# Optimal Poiseuille flow in a finite elastic dyadic tree

Benjamin Mauroy; Nicolas Meunier

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

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

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topMauroy, 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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- F.G. Salerno and M.S. Ludwig, Elastic moduli of excised constricted rat lungs. J. Appl. Physiol.86 (1999) 66–70.
- E.R. Weibel, Morphometry of the Human Lung. Springer, Verlag (1963).
- E.R. Weibel, The Pathway for Oxygen. Harvard University Press (1984).
- G.B. West, J.H. Brown and B.J. Enquist, A general model for the origin of allometric scaling laws in biology. Science276 (1997) 122–126.
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