A micro-mechanical model for the fibrous tissues of vocal folds

Mechanics of gelatin-based hydrogels during finite strain tension, compression and shear

“…Knowing that, our results show that the average properties of the Ge-GA hydrogel (stiffness and strength) are quite comparable (albeit higher) to those of the two vocal-fold layers in transverse compression and longitudinal shear, i.e., under loading conditions where fibers unfolding, tension and rotation are limited, while the mechanical contribution of the isotropic matrix is much more critical (Terzolo et al, 2022). Higher quantitative discrepancies are also found with the tensile response of the entire fold and its upper layer, due to the progressive recruitement and reorientation of the collagen fibers towards the load direction in this case (Min et al, 1995;Gasser et al, 2006;Terzolo et al, 2022). For instance, at a strain of 0.1 (absolute value), the stress level in the Ge-GA sample is about 17 times lower than that achieved in the lamina propria in tension (mean value on both donors), while it is about 5 times higher in compression and 4 times higher in shear.…”

“…Firstly, it is important to remind that both lamina propria and vocalis can be seen as 3D incompressible composite structures made of a gel-like matrix reinforced by a network of collagen fibers, with wavy shapes and preferred orientations at rest ( Kelleher et al, 2013 ; Miri et al, 2013 ; Bailly et al, 2018 ; Terzolo et al, 2022 ). Knowing that, our results show that the average properties of the Ge-GA hydrogel (stiffness and strength) are quite comparable (albeit higher) to those of the two vocal-fold layers in transverse compression and longitudinal shear, i.e., under loading conditions where fibers unfolding, tension and rotation are limited, while the mechanical contribution of the isotropic matrix is much more critical ( Terzolo et al, 2022 ). Higher quantitative discrepancies are also found with the tensile response of the entire fold and its upper layer, due to the progressive recruitement and reorientation of the collagen fibers towards the load direction in this case ( Min et al, 1995 ; Gasser et al, 2006 ; Terzolo et al, 2022 ).…”

“…For instance, at a strain of 0.1 (absolute value), the stress level in the Ge-GA sample is about 17 times lower than that achieved in the lamina propria in tension (mean value on both donors), while it is about 5 times higher in compression and 4 times higher in shear. Note that in tension, deviations from the vocalis muscle become far less pronounced, because the muscle fibers are straighter and softer than the collagen fibers of the lamina propria at rest ( Bailly et al, 2018 ; Terzolo et al, 2022 ).…”

Flow-induced oscillations of vocal-fold replicas with tuned extensibility and material properties

“…In parallel, over the past decades, a number of theoretical and numerical studies have also addressed the impact of vocal-fold mechanical properties on phonation 30 , 31 , using either vibrating string/beam models of vocal folds to study their natural mode frequencies 32 – 35 , reduced-order phonation models with simplified fluid-structure interactions (e.g., 36 – 40 ) or highly resolved ones commonly based on 3D finite-element methods to simulate tissues biomechanics (e.g., 41 – 44 ). In particular, variations in the tensile, shear and bending stiffness of the vocal folds, as well as in the stresses they undergo during longitudinal elongation (i.e., in the anterior–posterior direction), should contribute strongly to the regulation of their natural vibration frequencies 32 – 35 . This is ascribed to the non-linear and anisotropic mechanical properties of the native tissues at the macroscale, driven by their fibrous arrangement at the microscale 34 , 35 .…”

“…In particular, variations in the tensile, shear and bending stiffness of the vocal folds, as well as in the stresses they undergo during longitudinal elongation (i.e., in the anterior–posterior direction), should contribute strongly to the regulation of their natural vibration frequencies 32 – 35 . This is ascribed to the non-linear and anisotropic mechanical properties of the native tissues at the macroscale, driven by their fibrous arrangement at the microscale 34 , 35 . When interacting with airflow, a slight computed change in vocal-fold stiffness can alter their eigenmodes (i.e., structure resonances) and coupling, inducing a sudden change in phonation onset frequency 36 , 37 , 40 , 43 , vocal-fold vibration pattern 36 , 37 , 40 , 43 including glottal opening, open quotient and closing velocity 43 , airflow rate 40 , 43 and sound production efficiency 36 , 37 .…”