Determination of concentration distribution of trace elements near the detection limit

Abstract

The results of a numerical simulation, performed to check the validity of a method developed for reconstruction of concentration distributions truncated by the detection limit, are reported in the context of trace element analysis in biomedical samples by total-reflection X-ray fluorescence. This method, by correcting a distribution over the whole range of concentrations in a population of samples, restores a number of measurements reporting results below the detection limit. We show by Monte Carlo simulations, assuming lognormal distributions to describe both the concentrations measured as well as the detection limits in the biomedical samples, that the method developed is accurate to within 5% for most typical situations. Moreover, we demonstrate that the factor limiting the accuracy of the correction is the number of measurements, not the correction procedure itself. We have found in simulations that the reconstruction of a concentration distribution, for a typical population size of N=100, is possible when the concentrations are measured only in 20–30% of samples. On the other hand, we show that by ignoring the truncation of a concentration distribution by the detection limit, the results can be systematically biased by as much as 50%. The method developed is applied to the analysis of trace elements in human breast tissue samples by total-reflection X-ray fluorescence (TXRF). The results are also discussed in terms of the size of the population studied.