Spatially varying properties of the vocal ligament contribute to its eigenfrequency response

Abstract

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.

The anisotropic hyperelastic biomechanical response of the vocal ligament and implications for frequency regulation: A case study

“…We speculate that the microstructural arrangement likely varies based upon the anterior-posterior location along the vocal ligament as indicated by the heterogeneous elastic response measured in previous studies. 22,30 A more complete analysis should include the fiber dispersion at several locations along the vocal ligament to account for the histological heterogeneity. A recent study has documented the dispersion and density of collagenous fibers of the vocal ligament with more samples and provided a statistical range.…”

“…21 The anisotropy, expressed as the ratio of the anterior-posterior elastic modulus and the longitudinal shear, was found to range typically from 15 to 40, while for an incompressible, isotropic tissue the ratio would equal three. As it was shown in Kelleher et al, 22,23 the effect of shear deformation can be of substantial magnitude in the vibration of vocal fold tissue, and thus seems crucial for accurate predictions of the fundamental frequency. Furthermore, it is understood that during the stretching of a tissue (i.e., during posturing of the vocal folds) a re-orientation of the fibrous proteins can occur which will alter the effective anisotropy.…”

“…Since vocal fold tissue has been shown to be heterogeneous, it was important that the elastic properties be measured in the same region. 22,30 However, for the constitutive and vibration modeling the elastic properties of the overall tissue (i.e., from the anterior commissure to the vocal process) were used.…”

Mechanical Characterization of Vocal Fold Tissue: A Review Study

“…42 Recently, noncontact optical measurement was applied to determine tissue deformation in the traction testing. 43,44 The applied displacement by testers was found to be significantly larger than the true deformation in the sample, thus underestimating the Young modulus. The heterogeneity of the deformation field was used to estimate local elastic modulus values.…”

“…The smallest deformation at the midmembranous vocal fold region yielded a 10 times stiffer region than the anterior and posterior regions. Because Kelleher et al 43 kept the vocal fold samples in air to avoid optical distortions while dripping buffer solution onto the sample, the effects of tissue dehydration 44 were significant.…”