The radiation quality factor as an Ornstein-Uhlenbeck process

Radiation protection strategies for extended or deep space missions rely on accurate and robust estimates of exposure dose and corresponding risk to crew health, systems functions, and mission safety in general. Simulation and modeling of dose and risk associated with such exposures are, to various degrees, made difficult by the inherent complexity and variability in characterizing the radiation environment, its passage and interaction with matter, and its biological effects. One of the more important contributors to the overall uncertainty in dose or risk assessment is the empirical variability in the radiation quality factor, Q, which is typically used to differentiate such effects. Motivated in part by recent Monte-Carlo based simulations of this variability, we propose and demonstrate a stochastic dynamic model for Q based on the Ornstein-Uhlenbeck process. The proposed model's probability density function is a Gaussian in Q and with a linearly (in the logarithm of the LET variable) growing variance, but with rather complex scaling properties. The model's density function is shown to be quite sensitive to any functional parameterization of the mean (deterministic) behavior of the quality factor with a discontinuous first derivative in LET. The proposed linear stochastic model is also shown to be insensitive, however, to the precise functional form of the deterministic Q.