Transfer functions for a one-dimensional fluid-poroelastic system subject to an ultrasonic pulse |
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Authors: | James L. BuchananRobert P. Gilbert Miao-jung Ou |
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Affiliation: | a Mathematics Department, United States Naval Academy, Annapolis, MD 21402, USAb Department of Mathematical Sciences, University of Delaware, Newark, DE 19711, USA |
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Abstract: | A one-dimensional model of an in vitro experiment, in which a specimen of cancellous bone is immersed in water and insonified by an ultrasonic pulse, is considered. The modification of the poroelastic model of Biot due to Johnson et al. [D.L. Johnson, J. Koplik, R. Dashen, Theory of dynamic permeability and tortuosity in fluid-saturated porous media, J. Fluid Mech. 176 (1987) 379-402] is used for the cancellous bone segment. By working with series expansions of the Laplace transform in terms of travel-time exponentials, a series of transfer functions for the reflection and transmission of fast and slow waves at the fluid-poroelastic interfaces are derived. The approach obviates numerical solution beyond the discretization involved in the use of the fast Fourier transform. |
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Keywords: | Poroelastic materials Laplace transforms Biot&rsquo s equations Numerical methods Fast Fourier transforms |
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