The fast growth of malignant tumours frequently results in regions of the tumour becoming low in oxygen (hypoxic). Tissue hypoxia is important because hypoxic tumours are thought to be particularly aggressive and are difficult to treat because they are resistant to radiotherapy. We are using mathematical models to investigate the relationship between tissue hypoxia and the interpretation of positron emission tomography (PET) scans: the poor spatial resolution and low image contrast mean that tumours that appear identical in a PET scan may have significantly different underlying tissue structures making treatment planning difficult.