Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA.
Bull Math Biol. 2010 May;72(4):830-68. doi: 10.1007/s11538-009-9471-1. Epub 2010 Jan 6.
The motivation of this work stems from two critical experimental observations associated with corneal angiogenesis: (1) angiogenesis will not succeed without endothelial cell proliferation, and (2) proliferation mainly occurs at the leading edge of developing sprouts (Sholley et al., Lab. Invest. 51:624-634, 1984). To discover the underlying mechanisms of these phenomena, we develop a cell-based mathematical model that integrates a mechanical model of elongation with a biochemical model of cell phenotype variation regulated by angiopoietins within a developing sprout. This model allows for a detailed study of the relative roles of endothelial cell migration, proliferation, and maturation. The model is validated by quantitatively comparing its predictions with data derived from corneal angiogenesis experiments. We conclude that cell elasticity and cell-to-cell adhesion allow only limited sprout extension in the absence of proliferation, and the maturation process combined with bioavailability of VEGF can explain the localization of proliferation to the leading edge. We also use this model to investigate the effects of X-ray irradiation, Ang-2 inhibition, and extracellular matrix anisotropy on sprout morphology and extension.
（1）没有内皮细胞增殖，血管生成就不会成功；（2）增殖主要发生在正在发育的芽的前沿（Sholley 等人，Lab Invest. 51:624-634, 1984）。为了发现这些现象的潜在机制，我们开发了一种基于细胞的数学模型，该模型将伸长的力学模型与由发育中的芽内血管生成素调节的细胞表型变化的生化模型相结合。该模型可以详细研究内皮细胞迁移、增殖和成熟的相对作用。通过将其预测与来自角膜血管生成实验的数据进行定量比较，对模型进行了验证。我们的结论是，在没有增殖的情况下，细胞弹性和细胞间粘附只允许有限的芽延伸，而成熟过程与 VEGF 的生物利用度相结合可以解释增殖定位在前沿。我们还使用该模型研究了 X 射线照射、Ang-2 抑制和细胞外基质各向异性对芽形态和延伸的影响。
