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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (4): 455-462.doi: https://doi.org/10.1007/s10483-009-0406-y

• Articles • 上一篇    下一篇

Two-dimensional discrete mathematical model of tumor-induced angiogenesis

赵改平1 陈二云2 吴洁3 许世雄3 M.W.Collins4 龙泉4   

    1. School of Medical Instrument and Food Engineering,University of Shanghai for Science and Technology, Shanghai 200093,  P. R. China
    2. School of Energy and Power Engineering, University of Shanghai for Science and Technology,Shanghai 200093, P. R. China;
    3. Department of Mechanics and Engineering Science,Fudan University,Shanghai 200433, P. R. China;
    4. Brunel Institute for Bioengineering, School of Engineering and Design
  • 收稿日期:2008-08-01 修回日期:2009-02-13 出版日期:2009-04-16 发布日期:2009-04-16

Two-dimensional discrete mathematical model of tumor-induced angiogenesis

Gai-Ping ZHAO1, Er-Yun CHEN2, Ji WU3, Shi-Xiong XU3, M.W.Collins4, Quan LONG4   

    1. School of Medical Instrument and Food Engineering,University of Shanghai for Science and Technology, Shanghai 200093,  P. R. China
    2. School of Energy and Power Engineering, University of Shanghai for Science and Technology,Shanghai 200093, P. R. China;
    3. Department of Mechanics and Engineering Science,Fudan University,Shanghai 200433, P. R. China;
    4. Brunel Institute for Bioengineering, School of Engineering and Design
  • Received:2008-08-01 Revised:2009-02-13 Online:2009-04-16 Published:2009-04-16

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摘要： A 2D discrete mathematical model of a nine-point finite difference scheme is built to simulate tumor-induced angiogenesis. Nine motion directions of an individual endothelial cell and two parent vessels are extended in the present model.  The process of tumor-induced angiogenesis is performed by coupling random motility, chemotaxis, and haptotaxis of endothelial cell in different mechanical environments inside and outside the tumor. The results show that nearly realistic tumor microvascular networks with neoplastic pathophysiological characteristics can be generated from the present model. Moreover, the theoretical capillary networks generated in numerical simulations of the discrete model may provide useful information for further clinical research.

Abstract: A 2D discrete mathematical model of a nine-point finite difference scheme is built to simulate tumor-induced angiogenesis. Nine motion directions of an individual endothelial cell and two parent vessels are extended in the present model.  The process of tumor-induced angiogenesis is performed by coupling random motility, chemotaxis, and haptotaxis of endothelial cell in different mechanical environments inside and outside the tumor. The results show that nearly realistic tumor microvascular networks with neoplastic pathophysiological characteristics can be generated from the present model. Moreover, the theoretical capillary networks generated in numerical simulations of the discrete model may provide useful information for further clinical research.

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