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We use a stochastic birth-death model for a population of cells to estimatethe normal tissue complication probability (NTCP) under a particularradiotherapy protocol. We specifically allow for interaction between cells, viaa nonlinear logistic growth model. To capture some of the effects of intrinsicnoise in the population we develop several approximations of NTCP, usingKramers-Moyal expansion techniques. These approaches provide an approximationto the first and second moments of a general first-passage time problem in thelimit of large, but finite populations. We use this method to study NTCP in asimple model of normal cells and in a model of normal and damaged cells. Wealso study a combined model of normal tissue cells and tumour cells. Based onexisting methods to calculate tumour control probabilities, and our procedureto approximate NTCP, we estimate the probability of complication free tumourcontrol.

Calculating normal tissue complication probabilities and probabilities  of complication-free tumour control from stochastic models of population  dynamics