RBE Estimates

At low dose or fluence, RBE was calculated using the TE model, and is given by the ratio of linear induction coefficients. Here we used RBE_{γ Acute}, which compares low dose particle responses to acute γ-ray exposures using a linear fit of acute γ-ray responses doses near 1 Gy^{1, 10}, with linear coefficient denoted as α_γ. For the HG experiment the highest γ- ray dose of 7 Gy is not included in the RBE_{γ Acute} estimate. This approach is used in the NASA quality factor (QF) model¹ in order to be consistent with the linear response model used to represent the Atomic-bomb survivor solid cancer incidence data while reducing uncertainties related to low dose and dose-rate γ-ray responses.

The functional form of the RBE function at low dose where cell survival effects can be ignored are based on the linear or targeted effects assumption (TE), which uses a linear fit to acute γ-ray responses as the reference radiation is given by:

We also considered RBE in the NTE model, however RBE estimates are dose dependent and do not limit to a constant value at low dose. Here it is convenient to define a cross-over dose where the contributions from the TE and NTE terms in the Hazard function of Equation (⁶) are equal:

The RBE in the NTE model is a function of the particles absorbed dose, D and is given by²⁰: