First-passage times and normal tissue complication probabilities in the limit of large populations

Peter Hufton, Elizabeth Buckingham-Jeffery, Tobias Galla

Research output: Contribution to journalArticlepeer-review


The time of a stochastic process first passing through a boundary is important to many diverse applications. However, we can rarely compute the analytical distribution of these first-passage times. We develop an approximation to the first and second moments of a general first-passage time problem in the limit of large, but finite, populations using Kramers–Moyal expansion techniques. We demonstrate these results by application to a stochastic birth-death model for a population of cells in order to develop several approximations to the normal tissue complication probability (NTCP): a problem arising in the radiation treatment of cancers. We specifically allow for interaction between cells, via a nonlinear logistic growth model, and our approximations capture the effects of intrinsic noise on NTCP. We consider examples of NTCP in both a simple model of normal cells and in a model of normal and damaged cells. Our analytical approximation of NTCP could help optimise radiotherapy planning, for example by estimating the probability of complication-free tumour under different treatment protocols.
Original languageEnglish
JournalScientific Reports
Early online date29 May 2021
Publication statusE-pub ahead of print - 29 May 2021


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