## Materials and Methods
### Overlapping Models and Calculation of the Volumes  
GOM Inspect (GOM GmbH, Braunschweig, Germany) is the software dedicated to the analysis of 3D measuring data for quality control, product development, and production. GOM software is used to evaluate 3D measuring data derived from GOM systems, 3D scanners, laser scanners, CTs and other sources, such as _STL (stereolithography file type, made basing on Standard Triangle Language)_ models. The procedure of the overlapping of volumes is one among many possible methods to evaluate the volumetric bone growth that took place following the SB implant. Two 3D models are needed to perform the overlapping: The one built through pre-operation CT and the one constructed through post-operation CT.  
Once models reproduce the patient's anatomy faithfully, it is possible to import the two geometric models into GOM Inspect to measure the differences between them. This image matching has to be done on images taken before the surgery _versus_ those taken at least six months after when the patient is undergoing a control CT: Such timeframe allows seeing the beginning of the remodeling process supported by SB [29]. Moreover, this step overlap is necessary to get a comparison between the two models. The reference system of one model is converted into the reference system of the other model, to get a correct overlapping and avoid errors. It is very important to have a perfect alignment of the measuring model to the nominal model. Figure 2 shows an example of the pre-operative model imported as a mesh file (in gray) and the post-operative template imported as a CAD body file (in blue).  
Figure 2: Example of the pre-operative model imported as a mesh file (in gray) and the post-operative template imported as a CAD body file (in blue).  
It is crucial, in the overlapping procedure, to perform all possible alignment modes. Two types of alignment have been developed: 1) automatic pre-alignment and 2) alignments made by points. Pre-alignment is an automatic alignment created by the software through robust, effective algorithms. It works by recognizing three-dimensional features, such as edges or angles. Alignment by point consists of defining in the reference model a number of relevant anatomical points that are constant and also easily identifiable in the control model. The chosen points do not change in the two models enabling the chosen points to be perfectly aligned. After alignment, measurements are performed thanks to the GOM Inspects tools, which also provides the models' deviations and the measurements of increased bone volume (\(\Delta\)V). That \(\Delta\)V is the bone material regenerated from the SB graft.  
The other method used to evaluate the volumetric bone growth is the Boolean subtraction between the two solid models. The software that carries out the subtraction is 3-Matic Medical (Materialise). With 3-Matic, the Boolean subtraction is performed on the 3D models obtained starting from two CT scans: one before the surgery and the other one always at least 6 months after the surgery. After an automatic alignment, the models obtained from the CT scan before surgery is subtracted from the model obtained from the CT scan after surgery. The software shows the remaining volume, which coincides with the bone regenerated (Figure 3).