Relative Biological Effectiveness (RBE) of Monoenergetic Protons: Comparison of Empirical and Biophysical Models

A constant proton relative biological effectiveness (RBE) of 1.1 for tumor control is currently used in proton therapy treatment planning. However, in vitro, in vivo and clinical experiences indicate that proton RBE varies with kinetic energy and, therefore, tissue depth within proton Bragg peaks. A number of published RBE models capture variations in proton RBE with depth. The published models can be sub-divided into empirical (or phenomenological) and biophysical (or mechanistic-inspired) RBE models. Empirical RBE models usually characterize the beam quality through the dose-averaged linear energy transfer (${\mathrm{LET}}_{\mathrm{D}}$), while most biophysical RBE models relate RBE to the dose-averaged lineal energy (${\mathrm{y}}_{\mathrm{D}}$). In this work, an analytic microdosimetry model and the Monte Carlo damage simulation code (MCDS) were utilized for the evaluation of the ${\mathrm{LET}}_{\mathrm{D}}$ and ${\mathrm{y}}_{\mathrm{D}}$ of monoenergetic proton beams in the clinically relevant energy range of 1–250 MeV. The calculated ${\mathrm{LET}}_{\mathrm{D}}$ and ${\mathrm{y}}_{\mathrm{D}}$ values were then used for the estimation of the RBE for five different cell types at three dose levels (2 Gy, 5 Gy and 7 Gy). Comparisons are made between nine empirical RBE models and two biophysical models, namely, the theory of dual radiation action (TDRA) and the microdosimetric kinetic model (MKM). The results show that, at conventional dose fractions (~2 Gy) and for proton energies which correspond to the proximal and central regions of the spread-out Bragg peak (SOBP), RBE varies from 1.0 to 1.2. At lower proton energies related to the distal SOBP, we find significant deviations from a constant $\mathrm{RBE}$ of 1.1, especially for late-responding tissues (low ${(\alpha /\beta )}_R$ of ~1.5–3.5 Gy) where proton RBE may reach 1.3 to 1.5. For hypofractionated dose fractions (5–7 Gy), deviations from a constant $\mathrm{RBE}$ of 1.1 are smaller, but may still be sizeable, yielding RBE values between 1.15 and 1.3. However, large discrepancies among the different models were observed that make the selection of a variable RBE across the SOBP uncertain.