The corneal micropocket assay is an experimental protocol for studying vessel network formation, or neovascularization, in vivo. The assay is attractive due to the ease with which the developing vessel network can be observed in the same animal over time. However, it is difficult to relate observations of neovascularization in the hemispherical geometry of the cornea to predictions from mathematical (in silico) models and observations from in vitro models, which mostly adopt planar geometries. Here, we develop a three-dimensional, off-lattice mathematical model of neovascularization in the cornea, with a new repulsion model for the interaction of vessels with tissue boundaries. The model allows us to: i) investigate how the hemispherical geometry of the cornea influences vessel network formation and ii) identify the metrics of neovascularization that are most robust to geometrical differences between typical in silico, in vitro and in vivo tissue domains. We predict that two-dimensional geometries lead to increased vessel 'merging', or anastomosis, relative to three-dimensional versions, with differences being most pronounced when circular geometries are adopted. Cuboidal geometries lead to patterns of neovascularization that most closely mimic the in vivo case. The 'distance of the vascular front to the limbus' is found to be a robust metric of neovascularization across the studied tissue domains, while densities of tip cells and vessels and 'vascularized fraction' are more sensitive to domain choice. Given the widespread adoption and attractive simplicity of planar tissue domains, the differences identified in the present study should prove useful in relating the results of previous and future in silico and in vitro studies of neovascularization to in vivo observations in the cornea.
Author summaryNeovascularization, or the formation of new blood vessels, is an important process in development, wound healing and cancer. The corneal micropocket assay is used to better understand the process and, in the case of cancer, how it can be controlled with drug therapies for improved patient outcomes. In the assay, the hemispherical shape of the cornea can influence the way the vessel network forms. This makes it difficult to directly compare results from experiments with the predictions of mathematical models or cell culture experiments, which are