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Multiscale modelling of sound propagation through the lung parenchyma∗

Published online by Cambridge University Press:  15 November 2013

Paul Cazeaux  and
Jan S. Hesthaven
Paul Cazeaux
Affiliation:
UniversitéPierre et Marie Curie-Paris 6, UMR 7598, Laboratoire J.-L. Lions, 75005 Paris, France Inria Projet REO, Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France. cazeaux@ann.jussieu.fr
Jan S. Hesthaven
Affiliation:
Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, USA; JanHesthaven@brown.edu
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Abstract

In this paper we develop and study numerically a model to describe some aspects of sound propagation in the human lung, considered as a deformable and viscoelastic porous medium (the parenchyma) with millions of alveoli filled with air. Transmission of sound through the lung above 1 kHz is known to be highly frequency-dependent. We pursue the key idea that the viscoelastic parenchyma structure is highly heterogeneous on the small scale ε and use two-scale homogenization techniques to derive effective acoustic equations for asymptotically small ε. This process turns out to introduce new memory effects. The effective material parameters are determined from the solution of frequency-dependent micro-structure cell problems. We propose a numerical approach to investigate the sound propagation in the homogenized parenchyma using a Discontinuous Galerkin formulation. Numerical examples are presented.

Keywords

Mathematical modelingperiodic homogenizationviscoelastic mediafluid-structure interactionDiscontinuous Galerkin methods
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 1 , January 2014 , pp. 27 - 52
Copyright
© EDP Sciences, SMAI 2013

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