A closed-form description of tumour control with fractionated radiotherapy and repopulation.
OBJECTIVE
To derive a closed form expression of tumour control probability (TCP) following the geometric stochastic approach of Tucker and Taylor.


METHODS
A model was constructed based upon a Galton-Watson branching process with cell killing represented by a Bernoulli random variable, and repopulation represented by a Yule Fury process. A closed-form expression of the probability-generating function was derived, which yielded an explicit expression for the mean number of surviving clonogens and the TCP.


RESULTS
The mean number of surviving cells, after i clonogens have been treated with n fractions of irradiation, was [equation: see text], where s is the surviving fraction, lambda is the rate of cell division, and delta t is the interfraction time interval. The tumour control probability was [equation: see text].


CONCLUSIONS
Tucker and Taylor provided improvements upon the conventional Poisson model for TCP, mainly through numerical simulation. Here a model based upon their geometric stochastic approach has been derived in closed form. The resultant equations provide a simpler alternative to numerical simulation allowing the effects of fractionated radiotherapy on a replicating population of tumour cells to be more easily predicted.
Kendal
W S
WS
Department of Radiation Oncology, The Ottawa Regional Cancer Center, Ontario, Canada.
D002455:Cell Division / Q000528:radiation effects; D002470:Cell Survival / Q000528:radiation effects; D008432:Mathematical Computing; D008954:Models, Biological; D009369:Neoplasms / Q000473:pathology* / Q000532:radiotherapy*