## 4 Results and Discussion
### Effect of Melanin Content in the Epidermis on Laser Fluence Selection  
The effects of melanin content in the epidermis were investigated from 1% to 9% on a real vessel under 595 nm PDL irradiation. Figure 17 shows \(S_{rpu}\) of a vessel buried in the median layer (0.375 mm) at \(f_{m}\) of 1% or 5%. The laser fluence of the vessel rupture increases with the melanin content. For example, in the blood vessel of stdGC = 41.3, the bleeding threshold increases from 4 J/cm\({}^{2}\) to 6 J/cm\({}^{2}\) when \(f_{m}\) increases from 1% to 5% because the light absorption capacity of the epidermis increases with melanin content (Table 2). Subsequently, the relevant absorption ratio of the blood vessel decreases. Therefore, a high laser fluence is required to rupture the targeted blood vessel. With an increase in laser fluence, \(S_{rpu}\) of the vessel with different values of stdGC continues to increase and gradually achieves a significant effect (6.9% \(<S_{rup}<\) 12.6%). However, when the laser fluence continues to increase, \(S_{rup}\) rapidly exceeds the upper limit (12.6%), and the skin experiences a side effect.  
For \(f_{m}=1\%\), three vessels with different values of stdGC simultaneously reach the rupture threshold at \(E=4\) J/cm\({}^{2}\). Among them, the vessels with a large stdGC have a large Gaussian curvature at the saddle point of the vessel surface. As a consequence, rupture and bleeding occur easily. When the laser fluence exceeds 5 J/cm\({}^{2}\), the rupture area of the vessel with a small stdGC increases faster than that with a large stdGC because the lumen of the vessel with a small stdGC is relatively straight. As a result, the disturbance to the blood flow and the generated bubbles is weak. The bubbles grow and come in contact with the vessel wall without restriction, leading to a large high-pressure area on the vessel wall and rupture. At \(f_{m}=1\%\), when the laser fluence reaches 9 J/cm\({}^{2}\), the gap in the rupture area of the three vessels is sharply narrowed because high energy greatly reduces the curvature effect. Similar results are obtained at \(f_{m}=5\%\).  
In laser dermatologic surgery, CSC with R134a is an efficient technique to avoid epidermal damage among white people because of light energy absorption by melanin. However, even with CSC protection, people with dark pigmentation may suffer from epidermal damage. Previous studies showed that thermal damage occurs when the central temperature of the epidermis \(T_{cc}\) is higher than 80 \({}^{\circ}\)C at the end of laser irradiation [40]. Therefore, the PDL fluence threshold of epidermal injury \(E_{e,R134a}\) is defined as the laser fluence leading to \(T_{cc}=80\)\({}^{\circ}\)C with R134a cooling. \(E_{e,R134a}\) increases with an increase in the cooling effect of cryogen. \(E_{e\!f\!f}\) should be higher than \(E_{e,R134a}\) to ensure the safety of the epidermis in the treatment of vascular lesions.  
Figure 17: Purpura rate of blood vessels at a depth of 0.375 mm (the laser fluence of vessel rupture is marked by the black circles): (**a**) \(f_{m}=1\%\) (**b**) \(f_{m}=5\%\).  
Figure 18 shows \(E_{\mathit{eff}}\) at different melanin contents and a vessel depth of 0.375 mm. \(E_{\mathit{eff}}\) varies by 1-2 J/cm\({}^{2}\) with the degree of curvature regardless of \(f_{m}\). With the present CSC technology, for white (\(f_{m}=1\%\)) and light-yellow (\(f_{m}=3\%\)) people, the epidermis remains undamaged when \(E_{\mathit{eff}}\) is used. For dark-yellow people (\(f_{m}=5\%\)), \(E_{\mathit{eff}}\) of a large-stdGC vessel exceeds \(E_{\mathit{r},R134a}\). Therefore, \(E_{\mathit{r},R134a}\) should be improved by strengthening the cooling capacity of cryogen. For brown (\(f_{m}=7\%\)) and black (\(f_{m}=9\%\)) people, \(E_{\mathit{eff}}\) is higher than \(E_{\mathit{r},R134a}\). The near-infrared laser instead of PDL should be used to treat darkly pigmented patients because of its weak absorption of melanin.