血管新生の数理モデル  [in Japanese] A Mathematical Modeling of Angiogenesis  [in Japanese]

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<p><b>概要.</b>血管新生を記述する単純な数理モデルを考察する.最近の血管新生における内皮細胞運動のタイムラプス撮影の実験を参考に,内皮細胞の新生血管先端での密度のみにより,新生血管の伸長と分岐が定まることを仮定すると,非線形連立常微分方程式によって記述されるモデルが導かれる.細胞分裂および VEGFなどの内皮細胞の運動を活性化する因子の影響も取り入れ,厳密解および数値シミュレーションの結果を示す.</p>

<p><i>Abstract.</i> We investigate a simple mathematical model for angiogenesis. From recent time-lapse imaging experiments on the dynamics of endothelial cells (ECs) in angiogenesis, we suppose that elongation and bifurcation of neogenetic vessel is determined by only the density of ECs near the tip, and introduce a model described by nonlinear simultaneous differential equations. We also incorporate proliferation of ECs and activation factor such as VEGF and show the exact solutions to that model and numerical simulations. </p>

Journal

  • Transactions of the Japan Society for Industrial and Applied Mathematics

    Transactions of the Japan Society for Industrial and Applied Mathematics 26(1), 105-123, 2016

    The Japan Society for Industrial and Applied Mathematics

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