Background estimation methods for quantitative x-ray fluorescence analysis of gold nanoparticles in biomedical applications

Accurate background estimation to isolate the fluorescence signals is an important issue for quantitative X-ray fluorescence (XRF) analysis of gold nanoparticles (GNPs). Though a good estimation can be obtained experimentally through acquiring the background spectrum of water solution, it inevitably leads to unnecessary second exposure in reality. Thus, several numerical methods such as trapezoidal shape estimation, interpolation by polynomial fitting and SNIP (Statistics sensitive Nonlinear Iterative Peak-Clipping) algorithm are proposed to achieve this goal. This paper aims to evaluate the estimation results calculated by these numerical methods through comparing with that acquired using the experimental way, in term of mean squared error (MSE). Four GNP/water solutions with various concentrations from 0.0% to 1.0% by weight are prepared. Then, ten spectra are acquired for each solution for further analysis, under the identical condition of using pencil beam x-ray and single spectrometer. Finally, the experimental and numerical methods are performed on these spectra within the optimally determined energy window and their statistical characteristics are analyzed and compared. These numerical background estimation methods as well as the evaluation methods can be easily extended to analyze the fluorescence signals of other nanoparticle biomarkers such as gadolinium, platinum and Barium in multiple biomedical applications.