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).

Figure 1

The complex composite microstructure in vocal fold tissue. (a) vocal fold (b) the three layers of the lamina propria of the vocal fold (From reference 44). (c) The basement membrane zone where is full of various fibers. (From reference 43).

Figure 2

The fluid-saturated porous solid theory of the vocal fold tissue. (a) A bunch of fiber lies along the anterior-posterior direction of the vocal fold. (b) The sketch map of the porous solid. (c)-(d) The vibration of a bunch of fiber in vocal fold.

Figure 3

The liquid movement when vocal fold begin vibrating. In spatial, the maximum velocity occurs at the L/4 and 3L/4 positions. In posterior side of vocal fold, the velocity of liquid is always positive, but in the anterior side, the velocity of liquid in vocal fold is always negative. The liquid both in anterior side and in the posterior side will move toward the midmembranous region vocal fold is vibrating. Moreover, the velocity of the liquid is positive proportional to the vibration frequency and amplitude [see Eq.(28)]

Figure 4

The liquid in vocal fold follow a cosine distribution in the anterior-posterior direction after a stable vibration is sustained. For the region 0 < y < L/4 and 3L/4 < y < L, Δρ_F is negative, which means the liquid are lost in these regions. For the region L/4 < y < 3L/4, Δρ_F is positive and the maximum Δρ_F is located at the midpoint of vocal fold, which means the liquid is accumulated in this region. The figures (a) and (b) are modified from the figures in reference 43.

Figure 5

Pressure plotted with respect to frequency squared and amplitude squared measured from the physical blood vessel. (From reference 33).