A track-event theory of cell survival

When fractionation schemes for hypofractionation and stereotactic body radiotherapy are considered, a reliable cell survival model at high dose is needed for calculating doses of similar biological effectiveness. In this work a simple model for cell survival which is valid also at high dose is developed from Poisson statistics.

An event is defined by two double strand breaks (DSB) on the same or different chromosomes. An event is always lethal due to direct lethal damage or lethal binary misrepair by the formation of chromosome aberrations. Two different mechanisms can produce events: one-track events (OTE) or two-track-events (TTE). The target for an OTE is always a lethal event, the target for an TTE is one DSB. At least two TTEs on the same or different chromosomes are necessary to produce an event. Both, the OTE and the TTE are statistically independent. From the stochastic nature of cell kill which is described by the Poisson distribution the cell survival probability was derived.

It was shown that a solution based on Poisson statistics exists for cell survival. It exhibits exponential cell survival at high dose and a finite gradient of cell survival at vanishing dose, which is in agreement with experimental cell studies. The model fits the experimental data nearly as well as the three-parameter formula of Hug-Kellerer and is only based on two free parameters. It is shown that the LQ formalism is an approximation of the model derived in this work. It could be also shown that the derived model predicts a fractionated cell survival experiment better than the LQ-model.

It was shown that cell survival can be described with a simple analytical formula on the basis of Poisson statistics. This solution represents in the limit of large dose the typical exponential behavior and predicts cell survival after fractionated dose application better than the LQ-model.