A novel 3D technique to assess symmetry of hemi pelvises

Anatomical reconstruction of pelvic fractures has been shown to affect functional outcome. Using the contra lateral side of the extremities to create a template for an ipsilateral reconstruction is common practice in orthopedic surgery. We aimed to assess whether hemi pelvises are symmetrical in terms of translation and rotation using 3D reconstruction, point to point mirroring and merging of the 3D created volumes, a method with previous proven high precision and accuracy. CT images of ten randomly selected patients were used. The DICOM images were converted to STL files. Three dimensional images of left hemi pelvis were reversed and merged with the right side. The posterior aspect of the pelvises was considered static and the anterior aspect as moving. Differences in translation and rotation were measured. There were no statistically significant differences between right and left hemi pelvis. The 95% confidence interval (CI) for all mean angular differences between right hemi pelvis and mirrored left hemi pelvis were − 2° to 1.5°. The 95% CI for all mean translational differences between these two objects were − 2.3 to 2.9 mm. Differences between the right hemi pelvis and the mirrored images of the left hemi pelvis for any patient greater than 3 mm or 2 degrees could be excluded with a 95% confidence. The left and right hemi pelvis of healthy adults are symmetrical enough. The pre-operative planning based on a healthy contra lateral side seems reasonable.

2 × 128 × 0.625 mm. A Field of View (FOV) of 200-500 mm and matrix of 512 was used. The filter used was the iDose4 Premium Package. The tube current was set to 89-134 mAs and a dose of 520-920 mGy*cm. The average tube voltage used was 100 Kv.
Images of the right hemi pelvis and mirrored images of left hemi pelvis were saved (Fig. 2). The software in 3D Trauma package uses two parameters to find the optimal segmentation; first the user differentiates the femur from the pelvis by clicking on their respective surfaces in the software. Secondly, the first commando in combination with the Hounsfield Unit values (HU-values) is used to find where one bone ends and the other starts (i.e. optimal segmentation). Analyses of images were done using CT Motion Analysis (CTMA). This software can precisely find the relative movement of an object between two different CT-stacks. In both CT-stacks up to 100 000 measurement points on the surface of the object of interest spreads randomly. The random points create geometrical patterns. Thereafter, the software rotates and translates the object in the second CT-stack to get the best possible match in the first CT-stack as closely as possible (Fig. 2). This procedure is done by minimizing the distance between the two groups of points. This procedure is called "Algorithmic approach for best fit of the identical surfaces" and is described by Maguire et al 14 .
As the used surfaces are much larger than any artifact areas, impact of the artifacts is limited on the matching process. The process is done first for a reference object which is defined as stationary, with which the frame of reference is created. Thereafter, the movement of the object of interest is measured in the same way and the second part is defined as the moving part. The process has been previously described in greater detail 2,13 .
Based on our previous experience from using this software, 10 000 points with a mean distance difference between meshes of 0.5 mm or less was chosen 2,13 . No smoothing was used in the CTMA software.
Translations and particularly rotations of the 3D objects in the space are measured respect another objects and references. In our proposed technique the posterior aspect of the mirrored images of the left hemi pelvis are merged with the right hemi pelvis in order to create this stationary reference volume. Further the anterior aspect of the mirrored images of the left hemi pelvis is merged with the right hemi pelvis's counterpart and registered as a moving object. The posterior part of the right and left hemi pelvises, excluding acetabular vault and including the posterior superior iliac spine, posterior inferior iliac spine and parts of the pelvic wing of each STL created 3D volume were merged with the mirrored contralateral side (Fig. 2). These merged images were saved as static, or nonmoving parts, and were used as reference volumes. Furthermore, the anterior part of the hemi pelvises, excluding acetabulum but including superior/inferior rami were merged.
Translational and rotational changes in 3 different Euler axes (X, Y and Z) was calculated in the CTMA package 15,16 . As per DICOM standard these axes and the rotations were defined; axis X from the patient's left to the right, axis Y from the patient's front to back and axis Z from the patient's feet to head. A clockwise rotation  Statistics. Accuracy was analyzed as per Root Mean Square Error (RMSE) with mean, median and 95% confidence interval (CI) of the mean 17 . Shapiro-Wilk and Kolmogorov-Smirnov tests were used to test the distribution of normality. Statistical analysis was performed using IBM SPSS Statistics version 25 for Windows. A p-value < 0.05 was considered statistically significant.

Results
The mean age of the study population was 54 ± 20 years. Six of the study population were males and the other four were females. There were eight cases of white British origin, one black African and one from the middle east. Differences in rotation and translation in X, Y and Z-axes of COMs are presented in Table 1. Table 2 is presenting Mean, Median and 95% CI of the measurements according to RMSE. All variables were normally distributed. Table 3 is showing normality analysis of the variables. Figures 3 and 4 illustrates the normal distribution of differences alongside the coordinates showing 95% CI of the mean differences and Interquartile Range (IQR) of the differences covering 0.
The 95% for all mean angular differences between right hemi pelvis and mirrored left hemi pelvis were − 2.011 to 1.534. The 95% for all mean translational differences between these two objects were − 2.273 to 2.893. Differences between the right hemi pelvis and the mirrored images of the left hemi pelvis for any patient greater than 3 mm or 2 degrees could be excluded with a 95% confidence.

Discussion
The main finding of our study was that the mirrored images of the left hemi pelvis were highly symmetrical with the right hemi pelvis. Differences between the right hemi pelvis and the mirrored images of the left hemi pelvis for any patient greater than 3 mm or 2 degrees could be excluded with a 95% confidence. These small differences seem to have no clinical implications for pelvic surgeons planning their surgery or templating their implants 1,18 .
Osterhoff et al. recently published an article using mirror images of contralateral pelvis and 3D templates of peri-acetabular plates in order to test symmetricity of left versus right acetabulum 19 . The authors found no statistically significant differences between right and left acetabulum when measuring the distances between a mirrored pre-contoured acetabular plate to the acetabular bone 19 . While the authors offer a new technique to define symmetricity of contralateral acetabulum based on distances, no direct measurement technique has been introduced to measure the rotational differences between the two volumes.
Badii et al., utilising CT scans alongside manual measurement found a range of asymmetry; − 11 to 7 mm difference between right and left hemi pelvis. The authors described a manual technique using the distance between the iliac crest to the acetabulum bilaterally 12 . However, manual calculations are highly subject to bias because of intra-and inter observer reliability issues. Finding reference points and reproduction of the different measurement techniques is difficult 4 . Measuring rotational differences between two hemi-pelvises has been a recurrent problematic issue in previous studies 4, 6 .
In an equivalent fashion using reverse engineering Ead et al. have been successful showing that first hemi pelvises are symmetrical and further that the contra lateral hemi pelvis can be used as a surrogate for reconstruction of the injured side 20,21 . However, the authors use engineering techniques not easily available to the clinicians.
We have been able to introduce a new technique using fusion of the volume using two software packages (3D trauma and CTMA). Application of CTMA in a pelvic fracture model in a previous study showed a precision of ± 0.2 mm for translation and ± 0.2°for rotation 13 . www.nature.com/scientificreports/ In this study, we used translation of two points in the symphysis pubis with respect to the merged images in the posterior aspect of the pelvises. Osterhoff et al. used the mid portion of the pelvises where the acetabulum is located. If we had merged the images posteriorly and included areas very close to the acetabulum, we would have been able to report a narrower confidence interval of the mean differences similar to that presented by the Ostehoff et al. (± 0.2 mm). However, we decided to use the pubic symphysis in our study as it was aimed to investigate the entire pelvis rather than acetabulum only 22 .
In the era of three-dimensional planning and 3D printing of pre-contoured implants, knowledge regarding symmetricity of the hemi pelvises using a highly precise technique is useful. Additionally, the technique can be used for the reconstructed pelvis to check the quality of post-operative reconstruction [8][9][10]23,24 .
Our study had some clear limitations. One limitation is its small sample size. The reason why we accepted this sample size was that sensitivity of the software used to detect small translations and rotations compared to what is important for the clinicians. For example, if the accuracy of the software was even ± 1 mm to detect translation and our confidence band was ± 3 mm, then a sample size as small as 6 would be enough. As we were not sure which effect size we were looking for we kept the characteristic of our study as observational. However, as our normality tests showed that our variables are coming from a normal population, increasing the sample size would probably have only contributed to a narrower confidence band. Another explanation why we did not choose a larger sample size is that the procedure at the moment is time consuming. At the moment the procedure

Conclusion
Hemi pelvises of healthy adults appear to show enough symmetry to be used for pre-contouring of implants and planning of pelvic fracture surgery.
Received: 29 March 2020; Accepted: 16 October 2020  Table 3. Illustrates test of normality. a Lilliefors Significance Correction. *This is a lower bound of the true significance.