Phonation threshold pressure: Comparison of calculations and measurements taken with physical models of the vocal fold mucosa

Abstract

In an important paper on the physics of small amplitude oscillations, Titze showed that the essence of the vertical phase difference, which allows energy to be transferred from the flowing air to the motion of the vocal folds, could be captured in a surface wave model, and he derived a formula for the phonation threshold pressure with an explicit dependence on the geometrical and biomechanical properties of the vocal folds. The formula inspired a series of experiments [e.g., R. Chan and I. Titze, J. Acoust. Soc. Am 119, 2351-2362 (2006)]. Although the experiments support many aspects of Titze's formula, including a linear dependence on the glottal half-width, the behavior of the experiments at the smallest values of this parameter is not consistent with the formula. It is shown that a key element for removing this discrepancy lies in a careful examination of the properties of the entrance loss coefficient. In particular, measurements of the entrance loss coefficient at small widths done with a physical model of the glottis (M5) show that this coefficient varies inversely with the glottal width. A numerical solution of the time-dependent equations of the surface wave model shows that adding a supraglottal vocal tract lowers the phonation threshold pressure by an amount approximately consistent with Chan and Titze's experiments.

Phonation threshold pressure and the elastic shear modulus: Comparison of two-mass model calculations with experiments

“…This prediction is not consistent with Chan and Titze's 2006 measurements, 6 where the linear trend of the threshold pressure data clearly does not approach zero. As shown in our earlier work with Titze's surface wave model, 7 the key to resolving this discrepancy is to introduce a parameterization of the entrance loss coefficient that includes an inverse dependence on the glottal half-width. It is shown that this parameterization may be readily incorporated into the two-mass model of Ishizaka and Flanagan.…”

“…This situation was explored further in Ref. 7, where Lucero's suggestion 27 of using Poiseuille's approach to describe viscous effects of the flowing air within the glottis to explain the upward trends was analyzed. There it was shown that Poiseuille's approach to viscous effects should also lead to upward trends in Chan and Titze's 2006 measurements at small glottal widths.…”

“…which does not approach zero as the half-width approaches zero and which produces much better fits 7 to the data collected by Chan and Titze 6 in 2006 than Eq.…”

“…A recent study 7 showed that the key to resolving this discrepancy lies in recognizing that the entrance loss coefficient [8][9][10][11] is not constant at small half-widths but becomes large as the half-width becomes small. There it was also shown that a reasonable parameterization of this coefficient is…”

Experimental validation of a three-dimensional reduced-order continuum model of phonation

“…Note that Zhang and Luu (2012), which used a similar 1D flow model but without accounting for the glottal flow viscous loss, also reported a stronger fluidstructure interaction in their numerical model than in their experiment. These issues need to be further explored in future studies, using more accurate vocal fold material properties data, a better representation of the experimental setup, and gradually refined flow models [e.g., including the glottal channel curvature effect, or using more accurate models of the glottal flow viscous loss (Fulcher and Scherer, 2011)]. Such studies would help to reveal the effects on phonation of the various flow features that are neglected in 1D flow models.…”