# Estimation of Dose Enhancement for Inhomogeneous Distribution of Nanoparticles: A Monte Carlo Study
###### Abstract  
High atomic number nanoparticles are of increasing interest in radiotherapy due to their significant positive impact on the local dose applied to the treatment site. In this work, three types of metal nanoparticles were utilized to investigate their dose enhancement based on the GATE Monte Carlo simulation tool. Gold, gadolinium, and silver were implanted at three different concentrations to a 1 cm radius sphere to mimic a cancerous tumor inside a 10 \(\times\) 10 \(\times\) 30 cm\({}^{3}\) water phantom. The innermost layer of the tumor represents a necrotic region, where the metal nanoparticles uptake is assumed to be zero, arising from hypoxic conditions. The nanoparticles were defined using the mixture technique, where nanoparticles are added to the chemical composition of the tumor. A directional 2 \(\times\) 2 cm\({}^{2}\) monoenergetic photon beam was used with several energies ranging from 50 keV to 4000 keV. The dose enhancement factor (DEF) was measured for all three metal nanoparticles under all beam energies. The maximum DEF was -7 for silver nanoparticles with the 50 keV beam energy at the highest nanoparticle concentration of 30 mg/g of water. Gold followed the same trend as it registered the highest DEF at the 50 keV beam energy with the highest concentration of nanoparticles at 30 mg/g, while gadolinium registered the highest at 100 keV. metal nanoparticles; GATE Monte Carlo simulation; necrotic region; dose enhancement factor (DEF) 20212 with a high atomic number \(Z\)--gold [8], gadolinium, [9] bismuth, [10] and silver [11]--implanted inside a tumor can increase the production of secondary electrons and Auger electrons by the photoelectric effect when irradiated with photons of low energy \(E\), as the cross-section of this interaction varies as \(\frac{Z^{n}}{E^{n}}\) with 4 \(<n<\) 5 [12]. This local dose intensification, in turn, may enhance the radiation therapy effects [13]. Several studies have reported dose enhancement arising by the use of nanoparticles for both in vitro [14; 15] and in vivo animal studies [16; 17; 18; 19]. The majority of such studies have involved the study of gold nanoparticles in the kilovoltage X-ray energy range. However, it has become clear that the increased radiosensitivity reported in the literature results from a combination of the physical dose enhancement and additional chemical and biological effects associated with the type of nanoparticle in use [20]. Despite this body of work and commercial nanoparticles' availability, the clinical translation of nanoparticles has been limited [21], although reports from clinical trials are beginning to emerge [22]. Gold has been the predominant nanoparticle studied to date due to its high X-ray absorption coefficient at kilovoltage energies and the ability to manufacture the nanoparticle size, shape and surface properties to optimize particle stability, solubility and biological properties. However, other nanoparticles have also been studied to varying degrees, including gadolinium and titanium oxide nanotubes [23; 24; 25]. Nanoparticles are delivered to the tumor cells via the bloodstream. Cellular uptake of the NPs is a complex process controlled mainly by the tumor vasculature [26]. In numerous studies on dose enhancement, it was assumed that the distribution of NPs within the tumor is homogeneous [27; 28; 29; 30; 31]. However, this assumption might be unrealistic since the neo-vascularization is higher in the outer regions of the tumor than in its inner parts. The heterogeneous vascularization of the interstitial medium affects greatly the concentration distribution of the NP uptake [32]. It is expected that the concentration of NPs would be higher in the peripheral regions of the tumor. This may lead to an increase in viable tumor cell killing in real conditions of cancer radiotherapy, although this assumption is complicated by the potentially increased radio resistance of a hypoxic core [32; 33; 34; 35].