Multiple levels of stochasticity accounted for in different radiation biophysical models: from physics to biology.

Purpose: In the present paper we investigate how some stochastic effects are included in a class of radiobiological models with particular emphasis on how such randomnesses reflect into the predicted cell survival curve.

Materials and methods: We consider four different models, namely the Generalized Stochastic Microdosimetric Model GSM², in its original full form, the Dirac GSM² the Poisson GSM²$$ and the Repair-Misrepair Model (RMR). While GSM²$$ and the RMR models are known in literature, the Dirac and the Poisson GSM²$$ have been newly introduced in this work. We further numerically investigate via Monte Carlo simulation of four different particle beams, how the proposed stochastic approximations reflect into the predicted survival curves. To achieve these results, we consider different ion species at energies of interest for therapeutic applications, also including a mixed field scenario.

Results: We show how the Dirac GSM²$,$ the Poisson GSM²$$ and the RMR can be obtained from the GSM²$$ under suitable approximations on the stochasticity considered. We analytically derive the cell survival curve predicted by the four models, characterizing rigorously the high and low dose limits. We further study how the theoretical findings emerge also using Monte Carlo numerical simulations.

Conclusions: We show how different models include different levels of stochasticity in the description of cellular response to radiation. This translates into different cell survival predictions depending on the radiation quality.