Multiscale modelling of sound propagation through the lung parenchyma

Paul Cazeaux; Jan S. Hesthaven

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2014)

  • Volume: 48, Issue: 1, page 27-52
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Cazeaux, Paul, and Hesthaven, Jan S.. "Multiscale modelling of sound propagation through the lung parenchyma." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.1 (2014): 27-52. <http://eudml.org/doc/273201>.

@article{Cazeaux2014,
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.},
author = {Cazeaux, Paul, Hesthaven, Jan S.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {mathematical modeling; periodic homogenization; viscoelastic media; fluid-structure interaction; discontinuous Galerkin methods},
language = {eng},
number = {1},
pages = {27-52},
publisher = {EDP-Sciences},
title = {Multiscale modelling of sound propagation through the lung parenchyma},
url = {http://eudml.org/doc/273201},
volume = {48},
year = {2014},
}

TY - JOUR
AU - Cazeaux, Paul
AU - Hesthaven, Jan S.
TI - Multiscale modelling of sound propagation through the lung parenchyma
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 1
SP - 27
EP - 52
AB - 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.
LA - eng
KW - mathematical modeling; periodic homogenization; viscoelastic media; fluid-structure interaction; discontinuous Galerkin methods
UR - http://eudml.org/doc/273201
ER -

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