Department of Mathematics, University of Kocaeli, Kocaeli41380, Turkey.
Department of Mathematics, University of Kocaeli, Kocaeli41380, Turkey.
Math Biosci. 2018 Dec;306:32-48. doi: 10.1016/j.mbs.2018.10.007. Epub 2018 Oct 26.
We present a 2D mathematical model of tumor angiogenesis which is an extension of the 1D model originally presented in Levine et al. (2000) [1]. Our model is connected to that 1D model by some transmission and boundary conditions which carry certain cells, the endothelials, pericytes and macrophages from the vessel wall into the extra cellular matrix. In our extended model we also include a mechanism for the action of anti-angiogenic factors such as angiostatin. We present numerical simulations in which we obtain a very good "qualitative agreement" with the time of the onset of vascularization of tumors and with the fact that the capillary tip growth accelerates as it approaches the "tumor".
我们提出了一个二维的肿瘤血管生成数学模型，该模型是 Levine 等人在 2000 年提出的一维模型的扩展[1]。我们的模型通过一些传输和边界条件与一维模型相连接，这些条件将某些细胞，内皮细胞、周细胞和巨噬细胞从血管壁输送到细胞外基质中。在我们的扩展模型中，我们还包括了血管生成抑制因子如血管抑肽的作用机制。我们进行了数值模拟，结果与肿瘤血管生成的时间以及毛细血管尖端生长在接近“肿瘤”时加速的事实非常吻合，达到了很好的“定性一致性”。
