Innovation for mathematical medical applications of models based on stochastic processes.

2022 Fiscal Year Final Research Report

• Project/Area Number: 17K05358
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Saitama University
• Principal Investigator: DOKU Isamu 埼玉大学, 教育学部, 教授 (60207686)
• Project Period (FY): 2017-04-01 – 2023-03-31
• Keywords: 数理医学 / 確率過程モデル / ガン免疫応答 / 環境依存型モデル / 局所消滅性 / 免疫細胞エフェクター群 / 分枝過程 / 極限操作

Outline of Final Research Achievements

This research is a theoretical study that is aiming at contribution to the mathematical medicine, by establishing a random model based upon stochastic processes, applying it for various problems in the medical field, and deepening the mathematical understanding to peculiar phenomena. As for the characterization problem of local extinction for tumor-immunological response,
we have succeeded in proposing environment dependent model to describe cancer immune response, and also in realizing, in the sense of modelling, local extinction which just corresponds to the situation that the effector group drives away the cancer cells. Next we try to prove the existence of the limit called saturation point of immunity, and we have succeeded in showing the
existence of the limit indirectly by deriving the local extinction in finite time for the qualitative model obtained in the limit, instead of showing it directly.

Free Research Field

確率論、関数方程式論

Academic Significance and Societal Importance of the Research Achievements

確率過程に基づくランダムな数理モデルを構築し、それを医療科学分野の個別問題に適用し、モデル解析的手法を駆使して医療分野特有の現象の数理的理解および数理科学的解釈を深めることで、新領域である「数理医学」の発展に大いに寄与することができる好例を与えている。また、ガン細胞に対する免疫応答を記述する環境依存型モデルを提案し、免疫細胞によりガン細胞が局所的に駆逐される様子に対応する局所消滅性をモデル論的に再現することに成功したことで、ガン免疫応答に対する数理医学的な新たな研究の道筋を開いたという意味合いがある。