Abstract
Inter-individual size and shape (form) variation for the orbital floor and medial wall was assessed and compared with its posterior partition. Reconstruction of the posterior partition is known to be a surgical challenge in complex orbital defect repair when using standard manual implant contouring and positioning techniques. The size variation of both regions was assessed, alone and combined, in statistical form analysis using three-dimensional computer models of left and mirrored right orbits, obtained from 70 clinical computed tomography (CT) scans of adult European Caucasians with unaffected orbits. Major shape and size variability for both regions was observed, but to a larger extent for the entire orbital floor and medial wall, with males having significantly larger regions but with no differing shape patterns. Statistical modeling was used to identify characteristic shape patterns in given orbits. The size, shape and positioning of precontoured implants are decisive criteria for the adequate repair of complex orbital defects. The results indicate that optimal form conditions for prefabricated implants exist in a restricted area corresponding to the transition of the posterior orbital floor and medial wall.
The mainstay of a severe injured orbit repair is restitution of the preinjury bone anatomy in order to re-establish orbital form and function . Dislocation of orbital wall fragments leads to orbital widening, resulting in an enlarged orbital volume, it also induces displacement and dysfunction of orbital soft tissue structures . Traditional surgical techniques for restoring orbital wall defects involve freehand contouring and positioning of grafts which are technically difficult and prone to error.
In the present study, the authors evaluate the inter-individual variability of the orbital floor/medial wall region (FMW) and its posterior partition (pFMW), in order to establish a scientific anatomical basis and to define optimal conditions for preshaped orbital implants for complex orbital fracture repair ( Fig. 1 ). This includes the use of clinical computed tomography (CT) data from unaffected adult orbits, the creation of three-dimensional (3D) computer models, size measurements and 3D statistical modeling and analysis techniques, the latter comprising techniques of anatomical homologous point determination and evaluation. Statistical modeling identified characteristic shape patterns in given orbits.
Material and methods
Consecutive CT scans from 70 adult European Caucasians (35 females and 35 males), aged 20–88 years (mean ± SD 53 ± 19.4 years; 53.4 ± 17.8 for females, and 52.7 ± 21 for males) were retrospectively assessed using routine CT head protocols from patients undergoing diagnostic procedures for pathologies near, but not directly involving, the orbits (e.g. for paranasal sinus problems). Exclusion criteria included the presence of uni- or bilateral radiological signs of orbital pathology.
CT data were obtained on a standard multi-slice CT scanner (SOMATOM Sensation 10, Siemens AG, Erlangen, Germany) and comprised continuous 0.4–0.8 mm high resolution (512 × 512 matrix) axial slices in a bone window setting. After acquiring the patients’ meta-data (i.e. age, gender and ethnicity) all image data were stored in DICOM-format (Digital Imaging and Communications in Medicine), anonymized and transferred via compact disc to an off-line desktop computer and processed with Amira, a commercial software package for image visualization and data analysis (Visage Imaging GmbH, Berlin, Germany).
In Amira, semi-automated segmentation tools were used, associating DICOM threshold values of grey scales to bone. Very thin bony orbital structures led to the creation of partial volume averaging and required additional manual segmentation. 3D triangulated surfaces of the bony orbit were created and all image data of the right orbits were mirrored, resulting in 140 left sided orbits (i.e. 70 mirrored right and 70 left orbits).
The surface area of FMW and pFMW was determined using the Amira’s SurfaceAreaGet module. Related descriptive statistics, tests for normality, the independent sample t -test for testing gender related variability and the paired t -test for laterality evaluation were carried out using SPSS 14.0 (Statistic Package for the Social Sciences, SPSS Inc., Chicago, USA). A p -value <0.05 was considered significant.
In order to perform statistical form modeling in FMW and pFMW, homologous boundary and surface points had to be determined. For this, a statistical model analysis procedure was developed based on manual anatomical landmark tracing, computing anatomical–mathematical boundary landmarks and mathematically defined surface landmarks ( Fig. 1 ). Evaluation was carried out with special regard for anatomical regions lacking anatomical criteria as observed in the pFMW . In standard shape analysis, scaled region evaluation is performed, thus eliminating size as a factor, but in the present study, unscaled statistical modeling was carried out, allowing analysis of both the shape and size; this is termed statistical form analysis. Homology computing was finalized by creating corresponding mesh surfaces with an identical triangulation structure (1385 mesh points for FMW and 541 for pFMW).
The datasets with homologous landmarks were aligned using an unscaled generalized Procrustes Fit and analyzed using Principal Component Analysis (PCA), a state of the art method for statistical modeling and analysis . PCA was performed with MATLAB (The MatWorks GmbH, Bern, Switzerland) and results were expressed as PCA scatterplots, charts and simplified 3D visualizations. The size variability in the PCAs was characterized using the Frobenius Norm and MATLAB’s standard correlation test.
The scatterplots were also used to identify characteristic shape patterns of the FMW region, visualized in given orbits using Amira’s curvature module.
Results
FMW and pFMW surface area measurements showed normal distribution (Kolmogorov–Smirnov and Lilliefors significance level p ≥ 0.2). The area of the mean FMW in women and men was roughly four times larger than the corresponding mean pFMW ( Table 1 ). For both regions a significant gender dependent surface size variation was observed with males having significantly larger values (independent samples t -test (the null hypothesis of a t -test for equality of means could clearly be rejected with a p -value = 0.000 for FMW and for pFMW)). In the laterality evaluation of corresponding left and right orbits, the null hypothesis of the paired t -test could not be rejected for both regions, indicating no significant side difference (paired t -test p = 0.726 for FMW and 0.983 for pFMW). No significant correlations between age and both areas could be observed (Pearson correlation ≤ |0.071|).
| FMW | pFMW | |||
|---|---|---|---|---|
| Women | Men | Women | Men | |
| Min | 10.7221 | 12.0541 | 2.8990 | 3.4189 |
| Max | 14.3294 | 15.2328 | 4.8826 | 5.0048 |
| Mean | 12.530979 | 13.591720 | 3.854154 | 4.187711 |
| SD | 0.9589698 | 0.8173561 | 0.3830414 | 0.3342664 |
A statistical form model for both FMW and pFMW regions was evaluated. The results were compared with the corresponding mean shapes and visualized ( Fig. 2 ) with colour maps showing the degree of form variation and by vectors indicating the amount and direction of maximum values analyzed for all corresponding homologous mesh points.
High deviation of the FMW region (≥3 mm) was observed at the periphery and centrally at the transition from the anterior to the posterior orbital floor. Good form match (≤2 mm deviation) was obtained at the posterior medial orbital wall and the anterior orbital floor. The pFMW showed increased form variation at the anterior and posterior margins (i.e. anteriorly towards the lacrimal fossa and posteriorly below the optic foramen). In contrast to the orbital FMW region, maximum deviations (≥5 mm) were limited to the area corresponding to the infraorbital sulcus. 3D rendered standard deviations are shown in Fig. 3 .
Identification and categorization of patterns of form similarities were performed with the statistical models created by applying PCA. As expected, most significant variability was obtained in the first principal component (1st PC) ( Fig. 4 ). It showed a significant correlation between size and shape values at a p -level of ≤0.05 in both regions, indicating that most relevant form variation was due to size and not to shape variation. Other significant correlations between these parameters were observed in the 3rd PC and 4th PC for FMW and the 2nd PC and 3rd PC for pFMW. The remaining PCs showed variation patterns due to shape variation and were not correlated to size. Gender specific patterns of shape variation could not be observed in the PCA. The cumulative percentage of contribution of each PC is shown in Fig. 5 . The first five PCs cover about 60% FMW and more than 70% pFMW overall form variability. In Fig. 6 the fit of each individual FMW and pFMW was quantified and visualized by computing and plotting normalized average distances from the corresponding average values of FMW and pFMW. The overall average distance between mean form and its samples was 1.28 mm (±0.3 SD) for FMW and 0.86 (±0.26 SD) for pFMW.
