Optimal Poiseuille flow in a finite elastic dyadic tree
ESAIM: Modélisation mathématique et analyse numérique, Volume 42 (2008) no. 4, pp. 507-533.

In this paper we construct a model to describe some aspects of the deformation of the central region of the human lung considered as a continuous elastically deformable medium. To achieve this purpose, we study the 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 use of a fixed point theorem in order to find the optimal flow associated to a deformed tree. We also give some numerical results with interesting consequences on human lung deformation during expiration, particularly concerning the localization of the equal pressure point (EPP).

DOI: 10.1051/m2an:2008015
Classification: 74D05, 74Q10, 76S05, 92B05
Mots-clés : fixed point, Poiseuille flow, finite tree, elastic wall, lungs, equal pressure point
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Mauroy, Benjamin; Meunier, Nicolas. Optimal Poiseuille flow in a finite elastic dyadic tree. ESAIM: Modélisation mathématique et analyse numérique, Volume 42 (2008) no. 4, pp. 507-533. doi : 10.1051/m2an:2008015. http://www.numdam.org/articles/10.1051/m2an:2008015/

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