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Effects of poroelastic coefficients on normal vibration modes in vocal-fold tissues
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10.1121/1.3533692
/content/asa/journal/jasa/129/2/10.1121/1.3533692
http://aip.metastore.ingenta.com/content/asa/journal/jasa/129/2/10.1121/1.3533692

Figures

Image of FIG. 1.
FIG. 1.

Geometric configuration and boundary conditions of the vocal-fold model, where the gray faces indicate the fixed boundary conditions and the other faces are the free boundary conditions.

Image of FIG. 2.
FIG. 2.

(Color online) Convergence of the three lowest eigenfrequencies as a function of the order of the M and N matrices. (a) Q = 0.0 kPa and R = 0.0 kPa; (b) Q = 2.5 × 105 kPa and R = 0.0 kPa. In addition, for the sake of comparison with the elastic model, transverse Young’s modulus μ = 5.0 kPa and μ = 2.5 kPa are used for (a) and (b), respectively.

Image of FIG. 3.
FIG. 3.

The first three eigenmodes and eigenfrequencies in the poroelastic vocal-fold model with ρ 12 = –1.0 × 109 kg/m3, Q = 0 kPa, and R = 0 kPa. Mode shapes are viewed as coronal cross sections. (a) Eigenmode 1, analogous to the z-10 mode; (b) eigenmode 2, analogous to the x-10 mode; (c) eigenmode 3, analogous to the x-11 mode. These eigenmodes and eigenfrequencies are similar to those obtained using an elastic vocal-fold model with completely compressible tissue (ν = 0.0).

Image of FIG. 4.
FIG. 4.

The first three eigenmodes and eigenfrequency in the poroelastic vocal-fold model with ρ 12 = –1.0 × 109 kg/m3, 2Q + R = 0.5 × 106 kPa. Mode shapes are viewed as coronal cross sections. (a) Eigenmode 1, analogous to the z-10 mode; (b) eigenmode 2, analogous to the x-11 mode; and (c) eigenmode 3, analogous to the x-10 mode. These eigenmodes and eigenfrequencies are similar to those obtained using an elastic vocal-fold model with nearly incompressible tissue (ν = 0.9999).

Image of FIG. 5.
FIG. 5.

(Color online) Eigenfrequencies as a function of the coefficients Q and R. (a) Eigenfrequencies vs Q, where ρ 12 = –1.0 × 109 kg/m3 and R = 0.0 kPa. (b) Eigenfrequencies vs R, where ρ 12 = –1.0 × 109 kg/m3 and Q = 0.0 kPa.

Image of FIG. 6.
FIG. 6.

(Color online) Eigenfrequencies as a function of the solid content, where β = ρ s/ρ tissue and the mass coupling parameter ρ 12 = −1 × 109 kg/m3. (a) 2Q + R = 0 kPa; (b) 2Q + R = 0.5 × 106 kPa.

Image of FIG. 7.
FIG. 7.

(Color online) Eigenfrequencies as a function of the solid content, where ρ 12 = −1 × 103 kg/m3. (a) 2Q + R = 0 kPa; (b) 2Q + R = 0.5 × 106 kPa.

Image of FIG. 8.
FIG. 8.

(Color online) Eigenfrequencies as a function of Biot’s coefficient ρ 12. (a) Q = 0.0 kPa and R = 0.0 kPa; (b) Q = 0.25 × 106 kPa and R = 0.0 kPa. In addition, for the sake of comparison with the elastic model, transverse Young’s modulus μ = 5.0 and 2.5 kPa are used for (a) and (b), respectively.

Image of FIG. 9.
FIG. 9.

(Color online) Eigenfrequencies as a function of the coefficients R, where ρ 12 = –1 × 103 kg/m3 and Q = 0. 0 kPa.

Image of FIG. 10.
FIG. 10.

The first three eigenmodes and eigenfrequencies in the poroelastic vocal-fold model with ρ 12 = –1 × 103 kg/m3, Q = 0. 0 kPa, and R = 0.0 kPa. (a) The z-10-like mode; (b) the x-10-like mode; and (c) the x-11-like mode. The solid lines and the dashed lines represent the movements of the solid and liquid components, respectively.

Image of FIG. 11.
FIG. 11.

Five eigenmodes in the poroelastic vocal-fold model with ρ 12 = –1 × 103 kg/m3, Q = 0. 0 kPa, and R = 1.0 × 103 kPa, where the solid lines and the dashed lines represent the movements of the solid and liquid components. Modes B, C, and E are analogous to the z-10 mode, the x-11 mode, and the x-10 mode, respectively.

Image of FIG. 12.
FIG. 12.

Six eigenmodes and eigenfrequencies in the poroelastic vocal-fold model with ρ 12 = –1 × 103 kg/m3, Q = 0. 0 kPa, and R = 3.0 kPa, where the solid lines and the dashed lines represent the movements of the solid and liquid components. Modes B, E, and F are analogous to the z-10 mode, the x-10 mode, and the x-11 mode, respectively.

Tables

Generic image for table
TABLE I.

Parameter values used in the eigenmode analysis.

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/content/asa/journal/jasa/129/2/10.1121/1.3533692
2011-02-11
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Effects of poroelastic coefficients on normal vibration modes in vocal-fold tissues
http://aip.metastore.ingenta.com/content/asa/journal/jasa/129/2/10.1121/1.3533692
10.1121/1.3533692
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