A computational method to estimate the relative biological effectiveness and tumor control probability for low-LET proton irradiations

A constant relative biological effectiveness (RBE) value of 1.1 is used for proton therapy (PT) in many clinical treatment plans. However, several studies show that RBE varies with proton energy, linear energy transfer (LET), and oxygen concentration. This study presents a computational method based on the linear quadratic (LQ) and repair-misrepair-fixation (RMF) models to calculate tumor control probability (TCP) under varying oxygen conditions. We analyze the impact of hypoxia on the parameters of the LQ model, focusing on the ratio and RBE. The proposed method allows for TCP calculations across different oxygen concentrations and for various ion therapies, such as proton and carbon ion therapy. Our results show that increasing the LET from 1 to 12 keV/μm enhances TCP from 61% to 98% under aerobic conditions (21% O2), 45% to 98% under moderately hypoxic conditions (2% O2), and from 1% to 48% under severely hypoxic conditions (0.1% O2). These findings are compared with clinical trial data, demonstrating that hypoxia significantly affects TCP for low-LET radiations.