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Modelling radiation-induced cell death and tumour re-oxygenation: local versus global and instant versus delayed cell death

The resistance of hypoxic cells to radiation, due to the oxygen dependence of radiosensitivity, is well known and must be taken into account to accurately calculate the radiation induced cell death. A proper modelling of the response of tumours to radiation requires deriving the distribution of oxygen at a microscopic scale. This usually involves solving the reaction-diffusion equation in tumour voxels using a vascularization distribution model. Moreover, re-oxygenation arises during the course of radiotherapy, one reason being the increase of available oxygen caused by cell killing, which can turn hypoxic tumours into oxic. In this work we study the effect of cell death kinetics in tumour oxygenation modelling, analysing how it affects the timing of re-oxygenation, surviving fraction and tumour control. Two models of cell death are compared, an instantaneous cell killing, mimicking early apoptosis, and a delayed cell death scenario in which cells can die shortly after being damaged, as well as long after irradiation. For each of these scenarios, the decrease in oxygen consumption due to cell death can be computed globally (macroscopic voxel average) or locally (microscopic). A re-oxygenation model already used in the literature, the so called full re-oxygenation, is also considered. The impact of cell death kinetics and re-oxygenation on tumour responses is illustrated for two radiotherapy fractionation schemes: a conventional schedule, and a hypofractionated treatment. The results show large differences in the doses needed to achieve 50% tumour control for the investigated cell death models. Moreover, the models affect the tumour responses differently depending on the treatment schedule. This corroborates the complex nature of re-oxygenation, showing the need to take into account the kinetics of cell death in radiation response models.