The response of tumours with Gompertzian growth characteristics to fractionated radiotherapy

Proliferation of tumour cells during radiotherapy may be a significant factor determining response to treatment. In previous work based on the linear-quadratic (LQ) model, tumour cell proliferation was assumed to be independent of both tumour size and the temporal structure of treatment. This paper examines a form of tumour cell proliferation that is exponential at small tumour sizes and Gompertzian at larger sizes. This is integrated with the LQ description of tumour cell sterilization. It is assumed that exposure to therapeutic radiation changes the stale of tumour cells from viable to doomed. Doomed cells are assumed to be lost from the tumour mass with exponential kinetics. Six parameters are used to describe tumour response. Three of these are the standard 'LQ+time' (alpha, beta, T-pot) parameters. Two additional parameters are required to describe the shape of the tumour growth/regrowth curve (V-G, V-max). The sixth parameter (T-s) represents the rate of loss of doomed cells from the tumour. The model may be used to describe the effects of radiation therapy, both in terms of cure response (clonogenic cell sterilization) and also remission response (tumour regression and regrowth). An important feature of the model is that it enables the effects of temporally non-uniform treatments to be described. Preliminary modelling studies suggest that it may be possible to manipulate the temporal structures of fractionation schedules to increase the duration of remission at the expense of the probability of cure.