# Hybrid Spine Simulator Prototype for X-ray Free Pedicle Screws Fixation Training
## 3 Results  
The target visualization errors (both TVE2D and TVE3D) were estimated for each spine pose for a total of: 40 measurements for the lateral camera, \(\text{Cam}_{\text{Lat}}\) (4 markers detected in each of the 10 images); and 80 measurements for the top camera, \(\text{Cam}_{\text{Top}}\) (8 markers detected in each of the 10 images). Table 1 summarizes mean (\(\upmu\)) and standard deviation (\(\sigma\)) values for each of the 10 images. The total error was calculated for each vertebra (for a single spine pose), three times for each of the landmarks (landmarks on the vertebral body, pedicle and spinous process) for a total of 36 measurements. Table 2 summarizes mean (\(\upmu\)) and standard deviation (\(\sigma\)) values for each vertebra. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & **Pos 1** & **Pos 2** & **Pos 3** & **Pos 4** & **Pos 5** & **Pos 6** & **Pos 7** & **Pos 8** & **Pos 9** & **Pos 10** & **Total** \\ \hline \multirow{4}{*}{\(\text{Cam}_{\text{Lat}}\)} & TVE2D & \(\upmu\)= 8.1 & 9.1 & 10.1 & 10 & 6.5 & 8.8 & 7.4 & 7.5 & 5.5 & 6.6 & **8** \\  & (pixel) & \(\sigma\)= 7.7 & 7.8 & 9.9 & 9.2 & 5.5 & 9.2 & 8.4 & 8.5 & 6.1 & 6.4 & **4.1** \\ \cline{1-1} \cline{2-11}  & TVE3D & 0.7 & 0.9 & 1 & 1 & 0.6 & 0.9 & 0.8 & 0.8 & 0.6 & 0.7 & **0.8** \\  & (mm) & 0.3 & 0.4 & 0.4 & 0.7 & 0.3 & 0.4 & 0.3 & 0.4 & 0.3 & 0.5 & **0.4** \\ \hline \multirow{4}{*}{\(\text{Cam}_{\text{Top}}\)} & TVE2D & 5.9 & 6.5 & 4.9 & 4.7 & 4.5 & 6.6 & 6.6 & 3.9 & 4.1 & 6.8 & **5.5** \\  & (pixel) & 2.8 & 3.8 & 3.2 & 3.6 & 1.2 & 3.4 & 3.2 & 2.2 & 2.2 & 3.1 & **3** \\ \cline{1-1} \cline{2-11}  & TVE3D & 1.7 & 1.9 & 1.5 & 1.4 & 1.4 & 2 & 2 & 1.1 & 1.3 & 2 & **1.6** \\ \cline{1-1}  & [mm] & 0.8 & 1.1 & 0.9 & 1.1 & 0.4 & 1 & 1 & 0.6 & 0.7 & 0.9 & **0.4** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mean (\(\upmu\)) and standard deviation (\(\sigma\)) of target visualization errors (TVE2D and TVE3D values for each of the 10 poses. The obtained TVE3D and targeting errors confirm the feasibility of the proposed strategy to track the vertebral models/surgical tools, and to coherently visualize them both in AR Visualization mode and in Virtual X-ray Visualization as an aid for the training of pedicle screw implantation in lumbar vertebrae. The errors are indeed lower than half the size of lumbar pedicle radius which, according to [40], is 6.4-6.5 mm for L1 (left and right pedicle, respectively) increases from L1 to L4, and increased sharply at L5 reaching a mean size of 17.5-17.7 mm (left and right pedicle, respectively). The TVE3D of the Cam\({}_{\text{Top}}\) is an estimation of the error in the registration of vertebral models in the global (Cam\({}_{\text{Top}}\)) reference systems (Vertebra Registration Error). As for the targeting error we should consider the following sources of error: Vertebra Registration Error, error in the localization of the ArUco marker used to track the surgical tool in the global (Cam\({}_{\text{Top}}\)) reference system, inaccuracy of the users in the alignment of the tool tip with the marker, and finally the error in the tool calibration. The instrument calibration is required to infer the pose of the tool tip from the pose of the detected marker. In this study, we used a built-in marker to track the trocar mockup and we derived the calibration matrix from the CAD (computer-aided design) project; a procedure such as the pivot calibration [41] can be used instead for localizing a real surgical tool using a marker whose relative pose with the respect to the tool tip is unknown a priori. Given the obtained TVE3D and targeting error we can assume that, even using a real surgical tool, the final accuracy of the system would be enough for the proposed application (screw implantation in lumbar vertebrae). Figure 10 illustrates the simulated lateral (Figure 10a) and anterior-posterior (Figure 10b) fluoroscopic view of the spine during the targeting of one marker with the Jamshidi trocar mockup.