Multiscale modeling of the acoustic properties of lung parenchyma

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

Corresponding authors: malinsi@simula.no Oliver.Jensen@nottingham.ac.uk Richard.Tew@nottingham.ac.uk logg@simula.no

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.