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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(More)
Our work is motivated by numerical homogenization of materials such as concrete, modeled as composites structured as randomly distributed inclusions imbedded in a matrix. In this paper, we propose a method for the approximation of the periodic corrector problem based on boundary integral equations. The fully populated matrices obtained by the discretization(More)
In this paper, we are interested in the mathematical modeling of the propagation of sound waves in the lung parenchyma, which is a foam–like elastic material containing millions of air– filled alveoli. In this study, the parenchyma is governed by the linearized elasticity equations and the air by the acoustic wave equations. The geometric arrangement of the(More)
We are interested in the mathematical modeling of the deformation of the human lung tissue, called the lung parenchyma, during the respiration process. The parenchyma is a foam–like elastic material containing millions of air–filled alveoli connected by a tree– shaped network of airways. In this study, the parenchyma is governed by the linearized elasticity(More)
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