Two-dimensional discrete mathematical model of tumor-induced angiogenesis

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Two-dimensional discrete mathematical model of tumor-induced angiogenesis

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.水利论文#V/M ReRRajF

作 者: Gai-ping ZHAO Er-yun CHEN Jie WU Shi-xiong XU M.W. Collins Quan LONG  
作者单位:Gai-ping ZHAO(School of Medical Instrument and Food Engineering, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China)
*p:VD^.r.H2V0Er-yun CHEN(School of Energy and Power Engineering, University of Shanghai for Science and Technology,Shanghai 200093, P. R. China)
-IaSlopi0Jie WU,Shi-xiong XU(Department of Mechanics and Engineering Science, Fudan University,Shanghai 200433, P. R. China)水利论文;~1H*z+n's,n
M.W. Collins,Quan LONG(Brunel Institute for Bioengineering, School of Engineering and Design,Brunel University, Uxbridge, Middlesex, UK) 
刊 名:应用数学和力学(英文版)  EI SCI
英文刊名:APPLIED MATHEMATICS AND MECHANICS 
年,卷(期):2009 30(4) 
分类号:R318.01 TB115 
关键词:tumor angiogenesis   discrete mathematical model   nine-point scheme   nu-merical simulation  
机标关键词:endothelial cellfinite difference schemenumerical simulationsmathematical modeldiscrete modelinformationindividualchemotaxisrealisticdifferentextendedresultstwo 
基金项目:国家自然科学基金,Science Foundation for the Excellent Youth Scholars of Higher Education of Shanghai,Research Fund for the Doctoral Program of University of Shanghai for Science and Technology 
下一篇:Analytical solution to stagnation-point flow and heat transfer over a stretching
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