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Study on partial differential equations describing multi-scale life phenomenon

Research Project

Project/Area Number 25400148
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionFujita Health University

Principal Investigator

KUBO Akisato  藤田保健衛生大学, 保健学研究科, 教授 (60170023)

Co-Investigator(Kenkyū-buntansha) UMEZAWA EIZOU  藤田保健衛生大学, 医療科学部, 准教授 (50318359)
HOSHINO HIROKI  藤田保健衛生大学, 医療科学部, 准教授 (80238740)
HAYASHI NAOKI  藤田保健衛生大学, 医療科学部, 講師 (00549884)
Co-Investigator(Renkei-kenkyūsha) SAITO NORIKAZU  東京大学, 大学院数理科学研究科, 准教授 (00334706)
Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2013: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywordsマルチスケール / 非局所 / 腫瘍浸潤 / 腫瘍成長 / 数理モデル / 解の存在 / 漸近挙動 / シミュレーション / 非局所項 / 増殖項 / 数学解析 / 腫瘍浸潤現象 / 多重スケール現象 / 多重尺度 / 非線形発展方程式 / 時間大域解 / 解の挙動 / 腫瘍侵潤現象 / 数学的特徴づけ / 解の可解性 / 多重尺度項
Outline of Final Research Achievements

The mathematical models of tumor growth and invasion proposed by Chaplain et al. consistently preserves a multi-scaling structure. In this research subject we consider Chaplain-Lolas and Gerisch-Chaplain models specified in this point of view clearly.
(1)We first completed mathematical analysis of the former and then in the same line we sutudied the latter. We could show the time global existence and asymptotic behavior of the solution of the former in the original form. (2)However, in the latter we found the non-local term is not well-defined on the boundary, and Chaplain has finally accepted this point in his latest paper, and gave biological justification. When it was known, we have already gone into the last year of the subject research period, and cannot help considering it as the future one. (3)We have confirmed some visualization of the behavior of Glioma cells in the invisible area of invasive range by computer simulations, based on experiments in vitro.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (59 results)

All 2016 2015 2014 2013 Other

All Int'l Joint Research (1 results) Journal Article (19 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 17 results,  Acknowledgement Compliant: 7 results,  Open Access: 4 results) Presentation (34 results) (of which Int'l Joint Research: 3 results,  Invited: 9 results) Book (5 results)

  • [Int'l Joint Research] Universidad Politecnica de Madrid(スペイン)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Mathematical analysis of a model of chemotaxis with competition terms2016

    • Author(s)
      A. Kubo and J.Ignacio Tello
    • Journal Title

      Differential and Integral Equations

      Volume: 29 Pages: 441-454

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Global existence and asymptotic behaviour of solutions for nonlinear evolution equations related to tumour invasion2015

    • Author(s)
      A. Kubo and H. Hoshino and K. Kimura
    • Journal Title

      Dynamical Systems, Differential Equations and Applications, AIMS Proceedings

      Volume: * Pages: 733-744

    • DOI

      10.3934/proc.2015.0733

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Nonlinear evolution equations with strong dissipation and proliferation2015

    • Author(s)
      A. Kubo and H. Hoshino
    • Journal Title

      Current Trends in Analysis and Applications

      Volume: * Pages: 233-241

    • DOI

      10.1007/978-3-319-12577-0_28

    • ISBN
      9783319125763, 9783319125770
    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Nonlinear evolution equations with strong dissipation and proliferation2015

    • Author(s)
      Akisato Kubo and Hiroki Hoshino
    • Journal Title

      CurrentTrends in Analysis and its Applications(Springer)

      Volume: * Pages: 233-241

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Global existence and asymptotic behaviour of solutions for nonlinear evolution equations related to a tumour invasion2015

    • Author(s)
      Akisato Kubo,Hiroki Hoshino and Katsutaka Kimura
    • Journal Title

      The proceedings of 10 th AIMS conference

      Volume: * Pages: 1-13

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Mathematical analysis of tumour invasion with proliferation model and simulations2014

    • Author(s)
      Akisato Kubo and Katsutaka Kimura
    • Journal Title

      WSEAS Transactions on Biology and Biomedicine

      Volume: 11 Pages: 165-173

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Mathematical analysis of Glioblastoma invasion in 3D2014

    • Author(s)
      Akisato Kubo and Katsutaka Kimura
    • Journal Title

      Recent Advances in Applied Mathematics, Modelling and Simulation

      Volume: * Pages: 117-122

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Noncommutative spacetime realized in AdSn+1 space: Nonlocal field theory out of noncommutative spacetime2014

    • Author(s)
      S. Naka, H. Toyoda, T. Takanashi, and E. Umezawa
    • Journal Title

      Prog. Theor. Exp. Phys.

      Volume: * Issue: 4 Pages: 43B03-0

    • DOI

      10.1093/ptep/ptu022

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] An accurate and precise new method for measuring kurtosis of intravoxel incoherent motion2014

    • Author(s)
      E. Umezawa, D. Ishihara and S. Seko
    • Journal Title

      Proc. Intl. Soc. Mag. Reson. Med. 22

      Volume: * Pages: 22-22

    • Related Report
      2014 Research-status Report
  • [Journal Article] コバルト60定位手術的照射装置の違いが治療計画に及ぼす影響2014

    • Author(s)
      中澤寿人、内山幸男、萩原昌宏、小森雅孝、林直樹
    • Journal Title

      日本放射線技術学会雑誌

      Volume: 70(6) Pages: 556-561

    • NAID

      130004486917

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] 脊椎照合法を用いた体幹部画像誘導放射線治療における総合精度の検討2014

    • Author(s)
      中澤寿人、内山幸男、萩原昌宏、小森雅孝、林直樹
    • Journal Title

      日本放射線技術学会雑誌

      Volume: 70(5) Pages: 439-444

    • NAID

      130004486933

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Mathematical analysis of tumour invasion with proliferation2014

    • Author(s)
      Akisato Kubo
    • Journal Title

      Recent Advances in Energy, Envionment, Biology and Energy

      Volume: * Pages: 46-49

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Nonlinear evolution equations with strong dissipation and proliferation2014

    • Author(s)
      Akisato Kubo and Hiroki Hoshino
    • Journal Title

      The proceedings of 9th ISSAC Congress

      Volume: *

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Mathematical analysis of tumour invasion with proliferation model and simulation2014

    • Author(s)
      Akisato Kubo and Katsutaka Kimura
    • Journal Title

      WSEAS Transaction of Biology and Biomedicine

      Volume: *

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Dosimetric verification for intensity-modulated arc therapy plan by use of 2D diode array, radiochromic film and radiosensitive polymer gel2014

    • Author(s)
      Hayashi N, Malmin RL, Watanabe Y
    • Journal Title

      J Radiat Res

      Volume: Vol.55

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] 拡散 MRI に対する灌流の影響についての再考2013

    • Author(s)
      梅沢栄三, 岩井 恵里香, 田邉 沙織
    • Journal Title

      日本磁気共鳴医学会雑誌

      Volume: Vol. 33, No. 1 Pages: 54-58

    • NAID

      10031163475

    • Related Report
      2013 Research-status Report
  • [Journal Article] 拡散MRIにおける灌流の影響2013

    • Author(s)
      梅沢栄三
    • Journal Title

      画像診断

      Volume: Vol. 33, No.7 Pages: 806-816

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] ベータ分布をモデルとした高エネルギー電子線スペクトルの推定2013

    • Author(s)
      加藤秀起,林直樹,黒木燎平,安達由美子 ,鈴木志津馬
    • Journal Title

      日本放射線技術学会雑誌

      Volume: 第69巻12号 Pages: 1387-1393

    • NAID

      130003384235

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] 自作プログラムを用いた照射中のマルチリーフコリメータ動作の評価2013

    • Author(s)
      安達由美子,林直樹,加藤秀起,江原勲,矢田隆一,松永卓磨
    • Journal Title

      日本放射線技術学会雑誌

      Volume: 第69巻10号 Pages: 1130-1139

    • NAID

      10031196865

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] Mathematical analysis of tumour invasion model with proliferation and re-establishment2016

    • Author(s)
      A. Kubo
    • Organizer
      16th Application of mathematical methods and models in engineering
    • Place of Presentation
      Prague, Czech
    • Year and Date
      2016-03-19
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 非局所項をともなう細胞移動モデルの数学解析について2016

    • Author(s)
      久保明達
    • Organizer
      第23回応用解析シンポジウム
    • Place of Presentation
      神奈川県足柄下郡湯河原町ゆがわら万葉荘
    • Year and Date
      2016-03-01
    • Related Report
      2015 Annual Research Report
  • [Presentation] Nonlinear evolution equations and application to mathematical models2015

    • Author(s)
      A.Kubo
    • Organizer
      10th ISSAC conference
    • Place of Presentation
      Macao, China
    • Year and Date
      2015-08-03
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Nonlinear evolution equations arising from mathematical biology and medicine2015

    • Author(s)
      A.Kubo
    • Organizer
      EquaDiff2015
    • Place of Presentation
      Lyon, France
    • Year and Date
      2015-07-07
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Chaplain type of mathematical models and related topics2015

    • Author(s)
      Akisato Kubo
    • Organizer
      Mini-workshop on Models of Directional Movement and their Analysis
    • Place of Presentation
      Tohoku University
    • Year and Date
      2015-03-26 – 2015-03-28
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Traveling waves for a model of malignant tumor invasion and related topics2015

    • Author(s)
      Hiroki Hoshino
    • Organizer
      Mini-workshop on Models of Directional Movement and their Analysis
    • Place of Presentation
      Tohoku University
    • Year and Date
      2015-03-26 – 2015-03-28
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] ExacTrac導入時の物理・技術的品質管理2014

    • Author(s)
      林 直樹
    • Organizer
      第27回日本放射線腫瘍学会学術大会(ランチョンセミナー)
    • Place of Presentation
      横浜
    • Year and Date
      2014-12-11 – 2014-12-13
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Mathematical analysis of Glioblastoma invasion in 3D2014

    • Author(s)
      Akisato Kubo
    • Organizer
      The 8th International Conference on Applied Mathematics, Simulation, Modelling
    • Place of Presentation
      Florence, Italy
    • Year and Date
      2014-11-22 – 2014-11-24
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Independent monitor unit verification for passively proton therapy2014

    • Author(s)
      T. Yamakawa, N. Hayashi, etc.
    • Organizer
      14th Asia-Oceania Congress of Medical Physics
    • Place of Presentation
      Vietnam
    • Year and Date
      2014-10-23 – 2014-10-25
    • Related Report
      2014 Research-status Report
  • [Presentation] Commissioning of respiratory gating irradiation with spot scanning proton therapy unit : a fundamental study2014

    • Author(s)
      H. Hamano, N. Hayashi, etc.
    • Organizer
      14th Asia-Oceania Congress of Medical Physics
    • Place of Presentation
      Vietnam
    • Year and Date
      2014-10-23 – 2014-10-25
    • Related Report
      2014 Research-status Report
  • [Presentation] Intravoxel incoherent motionの尖度を測定する方法2014

    • Author(s)
      梅沢栄三, 石原大地, 世古翔太
    • Organizer
      第42回日本磁気共鳴医学会大会
    • Place of Presentation
      京都市
    • Year and Date
      2014-09-18 – 2014-09-20
    • Related Report
      2014 Research-status Report
  • [Presentation] 脳梗塞で ADC や kurtosis が変化するメカニズムの検討 -bi-exponential 模型と CHARMED の比較2014

    • Author(s)
      石原大地, 梅沢栄三, 世古翔太, 加藤良一
    • Organizer
      第42回日本磁気共鳴医学会大会
    • Place of Presentation
      京都市
    • Year and Date
      2014-09-18 – 2014-09-20
    • Related Report
      2014 Research-status Report
  • [Presentation] リニアックX線シミュレーションにおけるモンテカルロコード EGS5 と PHITS 間の比較2014

    • Author(s)
      黒木燎平,林 直樹,松永卓磨,濱野 裕,山川哲弘,加藤秀起
    • Organizer
      PHITS 研究会
    • Place of Presentation
      茨城
    • Year and Date
      2014-09-01
    • Related Report
      2014 Research-status Report
  • [Presentation] 各シミュレーション条件による並列計算の最適化2014

    • Author(s)
      濱野 裕,黒木燎平,山川哲弘,桂田昌輝,加藤秀起,林 直樹
    • Organizer
      PHITS 研究会
    • Place of Presentation
      茨城
    • Year and Date
      2014-09-01
    • Related Report
      2014 Research-status Report
  • [Presentation] Nonlinear evolution equations and application to mathematical models of medicine2014

    • Author(s)
      Akisato Kubo
    • Organizer
      The 10th AIMS Conference on Dynamical Systems, Differential Equations and Application
    • Place of Presentation
      Madrid, Spain
    • Year and Date
      2014-07-07 – 2014-07-11
    • Related Report
      2014 Research-status Report
  • [Presentation] Global existence in time of a model of chemotaxis2014

    • Author(s)
      Akisato Kubo
    • Organizer
      The 10th AIMS Conference on Dynamical Systems, Differential Equations and Application
    • Place of Presentation
      Madrid, Spain
    • Year and Date
      2014-07-07 – 2014-07-11
    • Related Report
      2014 Research-status Report
  • [Presentation] An accurate and precise new method for measuring kurtosis of intravoxel incoherent motion2014

    • Author(s)
      E. Umezawa, D. Ishihara and S. Seko
    • Organizer
      Joint Annual Meeting International Society for Magnetic Resonance in Medicine-European Society for Magnetic Resonance in Medicine and Biology 2014
    • Place of Presentation
      Milan, Italy
    • Year and Date
      2014-05-10 – 2014-05-16
    • Related Report
      2014 Research-status Report
  • [Presentation] 陽子線治療におけるモニタユニット独立計算ソフトウェアの開発2014

    • Author(s)
      山川哲弘,林 直樹,安達由美子,黒木燎平,安井啓祐,柴田洋希,加藤秀起
    • Organizer
      第70回日本放射線技術学会総会学術大会
    • Place of Presentation
      横浜
    • Year and Date
      2014-04-10 – 2014-04-14
    • Related Report
      2014 Research-status Report
  • [Presentation] 陽子線治療装置における放射化物による残留放射線の測定および放射化核種の同定2014

    • Author(s)
      濱野 裕,加藤秀起,鈴木志津馬,林 直樹,安井啓祐,柴田洋希
    • Organizer
      第70回日本放射線技術学会総会学術大会
    • Place of Presentation
      横浜
    • Year and Date
      2014-04-10 – 2014-04-14
    • Related Report
      2014 Research-status Report
  • [Presentation] 全身電子線照射の体表面線量分布(実測とモンテカルロシミュレーションによる比較)2014

    • Author(s)
      黒木燎平,加藤秀起,林 直樹,山川哲弘,山崎希世,濱野 裕,高木 等
    • Organizer
      第70回日本放射線技術学会総会学術大会
    • Place of Presentation
      横浜
    • Year and Date
      2014-04-10 – 2014-04-14
    • Related Report
      2014 Research-status Report
  • [Presentation] Mathematical analysis of tumour invasion with proliferation2014

    • Author(s)
      Akisato Kubo
    • Organizer
      11th International Conference of Mathematical Biology and Ecology
    • Place of Presentation
      Tenerife, Spain
    • Related Report
      2013 Research-status Report
  • [Presentation] U87MG細胞の遊走と3D侵潤2014

    • Author(s)
      久保明達
    • Organizer
      第21回応用解析研究会シンポジウム
    • Place of Presentation
      神奈川県
    • Related Report
      2013 Research-status Report
  • [Presentation] 拡散尖度に含まれる誤差2013

    • Author(s)
      梅沢栄三
    • Organizer
      第41回日本磁気共鳴医学会大会
    • Place of Presentation
      徳島
    • Related Report
      2013 Research-status Report
  • [Presentation] Development of an in-house program to calculate the monitor unit for proton therapy beam2013

    • Author(s)
      Naoki Hayashi, Yui Watanabe, Yumiko Adachi, Naotsugu Manabe, Saki Yoshimura, Isao Ehara, Hideki Kato
    • Organizer
      The 105th scientific meeting of Japan Society of Medical Physics
    • Place of Presentation
      Yokohama
    • Related Report
      2013 Research-status Report
  • [Presentation] Development and assessment of an in-house program for calculating the monitor unit in proton therapy2013

    • Author(s)
      Naoki Hayashi, Yui Watanabe, Yumiko Adachi, Naotsugu Manabe, Saki Yoshimura, Isao Ehara, Hideki Kato
    • Organizer
      The 2nd ESTRO Forum in Geneva
    • Place of Presentation
      Geneva, Switzerland.
    • Related Report
      2013 Research-status Report
  • [Presentation] Clinical implementation of the dedicated program for MU calculation in proton beam therapy2013

    • Author(s)
      Hayashi N, Adachi Y, and Kato H
    • Organizer
      The 55th annual meeting of American Association of Physicist in Medicine
    • Place of Presentation
      Indianapolis, USA
    • Related Report
      2013 Research-status Report
  • [Presentation] Radiochromic film dosimetry on total body irradiation with photon and electron beams2013

    • Author(s)
      Hayashi N, Yamazaki K, Maeda M, Yamakawa T, Sarara R, Adachi Y, Kuroki R, Takagi H, Kato H
    • Organizer
      The 13th Asia-Oceania Congress of Medical Physics
    • Place of Presentation
      Singapore
    • Related Report
      2013 Research-status Report
  • [Presentation] Nonlinear wave equations with strong Dissipation and proliferation

    • Author(s)
      Akisato Kubo
    • Organizer
      9th ISAAC Congress
    • Place of Presentation
      Krakow, Poland
    • Related Report
      2013 Research-status Report
  • [Presentation] Esistence and non-existence of solutions of nonlinear evolution equations arising fromMathematical biology

    • Author(s)
      Akisato Kubo
    • Organizer
      Seminare de Istitut Camille-Jordan and Ecole Centrale de Lyon
    • Place of Presentation
      Lyon, France
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Quality assurance/control and risk management on high precision external beam radiotherapy: Approach as a third-party medical physicist

    • Author(s)
      Naoki Hayashi
    • Organizer
      Minimizing errors, maximizing quality workshop
    • Place of Presentation
      Tokyo
    • Related Report
      2013 Research-status Report
  • [Presentation] ラジオクロミックフィルムドジメトリにおける化学,物理,技術

    • Author(s)
      林 直樹
    • Organizer
      放射線治療品質管理講習会2013
    • Place of Presentation
      大阪
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] IMRTにおける線量分布検証~ラジオクロミックフィルムの取扱と検証法~

    • Author(s)
      林 直樹
    • Organizer
      第16回放射線治療品質管理講習会
    • Place of Presentation
      東京
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] IMRTにおける線量分布検証~ラジオクロミックフィルムの取扱と検証法~

    • Author(s)
      林 直樹
    • Organizer
      第17回放射線治療品質管理講習会
    • Place of Presentation
      大阪
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] フィルムを用いた線量分布検証の有効性と課題

    • Author(s)
      林 直樹
    • Organizer
      日本放射線腫瘍学会第27回日本高精度放射線外部照射研究会
    • Place of Presentation
      東京
    • Related Report
      2013 Research-status Report
    • Invited
  • [Book] 現象から微積分を学ぼう 第一版第3刷2015

    • Author(s)
      垣田高夫,久保明達,田沼一実
    • Total Pages
      348
    • Publisher
      日本評論社
    • Related Report
      2015 Annual Research Report
  • [Book] 現象から微積分を学ぼう 第1版第3刷2015

    • Author(s)
      垣田高夫、久保明達、田沼一実
    • Total Pages
      348
    • Publisher
      日本評論社
    • Related Report
      2014 Research-status Report
  • [Book] 診療放射線技術実践ガイド2014

    • Author(s)
      林直樹(分担執筆)
    • Total Pages
      1104
    • Publisher
      文光堂
    • Related Report
      2014 Research-status Report
  • [Book] これでわかる拡散 MRI 第3版2013

    • Author(s)
      青木茂樹,阿部修,増谷佳孝,高原太郎 編.(梅沢栄三)
    • Total Pages
      470
    • Publisher
      学研メディカル秀潤社
    • Related Report
      2013 Research-status Report
  • [Book] 医学物理士のための放射線治療品質管理講習会冊子 ラジオクロミックフィルムドジメトリにおける化学,物理,技術2013

    • Author(s)
      林 直樹
    • Total Pages
      201
    • Publisher
      医学物理士認定機構
    • Related Report
      2013 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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