## 3 Results
#### Case Study: The Skin Assessment  
Once the cranial vault had been restored, assessing the skin flap was performed, in the first stage, with the in silico analysis. The analysis was carried out in the Geomagic(r) Design X environment. First, the three anatomical planes were defined on the skull to serve as a reference for the definition of the paths. The sagittal plane was defined as the previously computed symmetry plane. The transverse plane was defined as the Frankfurt plane, i.e., the plane drawn through the top point of both the ear canals (the anatomical landmarks named porions) and the bottom border of the left orbital (the anatomical landmark named left orbital). The last plane, the coronal one, was defined perpendicular to the others and passing through the top point of the left ear canal. Since the defect was located in the upper part of the skull, the planes used for the analysis were sagittal and coronal. With the aim to cover a larger region than the defective one, 21 planes parallel to the sagittal and 30 planes parallel to the coronal was defined in both directions concerning the corresponding reference planes. All planes were equally spaced 5 mm apart. The resulting path pattern is shown in Figure 9.  
Once the path pattern had been defined, the difference between lengths of the corresponding paths was calculated. Tables 1 and 2 report such differences for the sagittal-oriented and the coronal-oriented paths. Figure 9 visually resumes the results of the assessment. Red-colored paths represent a skin shrinkage greater than 0.5 mm, and the orange-colored paths a skin shrinkage between 0 and 0.5 mm. Figure 9 shows that the skin shrinkage was mainly located on the lateral and frontal boundaries of the defect, with a particularly critical region along the 20 th coronal path, where more than 4 mm of skin was missing compared to the reconstructed skull shape. The analysis also showed the presence of a region in the center of the defect (frontal paths #12 to #19 and sagittal paths #8 to #12). The skin path was up to 10 mm longer than the corresponding bone-related path. This was probably due to the long-lasting suction action to which the skin flap had been subjected. Figure 9: Paths generated on the skin model. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c}
**1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** & **14** & **15** & **16** & **17** & **18** & **19** & **20** & **21** \\ \hline
0.14 & \(-\)0.02 & \(-\)0.60 & \(-\)3.76 & \(-\)0.82 & 3.26 & 8.08 & 10.52 & 15.46 & 14.88 & 14.09 & 12.13 & 9.37 & 8.05 & 0.98 & 0.12 & \(-\)0.13 & 0.14 & 0.05 & 0.00 & 1.48 \\ \end{tabular}
\end{table} 
Table 1: Sagittal planes paths (black numbers in Figure 9). Green values refer to safe zones, characterized by Red values highlight paths where the difference between corresponding paths is negative (skin shrinkage condition). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c}
**1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** & **14** & **15** & **16** & **17** & **18** & **19** & **20** \\ \hline
0.12 & \(-\)0.05 & \(-\)0.05 & \(-\)0.01 & 0.17 & \(-\)0.09 & \(-\)1.21 & \(-\)0.09 & 2.94 & 3.73 & 6.15 & 8.35 & 10.27 & 10.84 & 8.17 & 8.14 & 7.37 & 6.48 & 4.94 & \(-\)4.64 \\ \hline
**21** & **22** & **23** & **24** & **25** & **26** & **27** & **28** & **29** & **30** & & & & & & & & & & & \\ \end{tabular}
\end{table} 
Table 2: Frontal planes paths (white numbers in Figure 9). Green values refer to safe zones, characterized by Red values highlight paths where the difference between corresponding paths is negative (skin shrinkage condition). This stretched zone could have provided the extra skin enabling a safe craniplasty. Still, the presence of such a particularly impaired scalp did not allow to ensure such an assumption. To further explore and integrate these results, both the patient's defective and restored cranial vaults and her scalp were reproduced.