## 4 Results and Discussion
### Energy Threshold of Vessel Hemorrhage  
The area of vessel rupture is closely related to purpura caused by vessel hemorrhage. For the convenience of statistical analysis of the degree of purpura in clinical patients during laser therapy, the area ratio of purpura (bleeding) \(S_{ppu}\) is introduced as:  
\[S_{ppu}=\frac{S_{pu}}{N\cdot S_{spot}}, \tag{15}\]  
where \(S_{pu}\) is the total area of the purpura after laser treatment, \(N\) is the total number of laser pulses, and \(S_{spot}\) is the area of laser spot. For the DSC model in which the epidermis was removed, \(S_{ppu}\) shows the area ratio of bleeding.  
Fifty patients were treated with a 595 nm PDL in Laser Treatment Center, Department of Dermatology, Second Affiliated Hospital of Xi'an Jiaotong University to establish the relationship between \(S_{ppu}\) predicted through numerical simulation and the treatment criterion based on clinical \(S_{ppu}\). The study included 34 female and 16 male PWS patients, with phototypes II-IV on the Fiztpatrick scale and an average age of 28. \(S_{pu}\) was measured immediately after each patient was treated (Figure 14a). \(S_{spot}\) is the circular area with a spot diameter of 1 mm, and \(N\) is related to the morphological characteristics of vascular lesions.  
The reasonable range of \(S_{ppu}\) after treatment could be obtained in terms of the degree of disease recovery at the return visit after 1 month of treatment (Figure 14b). If the laser fluence was too high, the bleeding area was also too large, and side effects such as erythema, scar, or pigmentation appeared after treatment. If the re-examination showed that the scar remained visible, a patient was included in the group with side effects. If no side effects were found during the return visit, patients were divided into four groups based on the clearance rate. Therefore, a total of five groups were set as follows: (a) no effect (clearance rate \(<\) 30%); (b) weak effect (30% \(\leq\) clearance rate \(<\) 60%); (c) marked effect (60% \(\leq\) clearance rate \(<\) 90%); (d) rehabilitation (clearance rate \(\geq\) 90%); and (e) side effects (erythema, scar, or pigmentation).  
Only a suitable laser fluence could achieve an acceptable therapeutic effect. The medical community in dermatology has reached a consensus on the effectiveness in treating PWS nevus, that is, the effective cure rate is equal to the sum of the rate of marked effect and rehabilitation. Figure 15 shows the mean and confidence interval of \(S_{ppu}\) of the five groups. Mean \(S_{ppu}\) increases almost uniformly as the laser fluence increases, and the curative effect changes gradually from no effect to side effects. Ideal \(S_{ppu}\) should be higher than \(S_{ppu}\) of marked effects (c) and lower than \(S_{ppu}\) of side effects (d), that is, higher than 13.8% and lower than 25.1%, as shown in Figure 15. The volume fraction of lesions in patients with moderate PWS nevus is approximately 20%, which is twice the volume fraction of the DSC vessels; hence, the appropriate range of \(S_{ppu}\) in computation based on the DSC model should be between 6.9%  
Figure 14: Purpura and curative effect of patients with port wine stains and treated with a 595 nm pulsed dye laser (**a**) Purpura occurs immediately after irradiation. (**b**) Return visit after 1 month of treatment (marked effect).  
and 12.6%. Laser fluence leading to 6.9% \(\leq S_{\mathit{7 pu}}\leq\) 12.6% in the DSC model experiment is defined as the effective laser fluence \(E_{\mathit{eff}}\), i.e., the fluence threshold of appropriate vessel hemorrhage.