Abstract
Hypoxia is central to tumour evolution, growth, invasion and metastasis. Mathematical models of hypoxia based on reaction-diffusion equations provide seemingly incomplete descriptions as they fail to predict the measured oxygen concentrations in the tumour microenvironment. In an attempt to explain the discrepancies, we consider both the inhomogeneous distribution of oxygen-consuming cells in solid tumours and the dynamics of blood flow in the tumour microcirculation. We find that the low-frequency oscillations play an important role in the establishment of tumour hypoxia. The oscillations interact with consumption to inhibit oxygen diffusion in the microenvironment. This suggests that alpha-blockers-a class of drugs used to treat hypertension and stress disorders, and known to lower or even abolish low-frequency oscillations of arterial blood flow -may act as adjuvant drugs in the radiotherapy of solid tumours by enhancing the oxygen effect.