# Personalised High Tibal Osteotomy Surgery Is Accurate: An Assessment Using 3D Distance Mapping
## 2 Materials and Methods
### Distance Map Analysis  
The STL models generated in the three PRE, PLA, and POST stages were imported in computer-aided modelling and designing software (Geomagic, 3D Systems, Rock Hill, SC, USA) to implement DMA for the assessment of geometrical differences between pairs of selected model surfaces (Figure 2).  
DMA allows quantifying the shortest distance between the mesh points of two selected surfaces facing each other, one surface being called \"Test\" and the other \"Reference\". A 3D colour-coded map of distances was then generated and displayed on the Reference object, with each colour associated with a different surface-to-surface distance interval. For this, Geomagic's \"3D Comparison\" tool was used, the relevant parameters of which were set to calculate and to export a number of DMA-related values. To identify the minimum distances between surfaces, the parameters \"critical angle\" and \"maximum deviation\" were set to 180 deg and 10 to 20 mm, respectively; the former was set to allow recognition of the maximum deviation, while the latter was adjusted according to the specific comparison and the expected maximum values. By definition, differences shown by DMA on the Reference surface were marked as positive (represented by progressive yellow/red areas) or negative (represented by progressive light blue/dark areas) if the Test surfaces were outside (i.e., separation) or inside (i.e., penetration) the Reference surfaces, respectively. DMA output consisted of the following values: Positive Maximum Distance (PMD) and Negative Maximum Distance (NMD), Positive mean Distance (\(\overline{\text{PD}}\)) and Negative mean Distance (\(\overline{\text{ND}}\)), and DMA standard deviation (DSD). The two mean distances, together with the DSD, are the most useful in determining deviations between two surfaces, and these were the focus of the analysis (Appendix A provides all DMA outputs for completeness).  
Figure 1: Planning on CT scan-derived geometry allows placement of tibial cuts and design of personalised jig and plate. (**a**) Tibial cuts with surgical jig in closed position. (**b**) Surgical jig opened to required correction. (**c**) Osteotomy stabilised with personalised plate (NB planning also gives the appropriate screw length to use, screw lengths are indicated by color).  
The following surface-to-surface comparisons were performed via DMA, with relevant \"Reference\" and \"Test\" surfaces being reported in brackets:  
(i) POST tibia (\"Test\") versus PLA tibia (\"Reference\"), to check whether the planned new proximal tibial alignment had been achieved surgically;  
(ii) POST fixation plate (\"Test\") versus PLA fixation plate (\"Reference\"), to check possible fixation-plate deformation after surgery with respect to the reference planned design;  
(iii-a) PLA fixation plate (\"Test\") versus PLA tibia (\"Reference\"), to check planned plate-to-bone surface contour matching;  
(iii-b) POST fixation plate (\"Test\") versus POST tibia (\"Reference\"), to check the achieved plate-to-bone surface contour matching;  
(iv) POST tibial plateau (\"Test\") versus PRE tibial plateau (\"Reference\"), to check for changes in the plateau surface only (e.g., due to OA progression), independently from the correction performed with HTO.  
Of note, prior to the implementation of DMA, best-fit model registration based on the Iterative Closest Point (ICP) algorithm in Geomagic was performed considering the tibial  
Figure 2: Diagram of the DMA workflow.  
diaphysis in comparison step i, i.e., the only tibial position which remains identical among the comparisons, or the overall morphologies in all other cases.