A hybrid model for tumor-induced angiogenesis in the cornea in the presence of inhibitors

The present work formulates and analyzes, by means of numerical experiments, a model for tumor-induced angiogenesis in the presence of inhibitors in the cornea. Our model is a generalization of the earlier work of Tong and Yuan [S. Tong, F. Yuan, Numerical simulations of angiogenesis in the cornea, Microvascular Research 61 (2001) 14–27] to incorporate the role of inhibitors, relevant to experimental assays. The derived set of hybrid equations consists of partial differential equations for the tumor angiogenic factors and the inhibitors with a particle model for the motion of the endothelial cells. This is analyzed numerically in the two-dimensional setting. The relevant results are discussed and qualitative agreement with the experimental work is illustrated.