## 3 Results
### Parallel Blood Vessels  
First, we studied the skin model with parallel vessels because it is the basis for investigating other increasingly complex shading. A skin model with two cylindrical parallel vessels with a diameter of 120 \(\upmu\)m is shown in Figure 9. The axes of the two vessels are along the \(y\)-axis. The angle between the center-center line of the two circles and the horizontal line is defined as the shading angle (\(0\leq\theta_{shad}\leq 90^{\circ}\)) (Figure 9a). Parallel vessel pairs are represented by \(\theta_{shad}\) and the vessel distance \(H_{shad}\) (Figure 7a). The position of the superficial vessel is fixed at z = 250 \(\upmu\)m, x = 700 \(\upmu\)m to explore the effect of the deep vessel's position. For a convenient comparison, the energy deposition of a deep vessel before and after shading was calculated when \(H_{shad}\) changed from 150 \(\upmu\)m to 350 \(\upmu\)m or \(\theta_{shad}\) from 0\({}^{\circ}\) to 90\({}^{\circ}\). The deep vessel is fully shaded at \(\theta_{shad}\) = 90\({}^{\circ}\).  
Figure 10 shows the ratio of deep vessel deposition with shading to that without shading at different shading angles and distances. The shading effect is apparent with a large \(\theta_{shad}\) and a low \(H_{shad}\). For example, energy loss in the deep vessel with shading is only 8% (\(\omega\) = 8%) at \(\theta_{shad}\) = 0\({}^{\circ}\) and \(H_{shad}\) = 350 \(\upmu\)m. By contrast, it increases to 37% (\(\omega\) = 63%) at \(\theta_{shad}\) = 90\({}^{\circ}\) and \(H_{shad}\) = 150 \(\upmu\)m (Figure 10). This phenomenon can be explained by scattering theory. When incident light enters a turbid biological tissue, it will scatter and deviate from the original direction. For the shading angle, more photon energy is absorbed by the shallow blood vessel as \(\theta_{shad}\) increases. Subsequently, energy deposition in the deep blood  
Figure 8: Relative error distribution in 1\({}^{\circ}\) annular cylinder region.  
Figure 9: Cross-sectional view of the skin model with parallel PWS vessels.  
vessel decreases. Consequently, the scattered light transmits randomly and is less likely to propagate around the superficial vessel and be absorbed by the deep vessel. As the energy loss caused by the shading effect increases, the deep vessel receives insufficient thermal damage. Therefore, high laser fluence is required to rupture deeply buried or (and) fully shaded blood vessels.  
Figure 11 shows the energy deposition directly below the center of the beam at \(\theta_{shad}\) = 90\({}^{\circ}\) with \(H_{shad}\) of 150, 250, and 350 \(\upmu\)m. When the two vessels are arranged along the z direction, photon deposition in the deep vessels decreases gradually from 5.4% to 4.1% with an increase in \(H_{shad}\) from 150 \(\upmu\)m to 350 \(\upmu\)m (not shown) because photon energy attenuates less by scattering before reaching the relatively shallow-buried vessel. However, the absorption peak of the deep vessels is only approximately 60 J/cm\({}^{3}\) regardless of \(H_{shad}\). This value is considerably less than 140 J/cm\({}^{3}\) in the shallow vessel. This finding indicates that the deep vessel is difficult to damage through complete shading (\(\theta_{shad}\) = 90\({}^{\circ}\)) of the shallow vessel.