Monte Carlo X-ray transport simulation of small-angle X-ray scattering instruments using measured sample cross sections

Small-angle X-ray scattering (SAXS) has recently been proposed as a novel noninvasive in vivo molecular imaging technique to characterize molecular interactions deep within the body using high-contrast probes. This article describes a detailed Monte Carlo X-ray transport simulation technique that utilizes user-provided cross sections to describe X-ray interaction in virtual samples and explore SAXS instrument design choices. The accuracy of the simulation code is validated with sample material cross sections derived from analytical models and empirical measurements of a homogeneous spherical gold nanoparticle (GNP) monomer, a dimer and heterogeneous mixtures of the two in aqueous solution. Analytical and measured scattering profiles from these samples were converted to cross sections using an absolute water standard. Our Monte Carlo estimates of the fraction of dimers from analytically derived and empirically derived cross sections are strongly correlated, with less than 1.5 and 16% error, respectively, to the expected concentration of monomer and dimer species. In addition, a variety of monoenergetic X-ray beams were simulated to investigate coherent scattering versus radiation dose for a range of sample sizes. For GNP spheres in aqueous solution, the energy range that produces the most coherent scattering at the detector per deposited energy was between 31 and 49 keV for a sample thickness of 1 mm to 10 cm. The method described here for the detailed simulation of SAXS using measured and modeled cross sections will enable instrumentation optimization for in vivo molecular imaging applications.