Volume 48, Number 1, January-February 2014
|Page(s)||27 - 52|
|Published online||15 November 2013|
Multiscale modelling of sound propagation through the lung parenchyma∗
1 UniversitéPierre et Marie Curie-Paris
6, UMR 7598, Laboratoire J.-L. Lions, 75005
2 Inria Projet REO, Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France
3 Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, USA
Revised: 23 April 2013
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.
Mathematics Subject Classification: 93A30 / 35B27 / 35B40 / 74D05 / 65M60
Key words: Mathematical modeling / periodic homogenization / viscoelastic media / fluid-structure interaction / Discontinuous Galerkin methods
© EDP Sciences, SMAI 2013
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.