Numerical simulations of angiogenesis in the cornea.

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.