Tong S, Yuan F
Department of Biomedical Engineering, Duke University, Durham, North Carolina 27708, USA.
Microvasc Res. 2001 Jan;61(1):14-27. doi: 10.1006/mvre.2000.2282.
Angiogenesis plays important roles in many physiologic and pathologic processes in the body. To understand mechanisms of angiogenesis, we developed a mathematical model for quantitative analysis of various biological events involved in angiogenesis. Our model was focused on two-dimensional angiogenesis in the cornea. The model considered diffusion of angiogenic factors, uptake of these factors by endothelial cells, and randomness in the rate of sprout formation and the direction of sprout growth. Our simulation results indicated that redistribution and uptake of angiogenic factors during angiogenesis had significant effects on the structure of vascular networks. A decrease in the uptake rate resulted in increases in vessel density, self-loop formation, and front migration speed of vascular networks. The randomness in the direction of sprout formation determined the curvature of vessels, whereas the probability of sprout formation from a vessel segment had a significant effect on the total number of vessels in vascular networks. The vascular networks generated in numerical simulations were similar to those observed experimentally. The mathematical model developed in this study can be used to evaluate effects of individual factors on angiogenesis, understand mechanisms of interactions among different factors during angiogenesis, and generate experimentally testable hypotheses.
血管生成在机体的许多生理和病理过程中发挥着重要作用。为了解血管生成的机制，我们开发了一个数学模型，用于定量分析血管生成过程中涉及的各种生物学事件。我们的模型聚焦于角膜中的二维血管生成。该模型考虑了血管生成因子的扩散、内皮细胞对这些因子的摄取，以及芽生形成速率和芽生生长方向的随机性。我们的模拟结果表明，血管生成过程中血管生成因子的重新分布和摄取对血管网络结构有显著影响。摄取速率的降低导致血管密度增加、自环形成以及血管网络前端迁移速度加快。芽生形成方向的随机性决定了血管的曲率，而血管段形成芽生的概率对血管网络中血管的总数有显著影响。数值模拟中生成的血管网络与实验观察到的相似。本研究中开发的数学模型可用于评估单个因素对血管生成的影响，理解血管生成过程中不同因素之间的相互作用机制，并生成可通过实验验证的假设。
