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Multiscale modelling of sound propagation through the lungparenchyma∗

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. [email protected]
Jan S. Hesthaven
Affiliation:
Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, USA; [email protected]
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Abstract

In this paper we develop and study numerically a model to describe some aspects of soundpropagation in the human lung, considered as a deformable and viscoelastic porous medium(the parenchyma) with millions of alveoli filled with air. Transmission of sound throughthe lung above 1 kHz is known to be highly frequency-dependent. We pursue the key ideathat the viscoelastic parenchyma structure is highly heterogeneous on the small scaleε and use two-scale homogenization techniques to derive effectiveacoustic equations for asymptotically small ε. This process turns out tointroduce new memory effects. The effective material parameters are determined from thesolution of frequency-dependent micro-structure cell problems. We propose a numericalapproach to investigate the sound propagation in the homogenized parenchyma using aDiscontinuous 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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