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 i...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.展开更多
In this paper, the author studies the stability of the solution to a three-dimension-al gonorrhea discrete mathematical model by Liapunoy method. The parameter es-timator of the slability domain is obtained and the ra...In this paper, the author studies the stability of the solution to a three-dimension-al gonorrhea discrete mathematical model by Liapunoy method. The parameter es-timator of the slability domain is obtained and the rationality of the model is ex-plained in a theoretic way.展开更多
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)
文摘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.
文摘In this paper, the author studies the stability of the solution to a three-dimension-al gonorrhea discrete mathematical model by Liapunoy method. The parameter es-timator of the slability domain is obtained and the rationality of the model is ex-plained in a theoretic way.
