A calculation of the relative biological effectiveness of and brachytherapy sources using the concept of proximity function

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Abstract
The clinical application of encapsulated radioactive sources in brachytherapy plays an important role in the treatment of malignancy. 125I and 103Pd sources have been widely used in the permanent implant of prostate cancer. An important consideration for the choice of brachytherapy sources is their relative biological effectiveness (RBE). Previous calculations of this quantity have used the dose-averaged lineal energy, yD, as a measure of biological effectiveness. In this approach, however, the selection of a relevant site size remains an open question. Here we avoid this problem by using the generalized theory of dual radiation action to calculate the initial slope, alpha, of the dose-effect curves using the proximity function, t(x), and the biological response function, gamma(x). At low doses and/or low dose rates (e.g., prostate implants) the parameter alpha determines the RBE. Proximity function, t(x), is the probability distribution function of distances between pairs of sublesions; and the biological function, gamma(x), is the probability that two sublesions at a distance x apart results in a lesion. Functions t(x) have been calculated for each source using the Monte Carlo transport codes PHOEL and PROTON5. The function gamma(x) has been taken from a published analysis. The RBE values thus obtained are: 1.5 for 125I and 1.6 for 103Pd. The question of whether an "effective" site size exists where yD approximates best the variation of alpha with radiation quality is also addressed.

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