# Personalised High Tibal Osteotomy Surgery Is Accurate: An Assessment Using 3D Distance Mapping
## 3 Results
### DMA Variables  
The number of mesh points contained in the STL files for the three stages were (given as median values and mean \(\pm\) standard deviation, respectively) 123,542 and 105,081.9 \(\pm\) 45,068.8 for PRE tibia, 125,680 and 108,409.8 \(\pm\) 45,982.0 for POST tibia, 9617 and 11,888.1 \(\pm\) 6007.7 for PLA tibia, 24,502 and 24,375.3 \(\pm\) 922.0 for PLA fixation plate and 19,280, and 17,494.3 \(\pm\) 5165.1 for POST fixation plate. In addition, the triangle densities of the surface meshes described in the same STL files (defined as the total number of mesh STL triangles over the total STL area in mm\({}^{2}\)) were also calculated. These are also given as median values and mean \(\pm\) standard deviation, with units triangles/mm\({}^{2}\), respectively, and reported as follows: 10.7 and 9.2 \(\pm\) 3.7 for PRE tibia, 10.7 and 9.1 \(\pm\) 3.7 for POST tibia, 0.7 and 0.8 \(\pm\) 0.3 for PLA tibia, 13.8 and 13.5 \(\pm\) 0.7 for PLA fixation plate, and 11.2 and 10.1 \(\pm\) 2.9 for POST fixation plate. Reconstruction of the 3D bone model derived from image segmentation did not result in significant differences between the PRE and POST tibia, both in terms of number of mesh points and triangle density. Figure 3 provides boxplots showing the values of \(\overline{\text{PD}},\overline{\text{ND}}\), and DSD for all DMA comparisons, while numerical values are given in Table 1. In general, all these values were low, indicating a very high amount of correspondence between the surfaces considered in each comparison. 1. Overall, a good replication of PLA tibia morphology was achieved in POST (Figures 3 and 4), with average values for \(\overline{\text{PD}}\) of 1.4 mm and \(\overline{\text{ND}}\) of \(-\)0.9 mm, associated with very small DMA standard deviation (DSD average value 1.6 mm) over the entire patient cohort (Table 1). Most points were in the safe zone (Table 2), although discrepancies were observed, mainly due to the difficulty of excluding the bone allograft (used to fill the osteotomy cut which is the standard practice of the operating surgeon) during image segmentation, thus altering the morphology of the area around the osteotomy in POST with reference to the corresponding one in PLA. \begin{table}
\begin{tabular}{c c c c c} \hline
**DMA Comparison** & **Variable** & **Mean** & **Median** & **Standard Deviation** \\ \hline \multirow{4}{*}{(i) POST tibia vs. PLA tibia} & PD & 1.4 & 1.4 & 0.5 \\ \cline{2-5}  & ND & \(-\)0.9 & \(-\)0.8 & 0.4 \\ \cline{2-5}  & DSD & 1.6 & 1.4 & 0.5 \\ \cline{2-5}  & PD & 0.4 & 0.4 & 0.1 \\ \cline{2-5}  & ND & \(-\)0.2 & \(-\)0.2 & 0.1 \\ \cline{2-5}  & DSD & 0.4 & 0.4 & 0.1 \\ \hline \multirow{4}{*}{(iii-a) PLA plate vs. PLA tibia} & PD & 1.3 & 1.3 & 0.2 \\ \cline{2-5}  & ND & 0 & 0 & 0 \\ \cline{2-5}  & DSD & 0.5 & 0.4 & 0.2 \\ \hline \multirow{4}{*}{(iii-b) POST plate vs. POST tibia} & PD & 0.7 & 0.6 & 0.4 \\ \cline{2-5}  & ND & \(-\)0.3 & \(-\)0.3 & 0.2 \\ \cline{2-5}  & DSD & 0.6 & 0.5 & 0.2 \\ \hline \multirow{4}{*}{(iv) POST tibia plateau vs. PRE tib plateau} & PD & 0.4 & 0.4 & 0.2 \\ \cline{2-5}  & ND & \(-\)0.3 & \(-\)0.2 & 0.1 \\ \cline{1-1} \cline{2-5}  & DSD & 0.6 & 0.6 & 0.2 \\ \hline \end{tabular}
\end{table} 
Table 1: DMA outputs (units for all variables mm). \(\overline{\text{PD}}\) = Positive mean Distance, \(\overline{\text{ND}}\) = Negative mean Distance, DSD = DMA standard deviation. Figure 3: Boxplots for positive mean distance (\(\overline{\text{PD}}\)), negative mean distance (\(\overline{\text{ND}}\)), and DMA standard deviation (DSD) for all sets of surface comparisons. * (ii) The DMA values associated with the deformation of the fixation plate (average for \(\overline{\text{PD}}\) was 0.4 mm, \(\overline{\text{ND}}\) was \(-\)0.2 mm, with DSD of 0.4 mm) were all less than the critical value, i.e., 1 mm (Table 1) and with most of the points in the safety zone (Table 2).