area. The elastic modulus was calculated locally and was found to be approximately 10 times higher at the mid-point of the vocal ligament than in the anterior and posterior macula flavae regions. Based on the spatially varying material properties obtained, finite element models (isotropic and transversely isotropic) were created to investigate how the effects of varying cross-section, heterogeneous stiffness, and anisotropy could affect the fundamental frequency of vibration. It was found that the spatial cross-section variation and the spatially varying anisotropy (i.e. modulus ratio) are significant to predictions of the vibration characteristics. Fundamental frequencies predicted with a finite element model are discussed in view of rotatory inertia and contribution of transverse shear deformation.

In voice research, in vitro tensile stretch experiments of vocal fold tissues are commonly employed to determine the tissue biomechanical properties. In the standard stretch-release protocol, tissue deformation is computed from displacements applied to sutures inserted through the thyroid and arytenoid cartilages, with the cartilages assumed to be rigid. Here, a non-contact optical method was employed to determine the actual tissue deformation of vocal fold lamina propria specimens from three excised human larynges in uniaxial tensile tests. Specimen deformation was found to consist not only of deformation of the tissue itself, but also deformation of the cartilages, as well as suture alignment and tightening. Stress-stretch curves of a representative load cycle were characterized by an incompressible Ogden model. The initial longitudinal elastic modulus was found to be considerably higher if determined based on optical displacement measurements than typical values reported in the literature. The present findings could change the understanding of the mechanics underlying vocal fold vibration. Given the high longitudinal elastic modulus the lamina propria appeared to demonstrate a substantial level of anisotropy. Consequently, transverse shear could play a significant role in vocal fold vibration, and fundamental frequencies of phonation should be predicted by beam theories accounting for such effects.

One of the primary mechanisms to vary one's vocal frequency is through vocal fold length changes. As stress and deformation are linked to each other, it is hypothesized that the anisotropy in the biomechanical properties of the vocal fold tissue would affect the phonation characteristics. A biomechanical model of vibrational frequency rise during vocal fold elongation is developed which combines an advanced biomechanical characterization protocol of the vocal fold tissue with continuum beam models. Biomechanical response of the tissue is related to a microstructurally informed, anisotropic, nonlinear hyperelastic constitutive model. A microstructural characteristic (the dispersion of collagen) was represented through a statistical orientation function acquired from a second harmonic generation image of the vocal ligament. Continuum models of vibration were constructed based upon Euler-Bernoulli and Timoshenko beam theories, and applied to the study of the vibration of a vocal ligament specimen. From the natural frequency predictions in dependence of elongation, two competing processes in frequency control emerged, i.e., the applied tension raises the frequency while simultaneously shear deformation lowers the frequency. Shear becomes much more substantial at higher modes of vibration and for highly anisotropic tissues. The analysis was developed as a case study based on a human vocal ligament specimen.

The vocal folds are known to be mechanically anisotropic due to the microstructural arrangement of fibrous proteins such as collagen and elastin in the lamina propria. Even though this has been known for many years, the biomechanical anisotropic properties have rarely been experimentally studied. We propose that an indentation procedure can be used with uniaxial tension in order to obtain an estimate of the biomechanical anisotropy within a single specimen. Experiments were performed on the lamina propria of three male and three female human vocal folds dissected from excised larynges. Two experiments were conducted: each specimen was subjected to cyclic uniaxial tensile loading in the longitudinal (i.e. anterior-posterior) direction, and then to cyclic indentation loading in the transverse (i.e. medial-lateral) direction. The indentation experiment was modeled as contact on a transversely isotropic half-space using the Barnett-Lothe tensors. The longitudinal elastic modulus EL was computed from the tensile test, and the transverse elastic modulus ET and longitudinal shear modulus GL were obtained by inverse analysis of the indentation force-displacement response. It was discovered that the average of EL/ET was 14 for the vocal ligament and 39 for the vocal fold cover specimens. Also, the average of EL/GL, a parameter important for models of phonation, was 28 for the vocal ligament and 54 for the vocal fold cover specimens. These measurements of anisotropy could contribute to more accurate models of fundamental frequency regulation and provide potentially better insights into the mechanics of vocal fold vibration.

The physical mechanisms leading to the acoustic and perceptual qualities of voice are not well understood. This study examines the spatial distribution of biomechanical properties in human vocal folds and explores the consequences of these properties on phonation. Vocal fold lamina propria specimens isolated from nine excised human male larynges were tested in uniaxial tension (six from non-smokers, three from smokers). An optical method was employed to determine the local stretch, from which the elastic modulus of three segments in the anterior-posterior direction was calculated. Several specimens exhibited a significant heterogeneity in the modulus with the middle segment stiffer than the other segments. It was concluded that such modulus gradients are stronger in specimens from non-smokers than smokers. To understand the functional implications of a modulus gradient, the first eigenmode of vibration was calculated with a finite element model. With a modulus gradient, the vocal fold's eigenmode deflection was spread along the anterior-posterior length, whereas for a homogeneous modulus distribution, the deflection was more focused around the mid-coronal plane. Consequently, the strong modulus gradient may enable more complete glottal closure, which is important for normal phonation, while a more homogeneous modulus may be responsible for poor glottal closure and a perceived "breathy" voice.