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elastic wall

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Optimal Poiseuille flow in a finite elastic dyadic tree
Benjamin Mauroy, Nicolas Meunier
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 42 / Issue 4 / July 2008

Published online by Cambridge University Press:

27 May 2008, pp. 507-533

Print publication:

July 2008
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In this paper we construct a model to describe someaspects of the deformation of the central region of the human lung considered as acontinuous elastically deformable medium. To achieve this purpose, we studythe interaction between the pipes composing the tree and the fluid that goes through it. We use a stationary model to determine the deformed radius of each branch. Then, we solve a constrained minimization problem, so as to minimize the viscous (dissipated) energy in the tree. The key feature of our approach is the useof a fixed point theorem in order to find the optimal flow associatedto a deformed tree. We also give some numerical results withinteresting consequences on human lung deformation during expiration, particularlyconcerning the localization of the equal pressure point (EPP).