An optimal bronchial tree may be dangerous

Mauroy, Benjamin; Filoche, Marcel; Weibel, Ewald R.; Sapoval, B.

doi:10.1038/nature02287

Cited by 255 publications

(240 citation statements)

References 12 publications

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“…The bronchial tree of the human lung has over 10 5 conducting and 10 7 respiratory airways arrayed in an intricate pattern crucial for oxygen flow [1][2][3][4] . Classical studies of lung structure 5-8 raise the question of how the information required to generate a tree of such complexity is biologically encoded 9 .…”

Section: Introductionmentioning

confidence: 99%

The branching programme of mouse lung development

Metzger

Klein

Martin

et al. 2008

Nature

711

786

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Mammalian lungs are branched networks containing thousands to millions of airways arrayed in intricate patterns that are crucial for respiration. How such trees are generated during development, and how the developmental patterning information is encoded, have long fascinated biologists and mathematicians. However, models have been limited by a lack of information on the normal sequence and pattern of branching events. Here we present the complete three-dimensional branching pattern and lineage of the mouse bronchial tree, reconstructed from an analysis of hundreds of developmental intermediates. The branching process is remarkably stereotyped and elegant: the tree is generated by three geometrically simple local modes of branching used in three different orders throughout the lung. We propose that each mode of branching is controlled by a genetically-encoded subroutine, a series of local patterning and morphogenesis operations, which are themselves controlled by a more global master routine. We show that this hierarchical and modular program is genetically tractable, and it is ideally suited to encoding and evolving the complex networks of the lung and other branched organs.Many organs are composed of highly ramified tubular networks, each with a distinct architecture tailored to its physiological function. The bronchial tree of the human lung has over 10 5 conducting and 10 7 respiratory airways arrayed in an intricate pattern crucial for oxygen flow [1][2][3][4] . Classical studies of lung structure 5-8 raise the question of how the information required to generate a tree of such complexity is biologically encoded 9 . Individually configuring thousands or millions of branches would require a tremendous amount of patterning information, far more than is biologically plausible, to specify when and where each branch forms during development, and the size, shape, and direction of outgrowth of each branch. One possibility is that the process is not precisely controlled, for example if branching occurs randomly to fill available space. Another is that control is precise but coding is simplified by repeated use of a branching mechanism, as in Mandelbrot's fractal model and other elegant algorithms [10][11][12][13][14][15][16][17] . Even with these attractive models and recent progress in identifying lung development genes 18 , understanding of the program that directs branching remains rudimentary. This is largely due to the complexity of the bronchial tree, which makes it difficult to follow branching dynamics beyond the earliest events [19][20][21] . Although branching of the lung and other organs can occur in culture [22][23][24][25] , it is unlikely these recapitulate the full pattern. Here, we have determined the complete in vivo pattern of branching and branch lineage of the mouse bronchial tree, and show that it is generated using three geometrically distinct local modes of branching coupled in three different sequences. The branch lineage of the mouse bronchial treeThe bronchial tree develops by bran...

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Section: Introductionmentioning

confidence: 99%

The branching programme of mouse lung development

Metzger

Klein

Martin

et al. 2008

Nature

711

786

View full text Add to dashboard Cite

show abstract

“…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: Introductionmentioning

confidence: 85%

“…Thus, we use E = 6250 Pa for Young's modulus [9,11] of each bronchi walls. The tree is assumed to have eleven generations and to be of fractal structure: bronchi of one generation are homothetic to bronchi of the previous generation with a factor h = 0.82 [7,12,14]. Parenchyma pressures have been fitted relatively to trachea velocities from measures obtained in [4].…”

Section: Methodsmentioning

confidence: 99%

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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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“…Our goal are more modest here, since the geometry of the problems (only two dimensions) and the physical phenomena considered are much simpler, but we hope that rigorous results and methods will prove useful. We refer to [5,15,16] for accurate physical descriptions of the lungs' physiology and for studies concerning the diffusion of oxygen in the lungs.…”

Section: Introductionmentioning

confidence: 99%

Diffusion and propagation problems in some ramified domains with a fractal boundary

Achdou¹,

Sabot²,

Tchou³

2006

ESAIM: M2AN

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Abstract. This paper is devoted to some elliptic boundary value problems in a self-similar ramified domain of R 2 with a fractal boundary. Both the Laplace and Helmholtz equations are studied. A generalized Neumann boundary condition is imposed on the fractal boundary. Sobolev spaces on this domain are studied. In particular, extension and trace results are obtained. These results enable the investigation of the variational formulation of the above mentioned boundary value problems. Next, for homogeneous Neumann conditions, the emphasis is placed on transparent boundary conditions, which allow the computation of the solutions in the subdomains obtained by stopping the geometric construction after a finite number of steps. The proposed methods and algorithms will be used numerically in forecoming papers.Mathematics Subject Classification. 28A80, 35J05, 35J25, 65N.

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An optimal bronchial tree may be dangerous

Cited by 255 publications

References 12 publications

The branching programme of mouse lung development

The branching programme of mouse lung development

Optimal Poiseuille flow in a finite elastic dyadic tree

Diffusion and propagation problems in some ramified domains with a fractal boundary

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