Liquid Accumulation in Vibrating Vocal Fold Tissue: A Simplified Model Based on a Fluid-Saturated Porous Solid Theory

Abstract

The human vocal fold is treated as a continuous, transversally isotropic, porous solid saturated with liquid. A set of mathematical equations, based on the theory of fluid-saturated porous solids, is developed to formulate the vibration of the vocal fold tissue. As the fluid-saturated porous tissue model degenerates to the continuous elastic tissue model when the relative movement of liquid in the porous tissue is ignored, it can be considered a more general description of vocal fold tissue than the continuous, elastic model. Using the fluid-saturated porous tissue model, the vibration of a bunch of one-dimensional fibers in the vocal fold is analytically solved based on the small amplitude assumption. It is found that the vibration of the tissue will lead to the accumulation of excess liquid in the midmembranous vocal fold. The degree of liquid accumulation is positively proportional to the vibratory amplitude and frequency. The correspondence between the liquid distribution predicted by the porous tissue theory and the location of vocal nodules observed in clinical practice, provides theoretical evidence for the liquid accumulation hypothesis of vocal nodule formation (Jiang, Ph. D., dissertation, 1991, University of Iowa).

Mechanical Characterization of Vocal Fold Tissue: A Review Study

“…68,69 The governing equations of Biot's theory, 70 along with a linear stress-strain relationship of the porous solid and incompressibility of the pore fluid, were applied. From the orientation of the collagen fibrils in the tissue and the existence of Reinke's space, the authors assumed that the relative velocity between the liquid and solid phases in the transverse direction (ie, along the coronal plane) can be ignored in comparison with that in the longitudinal direction (ie, anterior-posterior direction).…”

“…The capability of the model in simulating vocal fold fluid accumulations was also studied. 69 Miri et al 71 introduced a linear, isotropic, poroviscoelastic formulation to simulate the response of the vocal fold tissue under indentation loads. They assumed that the interstitial fluid acts at the micrometer scale and its contribution can be separated from the nanoscale viscoelasticity of ECM.…”

Characterizing Liquid Redistribution in a Biphasic Vibrating Vocal Fold Using Finite Element Analysis

“…The combination of these mechanical forces is believed to stress the extracellular matrix and affect the pressures experienced by capillaries, potentially leading to fiber damage and capillary rupture (3), resulting in tissue remodeling and subsequent formation of benign lesions (4). While the interplay between all of the listed forces has yet to be thoroughly explored, currently particularly lacking in literature is an investigation of the mechanical effects of liquid redistribution, which only recently has been explored using computer modeling (2, 5, 6). …”

“…The limitation of all of the listed models is that they assume the vocal fold material to be a single phase, as opposed to a biphasic, entity. In order to study the interaction between the solid and liquid phases, models using a finite-difference method were developed that viewed the vocal fold as a transversely isotropic poroviscoelastic solid, where the tissue is modeled as a porous material with both viscous and elastic properties, with liquid-filled pores (2, 5, 6) and showed liquid accumulation in the anterior-posterior midline of the fold in amounts proportional to frequency and amplitude of oscillation (5). This midline accumulation, and subsequent rise in liquid pressure, has been previously observed in a mechanical model of a vibrating capillary (3), and is thought to contribute to benign vocal fold injury development (3, 13).…”

Effects of poroelastic coefficients on normal vibration modes in vocal-fold tissues

“…These studies significantly improve our knowledge about the mechanical properties and microstructures of these biological tissues. Recently, the poroelastic theory has also been used to describe the viscoelastic behavior of the vocal tissue (Zhang et al, 2008) and the liquid redistribution in the vocal fold during phonation (Tao et al, 2009;Tao et al 2010).…”