Assessment of equivalent uniform RBE-weighted dose in hypofractionated proton therapy for ocular melanoma

Objective.The equivalent uniform RBE-weighted dose (EUD_RBE) is computed in a model problem for hypofractionated proton therapy for ocular melanoma, considering the depth and dose dependence of the relative biological effectiveness (RBE).Approach.The EUD_RBEwas developed to compare the integrated cell survival in radiotherapy modalities with nonuniform distributions of the RBE and the physical dose. Our simulations of the EUD_RBEin hypofractionated proton radiotherapy are based on the linear quadratic (LQ) cell survival model from which the dose correction to the RBE can be evaluated using the theory of dual radiation action. This theory predicts that the higher LET radiation increases the linear component (α) of radiation damage, while the quadratic component (β) remains unchanged. The effect of depth dependence of the RBE was derived from a fit to experimental data across various spread-out Bragg peaks (SOBPs) and the distribution of the physical dose was considered uniform.Main results. There are two competing processes that affect the EUD_RBE: first, the EUD_RBEdecreases as the fractional dose increases, and second, the EUD_RBEincreases with increasing the relative fraction of tumors treated with high RBE at the distal edge of Bragg peak. Our simulations show that the combined effect of these two processes predicts an increase of the EUD_RBEby 9%-12% relative to the physical dose for the fractionation schedule 5 × 10 Gy (RBE) assuming a distal tumor margin of 5 mm.Significance. The increase in the RBE at the end of the proton range largely compensates for the decrease in the RBE for higher fractional proton doses, thus producing the EUD_RBEthat does not deviate substantially from the clinically used uniform value of RBE = 1.1. The EUD_RBEwill enable more optimized proton therapy plans and comparison with other modalities such as eye plaque brachytherapy.