Transfer functions for a one-dimensional fluid–poroelastic system subject to an ultrasonic pulse
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 permeabi...
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| Published in | Nonlinear analysis: real world applications Vol. 13; no. 3; pp. 1030 - 1043 |
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| Format | Journal Article |
| Language | English |
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01.06.2012
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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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| AbstractList | 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. 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. |
| Author | Gilbert, Robert P. Ou, Miao-jung Buchanan, James L. |
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| Cites_doi | 10.1121/1.418118 10.1017/S0022112087000727 10.1121/1.1908239 10.1121/1.2335420 10.1121/1.1755239 10.1121/1.391927 10.1121/1.1908241 10.1063/1.1728759 10.1115/1.4011606 10.1016/S8756-3282(99)00011-3 10.1121/1.1918315 10.1088/0031-9155/36/10/003 10.1121/1.399081 10.1121/1.402637 10.1121/1.386692 |
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| References | Johnson, Koplik, Dashen (br000060) 1987; 176 Hosokawa, Otani (br000015) 1997; 101 Biot (br000035) 1956; 28 Williams (br000010) 1992; 91 Biot (br000045) 1962; 33 Wu, Xue, Adler (br000075) 1990; 87 Haire, Langton (br000055) 1999; 24 McKelvie, Palmer (br000005) 1991; 10 Fellah, Chapelon, Berger, Lauriks, Depollier (br000020) 2004; 116 Biot (br000030) 1956; 28 Sebaa, Fellah, Fellah, Ogam, Wirgin, Mitri, Depollier, Lauriks (br000025) 2006; 120 Biot, Willis (br000040) 1957; 24 Stoll, Kan (br000065) 1981; 70 Stern, Bedford, Milwater (br000070) 1985; 77 Biot (br000050) 1962; 34 Stoll (10.1016/j.nonrwa.2011.02.001_br000065) 1981; 70 Hosokawa (10.1016/j.nonrwa.2011.02.001_br000015) 1997; 101 Haire (10.1016/j.nonrwa.2011.02.001_br000055) 1999; 24 Stern (10.1016/j.nonrwa.2011.02.001_br000070) 1985; 77 Fellah (10.1016/j.nonrwa.2011.02.001_br000020) 2004; 116 Williams (10.1016/j.nonrwa.2011.02.001_br000010) 1992; 91 Sebaa (10.1016/j.nonrwa.2011.02.001_br000025) 2006; 120 Biot (10.1016/j.nonrwa.2011.02.001_br000045) 1962; 33 Biot (10.1016/j.nonrwa.2011.02.001_br000050) 1962; 34 Johnson (10.1016/j.nonrwa.2011.02.001_br000060) 1987; 176 Wu (10.1016/j.nonrwa.2011.02.001_br000075) 1990; 87 Biot (10.1016/j.nonrwa.2011.02.001_br000040) 1957; 24 Biot (10.1016/j.nonrwa.2011.02.001_br000035) 1956; 28 Biot (10.1016/j.nonrwa.2011.02.001_br000030) 1956; 28 McKelvie (10.1016/j.nonrwa.2011.02.001_br000005) 1991; 10 |
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| Snippet | 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... 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... |
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| SubjectTerms | Biot’s equations Bones Discretization Fast Fourier transforms In vitro testing Laplace transforms Mathematical models Numerical methods Poroelastic materials Series expansion Tortuosity Transfer functions |
| Title | Transfer functions for a one-dimensional fluid–poroelastic system subject to an ultrasonic pulse |
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