Model-Informed Radiotherapy Schedule Selection Under Hypoxia: A Phenotype-Structured PDE Approach
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Tumour radiotherapy outcomes depend strongly on intra-tumour heterogeneity and on the local microenvironment. Hypoxia is a key component of this picture, as it can reduce radiation effectiveness and favour relapse. Dose timing also matters: varying dose per fraction and inter-fraction intervals may markedly delay tumour progression. The specific question we address is how oxygenation and continuous phenotypic adaptation shape efficient radiotherapy protocols within the class of dose–interval fractionations. To this aim, drawing on phenotype-structured population dynamics and building on recent eco-evolutionary modelling, we introduce a phenotype-structured PDE model for the tumour cell density coupled to an oxygen field (either uniform or spatially heterogeneous). A continuous trait u in [0,1] quantifies adaptation to adverse conditions, with emphasis on hypoxia tolerance and resistance to radiation-induced damage. Radiotherapy is described through a modified linear–quadratic formulation: radiosensitivity varies along the phenotypic axis and is further modulated by an oxygen enhancement ratio (OER), so that treatment can induce selection across the phenotypic spectrum. We use the model to compare non-standard schedules (including hypo/hyper-fractionation) under a normal-tissue constraint expressed via biologically effective dose (BED). Preliminary in silico scans over the dose–interval space suggest that hypoxic settings generate a clear efficacy frontier, with sizeable differences in time-to-progression (TTP) between schedules, whereas highly oxygenated conditions lead to much weaker protocol separation. Introducing spatially heterogeneous oxygen supply highlights an additional effect: vascular geometry and hypoxic niches can increase outcome variability and alter schedule robustness. Overall, the proposed framework provides a model-informed, mechanistic tool to interpret heterogeneous radiotherapy responses and to compare fractionation strategies in oxygen-limited tumours, supporting schedule selection across oxygenation scenarios.
