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Investigation of an anisotropic tortuosity in a Biot model of ultrasonic propagation in cancellous bone
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10.1121/1.2387132
/content/asa/journal/jasa/121/1/10.1121/1.2387132
http://aip.metastore.ingenta.com/content/asa/journal/jasa/121/1/10.1121/1.2387132

Figures

Image of FIG. 1.
FIG. 1.

The porous microstructure of cancellous bone from a bovine femur, showing a centimeter scale.

Image of FIG. 2.
FIG. 2.

Idealization of the structure of cancellous bone as an array of parallel bone-marrow layers.

Image of FIG. 3.
FIG. 3.

Predicted stratified tortuosity of Eq. (20) (solid line), and tubular tortuosity, (dashed line), versus the angle of propagation. The angle 0° is normal to the stratification.

Image of FIG. 4.
FIG. 4.

Predicted fast and slow wave phase velocities for the stratified Biot model (solid line) and the Schoenberg model (dashed line). Angles 0° and 90° are normal and parallel to the stratification, respectively.

Image of FIG. 5.
FIG. 5.

(a) Predicted fast and slow wave velocities versus the angle of propagation for the stratified Biot model (solid lines) and the Schoenberg model (dashed lines). The angle 0° is normal to layering. Models are evaluated at porosities of 0.82 and 0.65, corresponding to the range within samples. Data from Hughes et al. (Ref. 6) (∙, o, +, ∗, x, ◇), and Hosokawa and Otani (Ref. 16) (◻). (b) Predicted fast wave velocities versus angle of propagation for the Stratified Biot model for input porosities of 0.65, 0.77, and 0.82 [data from Hughes et al. (Ref. 6)].

Image of FIG. 6.
FIG. 6.

Predicted and measured fast wave phase velocities versus propagation angle for the Stratified Biot model (solid line) and a stratified Biot model including directional Young’s modulus (dashed line), evaluated at the upper and lower porosity limits. The angle 0° is normal to the structure [data from Hughes et al. (Ref. 6)].

Tables

Generic image for table
TABLE I.

Input parameters for the stratified Biot and Schoenberg models.

Generic image for table
TABLE II.

Input parameters for the stratified Biot and Schoenberg models.

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/content/asa/journal/jasa/121/1/10.1121/1.2387132
2007-01-01
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Investigation of an anisotropic tortuosity in a Biot model of ultrasonic propagation in cancellous bone
http://aip.metastore.ingenta.com/content/asa/journal/jasa/121/1/10.1121/1.2387132
10.1121/1.2387132
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