Angiogenesis and vessel co-option in a mathematical model of diffusive tumor growth: The role of chemotaxis. (7th March 2021) - Gandolfi, A.
Highlights: We propose a new model for the time–space evolution of vascularized tumors The model encompasses tumor aggression to healthy cells, generation and dynamics of the endothelial cells that form the tumor neovasculature. Detailed derivation of a new general family of models of the tumoral angiogenesis-related chemotaxis by means of a velocity-jump random walk model. The dynamics of oxygen concentration and of a tumor proangiogenic factor is modeled, taking into account a crowding effect that impairs proliferation and cells mobility. Analytical study of non-negativity of all variables and of post-invasion steady state. Abstract: This work considers the propagation of a tumor from the stage of a small avascular sphere in a host tissue and the progressive onset of a tumor neovasculature stimulated by a pro-angiogenic factor secreted by hypoxic cells. The way new vessels are formed involves cell sprouting from pre-existing vessels and following a trail via a chemotactic mechanism (CM). Namely, it is first proposed a detailed general family of models of the CM, based on a statistical mechanics approach. The key hypothesis is that the CM is composed by two components: i) the well–known bias induced by the angiogenic factor gradient; ii) the presence of stochastic changes of the velocity direction, thus giving rise to a diffusive component. Then, some further assumptions and simplifications are applied in order to derive a specific model to be used in the simulations. The tumor progression is favored by its acidic aggression towards the healthy cells. The model includes the evolution of many biological and chemical species. Numerical simulations show the onset of a traveling wave eventually replacing the host tissue with a fully vascularized tumor. The results of simulations agree with experimental measures of the vasculature density in tumors, even in the case of particularly hypoxic tumors.