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Optimal Poiseuille flow in a finite elastic dyadic tree

Published online by Cambridge University Press:  27 May 2008

Benjamin Mauroy
Affiliation:
Laboratoire MSC, Université Paris 7 (Denis Diderot), 2 place Jussieu, building 33/34, 75251 Paris Cedex 05, France. benjamin.mauroy@paris7.jussieu.fr
Nicolas Meunier
Affiliation:
Laboratoire de Mathématiques MAP5, Université Paris 5 (R. Descartes), 45 rue des Saints Pères, 75006 Paris, France. Nicolas.Meunier@math-info.univ-paris5.fr
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Abstract

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).

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2008

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