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We present a two-dimensional continuum model of tumor growth, which treatsthe tissue as a composition of six distinct fluid phases; their dynamics aregoverned by the equations of mass and momentum conservation. Our model dividesthe cancer cells phase into two sub-phases depending on their maturity state.The same approach is also applied for the vasculature phase, which is dividedinto young sprouts (products of angiogenesis), and fully formed-mature vessels.The remaining two phases correspond to healthy cells and extracellular material(ECM). Furthermore, the model foresees the existence of nutrient chemicalspecies, which are transferred within the tissue through diffusion or suppliedby the vasculature (blood vessels). The model is numerically solved with theFinite Elements Method and computations are performed with the commercialsoftware Comsol Multiphysics. The numerical simulations predict that maturecancer cells are well separated from young cancer cells, which form aprotective shield for the growing tumor. We study the effect of differentmitosis and death rates for mature and young cancer cells on the tumor growthrate, and predict accelerated rates when the mitosis rate of young cancer cellsis higher compared to mature cancer cells.

Assessment of intra-tumor heterogeneity in a two-dimensional vascular tumor growth model