The effect of tumour shrinkage on biologically effective dose, and possible implications for fractionated high dose rate brachytherapy.

A method for incorporating a tumour shrinkage factor into linear-quadratic (LQ) brachytherapy equations is proposed. When there is a significant degree of ongoing shrinkage throughout a course of brachytherapy, and when the sources are centrally situated within the tumour volume, the biologically effective dose (BED) to the tumour will be higher than that which is calculated with standard equations. Although the analytical method initially assumes that shrinkage is exponential with time, it is shown that the modified equations (for both high and low dose rate brachytherapy) are essentially analogous to existing BED equations, but with the addition of a simple linear time-dependent factor. In this article, which concentrates on the implications for fractionated high dose-rate brachytherapy, it is demonstrated that increasing the time interval between fractions will only improve the BED in some cases, the conditions for which may be identified in terms of the ratio K/z, where K is the daily dose required to combat tumour repopulation and z is the daily linear shrinkage rate. In the absence of predictive assay techniques, or where there is doubt as to whether or not the radiobiological conditions favour an increase in the interval between each dose delivery, relatively close spacing (i.e. acceleration) of brachytherapy fractions appears to be the most prudent option.