# Estimation of Dose Enhancement for Inhomogeneous Distribution of Nanoparticles: A Monte Carlo Study
## 3 Results
enhancement ranges from 5% to 574%, while beyond 400 keV, it becomes less than 10% for all types and concentrations. The maximum dose enhancement factors for both the tumor and non-tumor (healthy tissue) are shown in Figure 6. The maximum enhancement provides a more generalized understanding of different NPs behavior among different energies. For AgNPs, the maximum  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & \multirow{2}{*}{ \begin{tabular}{c} **Concentration** \\ **(mg/g)** \\ \end{tabular}  } & \multicolumn{10}{c}{**Energy (keV)**} \\ \cline{3-14}  & & **50** & **100** & **150** & **200** & **300** & **400** & **600** & **800** & **1000** & **1500** & **2000** & **4000** \\ \hline \multirow{3}{*}{Ag} & 10 & 2.98 & 1.66 & 1.27 & 1.12 & 1.06 & 1.12 & 1.05 & 1.04 & 1.03 & 1.04 & 1.02 & 1.02 \\  & 20 & 4.90 & 2.30 & 1.46 & 1.20 & 1.11 & 1.07 & 1.05 & 1.05 & 1.03 & 1.05 & 1.03 & 1.02 \\  & 30 & 6.74 & 2.90 & 1.65 & 1.31 & 1.11 & 1.05 & 1.05 & 1.04 & 1.04 & 1.04 & 1.03 & 1.03 \\ \hline \multirow{3}{*}{Gd} & 10 & 2.05 & 2.16 & 1.43 & 1.21 & 1.10 & 1.09 & 1.05 & 1.04 & 1.03 & 1.04 & 1.02 & 1.02 \\  & 20 & 3.03 & 3.12 & 1.83 & 1.39 & 1.17 & 1.08 & 1.07 & 1.05 & 1.04 & 1.04 & 1.03 & 1.03 \\  & 30 & 3.95 & 4.20 & 2.22 & 1.58 & 1.1 enhancement occurs at 50 keV and 30 mg/g concentration. GdNPs maximum enhancement occurs at 100 keV and 30 mg/g. At 50 keV, Ag has a slightly lower absorption probability than Au, as shown in Table 2.  
Nevertheless, 50 keV exceeds the K-edge energy for silver but not for gold, leading to the emission of 25 keV characteristic X-ray photons that are likely to be reabsorbed within the tumor, enhancing the dose further. As a result, AgNPs produce a higher DEF \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Energy (keV)**} & \multirow{2}{*}{**Material**} & **Mass Absorption** & **Mass Attenuation** \\  & & **Coefficient (cm\({}^{2}\)/g)** & **Coefficient (cm\({}^{2}\)/g)** \\ \hline \multirow{3}{*}{50} & Ag & 6.06 & 9.44 \\  & Gd & 3.24 & 3.85 \\  & Au & 6.12 & 7.25 \\ \hline \multirow{3}{*}{100} & Ag & 1.06 & 1.47 \\  & Gd & 1.84 & 3.10 \\  & Au & 2.07 & 5.15 \\ \hline \multirow{3}{*}{150} & Ag & 0.36 & 0.54 \\  & Gd & 0.72 & 1.10 \\ \cline{1-1}  & Au & 1.02 & 1.86 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mass absorption and attenuation coefficients for Ag, Gd and Au [58]. Figure 5: DEF along depth for (**a**) 50, (**b**) 100, (**c**) 150 and (**d**) 200 keV for 10, 20, and 30 mg/g concentrations of AuNPs. than AuNPs at 50 keV. As for GdNPs, the absorption probability is lower than AgNPs and AuNPs and no K-shell characteristic X-rays are emitted. Figure 6: The maximum DEF in the tumor for (**a**) AgNPs, (**c**) GdNPs, and (**e**) AuNPs. The maximum DEF in non-tumor volume in the beam path for (**b**) AgNPs, (**d**) GdNPs, and (**f**) AuNPs. At 100 keV, Au has the highest absorption probability and therefore produces the highest DEF, followed by Gd, which possesses a higher absorption probability than Ag. As energy increases further, the absorption probability difference between different NPs types and concentrations gradually decreases. Therefore, DEF becomes less affected by Z. The maximum number of scattering events within the tumor occurs when no NPs are present. This is due to water having the highest electronic density than any of the NP mixtures used in this study. Particle tracking showed that while adding NPs to the tumor reduces the scattering events within the tumor up to 21%, the scattering events occurring outside remained almost constant. This fact shows that scatter radiation does not have a significant impact on enhancing the dose to healthy tissue. Most X-rays are produced at the outer layer, which holds the highest concentration. Therefore, it is very likely for those photons to escape, as will be discussed later. This will increase the healthy tissue dose, especially for those tissues that are very close to the tumor.