## 3 Validation of CCPD Model
### Validation of the CCPD Model  
Both the skin model and the damage model are considered as important factors in the computation. In this section, three computational models are made by combination from either of the two blood vessel geometries and the two damage models. For simplicity, the three models were referred to as models A, B, and C, which are a PD model with an ideal vessel (a straight cylinder), a PD model with a real vessel, and a CCPD model with a real vessel. With \(P\) = 2500 Pa as the pressure damage threshold [7], the location and area of the vessel rupture in the three models were computed and compared with those of the experiments. \begin{table}
\begin{tabular}{c c c c} \hline  & **Property** & **Dermis** & **Blood** \\ \hline \multirow{4}{*}{Optical properties} & Absorption coefficient, \(\mu_{\mathrm{a}}\)/cm\({}^{-1}\) & 20 & 49.3 \\  & Scattering coefficient, \(\mu_{\mathrm{s}}\)/cm\({}^{-1}\) & 460 & 466 \\  & Anisotropy index, \(g\) & 0.8 & 0.995 \\  & Refractive index, \(n\) & 1.37 & 1.33 \\ \hline \multirow{3}{*}{Thermal properties} & Density, \(\rho\)/kg\(\cdot\)m\({}^{-3}\) & 1090 & 1060 \\  & Thermal conductivity, \(k\)/kW\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\) & 0.41 & 0.55 \\ \cline{1-1}  & Specific heat, \(c\)/kg\({}^{-1}\cdot\)K\({}^{-1}\) & 3500 & 3600 \\ \hline \end{tabular}
\end{table} 
Table 1: Optical and hydrodynamic properties of dermis and blood [7]. Figure 6: Local Gaussian curvature obtained from the mesh with different intervals. Figure 7: Influence of the mesh on the calculation of the Gaussian curvature on the bifurcated vessels. Based on our computation, the standard deviation of the Gaussian curvature (StdGC) of a single vessel ranged from 10 to 80. In this study, the blood vessels with a diameter of \(100\pm 10\)\(\upmu\)m were divided into three groups in terms of their StdGC: small (\(0\leq\) StdGC \(<25\)), medium (\(25\leq\) StdGC \(<50\)), and large (StdGC \(\geq 50\)). For each group, one typical vessel was chosen to analyze pressure distribution. Figure 8 shows the experimental snapshots and the reconstructed blood vessels. For the convenience of model comparison, the position of the ideal cylindrical vessel was adjusted to coincide with the reconstructed vessel (Figure 9). Figures 10-12 show the wall pressure distribution of the three models. Model A has the largest rupture area, whereas model B has the smallest rupture area because the tortuosity of the real vessel disturbs the blood flow, which restricts the growth of large bubbles or breaks them into small bubbles. Figure 8: Responses of blood vessels irradiated with a 595 nm laser with a pulse width of 6 ms (yellow arrow refers to the irradiated reconstructed vessel) (**a**) Before irradiation (stdGC = 20.5); (**b**) reconstructed model (stdGC = 20.5); (**c**) after irradiation (stdGC = 20.5); (**d**) before irradiation (stdGC = 41.3); (**e**) reconstructed model (stdGC = 41.3); (**f**) after irradiation (stdGC = 41.3); (**g**) before irradiation (stdGC = 64.5); (**h**) reconstructed model (stdGC = 64.5); and (**i**) after irradiation (stdGC = 64.5). Figure 9: Reconstructed vessel models with different curvatures and corresponding cylindrical vessel models (the dark red vessel is the 3D reconstructed vessel, and the light red vessel is the corresponding cylindrical vessel). The position of the ideal vessel was adjusted to coincide with the reconstructed vessel. Therefore, the contact area between the region of high pressure (gas phase) and the blood vessel wall reduces, leading to a small rupture area. The rupture area of the real vessel in model C is between those of models A and B, and the rupture site agrees with the large Gaussian curvature spot on the wall surface, such as the saddle point. Figure 8c,f,i illustrate that the high-pressure position and area in model C (the present CCPD model) are more consistent with those of rupture and bleeding in the animal experiments than those in the two other models. This finding confirms the validity and feasibility of the new model in predicting vessel hemorrhage.