| Project/Area Number |
16KT0022
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Multi-year Fund |
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| Section | 特設分野 |
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| Research Field |
Mathematical Sciences in Search of New Cooperation
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| Research Institution | Meiji University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
稲垣 正司 国立研究開発法人国立循環器病研究センター, 研究所, 非常勤研究員 (80359273)
上山 大信 武蔵野大学, 工学部, 教授 (20304389)
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| Project Period (FY) |
2016-07-19 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥18,460,000 (Direct Cost: ¥14,200,000、Indirect Cost: ¥4,260,000)
Fiscal Year 2018: ¥6,110,000 (Direct Cost: ¥4,700,000、Indirect Cost: ¥1,410,000)
Fiscal Year 2017: ¥6,110,000 (Direct Cost: ¥4,700,000、Indirect Cost: ¥1,410,000)
Fiscal Year 2016: ¥6,240,000 (Direct Cost: ¥4,800,000、Indirect Cost: ¥1,440,000)
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| Keywords | 反応拡散系 / 自由境界問題 / パターンダイナミクス / 数理医学 / 不整脈 / 特異摂動法 / 外部問題 / 心室細動 / 伝播現象 / フィッツフー・南雲方程式 / 興奮系 / 応用数学 / 非線形現象 |
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| Outline of Final Research Achievements |
Arrhythmia is a group of conditions in which the heartbeat is irregular.Typical examples are and atrial fibrillation and ventricular fibrillation. Mathematical understanding of the mechanism of arrhythmia can be expected to have a clinical implication. In this research project, we study the pattern dynamics of solutions of partial differential equations representing the electrical potential to understand the mechanism of arrhythmia. More precisely, we derived the free boundary problem and characterized all dynamics in one dimensional space. Moreover, we also studied the influence of the geometry of obstacle such as myocardial infarct lesion and derived the mathematical mechanism of spontaneous spiral formation by obstacles. We also investigated the effect of placement of multiple obstacles on the propagation of electrical potential.
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| Academic Significance and Societal Importance of the Research Achievements |
数学的には，ある種の非線型偏微分方程式の解のパターンダイナミクスを調べる手法（反応界面系）を提案した．反応界面系は，これまでの自由境界問題に較べて，ダイナミクスを捉えやすい特徴があり，これまで得られている自由境界問題ではわからなかったダイナミクスが取り扱えるようになった．
障害物の形状や配置が活動電位の伝播現象に与える影響を調べ，自発的スパイラル形成のメカニズムを得た．これらの研究から，将来，心筋梗塞巣の形状などの情報から心室細動が起きるリスク患者の推定ができるようになることが期待される．
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