# Optimal Poiseuille flow in a finite elastic dyadic tree

• Volume: 42, Issue: 4, page 507-533
• ISSN: 0764-583X

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## Abstract

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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).

## How to cite

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Mauroy, Benjamin, and Meunier, Nicolas. "Optimal Poiseuille flow in a finite elastic dyadic tree." ESAIM: Mathematical Modelling and Numerical Analysis 42.4 (2008): 507-533. <http://eudml.org/doc/250276>.

@article{Mauroy2008,
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). },
author = {Mauroy, Benjamin, Meunier, Nicolas},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Fixed point; Poiseuille flow; finite tree; elastic wall; lungs; equal pressure point.; fixed point; equal pressure point},
language = {eng},
month = {5},
number = {4},
pages = {507-533},
publisher = {EDP Sciences},
title = {Optimal Poiseuille flow in a finite elastic dyadic tree},
url = {http://eudml.org/doc/250276},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Mauroy, Benjamin
AU - Meunier, Nicolas
TI - Optimal Poiseuille flow in a finite elastic dyadic tree
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2008/5//
PB - EDP Sciences
VL - 42
IS - 4
SP - 507
EP - 533
AB - 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).
LA - eng
KW - Fixed point; Poiseuille flow; finite tree; elastic wall; lungs; equal pressure point.; fixed point; equal pressure point
UR - http://eudml.org/doc/250276
ER -

## References

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15. M.S. Zach, The physiology of forced expiration. Paed. Resp. Review1 (2000) 36–39.

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