Geodesic
Multiscale modeling of the acoustic properties of lung parenchyma
Malin Siklosi1 ; Oliver E. Jensen2 ; Richard H. Tew2 ; Anders Logg3
1 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
ESAIM. Proceedings, Tome 23 (2008), pp. 78-97.

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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.
DOI : 10.1051/proc:082306

Malin Siklosi 1 ; Oliver E. Jensen 2 ; Richard H. Tew 2 ; Anders Logg 3

1 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 
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     title = {Multiscale modeling of the acoustic properties of lung parenchyma},
     journal = {ESAIM. Proceedings},
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Malin Siklosi; Oliver E. Jensen; Richard H. Tew; Anders Logg. Multiscale modeling of the acoustic properties of lung parenchyma. ESAIM. Proceedings, Tome 23 (2008), pp. 78-97. doi : 10.1051/proc:082306. http://geodesic.mathdoc.fr/articles/10.1051/proc:082306/

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