Multiscale modelling of sound propagation through the lung parenchyma

Paul Cazeaux, Jan S. Hesthaven

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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 frequencydependent 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.

Original languageEnglish (US)
Pages (from-to)27-52
Number of pages26
JournalESAIM: Mathematical Modelling and Numerical Analysis
Issue number1
StatePublished - 2014

Bibliographical note

Publisher Copyright:
© EDP Sciences, SMAI 2013.


  • Discontinuous Galerkin methods
  • Fluid-structure interaction
  • Mathematical modeling
  • Periodic homogenization
  • Viscoelastic media


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