Vocal Fold Vibration

 

In 2005-2007, I used medical ultrasound to visualize the vibration patterns of my vocal folds. It was a surprise to find that the deep layer of my vocal folds vibrated in the up-down direction (while the mucosal wave of the vocal fold propagated upward). This speaks against the prevailing three-mass model (Story & Titze, 1995). The ultrasound imaging of my vocal fold led me to develop a water-wave model.

 

The mucosal wave (bright curve) propagates upward.

 

Figure 1. The three-mass model (left) and the water-wave model (right) of human vocal fold vibration. The red arrows represent the motion directions of the vocal ligament.

 

The superficial layer of lamina propria, also known as Reinke’s space, comprises loose fibers and interstitial proteins with a high water content. A study on the canine vocal fold reported that the average mass and volume fractions of the liquid component in the lamina propria tissue were approximately 83.0% and 86.7%, respectively (Phillips et al., 2009). Their results represent preliminary experimental evidence for the biphasic composition (solid-liquid) of lamina propria tissue.

An approach to the effects of the liquids in the vocal fold may be water-wave models. McGowan’s (1990) pioneer work made an analogy between the mucosal waves and the growth of wind waves on water, suggesting that a layered-structure model is more appropriate to describe mucosal wave dynamics as relative to a two-mass model. In a similar vein, we proposed a water wave model by assuming that the fibers in lamina propria are loosely folded so that the liquid-like nature dominates vocal fold vibration (Tsai et al., 2006). This model used Airy’s (1841) water wave theory to predict the global vibration of the vocal fold, while the effects of the fibrous frames in the lamina propria are treated as minor corrections. The updating of the water-wave model was the seawave-seabed model, in which we analogized Reinke’s space and the vocal ligament as the seawater and the water-saturated porous seabed, respectively. We suggested that the restoring forces of liquid motion in lamina propria may be provided by the tensioned epithelium.

The seawave-seabed model of vocal fold vibration may provide new insight into the mechanical roles of the vocal ligament. First, the elasticity of the vocal ligament might be responsible for attenuating the water wave near the bottom. In oceanography, friction with the seabed increases as waves approach intermediate/shallow water, and sometimes leads to problems of drift, erosion, and sedimentation, because the water particles move forth and back at the bottom. In the vocal fold, the displacement of tissue particles may attenuate rapidly in the tensioned vocal ligament. In the other word, the two layers of the vocal ligament may serve to match the impedances of Reinke’s space and the vocalis muscle, thereby minimizing viscous losses due to velocity differences in the vocal fold.

Another role of the vocal ligament may be as an energy-saving mechanism. Whereas intermediate/shallow water waves lose energy through friction at the bottom, the strings in the vocal ligament are able to convert a portion of kinetic energy into potential energy when displaced from their equilibrium positions. While these strings move to their equilibrium positions, they may accelerate the liquids, thereby supplying energy to water waves. This effect may improve the efficiency of loud vocalization. Although this hypothesis needs more experimental evidence, it is interesting to note that energy-saving springs can be found in numerous oscillation systems in animals, such as legs of mammals, insect flight, and dolphin/jellyfish/scallop swimming (Alexander, 2003).

[to be continued]

 

REFERENCES

Airy, G. B. (1841). Tides and waves. In Encyclopaedia Metropolitana (1817–1845), Mixed Sciences, Vol. 3, edited by H. J. Rose, et al.

Alexander, R. M. (2003). Functions of elastomeric proteins in animals. In Elastomeric Proteins: Structures, Biomechanical Properties, and Biological Roles, edited by P. R. Shewry, A. S. Tatham, and A. J. Bailey (Cambridge University Press), pp. 1–14.

McGowan, R. (1990). An analogy between the mucosal waves of the vocal folds and wind waves on water. Haskins Laboratories Status Report on Speech Research, 101/102, 243–249.

Phillips, R., Zhang, Y., Keuler, M., Tao, C., & Jiang, J. J. (2009). Measurement of liquid and solid component parameters in canine vocal fold lamina propria. J Acoust Soc Am., 125(4), 2282–2287.

Story, B. H., & Titze, I. R. (1995). Voice Simulation with a Body-Cover Model of the Vocal Folds. J. Acoust. Soc. Am., 97(2), 1249–1260.

Tsai, C. G., Chen, J. H., Shau, Y. W., & Hsiao, T. Y. (2009). Dynamic B-mode ultrasound imaging of vocal fold vibration during phonation. Ultrasound in Medicine & Biology, 35(11), 1812–1818.

Tsai, C. G., Hsiao, T. Y., Shau, Y. W., & Chen, J. H. (2006). Towards an intermediate water wave model of vocal fold vibration: Evidence from vocal-fold dynamic sonography. International Conference on Voice Physiology and Biomechanics, July 12–14, 2006, Tokyo, Japan.

 

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