Hypoxia-resistance heterogeneity in tumours: the impact of geometrical characterization of environmental niches and evolutionary trade-offs. A mathematical approach

In the study of cancer evolution and therapeutic strategies, scientific evidence shows that a key dynamics lies in the tumor-environment interaction. In particular, oxygen concentration plays a central role in the determination of the phenotypic heterogeneity of cancer cell populations, whose qualitative and geometric characteristics are predominant factors in the occurrence of relapses and failure of eradication. We propose a mathematical model able to describe the eco-evolutionary spatial dynamics of tumour cells in their adaptation to hypoxic microenvironments. As a main novelty with respect to the existing literature, we combine a phenotypic indicator reflecting the experimentally-observed metabolic trade-off between the hypoxia-resistance ability and the proliferative potential with a 2d geometric domain, without the constraint of radial symmetry. The model is settled in the mathematical framework of phenotype-structured population dynamics and it is formulated in terms of systems of coupled non-linear integro-differential equations. The computational outcomes demonstrate that hypoxia-induced selection results in a geometric characterization of phenotypic-defined tumour niches that impact on tumour aggressiveness and invasive ability. Furthermore, results show how the knowledge of environmental characteristics provides a predictive advantage on tumour mass development in terms of size, shape, and composition.