Effect of overall time when radiotherapy includes teletherapy and brachytherapy: a mathematical model

Abstract

By expanding the linear quadratic equations to allow for the interval of time between teletherapy and brachytherapy in a model which assumes continual exponential tumour regression following teletherapy, the loge cell kill resulting from brachytherapy is found to depend on radiosensitivity, tumour regression rate (lambda) and tumour clonogen doubling time (Tp). When lambda is relatively small the precise timing of brachytherapy following teletherapy is shown to influence the tumour cure probabilities. The model predicts a reduction in tumour control if brachytherapy is delayed when lambda values are small and Tp values are short, but when Tp values are long, deferral of brachytherapy may be advantageous. By differential calculus the occurrence of a minimum value of log cell kill can be found. Application of these concepts may improve the results of clinical radiotherapy.