# Estimation of Dose Enhancement for Inhomogeneous Distribution of Nanoparticles: A Monte Carlo Study
## 4 Discussion  
In this study, the GATE toolkit was used to determine the DEF resulting from inhomogeneous nanoparticle uptake for various energies. Although simplistic in the arrangement, this setup was considered appropriate to demonstrate the dose enhancements that may be expected for external beam radiation therapy for nanoparticles of different elemental compositions and concentrations. Ag, Gd, and Au were modeled in concentrations varying from 10 mg/g tissue to 30 mg/g tissue in a layered, non-homogeneous pattern with a necrotic core. The presented model focused on demonstrating the DEF in an inhomogeneous distribution of NPs. However, the model did not incorporate many factors that might affect the clinical application of NPs. These factors include the healthy tissue uptake of NPs, uptake and elimination rates, tumor stage, size, vascularization and depth.  
Tumor vascularization and formation of necrosis is dependent on the tumor stage. Tumor necrosis is believed to form at the center of solid tumors as tumors progress into advanced stages [59, 60]. Therefore, not all tumors, at the time of therapy, have necessarily developed a necrotic region. Additionally, the vascular distribution dependency on tumor stage would affect the distribution of NPs within the tumor.  
Very few DEF studies considered an inhomogeneous distribution of NPs. [PERSON] et al., evaluated the dose enhancement in an inhomogeneous, gold NP distribution for different tumor depths. The study used low-energy monoenergetic photon beams, including 55 and 95 keV photons. The maximum DEF obtained with 55 and 95 keV photons for 10 and 30 mg/g Au is somewhat higher than those obtained in this study for 50 and 100 keV [43].  
The results of the two studies are following the same trend and the enhancement is increasing with concentration and decreasing with energy. However, the disagreement in the DEF values is most likely caused by two factors. First, the tumor in their study is located closer to the surface. The maximum tumor depth considered in their study is 6.5 cm, while a fixed tumor depth of 14 cm was used in this study. This difference in depth, as discussed earlier, could affect the DEF. Second, the NPs inhomogeneous distribution is different. For instance, the maximum concentration in any layer in this study is approximately 40 mg/g when the AuNps overall concentration in the tumor is 30 mg/g. In their study, for a 30 mg/g overall concentration, the maximum is 54 mg/g, resulting in higher enhancement than reported in our study.  
This study showed NPs to be advantageous at low energies and of limited benefit around the megavoltage range. This is consistent with several studies that reported relatively small macroscopic enhancement factors with very high energy photons [61, 62]. Compton is known to be dominant over photoelectric interaction in the megavoltage range. Compton scattering is dependent on electronic density rather than the atomic number. Therefore, metals with a high atomic number are not very effective as dose enhancers in the megavoltage range.  
Typically, external radiation therapy is carried out using heterogenous X-rays. However, monoenergetic beams were used in this study. X-rays have a relatively complicated energy spectrum. Additionally, for a given kVp, the spectrum is slightly different from one manufacturer to another [63]. On the other hand, a monoenergetic beam is easier to model and its results are easier to interpret. The term \"beam quality\" is usually used to describe the beam penetrability and attenuation properties. A half-value layer is usually used to describe the quality of the X-ray beam, especially in the low energy range. Therefore, it can be used to find the X-ray beam with a quality corresponding to monoenergetic beam quality.