Model for initial vascular patterns in melanoma transplants

In this paper we present a simple mathematical model that adequately accounts for at least the initial vasculature that is established in a melanoma transplant. It is assumed that the tumor produces a substance (tumor angiogenesis factor--TAF) that elicits capillary sprouts from the vascular bed of the host. These sprouts then invade the tumor along the gradient of TAF and cross-connect forming a vascular pathway that is similar to the experimental patterns observed in a hamster cheek pouch. This model is then extended to include the migration of loops. The rupture and formation of sprouts from these loops is assumed to depend on the strength of the stimulus (TAF). Under the assumption that the production of TAF is significantly reduced in a neighborhood of an established vessel, the network formed by the vessels in the tumor corresponds to the observed arboreal patterns.