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Origami Model for Breathing Alveoli

  • HirHiroko Kitaoka
  • Carlos A. M. Hoyos
  • Ryuji Takaki
Conference paper
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 669)

Abstract

We previously proposed a morphogenesis-based 4D model of the alveolar structure. However, the model exists only in computer, and is too complicated to be recognized in 2D display. Origami, a Japanese traditional craft, is a 4D object originated from 2D sheet. We introduce origami models approximating our computational alveolar model. One can make, see, and handle the models by oneself. Seeing is believing. We dare say “Making is convincing”.

Keywords

Alveolar Structure Morphogenetic Process Living Organ Alveolar Duct Alveolar Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

1 Similarity of Origami and the Living Organ

The living organ changes its shape from sheet-like arrangement of primitive cells to mature 3D structure through morphogenetic process. Functions of the living organ are realized by periodic changes in spatial arrangement of tissue elements of the organ. Origami, a Japanese traditional craft, is also a 3D structure originated from a sheet of paper. Origami is not fixed but movable by changing folding angles. Thus, both the living organ and origami are 4D systems originated from 2D sheet. If the structure, function, and morphogenesis of the organ can be expressed by origami, the origami model will be very useful for deeper understanding of the organ, because one can make, see, and handle it by oneself. The model will be also useful for developing artificial organs and biomimetic applications.

2 Four-Dimensional Model of the Alveolar Structure

We proposed a morphogenesis-based 4D model of the alveolar structure shown in Fig. 1 (Kitaoka et al. 2007). Our model was mathematically constructed based on the morphogenetic process (Burri 1991) and the distribution of material property of the alveolar wall (Mercer and Crapo 1990). The most characteristic point of the model is that size change during respiration is larger at the alveolar mouth (alveolar entrance ring) than its whole size, based on experimental facts (Mercer et al. 1987). The algorithm of the model construction mimics the morphogenetic process from a columnar duct into an alveolar duct with alveolar opening. First, smooth surfaces of the columnar duct are deformed convexly and concavely. Then, alveolar mouths are generated by attaching secondary septa at convex ridges.
Fig 1

Algorithm of Kitaoka’s 4D alveolar model

We have performed airflow simulation within a 4D alveolar sac model by the use of computational fluid dynamics (Fig. 2). The model contains 16 alveoli and 39,259 computational nodes. Airflow caused by the wall motion was computed by the use of arbitrary Laglangean Eulerian method of the finite element method (Solver: AcuSolve by AcuSim Inc, USA). Computed airflow is visualized by massless particles which are located at the open end at the initial condition and go inside during inspiration. A tidal deep breath was simulated for 4-second inspiration and 6-second expiration whose volume at the initial condition was 25% of that at full inspiration. Since the alveolar wall is expressed translucently in Fig. 2, deformation of alveolar mouths are recognizable. Alveolar mouths in the model are very narrow at the beginning of inspiration, and are widened during inspiration. Massless particles were used for visualization of the computed airflow, located at the open end. Although conventional textbooks of respiratory physiology tell us that there is little air flow in the alveolus (Lumb 2000), our simulation result showed apparent intra-alveolar flow through the alveolar mouth.
Fig. 2

Airflow simulation within an alveolar sac model

3 Origami Model for a Single Alveolus

Although a mathematically constructed 4D model is useful for numerical approach such as flow simulation, it exists only in computer, and is too complicated to be recognized in 2D display. Here, we introduce how to approximate the 4D alveolar model. Let’s fold a square sheet as shown in Fig. 3. When the folding angles at the real lines are 45 degrees, an open polyhedron (a part of 18-hedron) is generated. When the angles are 90 degrees, four vertexes touch each other and the open polyhedron becomes a closed cube. This conformation corresponds to that of the alveolus at the minimum volume (Mercer et al. 1987). Breathing motion of the alveolus can be mimicked by changing the folding angles between 45 and 90 degrees. If the folding angles are close to zero, it is hard to recover its 3D conformation due to lack of angular momentum. It corresponds to the condition of emphysematous alveoli. On the other hand, if there is liquid film inside of the origami and the surface tension of the liming liquid is high, the cube is collapsed by the surface tension, and loses its 3D conformation.
Fig. 3

Origami for a single alveolus

4 Origami Model for an Alveolar Duct

Multiple alveoli are generated from one rectangle sheet by dividing the sheet into smaller squares (Fig. 4). An alveolar duct is generated when the sheet is rounded. Note alveoli are generated on the backside of the sheet, too. The origami model for single alveolus has four triangles of which the alveolar mouth consists. However, when multiple alveoli are folded, those triangles become parts of bottoms of neighboring alveoli. Therefore, additional triangles corresponding to secondary septa are attached by cellophane tape. Finally, an alveolar duct by origami is breathing in your hands as you control motion of your hands. Although more complicated process is required for space-filling alveolar duct model, the basic method is the same.
Fig. 4

Origami for an alveolar duct

References

  1. Burri, P.H. (1991) Structural development of the human lung. In: Handbook of physiology, The respiratory system (pp. 8–21). Philadelphia, PA: Lippincott-Raven.Google Scholar
  2. Kitaoka, H., Nieman, G.F., Fujino, Y., Carney, D., DiRocco, J., and Kawase, I. (2007) A 4-dimensional model of the alveolar structure. J, Physiol. Sci. 57, 175–185.CrossRefGoogle Scholar
  3. Mercer, R., Laco, T.J.M., and Crapo, J.D. (1987) Three-dimensional reconstruction of alveoli in the rat lung for pressure-volume relationships. J. Appl. Physiol. 62, 1480–1487.PubMedGoogle Scholar
  4. Mercer, R. and Crapo, J.D. (1990) Spatial distribution of collagen and elastin fibers in the lungs. J. Appl. Physiol. 69, 756–765.PubMedGoogle Scholar
  5. Lumb, A.B. (2000) Distribution of pulmonary ventilation and perfusion. In: Nunn’s Applied Respiratory Physiology (pp. 163–199). Oxford: Butterworth Heinemann.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • HirHiroko Kitaoka
    • 1
  • Carlos A. M. Hoyos
    • 2
  • Ryuji Takaki
    • 3
  1. 1.Engineering Technology DivisionJSOL CorporationTokyoJapan
  2. 2.Department of EngineeringSingapore UniversitySingaporeSingapore
  3. 3.Kobe Design UniversityKobeJapan

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