Simulation of angiogenesis in a multiphase tumor growth model

• We introduce in our multiphase model for avascular tumor growth two new species.
• The new species are the tumor angiogenic factor (TAF) and endothelial cells (EC).
• Their diffusion and interaction simulate angiogenesis.
• Two numerical simulations of angiogenesis are proposed.
• The new capillary network will allow for simulating the chemotherapeutic agents delivery.

The avascular multiphase model for tumor growth, developed by the authors in previous works, is enhanced to include angiogenesis. The original model comprises the extracellular matrix (ECM) as porous solid phase and three fluid phases: living and necrotic tumor cells (TCs), host cells (HCs), and the interstitial fluid. In this paper we add transport of tumor angiogenic factor (TAF) and of endothelial cells. The density of the endothelial cells represents the newly created vessels in a smeared manner. Co-opted blood vessels can be added as line element with flow or can be taken into account as boundary condition. The model is hence of the continuum–discrete type. Two examples show the potential of the newly enhanced model. The first deals with growth of a 2D tumor spheroid in a square tissue domain. From a blood vessel, posed on one side of the domain, angiogenesis takes place through the migration of endothelial cells from the vessel to the tumor. The second one is the simulation of cutaneous melanoma growth with the diffusion of TAF from the living tumor cells and the consequent development of a new vessel network, represented by the endothelial cells density. The introduction of angiogenesis will allow for simulating the delivery of chemotherapeutic and nanoparticle-mediated agents to the vascular tumor, and for evaluation of the therapeutic effect.