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

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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  10. F. Preteux, C. Fetita, A. Capderou and P. Grenier, Modeling, segmentation, and caliber estimation of bronchi in high-resolution computerized tomography. J. Electron. Imaging8 (1999) 36–45.  
  11. F.G. Salerno and M.S. Ludwig, Elastic moduli of excised constricted rat lungs. J. Appl. Physiol.86 (1999) 66–70.  
  12. E.R. Weibel, Morphometry of the Human Lung. Springer, Verlag (1963).  
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  14. 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.  
  15. M.S. Zach, The physiology of forced expiration. Paed. Resp. Review1 (2000) 36–39.  

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