Two-Dimensional Discrete Mathematical Model of Tumor-Induced Angiogenesis
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摘要: 建立九点差分格式的二维离散数学模型，模拟肿瘤内外的血管生成．模型扩展了内皮细胞沿9个方向运动，考虑存在两根母血管的情况下，耦合内皮细胞在肿瘤内外不同力学环境下的随机、趋化和趋触性运动，数值生成了肿瘤内外异构的血管网．结果表明，该模型可以产生相对真实的具有接近肿瘤病理生理特性的血管网,可为临床研究提供有益的信息A·D2Abstract: 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.
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