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Introduction Joint Facet Tropism Was Previously Defined As the Difference 1 Introduction 2 Joint facet tropism was previously defined as the difference between right and left 3D orientation of the facet-joint 3 (Brailsford, 1929). Additionally, spine joints morphology (i.e. surface geometry) has been also shown to be of 4 clinical relevance while possibly determining degenerative processes (e.g. osteoarthritis, degenerative 5 spondylolisthesis) or injury mechanisms of the spine (Liu et al., 2017). Tropism together with facet 3D orientation 6 have been proposed as factors likely associated with laterality of specific diseases in both the lumbar spine (Alonso 7 et al., 2017; Gao et al., 2017; Kalichman et al., 2009) and the cervical spine (Rong et al., 2017b; Xu et al., 2016, 8 2014). However, considering the costovertebral joint complexes which are involved in both respiratory function 9 (Cappello and De Troyer, 2002) and thoracic spine stability (Brasiliense et al., 2011; Liebsch et al., 2017; Oda et 10 al., 1996; Takeuchi et al., 1999; Watkins et al., 2005), it is questionable how tropism could similarly affect costal 11 facets, but literature concerning costal facets remains qualitative (Drake et al., 2010; Moore et al., 2010; Struthers, 12 1874). In addition, costal facet geometry may partly explain the variability in rib motion during breathing 13 movement (Beyer et al., 2016, 2015). Finally, since the costal facets are also related to the orientation of the 14 transverse processes (Bastir et al., 2014; Gray et al., 2005) measurements of 3D morphometric features of both 15 vertebrae and costal facets can contribute to the understanding of functional and clinical aspects of the rib/vertebra 16 relationship. Thus, the aim of the present study was (1) to propose a methodology for determining location and 17 orientation of the costal facet on the transverse process of the thoracic vertebra Th1 to Th10; (2) to test the 18 hypotheses that tropism exists for costal facets as well as serial variation in orientation and shape among different 19 serial thoracic levels and 3) to investigate/explore the serial variation of the costal facet in the context of symmetric 20 and asymmetric features of the of the global vertebrae shape using 3D geometric morphometrics. 21 Material and Methods 22 3D reconstructions, anatomical landmarks and coordinate system 23 Thorax 3D reconstructions from anonymized CT-scan data of previous works (Beyer et al., 2017, 2016, 2015, 24 2014; Cassart et al., 1996) were used in the present study. According to the Helsinki protocol (Goodyear et al., 25 2007) and local Erasme Hospital Ethics Committee (P2005/021), all of the subjects signed a written consent that 26 allowed the use of these data for scientific purposes. A total of 140 vertebrae from Th1 to Th10 from a sample of 27 14 asymptomatic adults (including 6 males and 8 females; mean age 29.8 ± 5.1 years old) were processed. 28 Anatomical landmarks (ALs) were placed on 3D models in order to create a vertebra coordinate system (VCS) on 29 each thoracic vertebra using a custom made software called LhpFuionBox (http://lhpfusionbox.org/). The ALs 30 were located following adaptation of the method described in previous work (Beyer et al., 2016, 2015) but details 31 concerning ALs and axes of the coordinate system are depicted in figure 1. 32 Figure 1 33 Costal facet landmarks and geometry 34 A series of points (in average 95±43) were placed on the left and right costal facet of each thoracic vertebra (see 35 figure 2). Costal facet landmarks (CFLs) were occasionally undetermined at Th1 (21%), Th9 (4%) or Th10 (43%) 36 on a single or both sides, and eventually a total of 258 costal facets were analyzed. For most accurately determining 37 the location of the costal facet, the combination of both 3D models and CT slices were analyzed (see figure 2). 1 38 The CFLs were equally distributed on the entire joint facet and were then all expressed in the local vertebra 39 coordinate system (VCS). Figure 2 40 All feature calculations were performed by using in-house software implemented in the Matlab R 2014b platform 41 (MathWorks,Natick, Massachusetts). Spatial coordinates of the ALs and CFLs were processed as follows. Left 42 ALs coordinates were mirrored to the right side (Meskers et al., 1998) through the sagittal plane formed by the x- 43 axis and y-axis in order to compare right and left geometrical parameters of the costal facets. Spatial orientation 44 and location of the costal facet was determined as follows. First, the centroid of the CFLs of each costal facet was 45 computed. Second, a plane crossing the surface centroid was fitted to CFLs by minimizing orthogonal distance of 46 ALs to the plane using least-squares regression (see figure 2). The root mean square (RMS) distances from ALs 47 to the plane were calculated to estimate the out-of-plane deviation of the shape of the costal facet. In other words: 48 the greater the RMS the more concave the costal facet; and the smaller the RMS the flatter the facet. Third, a 3D 49 vector orthogonal to the best-fitted plane was computed to describe the 3D orientation of the joint facet. Finally, 50 orientation of the latter vector was expressed using inclination angle α (sagittal orientation) and declination angle 51 β (transverse orientation) as shown in the bottom of figure 3. A positive value for α and β angles corresponds to 52 superior and anterior orientation, respectively. Facet tropism was then estimated according to the absolute 53 difference between left and right values of both inclination and declination angles. To ensure the reproducibility 54 of the measurements, 40 costal facets of 20 vertebrae from 2 subjects were measured by a single observer at three 55 different sessions with more than 24 hours apart. Then, the mean standard deviation and coefficient of variation 56 were calculated for inclination and declination angle as well as for the distance from the best fit plane. 57 Figure 3 58 Statistical analysis 59 Statistical analysis was performed using Statistica software (Statistica 8.0© StatSoft. Inc., Tulsa, USA). Normality 60 test Kolmogorov-Smirnov was performed to evaluate data distribution. All variables followed normal distribution. 61 In order to evaluate the tropism, the averaged absolute difference between right and left measurements (i.e. 62 inclination and declination angles) was tested in a one-sample t-test against a fixed mean value of 0° which 63 corresponds to absolute symmetry. Values of p<0.05 were considered statistically significant. An analysis of 64 variance (ANOVA) was then used to estimate the difference between serial thoracic levels (Th1 to Th10). When 65 ANOVA demonstrated a significant effect, Tukey post-hoc test was used to determine the significant differences 66 at p=0.05. 67 3D Geometric Morphometric and Procrustes analysis on overall vertebra shape 68 The above-mentioned set of 16 landmarks (14 virtually placed and 2 additional ones computed as the centroid of 69 the costal facet) of the remaining 128 vertebra were used to determine shape variations of the thoracic vertebra in 70 relation to the location of the costal facet using the standard 3D geometric morphometric (GM) analysis 71 (O’Higgins, 2000; Zelditch et al., 2004). The 3D GM approach enables analysis of 3D shape using homologous 72 vertebra ALs defined above (Bookstein, 1997; Zelditch et al., 2004). In a geometric morphometric shape analysis 73 all specimens are measured by the same set of homologue landmarks leading to landmark configurations that are 74 subject to Generalized Procrustes Analysis (GPA) (Gower, 1975). GPA removes information of the landmark 75 coordinates related orientation, position and scale. By applying iterative least squares based registrations using 76 rotation, translation and rescaling, GPA minimizes the distances among homologous landmarks using of the 2 77 landmark configurations relative their mean shape (consensus) leading to a set of shape coordinates and a size 78 variable (centroid size) (Zelditch et al., 2004). After GPA, the shape coordinates can be analyzed by standardized 79 multivariate statistical analyses addressing specific hypotheses (Mitteroecker and Gunz, 2009). One key advantage 80 of GM over other morphometric methods is the direct correspondence of each specimen in shape space with a 81 given landmark configuration, which allows for powerful visualizations of statistical results (Zelditch et al., 2004). 82 Geometric morphometrics have been used to investigate symmetry and asymmetry (Klingenberg, 2015). To obtain 83 the symmetric and asymmetric components of total shape variation a method called “reflected relabeling” (Mardia 84 et al., 2000) is applied in which the original landmarks data of the full vertebrae are superimposed onto its mirrored 85 landmarks. Principal components analyses (PCA) were then carried out on the symmetric and on the asymmetric 86 components of shape data (Mitteroecker and Gunz, 2009) to investigate the seriality (that is, 3D shape change 87 between different serial levels). 88 With respect to the symmetric component we projected the shape data onto the first two principal components and 89 explore overall symmetric shape changes related to seriality. With respect to the more subtle, asymmetric part of 90 shape variation, we performed a second PCA followed by an ANOVA on the PC scores of the first three PC- 91 scores. This analysis was used to explore a potential systemic trend in asymmetry along different serial thoracic 92 vertebral levels. 93 94 Results 95 All tables of descriptive statistic are available in supplementary material. Results of the reproducibility analysis 96 displayed a mean standard deviation of 0.6 mm for the deviation from the best fit plane, 1.8° for inclination angle 97 and 1.9° for declination angle. Respectively, measurements showed a coefficient of variation of 15.6%, 9.0% and 98 5.6%.
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