Modelling of the oxygen enhancement ratio for ion beam radiation therapy.

The poor treatment prognosis for tumours with oxygen-deficient areas is usually attributed to the increased radioresistance of hypoxic cells. It can be expressed by the oxygen enhancement ratio (OER), which decreases with increasing linear energy transfer (LET) suggesting a potential clinical advantage of high-LET radiotherapy with heavy ion beams compared to low-LET photon or proton irradiation. The aim of this work is to review the experimental cell survival data from the literature and, based on them, to develop a simple OER model to estimate the clinical impact of OER variations. For this purpose, the standard linear-quadratic model and the Alper-Howard-Flanders model are used. According to our calculations for a carbon ion spread-out Bragg peak at clinically relevant intermediate oxygen levels (0.5-20 mmHg), the advantage of carbon ions might be relatively moderate, with OER values about 1%-15% smaller than for protons. Furthermore, the variations of OER with LET are much smaller in vivo than in vitro due to different oxygen partial pressures used in cell experiments or measured inside tumours. The proposed OER model is a simple tool to quantify the oxygen effect in a practical way and provides the possibility to do hypoxia-based biological optimization in treatment planning.