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Mechanism of spontaneous multi-scale pattern formation during develop,ment

Research Project

Project/Area Number 15KT0018
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeMulti-year Fund
Section特設分野
Research Field Mathematical Sciences in Search of New Cooperation
Research InstitutionKyushu University

Principal Investigator

Miura Takashi  九州大学, 医学研究院, 教授 (10324617)

Research Collaborator Uemura Akiyoshi  
Kawamura Shotaro  
Naroda Yuto  
Project Period (FY) 2015-07-10 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥16,250,000 (Direct Cost: ¥12,500,000、Indirect Cost: ¥3,750,000)
Fiscal Year 2018: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2017: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2016: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2015: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Keywords自発的パターン形成 / フラクタル / 網膜血管 / 頭蓋骨縫合線 / スケーリング則 / パターン形成 / スケーリング
Outline of Final Research Achievements

Biological organisms have complex form, like fractal structure. However, the mechanismn how the fractal structure is generated remain to be elucidated. In the present study, we use two biological systems, retina vasculature and skull suture interdigitation, and formulated biologically plausible mathematical model. Then we analytically showed that the model can generate patterns that show scaling behavior. In retina vasculature, combination of physiological law of vessel radii (Murray's law) and equal bifurcation can lead to the scaling behavior. In skull suture, noise term in the original PDE model can lead to the scaling behavior.

Academic Significance and Societal Importance of the Research Achievements

生物の形は複雑で、フラクタル構造が存在することは古くから指摘されていた。しかし、フラクタル次元の計測のみが行われて、なぜそのような形になるのか、その根本的なメカニズムは理解されていなかった。今回、網膜血管と頭蓋骨縫合線という二つの例について、パターン形成のメカニズムを数理モデルを作成することで理解し、そのメカニズムによってフラクタル構造が生成されうることを示した。

Report

(5 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (20 results)

All 2018 2017 2016 2015

All Journal Article (1 results) (of which Peer Reviewed: 1 results,  Acknowledgement Compliant: 1 results) Presentation (17 results) (of which Int'l Joint Research: 2 results,  Invited: 8 results) Book (2 results)

  • [Journal Article] A new mathematical model for pattern formation by cranial sutures.2016

    • Author(s)
      Kenji Yoshimura, Ryo Kobayashi, Tomohisa Ohmura, Yoshinaga Kajimoto,Takashi Miura.
    • Journal Title

      Journal of theorietical biology,

      Volume: 408 Pages: 66-74

    • DOI

      10.1016/j.jtbi.2016.08.003

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] 口蓋縫合のパターン形成の数理モデル2018

    • Author(s)
      澁澤伸英,遠藤淑恵,三浦岳
    • Organizer
      日本解剖学会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 頭蓋骨縫合線のパターン形成2018

    • Author(s)
      三浦 岳
    • Organizer
      反応拡散系のパターン形成とその応用
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Modeling of skull suture pattern formation2018

    • Author(s)
      三浦 岳
    • Organizer
      生物物理学会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 細胞壁と頭蓋骨:分野を超える数理2018

    • Author(s)
      三浦 岳
    • Organizer
      第15回生物数学の理論とその応用
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Mechanism of skull suture pattern formation2018

    • Author(s)
      三浦 岳
    • Organizer
      iWOMB2018
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 植物細胞壁の湾曲構造形成の理論モデル2017

    • Author(s)
      三浦 岳
    • Organizer
      AIMaP「反応拡散系と実験の融合」
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] 生物の形づくりの数理 -Mathematicaによるrapid prototyping-2017

    • Author(s)
      三浦 岳
    • Organizer
      ウルフラムコンファレンス2017
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Mechanism of lung branching morphogenesis2017

    • Author(s)
      三浦 岳
    • Organizer
      歯科基礎医学会
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Modeling vascular scaling law formation in retina vasculature2017

    • Author(s)
      河村正太郎
    • Organizer
      発生生物学会
    • Related Report
      2017 Research-status Report
  • [Presentation] A mathematical model to generate fractal structure in skull suture2017

    • Author(s)
      奈路田悠桃
    • Organizer
      数理生物学会
    • Related Report
      2017 Research-status Report
  • [Presentation] 精細管におけるwavetrain パターン形成のモデリング2017

    • Author(s)
      河村真里
    • Organizer
      数理生物学会
    • Related Report
      2017 Research-status Report
  • [Presentation] Mechanism of scaling law formation in developing retina vasculature2017

    • Author(s)
      飯塚統
    • Organizer
      数理生物学会
    • Related Report
      2017 Research-status Report
  • [Presentation] Origin of fractality of skull sutures2016

    • Author(s)
      ○Yuto Naroda, Kenji Yoshimura, Yoshinaga Kajimoto, Tomohisa Ohmura, Takashi Miura
    • Organizer
      JSMB2016
    • Place of Presentation
      Shiki Hall, Kyushu University(福岡)
    • Year and Date
      2016-09-07
    • Related Report
      2016 Research-status Report
  • [Presentation] Origin of fractality of skull sutures2016

    • Author(s)
      ○Yuto Naroda,Takashi Miura
    • Organizer
      JSDB Special Symposium: Frontier of Developmental Biology Hosted by JSDB
    • Place of Presentation
      Koshiba hall, University of Tokyo (東京)
    • Related Report
      2016 Research-status Report
  • [Presentation] 発生における マルチスケールの 自発的パターン形成現象2015

    • Author(s)
      三浦 岳
    • Organizer
      富山シンポジウム
    • Place of Presentation
      富山県教育文化会館
    • Year and Date
      2015-11-07
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Formation of fractal structure in skull suture2015

    • Author(s)
      Takashi Miura
    • Organizer
      ICIAM2015
    • Place of Presentation
      北京
    • Year and Date
      2015-08-10
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] 縫合線パターンのフラクタル性の起源2015

    • Author(s)
      三浦 岳
    • Organizer
      Craniosynostosis 研究会
    • Place of Presentation
      大阪医大
    • Year and Date
      2015-07-15
    • Related Report
      2015 Research-status Report
  • [Book] Fractal Geometry of the Brain2016

    • Author(s)
      Antonio Di Leva
    • Total Pages
      300
    • Publisher
      Springer
    • Related Report
      2015 Research-status Report
  • [Book] 発生の数理2015

    • Author(s)
      三浦 岳
    • Total Pages
      220
    • Publisher
      京都大学出版
    • Related Report
      2015 Research-status Report

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Published: 2015-07-14   Modified: 2020-03-30  

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