## 2 Materials and Methods
### In-Silico Skin Assessment  
The first step is a fully in silico procedure to provide a quantitative comparison between the actual scalp and the scalp needed to cover the restored cranial shape. It aims to investigate the presence of critical regions where the skin flap could be shrunken. The whole analysis can be carried out in CAD software by working on the 3D models obtained applying the traditional design framework for AM-fabricated cranial implants. The analysis is carried out by comparing the 3D model of the actual internal surface of the scalp and the reconstructed cranial vault. Both the 3D models can be retrieved from the patient's diagnostic image; the defect can be restored by following one of the procedures presented in the literature and discussed in the introduction. The models involved in the analysis must be registered, i.e., they must have the correct spatial relationship with each other. Usually, all the models are retrieved from the same diagnostic study, and, consequently, they are already registered. The analysis is based on the assumption that the internal surface of the scalp must have the same dimension or being larger than the outer surface of the skull with which it is in contact. Such comparison is carried out by measuring the length of a set of corresponding paths obtained on both surfaces. Operatively, the paths are found by defining two perpendicular sets of parallel planes (Figure 3). The intersection of each plane with the skin surface or with the reconstructed surface defines a path. As a result, two patterns of corresponding paths are obtained, as shown in Figure 4. The more the planes, the higher the resolution of the analysis. The planes are defined parallel to the three anatomical planes (sagittal, coronal, and transverse). Depending on the location of the defect, only two planes groups must be considered. For a lateral defect, planes parallel to coronal and transversal; for a frontal or posterior defect, planes parallel to sagittal and transversal; for a defect in the upper part of the cranial vault, planes parallel to sagittal and coronal planes must be considered. Figure 3: Perpendicular sets of parallel planes created in a CAD environment to map the defect area. To make the corresponding paths directly comparable, identical extremities should be identified. Accordingly, the user needs to define the endpoints of the paths outside the defective region where the surfaces are perfectly superimposed. This way, the endpoints belong to both surfaces and, consequently, to both the corresponding paths. Once that the extremities are identified, the paths can be trimmed to obtain their final definition. Subsequently, typical CAD functions can be used to query all the lengths of the so-generated trimmed paths and compute the differences between the lengths of each couple of corresponding paths. These data are then presented to the user in a series of tables and used as quantitative indications about the possible shrinkage of the scalp. If the analysis shows, for each path, a value of skin tissue higher than the one required by the preliminary skull reconstruction (i.e., each path on the inner surface of the scalp is longer than the corresponding path on the reconstructed skull), the device can be designed as typical on the restored skull, and the cranioplasty can be done without risk of subsequent complications of the skin flap. Otherwise, in the case of comparable values or smaller scalp length, the assessment provides the surgeon quantitative indications on the location and severity of any potential skin shrinkage. This information can help find alternative surgical pathways or constructive solutions for corrective devices that avoid using expanders. It is worth noting that, because of the difficulty to evaluate and simulate in silico the actual quality of the scalp and take its mechanical properties into consideration, assumptions on the skin flap elasticity are entirely avoided by this procedure.