Stochastic modeling of the cell killing effect for low- and high-LET radiation

Theoretical modeling of biological response to radiation describes qualitatively and quantitatively the results of radiobiological effects at the molecular, chromosomal, and cellular level. The repair-misrepair (RMR) model is the radiobiological model chosen for our study. It models deoxyribonucleic acid (DNA) damage formation and lesion repair through linear and quadratic processes. Double strand breaks (DSB) are a critical lesion in DNA. With increasing LET, the number of DSB per track traversing the cell nucleus increases. Using a compound Poisson process (CPP), we describe DNA damage formation. Three models were considered: a simple CPP using constant LET, a CPP using a chord length distribution, and a CPP using specific energy distribution. In the two first cases, and for low LET radiation the initial distribution of DSB was well approximated by a Poisson distribution, while for high LET radiation the initial distribution of DSB deviated slightly from a Poisson distribution. In the last case, DSB distribution was much broader than a pure Poisson distribution. Datasets from the literature for seven human cell lines, exhibiting various sensitivities to radiation were analyzed. We compared stochastic, CPP, and CPP using chord length distribution, with deterministic RMR models. For low LET radiation and at high dose rates the stochastic survival results agree well with the deterministic survival results. Also the stochastic model allows for non-linearity at low doses due to the accumulation of sub-lethal damage. At low dose rates deterministic results overestimate the surviving fraction compared to stochastic results. For high LET radiation stochastic and deterministic survival results agree. Stochastic survival results using specific energy distribution diverged from deterministic results by underestimating the surviving fraction at low and high LET radiation. The dose rate sparing curve, representing surviving fraction at a dose of 10Gy vs. dose rate shows that deterministic survival results are consistent with stochastic survival results, using CPP, or CPP with chord length distribution, for low and high dose rate values. Compared to deterministic aspects of DNA damage formation we concluded that stochastic aspects of DNA damage formation and repair using CPP or CPP with chord length distribution are not as prominent as reported in the earlier studies