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

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...

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Bibliographic Details
Published in:Scientific reports 2020-05, Vol.10 (1), p.8786-8786, Article 8786
Main Authors: Hufton, Peter G., Buckingham-Jeffery, Elizabeth, Galla, Tobias
Format: Article
Language:English
Subjects:
631/67/70
639/766/747
Apoptosis
Approximation
Cell division
Cell Proliferation - radiation effects
Cell Survival - radiation effects
Computer simulation
Growth models
Humanities and Social Sciences
Humans
Logistic Models
Models, Biological
multidisciplinary
Neoplasms - radiotherapy
Noise
Ordinary differential equations
Physics
Population
Probability
Protocol
Radiation therapy
Radiotherapy Planning, Computer-Assisted
Science
Science (multidisciplinary)
Stochastic Processes
Stochasticity
Tumors
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Summary: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.
ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-020-64618-9