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1 Introduction

2 facet tropism was previously defined as the difference between right and left 3D orientation of the facet-joint 3 (Brailsford, 1929). Additionally, spine morphology (i.e. surface geometry) has been also shown to be of 4 clinical relevance while possibly determining degenerative processes (e.g. , degenerative 5 ) 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, geometry may partly explain the variability in motion during 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/ 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 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).

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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 formed by the x- 43 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

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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%.

99 Inclination: 100 Inclination angle (α) increased gradually with increasing thoracic serial level from Th1 to Th10. In other words, 101 the sagittal orientation of the costal facet was gradually more cephalad in the lower thoracic levels (see figure 4). 102 The mean inclination was found to be -1.4° ± 9.5° at Th1, corresponding to a slightly caudal orientation relative 103 to the vertebra coordinate system. In more inferior levels, mean inclination ranged between 1.6°± 7.1° at Th2 to 104 38.0°± 10.0° at Th9. Analysis of variance demonstrated a significant effect of serial thoracic level (p<0.0001). 105 Globally, Tukey post-hoc test showed that adjacent levels did not significantly differ from each other (p>0.05).

106 Figure 4

107 Declination: 108 The mean declination angle (β) ranged between a minimum of 27.9° ± 10.4° at Th4 to a maximum of 46.6° ± 12.0° 109 at Th1 (see figure 5). Analysis of variance demonstrated a significant effect of thoracic level (p<0.0001). Globally, 110 Tukey post-hoc test showed also that level 1 differed from levels 2 to 9; and no significant difference (p>0.05) 111 was observed for adjacent 3 or 4 levels under the second one.

112 Figure 5

113 Deviation from the best-fit plane:

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114 The RMS distance from ALs to the best-fitted plane (see figure 6) ranged between 2.1 ± 0.9 mm at Th8 and 5.2 ± 115 2.2 mm at Th4. ANOVA showed a significant effect of thoracic level (p<0.001). RMS distance displayed a value 116 of 2.3 ± 1.0 mm at Th1, then a significant increase from Th2 to Th5 and a significant decrease from Th6 to Th10. 117 In other words, that costal facet is flattened at Th1 and from Th6 to Th10, and more concave between Th2 and 118 Th5.

119 Figure 6

120 Tropism

121 The mean absolute difference for inclination ranged from 4.9° ± 3.6° at Th4 to 12.2° ± 10.3° at Th10. The mean 122 absolute difference for declination ranged between 5.1° ± 4.2° at Th7 to 14.3° ± 5.8° at Th10. The absolute 123 difference for inclination angle differed significantly from zero (p<0.01) at all thoracic levels except Th10 124 (p=0.052). The absolute difference for declination angle also significantly differed from zero (p<0.01) at each 125 thoracic level. On average, regardless the thoracic level, the right-left absolute difference was 6.9° for inclination 126 and 7.7° for declination and differed significantly from zero (p<0.001).

127 Figure 7

128 Symmetry component from GM analysis 129 Analysis of symmetry enables for characterizing symmetric shape changes related to seriality. Results displayed a 130 clear organization on PC1 (51.5% of variance) and PC2 (22.1% of variance). These results characterized how 131 different are from one others and suggest dividing thoracic vertebrae in three shape groups; 132 upper thorax vertebrae Th1 to Th4, mid-thorax vertebrae Th5 to Th8 and specific lower thoracic vertebrae Th9 133 and Th10. The PCA shows a distribution of the upper levels along PC1 and lower levels along PC2. As usually 134 described, note the specific geometry results of Th1 with a frontal orientation of the transverse process (i.e. costal 135 facet), more horizontal spinous process, and a vertebral less circular. The upper thorax group (Th1 to 136 Th4) corresponds to a gradually increasing posterior orientation of the transverse process, a gradually increasing 137 caudal orientation of the spinous process and a gradual trend towards a more circular shape of the vertebral body. 138 Vertebrae of the mid-thorax group (Th5 and Th8) displayed a maximal caudal orientation and length of the spinous 139 process, a thicker (taller) and circular vertebral body as well as more posteriorly and superiorly oriented transverse 140 processes. Note that vertebrae between Th5 and Th8 have a very similar shape. Finally, the lower thorax group 141 displayed the shortest transverse processes, more horizontal spinous processes (oriented similarly to those of the 142 upper thorax group) and the thickest (tallest) and largest vertebral body. 143 Figure 8

144 Asymmetry component of the GM analysis 145 These results enables for characterizing the potential asymmetric component of shape variations along different 146 serial thoracic levels Following results on PC scores, no clear asymmetry components were demonstrated between 147 thoracic levels on PC1 and PC2 (p>0.05). However, a partial asymmetry component was displayed on PC3 (see 148 figure 9) with a significant influence of the thoracic level (p=0.0024). Tukey post-hoc test showed the main 149 difference between the upper thoracic vertebrae Th1-Th3 and the lower remaining ones. This difference globally 150 consists in a greater and more dorsal orientation of the transverse process on the left side at Th1 to Th3 and Th10

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151 and a similar deviation on the contralateral side at Th4 to Th9 (see figure 9 bottom). This result suggests a randomly 152 distributed asymmetry over thoracic levels. Figure 9 153 The PC 3 asymmetry describes also the relationship between relative length and relative orientation of the 154 transverse process in frontal and . In order to better visualize this phenomenon, the range of PC3 155 differences (i.e. between the maximum value at Th3 and the minimum value at Th5) was magnified up to 50 times 156 (see figure 10). Results show a relation between the asymmetry, length and orientation of the transverse process, 157 which is determined in the present measurements by the position of the costal facet. Note that a clear shift of the 158 body of the vertebra was also associated to the same side of the shortening and more frontal orientation of the 159 transverse process. Figure 10

160 Discussion 161 The present study proposes an innovative method that enables both qualitative and quantitative description of the 162 costal facet of the transverse processes in relation to the shape of the thoracic vertebra.

163 Concerning anatomical description, results have shown the serial change in orientation and position of 164 the costal facet over the different thoracic levels. These changes in orientation of the costal facet are in line with 165 the qualitative description of few textbooks (Gray et al., 2005; Moore et al., 2010; Roussos, 1995). 166 However, the declination angles obtained in the present work (figure 5) suggest that costal facet orientation in the 167 transverse plane does not strictly follow the gradual posterior orientation of the transverse processes among 168 thoracic levels (i.e. declination angle does not decrease gradually in the lower thoracic levels). In addition, results 169 concerning the shape showed that costal facet from Th2 to Th5 are more concave and the related costotransverse 170 joint may not be considered as an arthrodial joint (i.e. gliding joints formed by apposition of two planar surfaces), 171 but rather a trochoid/pivot one (i.e. rotary joint formed by apposition of a pivot-like surface turning within a partial 172 ring-like cavity). The present outcomes indicate a relationship between thoracic level and facet orientation, and an 173 average absolute difference of 7° between left/right orientations (more than three times the MSD of 1.6° for 174 inclination angle and 1.9° for declination angle) of the costal facet for both inclination and declination angle. While 175 the sample is relatively small, results suggest that tropism occurs not only at zygapophyseal joint facets (Masharawi 176 et al., 2008) but also at facets.

177 The present results may also be of interests for various clinical fields. Indeed, such quantitative data may 178 help in guiding medical procedure such as costotransverse joint injection in patients with pain (Deimel et al., 179 2013; Yoon et al., 2016) or planning interventions on thorax deformities (Little and Adam, 2011). Indeed, 180 combining the present results with other biomechanical parameters of the (Beyer et al., 2016, 181 2015; Lemosse et al., 1998) are of interest for modelling approach of dynamic interaction between spine and rib 182 cage (Kindig et al., 2015; Schlager et al., 2018). Physical examination of the thorax is also commonly used in 183 patients with musculoskeletal causes of chest pain (Jensen, 2001). Literature describes specific clinical assessment 184 and treatment of the costovertebral and/or costotransverse joint tenderness and manual therapies such as joint 185 mobilization procedures as a treatment tool (Edmondston and Singer, 1997; Lee, 2015). Considering the relevance 186 of facet orientation for ensuring the consistency of motion palpation procedure, the present outcomes may help in 187 reappraising several technical features (i.e. force orientation) of these manual methods.

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188 The present quantitative information about joint geometry may enable reappraising manual approaches 189 (i.e. orientation of the force produce by the practitioner for evaluating/mobilizing such joint) for clinical evaluation 190 or treatment of the thorax. 191 The GM results of asymmetry components are also in line with this hypothetic anatomical relationship 192 between the position of the costal facet and the overall shape of the thoracic vertebra (i.e. the lower the thoracic 193 vertebra, the more posterior and closer to the sagittal midline is the costal facet following the orientation of the 194 transverse process). Interestingly, magnification of the slight asymmetry observed in the present sample up to 50 195 times approximates a shape alteration that is very similar to the morphology observed in patients with scoliosis 196 (see figure 10). Thus, such asymmetry in costal facet location and in the body of the vertebra may represent a 197 relevant signal for determining ontogenetic scoliotic change of the thoracic spine. The overall asymmetry and 198 costal facet tropism could lead to similar compensation in the anterior joints of the thorax (i.e. costo-chondral and 199 chondro-sternal joints) since the overall mechanism consists of close kinematic chains. In a similar way, the effect 200 of such asymmetry could be related to side specific degenerative alteration of the thoracic or at 201 the costovertebral joints. Although such a relationship between tropism and degenerative disease have been 202 described previously in cervical (Rong et al., 2017b, 2017a; Xu et al., 2016, 2014) and lumbar spine (Alonso et 203 al., 2017; Gao et al., 2017; Kim et al., 2013; Liu et al., 2017; Zhou et al., 2018), these anatomo-clinical features 204 have to be further investigated for the thoracic spine. 205 In addition to the clinical implications, tropism associated with the variation of the orientation of the 206 transverse processes may have also some evolutionary implications. For example, the more dorsal orientation of 207 the transverse processess has been described as a potential plesiomorphy (i.e., an evolutionarily primitive 208 anatomical feature) observed in fossil hominins (Bastir et al., 2017; García-Martínez et al., 2017) but further 209 studies are required to confirm such hypothesis. 210 Concerning respiratory mechanics, the costal facet orientation is also suggested to influence the orientation of the 211 axis of rotation (AOR) of the rib (Saumarez, 1986) both for breathing motion and trunk rotation (Edmondston and 212 Singer, 1997; Lee, 2015). Previous work has shown that the side did not affect orientation of AOR between rib 213 levels in breathing (Beyer et al., 2016). Concurrently, the spatial dispersion of AOR orientation increases in lower 214 thoracic levels during rib rotation (Beyer et al., 2016, 2015) and authors suggested that specific regional variations 215 of joint geometry (Moore et al., 2010; Roussos, 1995) could explain axis dispersion. In the present study, the 216 decrease in out-of-plane distance in the lower thoracic levels (i.e. a costal facet closer to a plane in the lower levels) 217 is in accordance with this hypothesis. Indeed, a facet morphology close to a plane shape may allow slight 218 translatory displacements previously called “misfit” (Saumarez, 1986) that can lead to a change in both orientation 219 and position of the AOR (de Lange et al., 1990; Woltring et al., 1985).

220 Limitations: 221 There are several limitations to the present study. First, the data were obtained from CT imaging techniques, and 222 therefore the shape of the layer covering facets is lacking. Although the latter could slightly alter the 223 articular geometry, the resolution of the CT data obtained 0.5 mm with 1 mm interspacing still gives the 224 opportunity to estimate shape without being too far from reality. In addition, in order to optimize the palpation of 225 the ALs, both 3D models obtained from manual segmentation and CT slices were used trying to obtain the valid 226 and reliable results. In addition, the influence of landmark position may have altered the fitting process, however, 227 the reproducibility analysis showed acceptable results.

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228 Second, the sample analyzed in the present study includes small age range and therefore, results should be 229 interpreted with caution in older samples since degenerative changes can alter joint surfaces geometry. However, 230 considering that the subjects were randomly selected one might expect that the dispersion of results obtained in 231 the present study represents a substantial basis for morphometric consideration of the costal facet. Furthermore, 232 quantitative results obtained remain in line with anatomic descriptions found in literature (Moore et al., 2010; 233 Roussos, 1995). Finally, previous studies related to thoracic vertebrae morphometric analysis reported evidence 234 for sexual dimorphism in thoracic vertebrae (Bastir et al., 2014) and further research should investigate the sexual 235 dimorphism in these costal facets on a larger sample in relation to tropism.

236 Conclusion 237 The present study is the first to investigate quantitative geometry of the costal facet of the transverse processes in 238 relation to the overall shape of the thoracic vertebra. Our results demonstrate a solid signal of tropism and 239 asymmetric feature of the overall vertebra shape that should be further investigated on a larger sample that include 240 the analysis of different age groups and sexual dimorphism. Data obtained related to the change of location, shape 241 and orientation of the costal facet between thoracic levels can be further used for modelling approach and clinical 242 applications. The proposed method will be used to explore ontogenetic changes and evolutionary anatomy of the 243 costal facet in relation to the thorax functional aspects.

244 Acknowledgements 245 This research is funded by CGL2015-63648-P (Ministerio de Economía y Competitividad, Spain). We thank all 246 the members of the Virtual morphology Lab, and especially Nicole Torres and Daniel Garcia-Martinez for their 247 help with the GM software and helpful discussions. We also acknowledge the work of the reviewers, whose 248 comments helped improve this manuscript.

249 Disclosure of potential conflict of interest: 250 All authors declare that they have no conflict of interest.

251 References

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392

393 Figure 1 : 3D reconstruction and anatomical landmarks (type I and type II landmarks) of a typical vertebra with local 394 coordinate system. From left to right, inferior, superior and posterior view from left to right. Vertebra landmarks (V1 to V5 395 from (Beyer et al., 2015):.V1: Centre of inferior border of left pedicle (type II). V2: Centre of inferior border of right pedicle 396 (type II). V3: Superior junction of lamina (type II). V4: Posterior and superior apex of spinous process (type I). V5: Posterior 397 and inferior apex of spinous process (type I). In addition, four ALs were placed on upper and lower vertebra endplates 398 (displayed as green balls on the figure). ALs located on the endplates were used to compute their centroid (type III 399 landmark) that corresponds approximately to the center of the body of the vertebra. The vertebra coordinate system (VCS) 400 was then created using right rule with origin located at midpoint between V1 and V2; z-axis oriented from V1 to V2 401 and pointing to the right; x-axis normal to z-axis pointing to the centroid; y-axis normal to x-axis and z-axis pointing to the 402 top.

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403 .

404 Figure 2 : Top: CT-scan image in sagittal plane (left) and 3D model of a vertebra (right) that depicts the positioning of the 405 landmark on the costal facet. Bottom: Example of the processing of plane fitted to the costal facet landmarks, the vector 406 normal to the plane with origin at the centroid (type III landmark) of the costal facet. 407

408 409 Figure 3 : Illustration of the inclination (A) and declination (B) angles computation according to the vertebra coordinate 410 system. Positive values of α and β correspond to superior and anterior orientation respectively.

411 412 Figure 4 : Left: representation of the results obtained for inclination angles at each thoracic level. Right: Values obtained 413 for the inclination angles (in degree) at Th1 to Th10 regardless of the side. Note that n=22 for Th1, n=28 for Th2 to Th8, 414 n=27 for Th9 and n=13 for Th10.

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415

416 Figure 5 : Left: Values obtained for declination angles (in degree) at Th1 to Th10. Note that n=22 for Th1, n=28 for Th2 to 417 Th8, n=27 for Th9 and n=13 for Th10. Right: An example of 3D models of Th1 and Th4 is displayed for better visualization 418 of the change in declination angle between Th1 and Th4.

419

420 Figure 6 : Left: Out of plane distances represented by the root mean square (RMS) distance (in millimeter) from the 421 landmarks to the best fit plane at Th1 to Th10. Note that n=22 for Th1, n=28 for Th2 to Th8, n=27 for Th9 and n=13 for 422 Th10. Right: An example of the more concave facet at Th2 and flattened costal facet at Th7 is represented.

423

424 Figure 7 : Results of the absolute difference (in degree) between right and left inclination angle α (left) and declination 425 angle β (right). Note that n=11 for Th1, n=14 for Th2 to Th8, n=13 for Th9 and n=7 for Th10.

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426 427 Figure 8 : Right: Principal component analysis of the overall shape of the thoracic vertebra Th1 to Th10. Left: The scatterplot 428 of PC1 (51.5% of total variance) and PC2 (22.1% of total variance) illustrates shape distribution between thoracic levels Th1 429 to Th10. Details are explained in results section. The warps of the 3D models depict the mean shape change along PC1 and 430 PC2. The warps along PC1 from Th1 to Th6 displayed a gradual posterior orientation of the transverse process, a gradual 431 caudal orientation of the spinous process and a more squared vertebral body. Along PC2, from Th6 to Th10, the transverse 432 process are gradually smaller, the spinous process gradually more horizontal and short and the vertebral body becomes 433 thicker.

434 Figure 9 : Results of PC scores from the asymmetry component analysis along PC1 (top left), PC2 (top right) and PC3 (bottom) for each thoracic level Th1 to Th10. Note that only PC3 scores were significantly influenced by thoracic level. PC3 is related to the antero-posterior shift of the transverse processes depicted through the centroid of the costal facet as illustrated with the 3D warps.

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435

436 Figure 10 : 3D warps of Th6 vertebra mean shape along PC3. The magnitude of the shape change represents from 1 times 437 (left part) to 50 times (right part) the range of PC scores (between -0.002 to 0.005) on the positive PC3 axis. Details are 438 explained in the results section.

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