Transfer functions for a one-dimensional fluid–poroelastic system subject to an ultrasonic pulse

• Published in: Nonlinear analysis: real world applications Vol. 13; no. 3; pp. 1030 - 1043
• Main Authors: Buchanan, James L., Gilbert, Robert P., Ou, Miao-jung
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2012
• Subjects: Biot’s equations; Bones; Discretization; Fast Fourier transforms; In vitro testing; Laplace transforms; Mathematical models; Numerical methods; Poroelastic materials; Series expansion; Tortuosity; Transfer functions; Fast Fourier transforms; Laplace transforms; Poroelastic materials; Numerical methods; Biot’s equations
• ISSN: 1468-1218; 1878-5719
• DOI: 10.1016/j.nonrwa.2011.02.001

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.