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In the study of cancer evolution and therapeutic strategies, scientificevidence shows that a key dynamics lies in the tumor-environment interaction.In particular, oxygen concentration plays a central role in the determinationof the phenotypic heterogeneity of cancer cell populations, whose qualitativeand geometric characteristics are predominant factors in the occurrence ofrelapses and failure of eradication. We propose a mathematical model able todescribe the eco-evolutionary spatial dynamics of tumour cells in theiradaptation to hypoxic microenvironments. As a main novelty with respect to theexisting literature, we combine a phenotypic indicator reflecting theexperimentally-observed metabolic trade-off between the hypoxia-resistanceability and the proliferative potential with a 2d geometric domain, without theconstraint of radial symmetry. The model is settled in the mathematicalframework of phenotype-structured population dynamics and it is formulated interms of systems of coupled non-linear integro-differential equations. Thecomputational outcomes demonstrate that hypoxia-induced selection results in ageometric characterization of phenotypic-defined tumour niches that impact ontumour aggressiveness and invasive ability. Furthermore, results show how theknowledge of environmental characteristics provides a predictive advantage ontumour mass development in terms of size, shape, and composition.

mathematical modelling of natural phenomena

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