Two-Dimensional Discrete Mathematical Model of Tumor-Induced Angiogenesis

ZHAO Gai-ping; CHEN Er-yun; WU Jie; XU Shi-xiong; M. W. Collins; LONG Quan

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Article Navigation > Applied Mathematics and Mechanics > 2009 > 30(4): 425-431

ZHAO Gai-ping, CHEN Er-yun, WU Jie, XU Shi-xiong, M. W. Collins, LONG Quan. Two-Dimensional Discrete Mathematical Model of Tumor-Induced Angiogenesis[J]. Applied Mathematics and Mechanics, 2009, 30(4): 425-431.

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Two-Dimensional Discrete Mathematical Model of Tumor-Induced Angiogenesis

1.
School of Medical Instrument and Food Engineering, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China;
School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China;

Received Date: 2008-08-01
Rev Recd Date: 2009-02-13
Publish Date: 2009-04-15

Abstract

Abstract

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

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References(9)

References

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