## 1 Introduction
[PERSON] et al. [24] developed a numerical analysis model on the tumors injected with GNPs and confirmed the temperature distribution of tumors located on the skin surface and the surrounding tissues through the Monte Carlo method. The temperature in the medium for the size of various tumors, the intensity of the irradiated laser, and the volume fraction of GNPs in the tumor over time were evaluated, and thermal damage to the tumor and surrounding tissues was confirmed through the Arrhenius equation. [PERSON] et al. [25] confirmed the effect on the gold/gold sulfide (GGS) nanoshells in the NIR laser in photothermal therapy through numerical analysis and experiments. In their study, the intensity and period of the laser were adjusted, and the temperature distribution of the medium was confirmed according to whether GGS was  
Figure 1: Absorption coefficient of Hb, HbO\({}_{2}\), water for various wavelengths [18]. injected or not. In summarizing the studies through experiments and numerical analysis, it was confirmed that the tumor was killed by irradiating a laser to the tumor injected with the light absorption enhancer, and the temperature distribution in the medium according to various conditions was confirmed. Further, the thermal damage of the medium was confirmed through the Arrhenius equation. Although the Arrhenius damage integral is an appropriate indicator for quantifying thermal damage, this equation represents the thermal damage of tissues over time. It is challenging to quantitatively express the stages of various thermal damages to tissues determined by the level of temperature. Therefore, it is challenging to find the area corresponding to the apoptosis targeted in this study. It was also not possible to quantitatively present the results of apoptosis according to the size of the tumor, the intensity of the laser, the volume fraction of GNPs in the tumor, and the amount of thermal damage to surrounding normal tissues. In addition, skin cancer tumors exist at various depths from the skin surface, and the skin layer consists of several layers with different physical properties. There is insufficient research on the treatment of tumors located at various depths while considering the physical properties of each skin layer. Lastly, even if the temperature in the tumor reaches between 43 and 50 \({}^{\circ}\)C, which corresponds to the temperature range of apoptosis, whether apoptosis proceeds immediately or begins to proceed after a certain period has not been clearly investigated. Accordingly, in this study, the absorbed heat quantity and temperature distribution in the steady-state situation were evaluated according to changes in the various intensities of lasers, tumor location, size, and volume fraction of GNPs through numerical analysis, targeting skin cancer tumors at a certain depth from the skin surface to the reticular dermis layer. Therefore, this study attempted to estimate the apoptosis of the tumor, the thermal damage on the tumor, and surrounding normal tissues. To this end, we present the optimal laser intensity and the volume fraction of GNPs that produce the optimal photothermal therapy using the four variables proposed in our previous work.