Radiobiological modelling of dose-gradient effects in low dose rate, high dose rate and pulsed brachytherapy

This paper presents a generalization of a previously published methodology which quantified the radiobiological consequences of dose-gradient effects in brachytherapy applications. The methodology uses the linear-quadratic (LQ) formulation to identify an equivalent biologically effective dose (BED(eq)) which, if applied uniformly to a specified tissue volume, would produce the same net cell survival as that achieved by a given non-uniform brachytherapy application. Multiplying factors (MFs), which enable the equivalent BED for an enclosed volume to be estimated from the BED calculated at the dose reference surface, have been calculated and tabulated for both spherical and cylindrical geometries. The main types of brachytherapy (high dose rate (HDR), low dose rate (LDR) and pulsed (PB)) have been examined for a range of radiobiological parameters/dimensions. Equivalent BEDs are consistently higher than the BEDs calculated at the reference surface by an amount which depends on the treatment prescription (magnitude of the prescribed dose) at the reference point. MFs are closely related to the numerical BED values, irrespective of how the original BED was attained (e.g., via HDR, LDR or PB). Thus, an average MF can be used for a given prescribed BED as it will be largely independent of the assumed radiobiological parameters (radiosensitivity and alpha/beta) and standardized look-up tables may be applicable to all types of brachytherapy treatment. This analysis opens the way to more systematic approaches for correlating physical and biological effects in several types of brachytherapy and for the improved quantitative assessment and ranking of clinical treatments which involve a brachytherapy component.