Interplay between Geometry and Flow Distribution in an Airway Tree

Mauroy, Benjamin; Filoche, Marcel; Andrade, José S.; Sapoval, B.

doi:10.1103/physrevlett.90.148101

Cited by 70 publications

(64 citation statements)

References 23 publications

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“…In the middle part, mainly from the sixth generation to the sixteenth generation, the effects of inertia are smaller. This validates the Poiseuille regime (see [3,[5][6][7]12]), at least for rest respiratory regime. In this part of the tree, cartilage does not exist and there are interactions between the fluid and the walls of the pipes.…”

Section: Introductionsupporting

confidence: 81%

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Optimal Poiseuille flow in a finite elastic dyadic tree

Mauroy

Meunier

2008

ESAIM: M2AN

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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).Mathematics Subject Classification. 74D05, 74Q10, 76S05, 92B05.

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Section: Introductionsupporting

confidence: 81%

“…The bronchial tree of the human lung can be viewed as a dyadic net of pipes composed of 23 generations. More precisely, according to [5][6][7]12], we can distinguish three parts in this tree. In the first part, mainly from the first generation to the fifth generation, there is some cartilage and the pipes can be assumed to be rigid.…”

Section: Introductionmentioning

confidence: 99%

Optimal Poiseuille flow in a finite elastic dyadic tree

Mauroy

Meunier

2008

ESAIM: M2AN

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“…it obeys the Stokes equations) beyond generation 5 or 6 only. The flow in the upper part of the tree follows the Navier-Stokes equations (see [9]). Nevertheless, as our approach focuses on the asymptotic behaviour as the number of generations goes to infinity, we can apply it to the whole respiratory system, simply keeping in mind that the model is not valid for the first generations.…”

Section: Some Remarks On the Actual Respiration Treementioning

confidence: 99%

A viscoelastic model with non-local damping application to the human lungs

Grandmont

Maury²,

Meunier

2006

ESAIM: M2AN

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Abstract. In this paper we elaborate a model to describe some aspects of the human lung considered as a continuous, deformable, medium. To that purpose, we study the asymptotic behavior of a spring-mass system with dissipation. The key feature of our approach is the nature of this dissipation phenomena, which is related here to the flow of a viscous fluid through a dyadic tree of pipes (the branches), each exit of which being connected to an air pocket (alvelola) delimited by two successive masses. The first part focuses on the relation between fluxes and pressures at the outlets of a dyadic tree, assuming the flow within the tree obeys Poiseuille-like laws. In a second part, which contains the main convergence result, we intertwine the outlets of the tree with a spring-mass array. Letting again the number of generations (and therefore the number of masses) go to infinity, we show that the solutions to the finite dimensional problems converge in a weak sense to the solution of a wave-like partial differential equation with a non-local dissipative term.Mathematics Subject Classification. 74D05, 74Q10, 76S05, 92B05.

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“…The bronchial tree can then be modeled as a branching network of airways, represented as a dyadic resistive tree (see e.g. [28,29]). The airflow through the tree is then completely characterized by the knowledge of the individual resistances of the branches, which depends only on the dimensions of the bronchi and can be computed from available anatomical data [40].…”

Section: Introductionmentioning

confidence: 99%

Homogenization of a multiscale viscoelastic model with nonlocal damping, application to the human lungs

Cazeaux

Grandmont

2015

Math. Models Methods Appl. Sci.

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We are interested in the mathematical modeling of the deformation of the human lung tissue, called the lung parenchyma, during the respiration process. The parenchyma is a foam-like elastic material containing millions of air-filled alveoli connected by a treeshaped network of airways. In this study, the parenchyma is governed by the linearized elasticity equations and the air movement in the tree by the Poiseuille law in each airway. The geometric arrangement of the alveoli is assumed to be periodic with a small period ε > 0. We use the two-scale convergence theory to study the asymptotic behavior as ε goes to zero. The effect of the network of airways is described by a nonlocal operator and we propose a simple geometrical setting for which we show that this operator converges as ε goes to zero. We identify in the limit the equations modeling the homogenized behavior under an abstract convergence condition on this nonlocal operator. We derive some mechanical properties of the limit material by studying the homogenized equations: the limit model is nonlocal both in space and time if the parenchyma material is considered compressible, but only in space if it is incompressible. Finally, we propose a numerical method to solve the homogenized equations and we study numerically a few properties of the homogenized parenchyma model.

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Interplay between Geometry and Flow Distribution in an Airway Tree

Cited by 70 publications

References 23 publications

Optimal Poiseuille flow in a finite elastic dyadic tree

Optimal Poiseuille flow in a finite elastic dyadic tree

A viscoelastic model with non-local damping application to the human lungs

Homogenization of a multiscale viscoelastic model with nonlocal damping, application to the human lungs

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