Uncertainties in predicted radionuclide body burdens and doses from discrete stochastic source terms

Expressions are derived in three cases for the expectation and uncertainty of body burdens and doses calculated from a linear model of environmental transport and human metabolism in terms of expectation and uncertainty in inputs of discrete, stochastic random variables. Three cases are compared to determine the relationship of the expectations and uncertainties under varying assumptions. In the constant input case, the input is selected randomly at the outset of the simulation period [O,T] from the distribution to which the population is exposed and then is held constant throughout [O,T]. In the two time-varying cases, random and autoregressive, it was assumed that N discrete stochastic exposures to the input were made uncorrelated and partially correlated, respectively. Each exposure was constant during each time interval of length T/N. The expectation values of the body burdens and doses in the constant input case were identical to those in the random case and the autoregressive cases for stationary inputs. The uncertainties of the body burdens and the doses in the constant input case were identical in the limit of rapid metabolism to those of the random case and the autoregressive cases for stationary inputs. In the limit of slow metabolism, the uncertainties of the body burdens and the doses in the constant input case were N1/2 and (3N/4)1/2, respectively, greater than those in the random case and were ((1 + alpha)/[(1 - alpha)N])1/2 and (4(1 + alpha)/[3(1 - alpha)N])1/2, respectively, greater than those in the autoregressive case for stationary inputs and autocorrelation coefficient alpha. That is, increasing the number of sampling periods decreases the uncertainty and increasing the autocorrelation increases the uncertainty. In an example application for ingestion of 137Cs at Bikini Island, a weak form of both slow and rapid metabolism limits apply and give the result that the uncertainty of the body burden in the constant input case is 18 times greater than the random case. For alpha = 0.5, the uncertainty of the body burden in the autoregressive case is 1.7 times greater than the random case. The smooth transition of the autoregressive case from the random case to the constant input case is shown as alpha increases from 0 (random) to 1 (constant).