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ESAIM: Proc., 2008, Vol. 23, pp. 78-97
DOI: 10.1051/proc:082306
Multiscale modeling of the acoustic properties of lung parenchyma
Malin Siklosi1, Oliver E. Jensen2, Richard H. Tew2 and Anders Logg31 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
malinsi@simula.no
Oliver.Jensen@nottingham.ac.uk
Richard.Tew@nottingham.ac.uk
logg@simula.no
Published online: 26 July 2008
Abstract
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