Functional imaging of tumour hypoxia has been suggested as a tool for refining target definition and treatment optimization in radiotherapy. The approach, however, has been slow to be adopted clinically as most of the studies on the topic do not take into account the in-treatment changes of hypoxia. The present study aimed to introduce a function that quantifies the changes of oxygen distributions in repeated PET images taken during treatment. The proposed approach for determining the reoxygenation function was tested for feasibility on patients with head and neck cancer, repeatedly imaged with FMISO PET during radiotherapy. Reoxygenation functions were derived by solving the convolution between functions describing the oxygen distributions of successive images. The method was found to be mathematically feasible. The results indicate that the reoxygenation functions describing the change in oxygenation have distinct shapes prompting the hypothesis that oxygenation changes reflected by them might have predictive power for treatment outcome. Future studies on a larger patient population to search for predictive correlations based on the reoxygenation function are planned.