The Log-Normal Function As a Stochastic Model of the Distribution of Strontium-90 and Other Fission Products in Humans

Abstract

Data on the concentrations of 90Sr, 226Ra, Us, and some of the stable trace elements in human tissue as well as environmental samples were found, without exception, to follow log-normal distributions rather than normal distributions. Also, while the median of the 90Sr concentration in humans shifts for different time periods, areas of the world, and population age distributions, the geometric standard deviation has seemed recently to remain within the relatively narrow range of 1. 55-1. 67 for large population groups, so that about the same proportion of each population contains concentrations in excess of a given multiple of the median (or the average) concentration. The log-normal distribution fits the data better than the normal distribution, particularly in the "tail" of higher concentrations. This is the region most critical for the evaluation of the proportions of the population exceeding recommended limits of individual exposure. The repeated suitability of the log-normal permits the recommended limits of environmental contamination to be established with more confidence in predicting the proportions of the population exceeding any given level. The 1964-1965 U. S. Public Health Service measurements of 90Sr in the bones of U.S. children and young adults give parallel cumulative log-normal lines for the 90Sr concentration per gram of bone and per gram of Ca. These lines have approximately the same slope as Kulp and Schulert''s distribution for the variations in Sr concentration in total skeletal bone between adults in New York City in 1958, and the same slope as the distribution for stable strontium, indicating a characteristic variance in the log-normal distribution of strontium in bone within a limited geographic region. The average of the United States distribution in children and young adults was about 3.5 [mu][mu]Ci 90Sr/g Ca in Oct., 1964-March, 1965, the equilibrium level of 3. 5 [mu][mu]Ci/g predicted by Kulp and Schulert for 4-5 yr following the 1961 Soviet tests. The log-normal line fitted to the 1964-1965 U.S. data indicates that less than 3. 6 % of the United States population of age less than 25 will have bone doses exceeding twice the average. Extrapolation of the log-normal distribution would indicate that less than 0. 36 % of the population under age 25 would exceed 10.4 [mu][mu] Ci Sr/g Ca (3 times the average). The same percentages would apply to the corresponding multiples of the average 90Sr concentration per gram of bone. The applicability of the log-normal function for estimating internal, and possibly external, exposure distributions in the world population is also discussed.