A mathematical model for tumor angiogenesis with a travelling wave structure

The paper reviews a recent investigation on the onset of a tumor vessel network (stimulated by hypoxic cells) during tumor growth and invasion of the surrounding host tissue. The tumor aggression of normal cells creates an interface, which turns out to be the most active region for angiogenesis and which propagates as a travelling wave. The angiogenic process is governed by chemotaxis, whose modeling differs considerably from the classical gradient driven one for two reasons: (i) the velocity of the cells progressively creating the new vessels has a well defined physiological upper bound, (ii) a random change of direction creates a diffusion component. Numerical simulations and some new considerations about the travelling wave structure of the solution are provided.