Two-dimensional discrete mathematical model of tumor-induced angiogenesis  

作　　者：赵改平 陈二云 吴洁 许世雄 M.W.Collins 龙泉 

机构地区：[1]School of Medical Instrument and Food Engineering,University of Shanghai for Scienceand Technology [2]School of Energy and Power Engineering, University of Shanghai for Science and Technology [3]Department of Mechanics and Engineering Science, Fudan University [4]Brunel Institute for Bioengineering, School of Engineering and Design,Brunel University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2009年第4期455-462,共8页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China (No. 10772051);the ScienceFoundation for the Excellent Youth Scholars of Higher Education of Shanghai (No. 571215);the Research Fund for the Doctoral Program of University of Shanghai for Science and Technology(No. 10D214)

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.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.

关 键 词：tumor angiogenesis discrete mathematical model nine-point scheme nu-merical simulation 

分 类 号：R730.2[医药卫生—肿瘤] R311[医药卫生—临床医学]