Dependence of Monte Carlo microdosimetric computations on the simulation geometry of gold nanoparticles

Recently, interactions of x-rays with gold nanoparticles (GNPs) and the resulting dose enhancement have been studied using several Monte Carlo (MC) codes (Jones et al 2010 Med. Phys. 37 3809-16, Lechtman et al 2011 Phys. Med. Biol. 56 4631-47, McMahon et al 2011 Sci. Rep. 1 1-9, Leung et al 2011 Med. Phys. 38 624-31). These MC simulations were carried out in simplified geometries and provided encouraging preliminary data in support of GNP radiotherapy. As these studies showed, radiation transport computations of clinical beams to obtain dose enhancement from nanoparticles has several challenges, mostly arising from the requirement of high spatial resolution and from the approximations used at the interface between the macroscopic clinical beam transport and the nanoscopic electron transport originating in the nanoparticle or its vicinity. We investigate the impact of MC simulation geometry on the energy deposition due to the presence of GNPs, including the effects of particle clustering and morphology. Dose enhancement due to a single and multiple GNPs using various simulation geometries is computed using GEANT4 MC radiation transport code. Various approximations in the geometry and in the phase space transition from macro- to micro-beams incident on GNPs are analyzed. Simulations using GEANT4 are compared to a deterministic code CEPXS/ONEDANT for microscopic (nm-µm) geometry. Dependence on the following microscopic (µ) geometry parameters is investigated: µ-source-to-GNP distance (µSAD), µ-beam size (µS), and GNP size (µC). Because a micro-beam represents clinical beam properties at the microscopic scale, the effect of using different types of micro-beams is also investigated. In particular, a micro-beam with the phase space of a clinical beam versus a plane-parallel beam with an equivalent photon spectrum is characterized. Furthermore, the spatial anisotropy of energy deposition around a nanoparticle is analyzed. Finally, dependence of dose enhancement on the number of GNPs in a finite cluster of nanoparticles is determined. Simulations were performed for 100 nm GNPs irradiated in water phantom by various monoenergetic (11 keV-1 MeV) and spectral (50 kVp) sources. The dose enhancement ratio (DER) is very sensitive to the specific simulation geometry (µSAD, µS, µC parameters) and µ-source type. For a single GNP the spatial distribution of DER is found to be nearly isotropic with limited magnitude and relatively short range (∼100-200 nm for DER significantly greater than 1). For a cluster of GNPs both the magnitude and range are found much greater (∼1-2 µm). The relation between DER for a cluster of GNPs and a single GNP is strongly nonlinear. Relatively strong dependence of DER on the simulation micro-geometry cautions future studies and the interpretation of existing MC results obtained in different simulations geometries. The nonlinear relation between DER for a single and multiple GNPs suggests that parameters such as the number of adjacent nanoparticles per cell and the distances between the GNPs and the cellular target may be important in assessing the biological effectiveness associated with GNP.