Equivalent uniform RBE-weighted dose in eye plaque brachytherapy

Abstract

Background: Brachytherapy for ocular melanoma is based on the application of eye plaques with different spatial dose nonuniformity, time-dependent dose rates and relative biological effectiveness (RBE).

Purpose: We propose a parameter called the equivalent uniform RBE-weighted dose (EUD_RBE) that can be used for quantitative characterization of integrated cell survival in radiotherapy modalities with the variable RBE, dose nonuniformity and dose rate. The EUD_RBE is applied to brachytherapy with ¹²⁵I eye plaques designed by the Collaborative Ocular Melanoma Study (COMS).

Methods: The EUD_RBE is defined as the uniform dose distribution with RBE = 1 that causes equal cell survival for a given nonuniform dose distribution with the variable RBE > 1. The EUD_RBE can be used for comparison of cell survival for nonuniform dose distributions with different RBE, because they are compared to the reference dose with RBE = 1. The EUD_RBE is applied to brachytherapy with ¹²⁵I COMS eye plaques that are characterized by a steep dose gradient in tumor base-apex direction, protracted irradiation during time intervals of 3-8 days, and variable dose-rate dependent RBE with a maximum of about 1.4. The simulations are based on dose of 85 Gy prescribed to the farthest intraocular extent of the tumor (tumor apex). To compute the EUD_RBE in eye plaque brachytherapy and correct for protracted irradiation, the distributions of physical dose have been converted to non-uniform distributions of biologically effective dose (BED) to include the biological effects of sublethal cellular repair, Our radiobiological analysis considers the combined effects of different time-dependent dose rates, spatial dose non-uniformity, dose fractionation and different RBE and can be used to derive optimized dose regimens brachytherapy.

Results: Our simulations show that the EUD_RBE increases with the prescription depths and the maximum increase may achieve 6% for the tumor height of 12 mm. This effect stems from a steep dose gradient within the tumor that increases with the prescription depth. The simulations also show that the EUD_RBE increase may achieve 12% with increasing the dose rate when implant duration decreases. The combined effect of dose nonuniformity and dose rate may change the EUD_RBE up to 18% for the same dose prescription of 85 Gy to tumor apex. The absolute dose range of 48-61 Gy (RBE) for the EUD_RBE computed using 4 or 5 fractions is comparable to the dose prescriptions used in stereotactic body radiation therapy (SBRT) with megavoltage X-rays (RBE = 1) for different cancers. The tumor control probabilities in SBRT and eye plaque brachytherapy are very similar at the level of 80% or higher that support the hypothesis that the selected approximations for the EUD_RBE are valid.

Conclusions: The computed range of the EUD_RBE in ¹²⁵I COMS eye plaque brachytherapy suggests that the selected models and hypotheses are acceptable. The EUD_RBE can be useful for analysis of treatment outcomes and comparison of different dose regimens in eye plaque brachytherapy.

Keywords: BED; EUD; LQ model; RBE; eye plaque brachytherapy.