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Study on differential equations arising out of life phenomena in vivo

Research Project

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(Kenkyū-buntansha) 梅沢 栄三  藤田保健衛生大学, 衛生学部, 講師 (50318359)
斉藤 宣一  富山大学, 人間発達科学部, 准教授 (00334706)
手嶋 久三  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)
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
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
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 / 体内生命現象 / 腫瘍の血管新生 / 腫瘍浸潤 / 細胞接着 / 走化性 / 走触性 / 爆発解 / 腫瘍 / 侵潤 / 非局所項 / 腫瘍の増殖と転移 / パターン形成 / 数値シミュレーション / 数理医学 / 国際研究集会 / 2モデルの数学的同等性
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.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (28 results)

All 2010 2009 2008 2007 Other

All Journal Article (16 results) (of which Peer Reviewed: 14 results) Presentation (11 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

    • Related Report
      2009 Final Research Report
    • 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

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Mathematical analysis of some models of tumour growth2010

    • Author(s)
      久保明達
    • Journal Title

      Advances in Biological Researches(Proceedings of the 7^<th> WSEAS international conferences on mathematical biology and ecology)

      Pages: 446-451

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Mathematical analysis of some models of tumour growth and simulations2010

    • Author(s)
      久保明達
    • Journal Title

      WSEAS Transactions on Biology and Biomedecine Issue2, Vol.7

      Pages: 31-40

    • Related Report
      2009 Annual Research Report
    • 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

    • Related Report
      2009 Final Research Report
    • 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

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Existence and non-existence of global solutions to initial boundary value problems for nonlinear evolution eaquations with strong dissipation2009

    • Author(s)
      Akisato Kubo, J-P Loheac
    • Journal Title

      Nonlinear Analysis 71

      Pages: 2797-2806

    • Related Report
      2009 Annual Research Report
    • 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

      応用数理(日本応用数理学会編集) 19(4)

      Pages: 266-280

    • Related Report
      2009 Annual Research Report
    • 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

    • NAID

      10025696055

    • Related Report
      2009 Final Research Report
  • [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

    • NAID

      10027851272

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Blow up solutions of initial boundary value problems for nonlinear evolution equations with the strong dissipation2008

    • Author(s)
      久保明達
    • Journal Title

      Proceeding of 15th SAMS symposium (2008) 1

      Pages: 38-46

    • Related Report
      2008 Annual Research Report
  • [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

    • Related Report
      2009 Final Research Report
    • 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

    • Related Report
      2009 Final Research Report
    • 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

    • Related Report
      2009 Final Research Report
    • 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

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Mathematical models of tumour angiogenesis2007

    • Author(s)
      Akisato Kubo, Takashi Suzuki
    • Journal Title

      Journal of Computational and Applied Mathematics 204

      Pages: 48-55

    • Related Report
      2007 Annual Research Report
    • 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
    • Related Report
      2009 Final Research Report
  • [Presentation] Mathematical analysis of some models of tumour growth2010

    • Author(s)
      Akisato Kubo
    • Organizer
      The 7^<th> WSEAS international conferences on mathematical biology and ecology
    • Place of Presentation
      Cambridge, UK
    • Year and Date
      2010-02-24
    • Related Report
      2009 Annual Research Report
  • [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
    • Related Report
      2009 Final Research Report
  • [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
    • Related Report
      2009 Final Research Report
  • [Presentation] Blow up solutions of initial boundary value problems for nonlinear evolution equations with the strong dissipation2008

    • Author(s)
      久保明達
    • Organizer
      Fifth World Congress of Nonlinear Analysts
    • Place of Presentation
      Orland, Florida, USA
    • Year and Date
      2008-07-05
    • Related Report
      2008 Annual Research Report
  • [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
    • Related Report
      2009 Final Research Report
  • [Presentation] Mathematical Analysis of Models for Tumour Growth2008

    • Author(s)
      久保明達
    • Organizer
      European conference on Mathematical and Theoretical Biology 2008
    • Place of Presentation
      Edinburg, Scotland, England
    • Year and Date
      2008-07-03
    • Related Report
      2008 Annual Research Report
  • [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)
    • Related Report
      2009 Final Research Report
  • [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)
    • Related Report
      2009 Final Research Report
  • [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
    • Related Report
      2009 Final Research Report
  • [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)
    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

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

    • Related Report
      2009 Final Research Report

URL: 

Published: 2007-04-01   Modified: 2016-04-21  

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