A stochastic model for tumour control probability that accounts for repair from sublethal damage

The tumour control probability (TCP) is the probability that a treatment regimen of radiation therapy (RT) eradicates all tumour cells in a given tissue. To decrease the toxic effects on healthy cells, RT is usually delivered over a period of weeks in a series of fractions. This allows tumour cells to repair sublethal damage (RSD) caused by radiation. In this article, we introduce a stochastic model for tumour response to radiotherapy which accounts for the effects of RSD. The tumour is subdivided into two cell types: 'affected' cells which have been damaged by RT and 'unaffected' cells which have not. The model is formulated as a birth-death process for which we can derive an explicit formula for the TCP. We apply our model to prostate cancer, and find that the radiosensitivity parameters and the probability of sublethal damage during radiation are the parameters to which the TCP predictions are most sensitive. We compare our TCP predictions to those given by Zaider and Minerbo's one-class model (Zaider & Minerbo, 2000) and Dawson and Hillen's two-class model (Dawson & Hillen, 2006) and find that for low doses of radiation, our model predicts a lower TCP. Finally, we find that when the probability of sublethal damage during radiation is large, the mean field assumption overestimates the TCP.