## 2 Materials and Methods
### Physical Simulation  
To verify and integrate the results provided by the in silico simulation, the procedure considers an additional step with introducing a physical simulation on a patient-specific phantom reproducing the defective bone, the cranial implant, and the scalp. The authors have experimented with many materials and technologies to find the correct balance between costs, fidelity and times required for producing the different components. One of the cheapest and effective is by manufacturing the bone out of plastic via AM and the skin by casting a silicone with skin-like properties. The molds for the skin can also be produced via AM, which results in the best choice due to the limited costs associated with production in limited numbers and for the complex shapes that must be fabricated. The most suitable AM technologies for fabricating the skull and molds are fused-filament fabrication (FFF) or selective laser sintering (SLS). No specific properties are required from the plastic material. In both cases, state-of-the-art machines are perfectly capable of assuring the required  
Figure 4: (**a**) Paths created on the skin surface; (**b**) paths created on the reconstructed skull. accuracy, which could be estimated in a maximum deviation of 0.5 mm point-to-point from the digital surface. Regarding the scalp, it is important to mimic its real geometry (easily retrieved from the CT scan). Indeed, the quality and resolution of the anatomy acquisition affect the quality of the resulting virtual and physical model, and, consequently, the effectiveness of the subsequent evaluations. For this reason, CT is the data source of choice as it provides the data with the highest resolution. Nevertheless, an extreme resolution is not necessary. According to the authors' experience, a slice thickness up to 2 mm (which is an average resolution for a CT acquisition) is sufficient to obtain a satisfactory quality of the resulting 3D anatomic model. Accordingly, whenever CT images of the patient are available, there is usually no need for a new, higher resolution acquisition. The material used to reproduce the skin should be easily cut and sutured to allow the surgeon to perform all the required operations. The choice of a silicone able to effectively mimic the properties of the skin (especially by not overestimating its elasticity) is obviously the critical task. Much literature deals with this topic and can be taken as a reference to help in this choice [16]. To assemble the phantom, the skull (defective or restored) and the scalp are mounted together to replicate the patient's head (see Figure 5 for a schematic representation of the phantom). For the skull, a section performed on the axial plane is typically the best choice to isolate the area of the cranium that is of interest. This allows for an easier model to fabricate; whenever possible, it is convenient to eliminate the anterior skull bones to obtain simple anatomy. The models are fabricated, taking into consideration that the silicone skin and the skull should be placed in the correct position both in the presence of the defect and of the implant. Accordingly, the skin should possibly embrace the plastic skull around the area of the axial cut (red detail in Figure 5) to assure a correct position. Thanks to these models, surgeons can confirm the effectiveness of the assumptions suggested by the in silico analysis. In addition, physical reproduction is a powerful tool that integrates the data provided by the in silico analysis by introducing the mimicry of anatomical tissues and their mechanical properties. Moreover, surgeons can develop and simulate alternatives surgical strategies as well as devices to find the right combination that maximizes the chances of a positive outcome.