## 4 Discussion  
### Dependence of DDER on Treatment Depth  
It can be seen in Figure 1a,b that the DDERs were larger than one, when the depth ranges were 4-6 cm and 4-8 cm, respectively. However, when the depth was more than 6 and 8 cm for the FF and FFF photon beams, the DDERs were less than one, showing that the presence of Au NPs in water could not increase the dose in those depth ranges (i.e., 6-20 cm and 8-20 cm). The addition of Au NPs in water not only enhanced the dose, but also attenuated the photon beam along the depth. When the depth was shallow (i.e., 4-6 and 4-8 cm in Figure 1a,b), the effect of DDE was larger than the beam attenuation. The presence of low-energy photons in the beam at the shallow depth resulted in a dose enhancement [19]. On the other hand, when the depth was deeper and beyond 6 and 8 cm, the effect of beam attenuation became more significant. It is because most of the low-energy photons were absorbed in that depth range, leading to the DDER smaller than one [39]. This shows that the dose in an Au NP-added medium was smaller than the dose in water. In nanoparticle-enhanced radiotherapy, this happens when the NPs cannot be perfectly uptaken by the tumour, leaving particles distributed between the patient surface to the target [40]. This accumulation of NPs in the normal tissues would attenuate the photon beam targeting the tumour, and result in a lower DDE. However, from Table 1, the EEDRs for the FFF photon beams were larger than the FF, for the Au NPs in the depth range  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**(a)** & **10 MV FF** & **10 MV FFF** & **10 MV FF** & **10 MV FFF** & **10 MV FFF** \\ \hline Concentration & Au NPs & & Au NPs & Fe\({}_{2}\)O\({}_{3}\) NPs & Fe\({}_{2}\)O\({}_{3}\) NPs & \\
3 & & 1.000 & & 1.001 & 0.999 & 0.999 \\
7 & & 1.001 & & 1.003 & 0.998 & 0.998 \\
18 & & 1.002 & & 1.008 & 0.996 & 0.995 \\
30 & & 1.003 & & 1.013 & 0.993 & 0.992 \\
40 & & 1.004 & & 1.015 & 0.992 & 0.990 \\ \hline
**(b)** & **10 MV FF** & & **10 MV FFF** & **10 MV FF** & **10 MV FFF** & \\ \hline Concentration & Au NPs & & Au NPs & Fe\({}_{2}\)O\({}_{3}\) NPs & & Fe\({}_{2}\)O\({}_{3}\) NPs & \\
3 & & 1.000 & & 1.000 & 0.997 & 0.999 \\
7 & & 0.998 & & 0.999 & 0.997 & 0.996 \\
18 & & 0.996 & & 0.998 & 0.992 & 0.991 \\
30 & & 0.992 & & 0.997 & 0.986 & 0.984 \\
40 & & 0.989 & & 0.994 & 0.983 & 0.980 \\ \hline
**(c)** & **10 MV FF** & & **10 MV FFF** & **10 MV FF** & **10 MV FFF** & \\ \hline Concentration & Au NPs & & Au NPs & & Fe\({}_{2}\)O\({}_{3}\) NPs & & Fe\({}_{2}\)O\({}_{3}\) NPs & \\
3 & & 0.998 & & 0.999 & 0.998 & 0.998 \\
7 & & 0.996 & & 0.997 & 0.995 & 0.995 \\
18 & & 0.991 & & 0.992 & 0.988 & 0.987 \\
30 & & 0.984 & & 0.985 & 0.980 & 0.978 \\
40 & & 0.977 & & 0.979 & 0.974 & 0.971 \\ \hline
**(d)** & **10 MV FF** & & **10 MV FFF** & **10 MV FF** & **10 MV FFF** & **10 MV FFF** & \\ \hline Concentration & Au NPs & & Au NPs & & Fe\({}_{2}\)O\({}_{3}\) NPs & & Fe\({}_{2}\)O\({}_{3}\) NPs & \\ (mg/mL) & & & & & & \\
3 & & 0.998 & & 0.996 & 0.998 & 0.996 \\
7 & & 0.995 & & 0.995 & 0.994 & 0.992 \\
18 & & 0.986 & & 0.985 & 0.984 & 0.982 \\
30 & & 0.976 & & 0.973 & 0.973 & 0.971 \\
40 & & 0.967 & & 0.966 & 0.962 \\ \hline \hline \end{tabular}
\end{table}
Table 1: DDERs with variations of the NP material (Au and Fe\({}_{2}\)O\({}_{3}\)) and concentration for depth equal to (**a**) 5, (**b**) 10, (**c**) 15 and (**d**) 20 cm using the 10 MV FF and 10 MV FFF photon beams.  
between 5 and 15 cm. Since 5-15 cm is the typical treatment depth in radiotherapy [41], it can be seen that using the FFF photon beams can improve the low DDE due to beam attenuation.  
Similar results were observed in Figure 2a,b for the Fe\({}_{2}\)O\({}_{3}\) NPs. However, unlike Figure 1a,b, the DDER was all smaller than one in the depth range of 4-20 cm, using the FF and FFF photon beams. The DDE effect for the Fe\({}_{2}\)O\({}_{3}\) NPs is therefore lower than the Au NPs.