Different distributions of gold nanoparticles on the tumor and calculation of dose enhancement factor by Monte Carlo simulation

Abstract

Gold nanoparticles can be used to increase the dose of the tumor due to its high atomic number as well as being free from apparent toxicity. The aim of this study is to evaluate the effect of distribution of gold nanoparticles models, as well as changes in nanoparticle sizes and spectrum of radiation energy along with the effects of nanoparticle penetration into surrounding tissues in dose enhancement factor DEF. Three mathematical models were considered for distribution of gold nanoparticles in the tumor, such as 1-uniform, 2- non-uniform distribution with no penetration margin and 3- non-uniform distribution with penetration margin of 2.7 mm of gold nanoparticles. For this purpose, a cube-shaped water phantom of 50 cm size in each side and a cube with 1 cm side placed at depth of 2 cm below the upper surface of the cubic phantom as the tumor was defined, and then 3 models of nanoparticle distribution were modeled. MCNPX code was used to simulate 3 distribution models. DEF was evaluated for sizes of 20, 25, 30, 50, 70, 90 and 100 nm of gold nanoparticles, and 50, 95, 250 keV and 4 MeV photon energies. In uniform distribution model the maximum DEF was observed at 100 nm and 50 keV being equal to 2.90, in non-uniform distribution with no penetration margin, the maximum DEF was measured at 100 nm and 50 keV being 1.69, and in non-uniform distribution with penetration margin of 2.7 mm, the maximum DEF was measured at 100 nm and 50 keV as 1.38, and the results have been showed that the dose was increased by injecting nanoparticles into the tumor. It is concluded that the highest DEF could be achieved in low energy photons and larger sizes of nanoparticles. Non-uniform distribution of gold nanoparticles can increase the dose and also decrease the DEF in comparison with the uniform distribution. The non-uniform distribution of nanoparticles with penetration margin showed a lower DEF than the non-uniform distribution without any margin and uniform distribution. Meanwhile, utilization of the real X-ray spectrum brought about a smaller DEF in comparison to mono-energetic X-ray photons.

Monte Carlo studies in Gold Nanoparticles enhanced radiotherapy: The impact of modelled parameters in dose enhancement

“…AuNPs size [15,24,25,[29][30][31]34,[36][37][38][39], concentration [26,29,30,33,37,39] and the modelling of distribution [28,36,[38][39][40][41] are the main AuNPs properties under investigation in literature. Photon energy [12,22,[24][25][26]28,29,[31][32][33][34][36][37][38], the presence of flattening filter (FF) in clinical photon beams [15,27,30], simulation set up [42] and the user defined parameters [43] (Auger electrons activation, energy cut off, voxel size etc.) have been discussed in MC simulations from 2010 to 2019.…”

“…In other studies, AuNPs size has a negligible effect in dose enhancement when photon energies are in MV range [29,30,[36][37][38]. More specifically, Pakravan et al [30] reported the greatest difference in DEF values of 1.046 and 1.056 in case of 25 nm diameter and 200 nm respectively for a concentration of 36 mg AuNPs g _1 tumor and a 6 MV photon beam.…”

Intercomparison of Monte Carlo calculated dose enhancement ratios for gold nanoparticles irradiated by X-rays: Assessing the uncertainty and correct methodology for extended beams

“…Nevertheless, three studies have tried such straightforward simulation using the MCNP code and a hierarchical geometry with cubic voxels of decreasing size [17,20,44]. Spherical GNPs were placed in the centers of the lowest-level voxels that were filled with water.…”

“…All three papers report an increase in the average DER with increasing GNP size for a constant MFG [17,20,44]. This dependence on GNP size appears to be an artefact of the simulation, as the results are not compatible with what one would expect from energy conservation: As was shown by Koger and Kirkby [43], the fraction of the energy transferred to electrons by soft X-ray photon interactions inside a GNP and imparted to water by these electrons decreases with increasing GNP size.…”

“…While the lower mass fraction (which was also used in [20]) could be obtained by leaving 30% of the 1 µm 3 voxels without GNP, it is not described how the 18 mg/g was achieved. Kheshevarz et al [44] refer to the work of Mesbahi et al [17], but did not include the information about the smallest voxel size. In their work, the difference between uniform and non-uniform distribution of GNPs was studied, where the DERs for soft X-rays and the uniform distribution of 100 nm GNPs are compatible with what is expected from the mass-energy absorption coefficients and the results of Koger and Kirkby [43].…”