Optimizing the modified microdosimetric kinetic model input parameters for proton and $^4$He ion beam therapy application

Models able to predict relative biological effectiveness (RBE) values are necessary for an accurate determination of the biological effect with proton and $^4$He ion beams. This is particularly important when including RBE calculations in treatment planning studies comparing biologically optimized proton and $^4$He ion beam plans. In this work, we have tailored the predictions of the modified microdosimetric kinetic model (MKM), which is clinically applied for carbon ion beam therapy in Japan, to reproduce RBE with proton and $^4$He ion beams. We have tuned the input parameters of the MKM, i.e. the domain and nucleus radii, reproducing an experimental database of initial RBE data for proton and He ion beams. The modified MKM, with the best fit parameters obtained, has been used to reproduce in vitro cell survival data in clinically-relevant scenarios. A satisfactory agreement has been found for the studied cell lines, A549 and RENCA, with the mean absolute survival variation between the data and predictions within 2% and 5% for proton and $^4$He ion beams, respectively. Moreover, a sensitivity study has been performed varying the domain and nucleus radii and the quadratic parameter of the photon response curve. The promising agreement found in this work for the studied clinical-like scenarios supports the usage of the modified MKM for treatment planning studies in proton and $^4$He ion beam therapy.