Volume 23, 2008Mathematical and numerical modelling of the human lung
|Page(s)||78 - 97|
|Published online||26 July 2008|
Multiscale modeling of the acoustic properties of lung parenchyma
Center for Biomedical Computing, Simula Research Laboratory, P.O.Box 134, 1325 Lysaker, Norway
2 School of Mathematical Sciences, University ofNottingham, University Park, Nottingham NG7 2RD, UK &
3 Center for Biomedical Computing, Simula Research Laboratory / Department of Informatics, University of Oslo, P.O.Box 134, 1325 Lysaker, Norway
Lung parenchyma is a foam-like material consisting of millions of alveoli. Sound transmission through parenchyma plays an important role in the non-invasive diagnosis of many lung diseases. We model the parenchyma as a porous solid with air-filled pores and consider the Biot equations as a model for its acoustic properties. The Biot equations govern small-amplitude wave propagation in fluid-saturated porous solids, and include the effects of relative motion between the fluid and the solid frame. The Biot equations can be derived from a micro-structure model of the porous material, and the material parameters in the equations can be obtained from the solution of two independent micro-structure problems, a fluid-cell problem (governed by the unsteady Stokes equations) and a solid-cell problem. We review the homogenization approach for media with periodic micro-structure, and solve a fluid-cell problem numerically for an idealized two-dimensional micro-scale geometry for a wide range of frequencies. We also discuss sound speeds in lung tissue.
© EDP Sciences, ESAIM, 2008
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