## 4 Conclusions  
This study applied the use of properties of actual skin layers and the Monte Carlo method and derived quantitative information on the volume fraction of the GNRs injected into the tumor and the intensity of the laser that produces the optimal photothermal therapeutic effect according to the various locations of the tumor.  
First, the apoptosis ratio (\(\theta_{A}\)) was defined as the volume ratio corresponding to the temperature range of 43-50 \({}^{\circ}\)C, where apoptosis occurs in the tumor, to the total volume of the tumor tissue. It was confirmed that there is an intensity of the laser that yields the maximized apoptosis ratio according to the volume fraction of GNRs injected into the tumor. In addition, the intensity of the laser to maximize the apoptosis ratio was derived for the cases in which depth and length of the tumor increase or the volume fraction of GNRs decreases.  
The thermal hazard value (\(\theta_{H,n}\)), which is the degree of thermal damage to surrounding normal tissues, was defined as a weighted sum of the volumes in which the phenomena occur, giving weights to the biological phenomena occurring according to each temperature range. In the case of the thermal hazard value of normal tissue, the result value varies depending on the volume of the normal tissue. Thus, in this study, a distance of 50% of the length of the tumor tissue from the boundary of the tumor tissue was determined as the standard for the normal tissue. From the results, it was confirmed that the higher the volume fraction of GNRs injected into the tumor, the higher the thermal risk of surrounding normal tissues. It was also confirmed that as the length and depth of the tumor increased, the thermal risk of normal tissues decreased.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Geometry of Tumor Tissue**} & \multicolumn{3}{c}{**Optimal Treatment Conditions**} \\ \hline \(D_{t}\) [mm] & \(L_{t}\) [mm] & \(f_{p}\) & \(P\) & **Effective Apoptosis Ratio** \\ \hline \multirow{4}{*}{0.1} & 0.5 & \(10^{-5}\) & 0.08 & 0.7553 \\  & 1.5 & \(10^{-4.5}\) & 0.08 & 0.7944 \\  & 2.5 & \(10^{-5}\) & 0.09 & 0.8501 \\  & 3.5 & \(10^{-6}\) & 0.11 & 0.8751 \\  & 0.5 & \(10^{-5.5}\) & 0.1 & 0.7333 \\  & 1.5 & \(10^{-4.5}\) & 0.1 & 0.7646 \\  & 2.5 & \(10^{-5}\) & 0.11 & 0.8165 \\  & 3.5 & \(10^{-5.5}\) & 0.14 & 0.8479 \\  & 0.5 & \(10^{-6}\) & 0.11 & 0.7315 \\  & 1.5 & \(10^{-6}\) & 0.12 & 0.7363 \\  & 2.5 & \(10^{-5}\) & 0.13 & 0.7961 \\  & 3.5 & \(10^{-5.5}\) & 0.16 & 0.8181 \\  & 0.5 & \(10^{-4}\) & 0.11 & 0.7325 \\  & 1.5 & \(10^{-6}\) & 0.13 & 0.7327 \\  & 2.5 & \(10^{-5}\) & 0.14 & 0.7648 \\  & 3.5 & \(10^{-6}\) & 0.18 & 0.7896 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Best treatment effect condition for various geometry of tumor tissue.  
Lastly, to find conditions that maximize apoptosis in tumor tissue while minimizing thermal damage to surrounding normal tissues, which is the key purpose of photothermal therapy, the optimal therapeutic effect was confirmed according to the intensity of the laser and the volume fraction of GNRs by using an effective apoptosis ratio (\(\theta_{A,eff}\)) that simultaneously considers the apoptosis ratio and the thermal hazard value of surrounding normal tissues for various tumor depths and lengths.  
Through the wide parametric study of the results of this study, it is expected that the effective apoptosis ratio derived through the correlation among the various locations of tumors, the dose of GNRs, and the intensity of the laser can be used as the optimal conditions for improving treatment during photothermal therapy. In addition, it is expected that future studies will be able to confirm the characteristics of each nanoparticle by using various materials of light absorption enhancer and will be able to determine the accumulation and stability of GNPs through collaboration with clinicians.  
Not applicable.  
The authors declare no conflict of interest.