A three-dimensional model of the human  pulmonary acinus

Kitaoka, Hiroko; Tamura, Shinichi; Takaki, Ryuji

doi:10.1152/jappl.2000.88.6.2260

Cited by 63 publications

(57 citation statements)

References 14 publications

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“…This value is based on the stereological parameter surface-to-volume ratio (8) and is intuitively related to the model situation of the Hilbert acinus: if the acinus is considered as a dense set of cubes of side ᐉ, on average about four of the cube faces are used (18). From the data of Table 1, one obtains L p ͞ᐉ of order 700-900, which justifies the choice of the fourth generation Hilbert acinus to model the mammalian acini.…”

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confidence: 99%

Smaller is better—but not too small: A physical scale for the design of the mammalian pulmonary acinus

Sapoval

Filoche

Weibel

2002

Proc. Natl. Acad. Sci. U.S.A.

198

187

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The transfer of oxygen from air to blood in the lung involves three processes: ventilation through the airways, diffusion of oxygen in the air phase to the alveolar surface, and finally diffusion through tissue into the capillary blood. The latter two steps occur in the acinus, where the alveolar gas-exchange surface is arranged along the last few generations of airway branching. For the acinus to work efficiently, oxygen must reach the last branches of acinar airways, even though some of it is absorbed along the way. This ''screening effect'' is governed by the relative values of physical factors like diffusivity and permeability as well as size and design of the acinus. Physics predicts that efficient acini should be spacefilling surfaces and should not be too large. It is shown that the mammalian acini fulfill these requirements, small mammals being more efficient than large ones both at rest and in exercise.

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confidence: 99%

Smaller is better—but not too small: A physical scale for the design of the mammalian pulmonary acinus

Sapoval

Filoche

Weibel

2002

Proc. Natl. Acad. Sci. U.S.A.

198

187

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“…Morphology of this tissue has been misunderstood since many years, so that the pulmonary acini are arranged like a bunch of grapes. Recently, Kitaoka et al (2000) began to claim that the pulmonary acini are not like the bunch of grapes, where many vacant spaces are left out of the grapes, but like a 3D labyrinth made of branching paths, which fills the space completely and whose exit is connected to an end point of airway. At first, this claim met strong objections among medical scientists, but it is now getting more supports.…”

Section: Reconstruction Of Human Airway Systemmentioning

confidence: 99%

Branching Structures in Nature and Human Societies

Takaki¹

2016

Forma

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expressions of human relations and communication networks. Some of these examples appear in this review article.As a mathematical framework developed since many years we have the method developed by a geologist Horton (1945), who found so-called Horton's law in the tree-type river branching structures, which is introduced briefly in Sec. 2. This method has a great advantage in a sense that the geometrical properties of tree-type structures can be expressed in terms a single parameter. On the other hand, the network-type branching systems have been often treated successfully by scientists from various fields, but they were not based on a simple method similar to that of Horton. The present author has once proposed a method to treat network-type system for leaf veins and road systems, which was included in a monograph by the present author (Takaki, 1978) and not published as a scientific paper. It is introduced in Sec. 4.Of course, the framework of analysis of branching systems is not limited to the Horton's method, and some remarkable examples are introduced in the following sections. In particular, an application of the topology (one of mathematical fields) is made by a pathological scientist Shimizu (1992) for analysis of 3-dimensional (3D) network-type structures of blood vessels in human liver along with a topological concept called "Betti number".Here, it is expected that introductions of various method and concepts would give a larger scope of branching systems, which would stimulate further development of studies in future. Horton's Law for River Structures and Its Derivations Horton's lawA river made of branching streams has a shape belonging to the category of tree-type. The tree structure of riv- Branching Structures in Nature and Human Societies Ryuji TakakiTokyo University of Agriculture and Technology (emeritus professor), 2-23-12 Yuigahama, Kamakura, Kanagawa 248-0014, Japan E-mail address: jr.takaki@iris.ocn.ne.jp (Received July 19, 2015; Accepted March 25, 2016) Several examples of branching structures in the nature, social structures and the human body are introduced, and results of their analyses are given. It is shown that the Horton's law, which is confirmed for river branching structures, is satisfied also in variety of branching structures in the nature and human societies. It is suggested that these structures are constructed owing to mechanisms similar to that for river structure. As for the branching structures in human body some trials are introduced to construct them numerically by the use of mathematical models. The object of this review article is to show that the analyses of branching forms are interesting topics as the science of forms.

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“…Another related article is [23], where a computational algorithm is proposed in order to generate the acinus geometry. In [20] the propagation of elastic waves in the thorax is studied.…”

Section: Prefacementioning

confidence: 99%

“…The main idea is to replace (23) in (13) and, by comparison of the powers of ε, we find local differential problems (in the rapid variable y) parameterized by the macroscopic variable x for d 0 , d 1 and d 2 . Using (24) it is possible to expand the terms σ(d ε )n and divσ(d ε ).…”

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Homogenization of Elastic Media with Gaseous Inclusions

Baffico¹,

Grandmont²,

Maday³

et al. 2008

Multiscale Model. Simul.

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We study the asymptotic behavior of a system modeling a composite material made of an elastic periodically perforated support, with period ε > 0, and a perfect gas placed in each of these perforations, as ε goes to zero. The model we use is linear corresponding to deformations around a reference configuration. We apply both two-scale asymptotic expansion and two-scale convergence methods in order to identify the limit behaviors as ε goes to 0. We state that in the limit, we get a two-scale linear elasticity-like boundary value problem. From this problem, we identify the corresponding homogenized and periodic cell equations which allows us to find the first corrector term. The analysis is performed both in the case of an incompressible and compressible material. We derive some mechanical properties of the limit materials by studying the homogenized coefficients. Finally, we numerically calculate the homogenized coefficients in the incompressible case, for different types of elastic materials.

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A three-dimensional model of the human pulmonary acinus

Cited by 63 publications

References 14 publications

Smaller is better—but not too small: A physical scale for the design of the mammalian pulmonary acinus

Smaller is better—but not too small: A physical scale for the design of the mammalian pulmonary acinus

Branching Structures in Nature and Human Societies

Homogenization of Elastic Media with Gaseous Inclusions

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