| Project/Area Number |
25400148
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Fujita Health University |
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Principal Investigator |
KUBO Akisato 藤田保健衛生大学, 保健学研究科, 教授 (60170023)
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| 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)
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| Co-Investigator(Renkei-kenkyūsha) |
SAITO NORIKAZU 東京大学, 大学院数理科学研究科, 准教授 (00334706)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| 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)
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| 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 |
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| 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.
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