Geodesic
Optimal Poiseuille flow in a finite elastic dyadic tree
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 4, pp. 507-533

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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).

DOI : 10.1051/m2an:2008015
Classification : 74D05, 74Q10, 76S05, 92B05
Keywords: fixed point, Poiseuille flow, finite tree, elastic wall, lungs, equal pressure point 
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     title = {Optimal {Poiseuille} flow in a finite elastic dyadic tree},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {507--533},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {4},
     year = {2008},
     doi = {10.1051/m2an:2008015},
     mrnumber = {2437772},
     zbl = {1203.74033},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008015/}
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Mauroy, Benjamin; Meunier, Nicolas. Optimal Poiseuille flow in a finite elastic dyadic tree. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 4, pp. 507-533. doi: 10.1051/m2an:2008015

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