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Microscale oxygenation plays a prominent role in tumour progression.Spatiotemporal variability of oxygen distribution in the tumourmicroenvironment contributes to cellular heterogeneity and to the emergence ofnormoxic and hypoxic populations. Local levels of oxygen strongly affect theresponse of tumours to the administration of different therapeutic modalitiesand, more generally, to the phenomenon of resistance to treatments. Severalinterventions have been proposed to improve tumour oxygenation, being theelevation of the local temperature (hyperthermia) an important one. While otherfactors such as the metabolic activity have to be considered, the proficiencyof the tumour vascular system is a key factor both for the tissue oxygenationand for its temperature maps. Consequently, the interplay of these factors hasattracted considerable attention from the mathematical modelling perspective.Here we put forward a transport-based system of partial differential equationsaimed at describing the dynamics of healthy and tumour cell subpopulations atthe microscale in a region placed between two blood vessels. By using thismodel with diverse flow conditions, we analyse the oxygen and temperatureprofiles that arise in different scenarios of vascular status, both during freeprogression and under thermal therapy. We find that low oxygen levels areassociated to elevations of temperature in locations preferentially populatedby hypoxic cells, and hyperthermia-induced cell death, being strongly dependenton blood flow, would only appear under highly disrupted conditions of the localvasculature. This results in a noticeable effect of heat on hypoxic cells.Additionally, when pronounced cell death occurs, it is followed by asignificant increase in the oxygen levels.

Modelling the effect of vascular status on tumour evolution and outcome after thermal therapy