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2009 Fiscal Year Final Research Report

Study on differential equations arising out of life phenomena in vivo

Research Project

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Project/Area Number 19540200
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionFujita Health University

Principal Investigator

KUBO Akisato  Fujita Health University, 医療科学部, 教授 (60170023)

Co-Investigator(Renkei-kenkyūsha) UMEZAWA Eizou  藤田保健衛生大学, 医療科学部, 准教授 (50318359)
SAITO Norikazu  東京大学, 大学院・数理科学研究科, 准教授 (00334706)
TESHIMA Kyuzo  お茶の水女子大学, 大学院・人間文化創成科学研究科研究院, 研究員 (70288471)
Project Period (FY) 2007 – 2009
Keywords生命現象 / 数理モデル / 数学解析 / 腫瘍の成長 / 腫瘍の侵潤 / 腫瘍血管新生 / 非線形発展方程式 / 時間大域解
Research Abstract

(1) We invited Professor M.Chaplain from Dundee University, UK to Japan for a week, September, 2007. On this occasion we organized the international conference" "Workshop on Mathematical Modelling and Analysis of Biological Pattern Formations and the Related Topics" (25-26, September, Nagoya University) (http://www.fujita-hu.ac.jp/~akikubo/).
(2) We investigated mathematical model of tumour growth and invasion by M.Chaplain and G.Lolas, 2006. The principal investigator and co-investigators have to spend much time to overcome this difficulty.
(3) We succeeded to obtain the mathematically exact relation between Othmer and Stevens model and Anderson and Chaplain model of tumour induced angiogenesis. Our result allow us to connect them from one to another only by formal calculation and substitution.
(4) We tried to improve our mathematical way used in a sequence of mathematical models of tumour angiogenesis and tumour invasion by Anderson and Chaplain in order to study the latest model of nonlocal tumour invasion by Gerish and Chaplain (2007).
2009
(5) The principal investigator and co-investigators of this project studied an initial 0-Neumann boundary problem of nonlinear evolution equations in more general frame work. Finally to complete touch to this project we could give a characterization of a sequence of tumour growth models studied in this project by this framework of existence theorem and properties of the solution of our nonlinear evolution equations(see research activities 1,2,3).
(6) The main investigator and his collaborator applied the method used by Levine and Sleeman (1998) in initial Neumann boundary value problems of the evolution equation and succeeded to show the existence of blow up solution under Dirichlet boundary condition(see research activities 4)
(7) Based on the mathematical analysis in (2)to (6), we made computer simulations for each problem.

  • Research Products

    (19 results)

All 2010 2009 2008 2007 Other

All Journal Article (10 results) (of which Peer Reviewed: 9 results) Presentation (8 results) Remarks (1 results)

  • [Journal Article] Mathematical analysis of some models of tumour growth and simulations2010

    • Author(s)
      A. Kubo
    • Journal Title

      WSEAS Transactions on Biology and Biomedicine

      Pages: 31-40

    • Peer Reviewed
  • [Journal Article] Mathematical analysis of some models of tumour growth2010

    • Author(s)
      A. Kubo
    • Journal Title

      Advances in Biological research

      Pages: 446-451

    • Peer Reviewed
  • [Journal Article] 走化性を伴う腫瘍成長モデルとその数理2009

    • Author(s)
      久保明達, 小林英敏
    • Journal Title

      日本応用数理学会誌「応用数理」 19巻4号

      Pages: 50-64

    • Peer Reviewed
  • [Journal Article] Existence and non-existence of Global soutions to initial boundary balue problems for nonlinear evolution equations with the strong dissipation2009

    • Author(s)
      A. Kubo, J.P. Loheac
    • Journal Title

      Nonlinear Analysis Series A : Theory, Methods Applications 71

      Pages: 2797-2806

    • Peer Reviewed
  • [Journal Article] Multi-shelled q-ball imaging:高次モーメントを利用した方向分布関数による神経路走行方向の検出2008

    • Author(s)
      梅沢栄三, (他4人)
    • Journal Title

      日本磁気共鳴医学会雑誌 28(1)(大会長賞記録)

      Pages: 74-81

  • [Journal Article] Multi-Shelled Q-Ball Imaging : Moment-Based Orientation Distribution Function2008

    • Author(s)
      E. Umezawa, et al.
    • Journal Title

      Proceedings of the International Society for Magnetic Resonance in Medicine 16th Scientific Meetings and Exhibition 1865

    • Peer Reviewed
  • [Journal Article] Characterization of mathematical models of tumour angiogenesis2007

    • Author(s)
      A. Kubo
    • Journal Title

      Proceedings of the 3^<rd> International Conference on Mathematical Biology and Ecology

      Pages: 17-19

    • Peer Reviewed
  • [Journal Article] Mathematical models of tumour angiogenesis2007

    • Author(s)
      A. Kubo, T. Suzuki
    • Journal Title

      Journal of Computational and Applied Mathematics 204

      Pages: 48-55

    • Peer Reviewed
  • [Journal Article] Flux-free finite element method with Lagrange mutipliers for two-fluid flows2007

    • Author(s)
      K. Ohmori, N. Saito
    • Journal Title

      Journal of Scientific Computing Vol.32,No.2

      Pages: 147-173

    • Peer Reviewed
  • [Journal Article] Conservative upwind finite element method for a simplified Keller-Segel system modelling chemotaxis2007

    • Author(s)
      N. Saito
    • Journal Title

      IMA Journal of Numerical Analysis Vol.27,No.2

      Pages: 332-365

    • Peer Reviewed
  • [Presentation] Mathematical analysis of some models of tumour growth2010

    • Author(s)
      A. Kubo
    • Organizer
      7^<th> WSEAS International Conference on Mathematical Biology and Ecology
    • Place of Presentation
      Cambridge, UK
    • Year and Date
      2010-02-24
  • [Presentation] 臨床機によるmulti-shelled q-ball imagingの試行2009

    • Author(s)
      梅沢栄三, 〓山喜文, 他
    • Organizer
      第37回日本磁気共鳴医学会大会
    • Place of Presentation
      横浜
    • Year and Date
      20090910-20090924
  • [Presentation] Multi-shelled q-ball imagingに基づくTractographyの数値シミュレーションによる検証2008

    • Author(s)
      梅沢栄三, 森政裕, 他
    • Organizer
      第36回日本磁気共鳴医学会大会
    • Place of Presentation
      旭川(ポスター発表)
    • Year and Date
      20080930-20081003
  • [Presentation] Multi-Shelled Q-Ball Imaging: Moment-Based Orientation Distribution Function2008

    • Author(s)
      E. Umezawa, M. Yoshikawa, et al.
    • Organizer
      International Society for Magnetic Resonance in Medicine 16th Scientific Meetings and Exhibition
    • Place of Presentation
      Toronto(poster)
    • Year and Date
      20080504-20080508
  • [Presentation] Blowup solutions of initial boundary value problems for nonlinear evolution equations with the strong dissipation2008

    • Author(s)
      A. Kubo
    • Organizer
      5^<th> World Congress of Nonlinear Analysis
    • Place of Presentation
      Olando, Florida, USA
    • Year and Date
      2008-07-05
  • [Presentation] Mathematical analysis of models for tumour growth2008

    • Author(s)
      A. Kubo
    • Organizer
      European Conference on Mathematical and Theoretical Biology
    • Place of Presentation
      Edingburg, UK
    • Year and Date
      2008-07-03
  • [Presentation] Multi-shelled q-ball imaging:高次モーメントを利用した方向分布関数による神経路走行方向の検出2007

    • Author(s)
      梅沢栄三, 吉川真代, 他
    • Organizer
      第35回日本磁気共鳴医学会大会
    • Place of Presentation
      神戸(ポスター発表)
    • Year and Date
      20070927-20070929
  • [Presentation] Mathematical analysis of Anderson and Chaplain models2007

    • Author(s)
      A. Kubo
    • Organizer
      Workshop on Mathematical Modelling and Analysis of Biological Pattern Formations and the Related Topics
    • Place of Presentation
      Nagoya, Japan
    • Year and Date
      2007-09-26
  • [Remarks]

    • URL

      http://www.fujita-hu.ac.jp/~akikubo/

URL: 

Published: 2011-06-18   Modified: 2016-04-21  

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