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Research Papers

The Role of Finite Displacements in Vocal Fold Modeling

[+] Author and Article Information
Haoxiang Luo

Department of Mechanical Engineering,
Vanderbilt University,
2301 Vanderbilt Place,
Nashville, TN 37235

James F. Doyle

School of Aeronautics and Astronautics,
Purdue University,
West Lafayette, IN 47907-2045

Bernard Rousseau

Departments of Otolaryngology and
Hearing and Speech Sciences,
Vanderbilt University,
1215 21st Avenue South,
Nashville, TN 37232

Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received February 26, 2013; final manuscript received August 22, 2013; accepted manuscript posted September 6, 2013; published online October 1, 2013. Assoc. Editor: Ender A. Finol.

J Biomech Eng 135(11), 111008 (Oct 01, 2013) (8 pages) Paper No: BIO-13-1103; doi: 10.1115/1.4025330 History: Received February 26, 2013; Revised August 22, 2013; Accepted September 06, 2013

Human vocal folds experience flow-induced vibrations during phonation. In previous computational models, the vocal fold dynamics has been treated with linear elasticity theory in which both the strain and the displacement of the tissue are assumed to be infinitesimal (referred to as model I). The effect of the nonlinear strain, or geometric nonlinearity, caused by finite displacements is yet not clear. In this work, a two-dimensional model is used to study the effect of geometric nonlinearity (referred to as model II) on the vocal fold and the airflow. The result shows that even though the deformation is under 1 mm, i.e., less than 10% of the size of the vocal fold, the geometric nonlinear effect is still significant. Specifically, model I underpredicts the gap width, the flow rate, and the impact stress on the medial surfaces as compared to model II. The study further shows that the differences are caused by the contact mechanics and, more importantly, the fluid-structure interaction that magnifies the error from the small-displacement assumption. The results suggest that using the large-displacement formulation in a computational model would be more appropriate for accurate simulations of the vocal fold dynamics.

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Figures

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Fig. 1

A 2D model for studying the role of geometric nonlinearity in the vocal fold dynamics

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Fig. 2

The lowest four eigenmodes of the current vocal fold model. (a) The first mode at f1 = 86.9 Hz, (b) the second mode at f2 = 192.2 Hz, (c) the third mode at f3 = 217.5 Hz, and (d) the fourth mode at f4 = 372.9 Hz. The dashed line is for the rest shape, and the solid line is for deformed shape.

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Fig. 3

The time history of the glottal gap width for model II with Psub = 0.6 kPa. (a) Initial transition period and (b) the established vibration.

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Fig. 4

The vibration pattern of the vocal folds simulated by model I (a), (b), and (c) and model II (d), (e), and (f). The subglottal pressure is (a) and (d) Psub = 0.6 kPa, (b) and (e) Psub = 0.7 kPa, and (c) and (f) Psub = 0.8 kPa. The solid line and dashed line represent the open and closed phases, respectively. The circle shown in (a) is the marker point that will be used in the PSD analysis.

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Fig. 11

Displacement of the reference point in the static load test, the dynamic load test, and the coupled FSI simulation. (a) The total displacement and (b) the y-displacement.

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Fig. 10

(a) Illustration of the load tests of the current vocal fold model. The reference point marked by a circle is used to measure the displacement. (b) and (c) p/Psub from the FSI simulation during vocal fold opening for (b) Psub = 0.6 kPa and (c) Psub = 0.8 kPa.

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Fig. 9

Instantaneous vorticity contours during vocal fold opening for (a) model I and (b) model II at Psub = 0.8 kPa

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Fig. 8

(a) The time-averaged flow rate (per unit span) and (b) the waveform of the flow rate at Psub = 0.8 kPa. The dashed line is for model I and the solid line for model II.

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Fig. 7

The impact stress (a) and the total contact force (per unit length in span) (b) during vocal fold collision. The dashed line is for model I and the solid line for model II.

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Fig. 6

(a) The gap width during the open phase versus Psub. (b) The waveform of the gap width at Psub = 0.6 kPa. In both (a) and (b), the dashed line is for model I and the solid line for model II.

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Fig. 5

The PSD analysis of the oscillation of a point at the medial surface for Psub =  0.7 and 0.8 kPa. The two dashed lines indicate the eigenfrequencies f2 and f3.

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