Daphne Guenoun

Martine Pithioux

Jean-Christophe Souplet

Sandrine Guis

Thomas Le Corroller

Alaxandre Fouré

Vanessa Pauly

Jean-Pierre Mattei

Monique Bernard

Maxime Guye

J-C Souplet

T Corroller

J.-P Mattei

M Bernar

P Chabrand

P Champsaur

D Bendahan

Ultra-high Field MRI Microarchitecture Analysis Improves the Prediction of Proximal Femur Fracture: A Combined Study with Ex Vivo Biomechanical Tests

Keywords: femur, osteoporosis, magnetic resonance imaging, cancellous Bone, 7 Tesla

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Fracture of the proximal femur is a major health burden in post-menopausal women and elderly persons. It represents the main source of osteoporosis-related mortality and morbidity [START_REF] Cooper | Hip fractures in the elderly: a world-wide projection[END_REF].

Osteoporosis is an age-related progressive skeletal disease characterized by a reduced bone mass and microarchitectural alterations resulting in an increased bone fragility and susceptibility to fracture [2]. Bone strength is routinely evaluated from areal bone mineral density (ABDM) measurements using dual-energy X-ray absorptiometry (DXA) [START_REF] Cummings | Bone density at various sites for prediction of hip fractures. The Study of Osteoporotic Fractures Research Group[END_REF][START_REF] Cummings | Risk factors for hip fracture in white women. Study of Osteoporotic Fractures Research Group[END_REF]. Patients are commonly diagnosed as osteoporotic on the basis of the ABDM T-score [START_REF] Kanis | Diagnosis of osteoporosis and assessment of fracture risk[END_REF][START_REF] Marshall | Meta-analysis of how well measures of bone mineral density predict occurrence of osteoporotic fractures[END_REF]. A score lower than 2.5 standard deviations (SDs) below the mean ABDM value quantified in a group of young control subjects (< 30-year-old) of the same gender and ethnicity is considered as outside the normal range [START_REF] Kanis | Diagnosis of osteoporosis and assessment of fracture risk[END_REF][START_REF] Marshall | Meta-analysis of how well measures of bone mineral density predict occurrence of osteoporotic fractures[END_REF]. However, the diagnostic value of DXA-based ABDM has been recognized as limited for the prediction of fracture risk thereby indicating that ABDM would not allow bone microarchitecture assessment. Accordingly, low ABDM values would account for only 28% of hip fractures [START_REF] Chang | MRI of the hip at 7T: feasibility of bone microarchitecture, high-resolution cartilage, and clinical imaging[END_REF]. Similarly, a significant percentage of fractures has been reported in women with ABDM values above the accepted threshold [START_REF] Cummings | Are patients with hip fractures more osteoporotic? Review of the evidence[END_REF][START_REF] Schuit | Fracture incidence and association with bone mineral density in elderly men and women: the Rotterdam Study[END_REF][START_REF] Wainwright | Study of osteoporotic fractures research Group. Hip fracture in women without osteoporosis[END_REF]. While microarchitecture deterioration has actually been included in the definition of osteoporosis this aspect is not assessed using ABDM measurements [START_REF] Link | Osteoporosis imaging: state of the art and advanced imaging[END_REF]. Interestingly, bone microarchitecture can be assessed using highresolution quantitative computed tomography (QCT) [START_REF] Lespessailles | Imaging techniques for evaluating bone microarchitecture[END_REF] but the corresponding tool is poorly available and has never been used for large groups of subjects [START_REF] Adams | Quantitative computed tomography[END_REF].

Considering its non-radiating nature and the progress regarding radiofrequency coil technology and field strength, magnetic resonance imaging (MRI) of proximal femur microarchitecture has become possible [START_REF] Chang | MRI of the hip at 7T: feasibility of bone microarchitecture, high-resolution cartilage, and clinical imaging[END_REF][START_REF] Link | Structure analysis of high resolution magnetic resonance imaging of the proximal femur: in vitro correlation with biomechanical strength and BMD[END_REF][START_REF] Chang | 3-T MR Imaging of proximal femur microarchitecture in subjects with and without fragility fracture and nonosteoporotic proximal femur bone mineral density[END_REF]. It has been recently reported that postmenopausal women with a higher fracture risk can be distinguished from those with lower fracture risk on the basis of measurements obtained from ultra-high field (UHF) MRI [START_REF] Chang | 3-T MR Imaging of proximal femur microarchitecture in subjects with and without fragility fracture and nonosteoporotic proximal femur bone mineral density[END_REF]. On that basis, it has been suggested that UHF MRI can provide information about bone quality that are different and likely complementary than those provided by DXA. Although the very first results are promising, comparative analysis between MRI and biomechanical metrics are still very scarce with only one study performed at 1.5-T [START_REF] Link | Structure analysis of high resolution magnetic resonance imaging of the proximal femur: in vitro correlation with biomechanical strength and BMD[END_REF].

The purpose of this study was to investigate bone microarchitecture of cadaveric proximal femurs using UHF MRI and to compare the corresponding metrics with failure load assessed during mechanical compression tests and ABDM measured using DXA.

MATERIALS AND METHODS

Femoral specimens

Ten cadaveric proximal femora of 5 human donors (5 women; mean age= 86.2 ± 3.8 (SD) years; range : 82.5-90 years) were obtained within 10 days after death, according to the institutional safety and ethics regulations. Donor consent for research purposes was obtained prior to death.

No information was available regarding the cause of death or previous diseases. Donors with scars in the region of proximal femur were excluded. All specimens were carefully cleaned of soft tissue and the femoral diaphysis was cut 10 cm below the lesser trochanter to facilitate bone attachment for mechanical testing. Specimens were stored at -20°C and progressively thawed at room temperature 6 hours before testing. A single defrosting cycle was required.

CT measurements

Each femur was scanned using a Light Speed ® VCT 64 unit (General-Electric Healthcare) in order to detect femoral lesion (tumor) or fracture, and gas bubbles due to tissue degradation with the following parameters: field of view 12 cm slice thickness, 0.625; interval, 0.625 mm; tube current, 365 mA; and tube potential, 120 KV.

DXA measurements

Specimens were positioned similarly to what is conventionally done for in vivo examination with a mild internal rotation. They were placed in a vessel filled with tap water up to 15 cm in height to simulate soft tissue [START_REF] Corroller | Combination of texture analysis and bone mineral density improves the prediction of fracture load in human femurs[END_REF]. DXA measurements were performed with a Prodigy ® Scanner (General-Electric Healthcare). ABDM was measured in three regions of interest (ROIs) for each specimen (i.e., femoral neck, intertrochanteric and greater trochanter regions). The total proximal ABDM was computed.

MRI

Each specimen was scanned using a 7-T whole-body MRI scanner (Siemens Healthineers) and a 28-channel proton coil. Once the initial MRI localized images were obtained for the three orthogonal planes, an interactive localized B 0 shimming was performed using the second-order shimming procedure provided by the manufacturer. High-resolution gradient recalled-echo images of each femur were acquired in the coronal plane using the following parameters: field of view, 140 × 140 mm²; acquisition matrix size, 832  832; contiguous slice thickness, 0.5 mm; TR/TE, 20/6 msec; flip angle, 15°; number of repetitions, = 3; number of slices, = 58; in-plane voxel size, 0.17 x 0.17 mm. The corresponding acquisition time was 37 min 36 s.

Each image was initially corrected for any remaining signal inhomogeneities using the N4 algorithm [START_REF] Tustison | N4ITK: improved N3 bias correction[END_REF]. Using an open-source digital measurement software (ImageJ, NIH,) [START_REF] Doube | BoneJ: free and extensible bone image analysis in ImageJ[END_REF], images were binarized and thresholded as previously described [START_REF] Prewitt | The analysis of cell images[END_REF]. For each slice, a 10 x 10 x 10 mm volume of interest (VOI) positioned at mid-distance between the top and the bottom of the greater trochanter was selected (i.e., 60 x60 pixels in 20 slices) (Fig. 1). Bone volume fraction, trabecular thickness (Tb.Th), trabecular spacing (Tb.Sp), fractal dimension (FD), Euler characteristics, connectivity density and the degree of anisotropy (DA) were computed within the VOI using BoneJ an ImageJ module dedicated to bone images analysis.

Bone volume fraction corresponds to

. Bone volume fraction is commonly related to porosity and has been considered as a surrogate of volumetric bone density rather than a strict measure of bone microarchitecture [START_REF] Fields | Role of trabecular microarchitecture in whole-vertebral body biomechanical behavior[END_REF].

Fractal dimension is a bone texture parameter with the fractal dimension of bone-marrow surface giving some information on the degree of complexity or disorder of the bone microarchitecture. Fractal analysis expresses the roughness of the texture and characterizes the self-similarity of its gray-level variations over different scales [START_REF] Brunet-Imbault | A new anisotropy index on trabecular bone radiographic images using the fast Fourier transform[END_REF]. Texture parameters have been reported as indirect indices of the 3D microarchitecture [START_REF] Pothuaud | Fractal dimension of trabecular bone projection texture is related to three-dimensional microarchitecture[END_REF].

The number of connected structures in a network can be determined from the Euler characteristic [START_REF] Vasilić | Classification of trabeculae into three-dimensional rodlike and platelike structures via local inertial anisotropy[END_REF]. Trabecular bone can be considered as a network and its connectivity density can be calculated from the ratio between the connectivity estimate and the volume of the sample (~ number of trabeculae per unit volume) [START_REF] Doube | BoneJ: free and extensible bone image analysis in ImageJ[END_REF].

Anisotropy corresponds to the preferential spatial directional organization of a material.

Trabecular bone is typically an anisotropic material with variable mechanical properties according to the direction of the applied strength, the maximum resistance being parallel to the main line of spans. The spans which first disappear in osteoporosis are the ones which undergo the least mechanical strengths [START_REF] Pothuaud | Fractal dimension of trabecular bone projection texture is related to three-dimensional microarchitecture[END_REF] Analyses were performed by two independent operators, a 7-year-experience skeletal radiologist (D.G.) and a engineer doctor specialized in MRI (J.C.S.).

Mechanical testing

Each specimen was loaded to failure in a universal testing machine (Instron 5566, Instron).

Femur orientation within the loading apparatus was chosen so as to simulate a sideways fall on the greater trochanter [START_REF] Eeckstein | Reproducibility and side differences of mechanical tests for determining the structural strength of the proximal femur[END_REF][START_REF] Manske | Cortical and trabecular bone in the femoral neck both contribute to proximal femur failure load prediction[END_REF]. Specimens were fixed in resin (Epoxy Axon F23) at 15° internal rotation and the femoral shaft was oriented at 10° adduction within the apparatus. The load was applied to the greater trochanter through a pad, which simulated a soft tissue cover, and the femoral head was molded with resin to ensure force distribution over a greater surface area. The load was applied to the greater trochanter at a displacement rate of 10 mm/min. Failure load (in Newton) was defined as the first local maximum after which the load declined by more than 10%. Then, fractures were visually classified according to clinical criteria (femoral neck, intertrochanteric, subtrochanteric, or isolated greater trochanteric fractures) [START_REF] Zuckerman | Hip fracture[END_REF].

Statistical analysis

Each parameter was described using mean and standard deviation (SD), median and quartiles [Q1; Q3]. We firstly verified that the distribution of the parameters was not statistically different from the normal distribution using the Kolmogorov-Smirnov with exact P-value.

The inter-rater reliability of microarchitecture characterization was assessed with the intraclass correlation coefficient (ICC) for each microarchitecture variable. The average coefficient of variation between rater was presented as CV.

Then, we assessed the correlation between failure load and each of the parameters and between the parameters themselves using Pearson correlations coefficients (r) after having verified the linear relationship with scatter plots. The level of significance was set at P < 0.05.

To evaluate whether microarchitecture parameters combined to ABDM improved the accuracy of the model multivariate ridge regressions analyses (with femoral failure as the dependent factor) were performed. We used the coefficient of determination of the model (R²) to compare quality of the model with ABDM alone (R²) vs ABDM and different combinations of microarchitecture parameters (adjusted R² named adjR²). The R² indicates the percentage of the variance in the dependent variable (the femoral failure) that the independent variables (microarchitecture parameters and ABDM) explain collectively. We first reported the R² of the univariate linear regression with ABDM as the only independent variables (R²). Then, we reported the R² of the multivariate linear ridge regression with ABDM combined with one of the microarchitecture parameters adjusted (adjR²). For each microarchitecture parameters, we measured the % of improvements of the R² using the following computation:

. The % of improvement measures to what extent the addition of each of microarchitecture parameters allows to better explain the variation of the femoral failure. The ridge regression was used to take account for co-linearity due to correlation between microarchitecture parameters.

Finally, a multivariate ridge regression analysis was performed with the whole set of microarchitecture parameters and ABDM as independent variables. We used a backward stepwise analysis (elimination one parameter after the other) to only include parameters significantly associated with femoral failure at the P value <0.05. Statistical analyses were performed using SPSS V20 and ridge regression was performed using the SAS® software.

RESULTS

The mean ABDM for the total hip in our cohort was 0.72 ± 0.1 (SD) g/cm 2 (range: 0.62 -0.86 g/cm 2 ). During the compression test, a fracture could be detected for a mean failure load of 1238.5 ± 507.4(SD) N (range: 710.6 -2113 N) (mean=1034 N, Q1= 809.6, Q3= 1776.3). We observed 1 femoral neck and 9 intertrochanteric fractures. No subtrochanteric or isolated greater trochanteric fracture was observed. Microarchitecture metrics are reported in Table 1 along with the corresponding descriptive statistics.

The ICCs for the microarchitecture measurements performed in the greater trochanter were 0.90 (CV = 6.2%) for bone volume fraction, 0.89 (CV=6.6%) for trabecular thickness, and 0.80 (CV = 5.6%) for trabecular spacing, 0.81 (CV = 10.1%) for the degree of anisotropy, 0.88 (CV=9.5%)

for connectivity density, 0.91 (CV = 4.7%) for fractal dimension and 0.88 (CV = 6.2%) for Euler characteristics.

All of the microarchitecture metrics but connectivity density were significantly correlated with failure load and with each other (Table 1; Fig. 2). Bone volume fraction had the highest correlation with failure load (r= 0.736; P=0.01) Most of the microarchitecture parameters strongly correlated with each other but only the degree of anisotropy correlated with trabecular thickness (Table 2). The connectivity parameters (i.e., Euler characteristics and connectivity density) significantly correlated with each other (P=0.0001). Euler characteristics was significantly correlated with load failure (P=0.044) whereas connectivity density was not (P=0.063).

Ridge regression analysis demonstrated that correlation with fracture load prediction could be significantly increased from R²=0.418 to adjR²=0.69 when bone microarchitecture parameters metrics were combined with ABDM (Table 3). More specifically, Euler characteristics was the variable with the largest influence on the R² increase when combined to ABDM: when ABDM was combined with Euler characteristics the adjR² yielded the value of 0.69 (improvement of 64.6%).When connectivity density was combined to ABDM, the adjR² yielded the value of 0.67 (60.3% of improvement); while fractal dimension was combined with ABDM, the adjR² yielded the value of 0.69 (62.9% of improvement). Similarly, improvement in failure load correlation was 54.3% when combining bone fraction and ABDM, 60.5% when combining trabecular spacing and ABDM, 22.2%when combining trabecular thickness and ABDM, and 7.6% when combining the degree of anisotropy and ABDM.

Using a ridge multivariate regression analysis including all the microarchitecture metrics and ABDM and after a backward elimination of the non-significant parameters (at alpha level equal to 0.05), fractal dimension was the single eliminated parameter.

DISCUSSION

In the present study we assessed proximal femoral bone microarchitecture using UHF-MRI and compared the corresponding results with those from DXA and mechanical compression tests.

The correlations between bone microarchitecture parameters and mechanical compression tests were better than in those reported in further studies.

In our study, ABDM significantly correlated with failure load in line with two previous studies [START_REF] Corroller | Combination of texture analysis and bone mineral density improves the prediction of fracture load in human femurs[END_REF][START_REF] Seo | Efficacy of dual energy X-ray absorptiometry for evaluation of biomechanical properties: bone mineral density and actual bone strength[END_REF]. The microarchitecture (bone volume fraction, trabecular thickness, trabecular spacing, the degree of anisotropy and Euler characteristics) and texture metrics (fractal dimension) also significantly correlated with bone strength in line with previous study [l5]. In addition, ABDM and microarchitecture metrics were not related thereby indicating, as previously suggested, that MRI and DXA provide different information regarding bone quality and fracture risk [START_REF] Chang | 3-T MR Imaging of proximal femur microarchitecture in subjects with and without fragility fracture and nonosteoporotic proximal femur bone mineral density[END_REF]. Interestingly, the statistical power of the correlation between the microarchitecture and the mechanical metrics was improved when both ABDM and a microarchitecture variable were combined further supporting that both indices are not providing similar information and that the combination can be of diagnostic interest [START_REF] Chang | 3-T MR Imaging of proximal femur microarchitecture in subjects with and without fragility fracture and nonosteoporotic proximal femur bone mineral density[END_REF].

Among the microarchitecture metrics, bone volume fraction displayed the largest correlation with failure load. These results further support those from previous MRI studies conducted in the distal radius, ankle, distal femur, wrist and vertebrae [START_REF] Link | Structure analysis of high resolution magnetic resonance imaging of the proximal femur: in vitro correlation with biomechanical strength and BMD[END_REF][START_REF] Majumdar | Trabecular bone architecture in the distal radius using magnetic resonance imaging in subjects with fractures of the proximal femur[END_REF][START_REF] Link | In vivo high resolution MRI of the calcaneus: differences in trabecular structure in osteoporosis patients[END_REF]. On the basis fragility fractures [START_REF] Chang | 3 Tesla MRI detects deterioration in proximal femur microarchitecture and strength in long-term glucocorticoid users compared with controls[END_REF]. In a study conducted at 3-T in 60 postmenopausal women, the authors did not report significant bone volume fraction difference between the control group and the group with osteoporotic fractures thereby illustrating that the higher resolution obtained at UHF might account for this apparently paradoxical result [START_REF] Chang | 3-T MR Imaging of proximal femur microarchitecture in subjects with and without fragility fracture and nonosteoporotic proximal femur bone mineral density[END_REF]. Link et al. found a significant correlation between bone volume fraction measured in the great trochanter and biomechanical testing in the femoral neck (r= 0.62) [START_REF] Link | Structure analysis of high resolution magnetic resonance imaging of the proximal femur: in vitro correlation with biomechanical strength and BMD[END_REF]. This correlation was validated when measurements were performed using 0.9 mm thickness MRI slices but not when thickness was reduced to 0.3 mm (r = 0.32) likely resulting from a reduced signal-to-noise ratio. In the present study, strong correlations were found between bone volume fraction and other microarchitecture metrics suggesting a potential overlap between these variables for the assessment of bone quality.

Trabecular thickness and trabecular spacing were also very significantly correlated with failure load with correlation coefficient larger than those computed using ABDM values. This result supports those from previous studies which have illustrated that trabecular volume and trabeculae space both increased with age [START_REF] Milovanovic | Microstructural basis for particular vulnerability of the superolateral neck trabecular bone in the postmenopausal women with hip fractures[END_REF]. Combining trabecular spacing with ABDM significantly improved the failure load identification whereas combining trabecular thickness with BMD did not, probably due to a lack of power of the study. Both Euler characteristic (64.8%). and connectivity density (60.3%) had a large impact on the fracture identification from the combination between microarchitecture metrics and ABDM thereby illustrating a great potential for the assessment of bone strength in vivo from combined measurements. One can be surprised by this result because connectivity density was not significantly correlated to failure load (r=0.606, p=0.063), maybe due to a lack of power of the study because p is close to significance. Nevertheless, in our study, connectivity density and ABDM did not correlate (r=0.145, P=0.688), they therefore provide different information on the failure load. And when adjusted on ABDM, connectivity density provides significant information on failure load.

In our study, the degree of anisotropy was significantly correlated with failure load in agreement with previous results indicating that anisotropy is one of the main accounting factors of the bone mechanical resistance [START_REF] Majumdar | Trabecular bone architecture in the distal radius using magnetic resonance imaging in subjects with fractures of the proximal femur[END_REF]. Combining the degree of anisotropy and ABDM did not significantly improve the relationship between the microarchitecture and mechanical parameters in agreement to what has been previously suggested [START_REF] Majumdar | Trabecular bone architecture in the distal radius using magnetic resonance imaging in subjects with fractures of the proximal femur[END_REF]. Indeed, in our study the degree of anisotropy and ABDM are significantly linked (r= 0.637, P=0.048), that is why the degree of anisotropy does not provide any additional information on failure load vs. ABDM.

In the present study, fractal dimension was strongly correlated with both other microarchitecture metrics and failure load, and the failure load information was improved if fractal dimension was combined to ABDM. These results confirm those obtained from DXA measurements and using the trabecular bone score indicating that trabecular bone score combined with ABDM incrementally improved fracture assessment in postmenopausal women [START_REF] Hans | Bone microarchitecture assessed by TBS predicts osteoporotic fractures independent of bone density: the Manitoba study[END_REF].

The VOIs used for the microarchitecture measurements were positioned in the greater trochanter according to previous results [START_REF] Chang | 3-T MR Imaging of proximal femur microarchitecture in subjects with and without fragility fracture and nonosteoporotic proximal femur bone mineral density[END_REF] and given the high image quality there. Gas bubbles were present in the region of the femoral neck likely due to the metabolic processes occurring in ex-vivo specimen. Those gas bubbles generate important artifacts in MRI. A small VOI (1x1x1cm) similar as the recent study of Chang et al. [START_REF] Chang | 3-T MR Imaging of proximal femur microarchitecture in subjects with and without fragility fracture and nonosteoporotic proximal femur bone mineral density[END_REF] was chosen in order to avoid bubbles.

In addition, during the biomechanical tests, most of the femoral fractures occurred in the intertrochanteric region (only one in the femoral neck). Considering that our in-plane resolution was within the range of trabecular size, microstructure metrics could have been slightly biased due to partial volume effects. As previously indicated, the resolution we obtained might have caused artefactual widening of trabeculae. However, the correlative analyses with mechanical variables are still valid and of high interest. In addition, the resolution we obtained using UHF MRI (voxel size = 0.17 x 0.17 x 0.5mm) was almost equivalent to the resolution that can be achieved using HR-QCT [START_REF] Sornay-Rendu | Alterations of cortical and trabecular architecture are associated with fractures in postmenopausal women, partially independent of decreased BMD measured by DXA: the OFELY study[END_REF] and similar to the resolution previously reported at 7-T [START_REF] Bhagat | Performance of μMRI-Based virtual bone biopsy for structural and mechanical analysis at the distal tibia at 7T field strength[END_REF]. Due to image blurring and X-ray exposure, HR-QCT cannot be used in clinical routine so that UHF MRI could be considered as an interesting alternative [START_REF] Lespessailles | Imaging techniques for evaluating bone microarchitecture[END_REF]. Acquisition time (37 min) was still too long for a clinical context but might be shortened using other MRI pulse sequences such as 3D fast spin-echo with out-of-slab cancellation [START_REF] Magland | 3D fast spin echo with out-of-slab cancellation: a technique for high-resolution structural imaging of trabecular bone at 7 Tesla[END_REF].

Our study has some limitations. Our results have been obtained from a small number of specimens, although this number is similar to the amount used in some other studies [START_REF] Link | In vivo high resolution MRI of the calcaneus: differences in trabecular structure in osteoporosis patients[END_REF].

Samples preparation including a freezing-defreezing process and soft tissue removal might have altered the cadaveric samples and biased the corresponding results. Considering that the range of ABDM values reported in the present study was similar to those previously published ex-vivo [16, 28,] this bias might be considered as minor. As hematopoietic bone marrow could be detected in vivo, one can wonder about a potential contamination of hematopoietic bone marrow for the signal processing [START_REF] Link | Structure analysis of high resolution magnetic resonance imaging of the proximal femur: in vitro correlation with biomechanical strength and BMD[END_REF]. In our old cadaveric specimens, active red marrow is not expected and corresponding hyperintensities were not observed.

In conclusion, the results of the present study demonstrate that microarchitecture metrics quantified from excised proximal femur using UHF MRI are correlated with biomechanical strength and could provide an additional assessment tool of bone quality. Combined with ABDM values, these parameters might improve the prediction of load failure in previously undetected osteoporotic patients.

Acknowledgment

  of 1.5-T MRI measurements (slice thickness = 300 µm, in plane resolution = 117 µm), Majumdar et al. reported a lower bone volume fraction in the distal radius of subjects with fragility fractures (mean bone volume fraction = 0.23) as compared to controls (mean bone volume fraction = 0.29) while Link et al. showed similar results in the calcaneal bone and in the proximal femur (mean bone volume fraction=0.33) [14, 28, 29]. In our population of women cadavers without femoral fractures, mean bone volume fraction at the proximal femur was slightly larger i.e. 0.37 and the same as mean values reported by Chang et al. in women with

Figure 1 :

 1 Figure 1: Typical coronal MRI of a cadaveric femur in saline. A is the original image and B is

Figure 2 :

 2 Figure 2: Graph displaying the relation observed between bone volume fraction (BVF) on

Table legend Table 1 :

 legend1 Mean, standard deviation (SD), quartile Q1 and Q3, median, for each imaging variable and Pearson correlation (r) between imaging variables and failure load. Areal bone mineral

density (ABDM), bone volume fraction (BVF), trabecular thickness (TT), trabecular spacing (TS), fractal dimension (FD), Euler characteristics (EC), connectivity density (CD), degree of anisotropy (DA).

Table 2 :

 2 Pearson's correlation coefficient between vertebral microarchitecture parameters and areal bone mineral density (ABMD). Correlation coefficients between bone volume fraction (BVF) and other microarchitecture parameters trabecular thickness (TT), trabecular spacing (TS), fractal dimension (FD), Euler Characteristics (EC), connectivity density (CD), degree of anisotropy (DA) obtained at UHF-MRI, and ABDM measured by DXA.

Table 3 :

 3 Multiple regression analysis of combinations of ABDM and microarchitecture parameters used to explain the femoral failure load. *significant difference between adjusted R² of ABDM alone and ABDM + microarchitecture parameters, P value < 0.05


Martial Plasse
email: martial.plasse@mnhn.fr

Eli Amson

Jérémie Bardin

Quentin Grimal

Damien Germain

metaphyses of non-avian reptiles (Crocodylia, Squamata and Testudines): Lifestyle, allometry and phylogeny

Keywords: bone functional adaptation, bone volume fraction, degree of anisotropy, epiphysation, histology ORCID

| INTRODUCTION

Bone is a tissue able to adapt to its external mechanical environment. This seminal insight, commonly referred to as "bone functional adaptation," has been originally described by Wilhelm Roux [START_REF] Roux | Beitrage zur Morphologie der funktionellen Anpassung[END_REF]. Within the bones, trabecular architecture is more responsive and malleable to external loads (for a review see [START_REF] Cowin | The false premise of Wolff's law[END_REF][START_REF] Kivell | A review of trabecular bone functional adaptation: What have we learned from trabecular analyses in extant hominoids and what can we apply to fossils[END_REF]. During bone modeling, osteocytes embedded in the bone matrix act as mechano-sensors and send strain-related signals to other cells [START_REF] Huiskes | Effects of mechanical forces on maintenance and adaptation of form in trabecular bone[END_REF]. They recruit osteoblasts, which create bone, and osteoclasts, which resorb bone [START_REF] Gerhard | In silico biology of bone modelling and remodelling: Adaptation[END_REF], processes which result in bone functional adaptation [START_REF] Martin | Growth, modeling and remodeling of bone[END_REF].

A change of loading regimes on bone can modify the trabecular architecture. Many experimental studies support this hypothesis. For instance, macaques trained to walk bipedally have shown significantly different shape of femur and ilium than wild (quadrupedal) ones [START_REF] Volpato | Textural characteristics of the iliac-femoral trabecular pattern in a bipedally trained Japanese macaque[END_REF]. Therefore, different locomotor behaviors may leave different signatures inside bones. Indeed, in the above-cited bipedally trained macaque, the trabecular architecture of the iliac body became more anisotropic, thicker, and more structured vertically oriented [START_REF] Volpato | Textural characteristics of the iliac-femoral trabecular pattern in a bipedally trained Japanese macaque[END_REF].

In the same way, sheep exercised daily to trot on inclined treadmills have developed thicker trabeculae with a higher bone volume fraction in their distal radius [START_REF] Barak | A Wolff in sheep's clothing: Trabecular bone adaptation in response to changes in joint loading orientation[END_REF]. A similar adaptation in trabecular architecture has been shown in rabbits by the application of in vivo cyclic loading on the hind limbs [START_REF] Van Der Meulen | Cancellous bone adaptation to in vivo loading in a rabbit model[END_REF].

Many studies have attempted to test for correlations between trabecular architecture and locomotor behavior. In primates, trabecular architecture can be different in the femoral head according to the locomotor behavior: between leaping and nonleaping strepsirrhines (Ryan & Ketcham, 2002a), among locomotor behaviors (quadruped, climber, biped, quadrumanous, brachiator) of anthropoids [START_REF] Ryan | Unique suites of trabecular bone features characterize locomotor behavior in human and non-human anthropoid primates[END_REF], between hunter-gatherer populations and agricultural societies [START_REF] Ryan | Gracility of the modern Homo sapiens skeleton is the result of decreased biomechanical loading[END_REF]. In contrast, other studies found that trabecular structures are highly similar among the proximal femoral necks of anthropoid locomotor behaviors, but also between their humeral and femoral head [START_REF] Fajardo | Nonhuman anthropoid primate femoral neck trabecular architecture and its relationship to locomotor mode[END_REF][START_REF] Ryan | Trabecular bone structure in the humeral and femoral heads of anthropoid primates[END_REF]. Other studies, focused on extant primates, have attempted to infer the locomotor behavior of extinct primates, for example, omomyids (Ryan & Ketcham, 2002b) or Australopithecus (Barak et al., 2013).

Lifestyle represents the environment where the animal usually lives (e.g., terrestrial, fossorial, climber, aquatic or amphibious). Many lifestyles can be encompassed by a same locomotor behavior and vice versa. For instance, species walking quadrupedally can have various lifestyles such as on land (terrestrial), underground (fossorial), in trees (climber) or at the bottom of lakes (aquatic/amphibious). In contrast to locomotor behavior, the link between trabecular architecture and lifestyle has been little studied and research in this field is scarce. In an analysis focused on the humeral and femoral head of four primates species, terrestrial taxa have shown more anisotropic trabecular architecture in comparison to arboreal ones [START_REF] Fajardo | Three-dimensional analysis of nonhuman primate trabecular architecture using micro-computed tomography[END_REF]. In another broader study on anthropoid primates, trabecular architecture from the humeral and femoral heads was found to be similar in arboreal and terrestrial locomotor groups [START_REF] Ryan | Unique suites of trabecular bone features characterize locomotor behavior in human and non-human anthropoid primates[END_REF]. In a study focused on the fore limb epiphyses of xenarthrans, trabeculae have shown the clearest functional signal through their anisotropy: armadillos, fully terrestrial and fossorial, have the most anisotropic trabecular architecture in xenarthrans [START_REF] Amson | Trabecular architecture in the forelimb epiphyses of extant xenarthrans (Mammalia)[END_REF]. In a study focused on the sciuromorph femoral head, four trabecular parameters have shown functional signals related to the various lifestyles found in this clade [START_REF] Mielke | Trabecular architecture in the sciuromorph femoral head: Allometry and functional adaptation[END_REF].

Thanks to the development of X-ray computed microtomography, 3D trabecular architecture could be extensively studied in birds (e.g., [START_REF] Bishop | Cancellous bone and theropod dinosaur locomotion. Part I-An examination of cancellous bone architecture in the hindlimb bones of theropods[END_REF][START_REF] Doube | Trabecular bone scales allometrically in mammals and birds[END_REF][START_REF] Fajardo | Postcranial skeletal pneumaticity: A case study in the use of quantitative microCT to assess vertebral structure in birds[END_REF][START_REF] Pontzer | Trabecular bone in the bird knee responds with high sensitivity to changes in load orientation[END_REF] and mammals (e.g., many orders [START_REF] Doube | Trabecular bone scales allometrically in mammals and birds[END_REF], bovids [START_REF] Mittra | Interrelationship of trabecular mechanical and microstructural properties in sheep trabecular bone[END_REF][START_REF] Sode | Resolution dependence of the non-metric trabecular structure indices[END_REF], lagomorphs [START_REF] Marchand | Standardized three-dimensional volumes of interest with adapted surfaces for more precise subchondral bone analyses by micro-computed tomography[END_REF][START_REF] Van Der Meulen | Cancellous bone adaptation to in vivo loading in a rabbit model[END_REF], primates [START_REF] Barak | Trabecular evidence for a human-like gait in Australopithecus africanus[END_REF][START_REF] Cunningham | Anticipating bipedalism: Trabecular organization in the newborn ilium[END_REF], Kivell, Skinner, Lazenby, & Hublin, 2011, Lazenby, Skinner, Kivell, & Hublin, 2011[START_REF] Sode | Resolution dependence of the non-metric trabecular structure indices[END_REF], rodents [START_REF] Carlson | Do different locomotor modes during growth modulate trabecular architecture in the murine hind limb?[END_REF][START_REF] Lambers | Trabecular bone adapts to long-term cyclic loading by increasing stiffness and normalization of dynamic morphometric rates[END_REF][START_REF] Sode | Resolution dependence of the non-metric trabecular structure indices[END_REF], sciuromorphs [START_REF] Mielke | Trabecular architecture in the sciuromorph femoral head: Allometry and functional adaptation[END_REF], suids [START_REF] Ben-Zvi | 3D architecture of trabecular bone in the pig mandible and femur: Inter-trabecular angle distributions[END_REF], and xenarthrans [START_REF] Amson | Trabecular architecture in the forelimb epiphyses of extant xenarthrans (Mammalia)[END_REF]). In comparison, 3D trabecular architecture of nonavian reptiles has received little attention. The extensive sampling of [START_REF] Doube | Trabecular bone scales allometrically in mammals and birds[END_REF] includes a single femur of Crocodylus niloticus. Recently, another study focused on the trabeculae of avian hind limb bones (femur, tibia, tibiotarsus, and fibula) to infer dinosaurian locomotion and these observations were compared to those made on crocodylians and lizards, that is, two species of Crocodylus and three of Varanus [START_REF] Bishop | Cancellous bone and theropod dinosaur locomotion. Part I-An examination of cancellous bone architecture in the hindlimb bones of theropods[END_REF]. One should note that the latter study only analyzed trabecular direction. Thus, few data exist about taxa using a sprawling posture.

The purpose of this article is to highlight relations between humeral trabecular architecture and lifestyle within various clades of reptiles (Crocodylia, Squamata, and Testudines). These groups exhibit a broad variability of lifestyles: aquatic, amphibious, generalist terrestrial, fossorial, or climbing. According to the paradigm of the bone functional adaptation, we predict: a terrestrial tetrapod will show trabeculae with a well-marked main orientation (mainly subject to gravity), while an aquatic tetrapod will show a more isotropic trabecular architecture (the gravity effect being strongly decreased). For an amphibious tetrapod, we expect its trabecular structure to be intermediate in that regard. A similar interpretation has allowed the inference that the stem-tetrapod Ossinodus spent considerable time on land, on the basis of essentially parallel trabeculae in its radius [START_REF] Bishop | Oldest pathology in a tetrapod bone illuminates the origin of terrestrial vertebrates[END_REF]. Our expectations are herein tested in statistical framework taking into account both allometric and phylogenetic effects.

| Specimens and functional categories

The humerus was selected for this study for several reasons. While the hind limb has been completely reduced in various taxa, for example, in Bipes biporus (Amphisbaenia), the fore limb is more commonly retained. Also, during tetrapod evolution, the fore limb is hypothesized to have been the first to gain a role in land/substrate locomotion, as suggested for Ichthyostega [START_REF] Pierce | Three-dimensional limb joint mobility in the early tetrapod Ichthyostega[END_REF]. The hind limb exapted only later in the evolution of the clade to walk on land. We sampled 10 squamates, eight turtles and two crocodylians (Table 1). Ideally, we tried to encompass most of the reptilian diversity choosing one specimen per family among the most disparate ones (except for the two species of the genus Varanus). All sampled specimens of squamates still possess an epiphyseal plate, except for Tiliqua, which ended its growth. Turtles and crocodylians do not develop epiphyseal plates. The specimen MNHN-ZA-AC-1889-384, from Gabon, belongs to the species Trionyx cryptopus, which is not valid anymore. It could be Cyclanorbis senegalensis (=Cryptopus senegalensis Dumeril & Bibron, 1835), which is not reported in Gabon for the moment (S. Bailon, pers. comm.).

We selected species in order to cover a broad spectrum of lifestyles: aquatic, amphibious, generalist terrestrial, fossorial and climber.

Lifestyle is difficult to assess, because it is a somewhat continuous variable. We defined as terrestrial a species that generally lives on the ground, although it might be able to occasionally dig underground or climb. A climbing species will be found most of the time on plants (arboreal) or on rocks (saxicolous). A fossorial species is able to dig burrows with claws or with the head. An amphibious species spends a considerable amount of time both on the ground and in the water. An aquatic species spends most its time in water and can show special aquatic adaptations such as swimming paddles. Lifestyle for each taxon with associated bibliographic references is given in Table 1.

Within reptiles, similar lifestyles have been acquired many times independently (Figure 1). Squamates are mainly terrestrial, but fossorial and climbing lifestyles appear to have been convergently acquired on several instances (see Figure 1). Amblyrhynchus is the only sampled amphibious taxon among extant squamates. Sampled crocodylians are only amphibious. Testudines are mainly amphibious, but the aquatic lifestyle was convergently acquired in Chelus and Caretta. Centrochelys is the only fossorial turtle in our sampling. Therefore, the sampled phylogeny and lifestyles do not perfectly correlate. Nevertheless, a two-block partial least squares analysis [START_REF] Adams | Phylogenetic ANOVA: Group-clade aggregation, biological challenges, and a refined permutation procedure[END_REF] suggests that the lifestyles groups are aggregated on the phylogeny (Figure 1) to some extent (r-PLS: 0.7224; p-value: .0162, see script in Supporting Information, file 1).

In addition to lifestyles, we also took into account locomotor postures (and associated bibliographic references, Table 1), which have already been correlated to the trabecular architecture. Extant tetrapods show two main types of limb posture: a "sprawling" posture in salamanders and lizards, in which the limbs project laterally from the body and an "erect" posture in mammals and birds, in which the limbs are held under the body [START_REF] Russell | Biomechanics and kinematics of limbbased locomotion in lizards: Review, synthesis and prospectus[END_REF]. Extant crocodylians are generally defined as semi-erect with the body held halfway between the positions of the two other limbs postures [START_REF] Reilly | Locomotion in Alligator mississippiensis: Kinematic effects of speed and posture and their relevance to the sprawling-to-erect paradigm[END_REF]. Squamates can show two "sprawling" postures: a "belly-dragging" sprawling posture (e.g., Tiliqua scincoides) in which the animal's weight partially rests on the trunk with a direct contact to the substrate or a "raised" sprawling posture (e.g., Iguana iguana) without ventral trunk-ground contact and in which the shoulder/hip and elbow/knee joints bear the animal's weight [START_REF] Nyakatura | Bridging "Romer's gap": Limb mechanics of an extant belly-dragging lizard inform debate on tetrapod locomotion during the early carboniferous[END_REF].

We also noted when the species is able to practice bipedalism, either involved in an escape behavior (e.g., Basiliscus) or in defensive posturing (e.g., many species of Varanus). In turtles, we distinguished two groups according to the locomotor preference: the "bottom-walkers" and the "good swimmers." Thus, inside the same locomotor behavior (e.g., quadrupedal locomotor behavior), many locomotor postures can be observed among tetrapods ("belly-dragging" sprawling, "raised" sprawling, or "erect" postures). Each clade of reptiles is characterized by its own locomotor postures (Figure 1). Squamates are all sprawlers, but belly dragging sprawling posture and/or raised sprawling posture were convergently acquired several times, which is also the case for occasional bipedalism. Testudines are either bottom walkers or good swimmers, but at least one of these postures appeared twice independently. As for lifestyles, postures do not perfectly aggregate on the phylogeny (Figure 1), but there is nevertheless a correlation (r-PLS: 0.8375, p-value: .001, see script in Supporting Information, file 1).

| Data acquisition

Left or right humeri, depending on the availability, were X-rayed using a computed tomography (CT) imaging system (AST-RX platform and Ge Sensing and inspection Technologies phoenix-ray v|tome|x L240-180 CT scanner) at the Muséum national d'Histoire naturelle (MNHN), with nanofocus RX source 180 kV/15 W and detector 400 × 400 mm with a matrix of 2,024 pixels (pixel size: 200 × 200 μm). The images were acquired with different scan parameters (exposure time, voltage, current and filter; see Supporting Information, file 2) according to the specimens and the voxel sizes ranged from 13.604 to 113.825 μm. The micro-CT data were processed utilizing datos|x reconstruction software (Phoenix|x-ray, release 2.0) and then exported as a 16 bits TIFF image stack.

Volumes of interest (VOIs) were selected with the software CT-Analyser (CTAnalyser Software V 1.16, Skyscan NV, Kontich, Belgium). We chose spherical VOIs centered in the proximal metaphysis, at the location where the pectoral process is the most developed, because this part is present across the whole dataset (Figure 2). We defined the VOIs to be as large as possible to sample as many trabeculae as possible, but without including cortical bone. This trabecular extraction was preferred to other traditional methods (same size VOIs or VOIs proportional to the epiphysis size) to obtain a maximum of trabeculae from small specimens. The rest of the process was performed with the Fiji package [START_REF] Schindelin | Fiji: An open-source platform for biological-image analysis[END_REF] and the BoneJ plugin [START_REF] Doube | BoneJ: Free and extensible bone image analysis in ImageJ[END_REF]. The extracted VOIs were binarized with T A B L E 1 List of specimens included in the analyses with corresponding clades, species, catalogue number, lifestyles, and locomotor postures (and their associated bibliographic references). The epiphysation degree is indicated in the column "epiphyseal plate": "Present" if the epiphysis shows an epiphyseal plate, due to the presence of secondary centers of ossification and "absent," if the epiphysis does not show an epiphyseal plate "Optimize Threshold > Threshold Only" and their isolated particles was removed with "Purify."

Then eight trabecular parameters were measured with BoneJ (raw measurements given in Table 2, means for each lifestyle in stack with BoneJ, the plugin would also consider the spacing between the sphere and the cube vertices. This external space was excluded from the calculation to measure a reliable value of Tb.Sp (Table 2). In the same way, BoneJ will calculate TV from the cubic stack and not from the spherical VOI. Thus, we calculated the spherical TV from its radius r (its diameter can be extracted with CTAn).

Body mass could not have been used as a body size proxy, as it was unknown for all specimens. The average body weight was also unknown for the great majority of the sampled species. Doube et al.

(2011) used femoral head radius for that purpose. In our dataset, the shape of humeral head varies greatly among the main clades: in articular view, it is subrectangular in Crocodylia, subovate in Squamata, and subcircular in Testudines. Defining a size proxy with an external measure would therefore be unreliable with such a diversity of humeral shapes. We hence favored TV as a body size proxy, which is directly measured on the specimens.

| Statistical analyses

All the computations were performed with R version 3.4.4 (R Core

Team, 2013). The eight following trabecular parameters were included in the analyses: Av.Br.Len, Tb.Th, Tb.Sp, BS/TV, BV/TV, Conn.D, DA, and Tb.N. We calculated size-corrected trabecular parameters, which are the residuals of linear regressions (lm function) of the original parameters against the size proxy TV (in this case, the "size-corrected" parameter name is preceded by "sc"). We performed various comparisons among these parameters depending on lifestyles or locomotor postures. We checked the normality of the distribution (shapiro. test function) and the homogeneity of variance (bartlett. test function). If these conditions were met, we perform a traditional analysis of Phylogeny: To test whether phylogeny influences the trabecular architecture, we used the Testudines phylogenetic tree topology and the divergence times from [START_REF] Shaffer | Phylogenomic analyses of 539 highly informative loci dates a fully resolved time tree for the major clades of living turtles (Testudines)[END_REF] and data from [START_REF] Zheng | Combining phylogenomic and supermatrix approaches, and a time-calibrated phylogeny for squamate reptiles (lizards and snakes) based on 52 genes and 4162 species[END_REF] for Crocodylia and Squamata. To measure the phylogenetic signal of each trabecular parameter, we calculated Pagel's lambda [START_REF] Pagel | Inferring the historical patterns of biological evolution[END_REF], Table 5), with the phylosig function of the "phytools" package [START_REF] Revell | Phytools: An R package for phylogenetic comparative biology (and other things)[END_REF]. The parameter λ is a measure of the observed scaling (a obs ) of the regression between each trabecular parameter and VOI edge length (both log-transformed) was compared with an expected scaling under isometry (a iso ). As TV is a volume (unit:

F I G U R E
mm 3 ), the a iso in our analysis will be equal to the third of values from [START_REF] Mielke | Trabecular architecture in the sciuromorph femoral head: Allometry and functional adaptation[END_REF], because its VOI edge length was expressed in mm. BV/TV and DA are dimensionless ratios for which a iso = 0 (see Table 6, Supporting Information, file 5). Av.Br.Len, Tb.Th, and Tb.Sp are expressed in mm (unit: length 1 ) and would increase under isometry with a iso = 1/3 (length divided by volume). BS/TV (a surface divided by a volume) and Tb.N (a number divided by a length) are expressed in mm -1 and will have an a iso = -1/3. Conn.D, expressed in number per mm 3 (unit: length -3 ), will have an a iso = -1. For each regression, we calculated the confidence intervals to 95% (confint function) of the observed slope (a obs ) to test a possible significant deviation between both scalings. An a iso significantly lower than a obs and absent from the a obs confidence intervals indicates positive allometry. An a iso significantly higher than a obs and absent from the a obs confidence intervals indicates negative allometry. An a obs nonsignificantly different to a iso (i.e., a iso in the a obs confidence intervals) indicates an isometry.

Lifestyles: We used the "lda" function [START_REF] Venables | Modern applied statistics with S[END_REF] from the MASS package to perform several linear discriminant analyses to obtain the best discrimination of various lifestyles. A linear discriminant analysis (LDA) maximizes the variance between groups and minimizes the variance inside each group. We used a leave-oneout cross-validation (CV) to determine the posterior probability for each taxon to belong to a functional group: each specimen is successively removed, then both the model and the prediction for this specific specimen are calculated. We chose to run the LDA according to different modalities (see Table 7, Supporting Information, files 6 and 8): with the raw data or with the size-corrected parameters (to investigate the influence of size in the discrimination) and with or without CV (to compare the predictive ability of the model and the discrimination within the morphological space). In each modality, we calculated the percentage of well-predicted lifestyles, which fit to the number of well-classified specimens divided by the number of specimens. In a first LDA (referred to as "basic"), we used the eight trabecular parameters and the five different lifestyles (aquatic, amphibious, terrestrial, fossorial, and climbing). To investigate the effect of BV/TV, which showed a significant phylogenetic signal (see Table 5), we chose to remove this parameter from a second one. We a priori performed linear correlations between trabecular parameters and we found that BS/TV was highly correlated to Conn.D and Tb.N (R 2 = .5957, pvalue = 6.72 × 10 -5 , and R 2 = .7542, p-value = 6.88.10 -7 , respectively) and Tb.Sp was highly correlated to Av.Br.Len and Tb.Th (R 2 = .6891, p-value = 5.93.10 -6 , and R 2 = .561, p-value = 1.45.10 -4 , respectively). To exclude highly correlated variables, we deleted BS/TV and Tb.Sp in a third one. For the fourth LDA, we performed a principal component analysis (PCA) with the function PCA from the package FactoMineR [START_REF] Lê | FactoMineR: An R package for multivariate analysis[END_REF]) and used the extracted scores for the individuals, always in the purpose to obtain a better discrimination with a minimum of variables. Three lifestyles include only two or three specimens. To avoid lifestyles overlap in the morphological spaces and to increase the discriminating power of LDAs, we reduced the number of categories by gathering them in the last LDAs. In a fifth LDA, we used the eight variables, but we gathered the aquatic and amphibious lifestyles in a "water" category, while we gathered the three other lifestyles in a "ground" category.

In a sixth LDA, we used three lifestyle categories: aquatic, amphibious and "ground" (the latter grouping the same three lifestyles). We also performed a phylogenetic Flexible Discriminant Analysis (pFDA;

Motani & Schmitz, 2011) with the "mda" package [START_REF] Hastie | Flexible discriminant analysis by optimal scoring[END_REF] to take into account the phylogeny, but this analysis did not give an improved discrimination of lifestyles as the best discrimination was obtained with a Pagel's lambda equals to zero.

To test our hypotheses on relationships between trabecular anisotropy and lifestyles, we performed additional statistical analyses, where we compared DA according to lifestyles. We do not need to compare scDA, because p-value of the linear regression of DA against TV (both log-transformed) is not significant (R 2 = .1537, pvalue = .087). In the first comparison, all specimens were included. In the second comparison, specimens for which the corresponding VOI comprised less than 50 trabeculae were excluded. Indeed, calculating the degree of anisotropy from a VOI containing few trabeculae is not really reliable. Thus, by using a histogram on the Connectivity parameter, we chose to determine the lower limit to 50 trabeculae (We cannot determine this limit from Tb.N or Conn.D, which are average numbers of trabeculae). In the last comparisons, we also compared VOIs with more than 50 trabeculae but independently in

| RESULTS

| Histomorphometric results

Within reptiles, on average, climbers have shorter trabeculae than members of others lifestyles (see Tables 2 and3). On average, aquatic reptiles show thicker and more spaced trabeculae. Depending on Conn.D and Tb.N, on average, trabeculae are more densely packed in amphibious reptiles. On average, amphibious reptiles show a higher BS/TV and a higher BV/TV. BV/TV is significantly lower in squamates than in the crocodylian-turtle clade (mean = 0.22 and 0.39, respectively; ANOVA: p-value = 1.17 × 10 -4 ; Tukey's test between Squamata and Testudines: p-value = 1.50 × 10 -4 ; Tukey's test between Squamata and Crocodylia: p-value = .011; Tukey's test between Testudines and Crocodylia: p-value = .99). On average, the degree of anisotropy is similar between the lifestyles.

In Squamata, trabeculae of the proximal humeral metaphysis have an average length of 238 μm, an average thickness of 115 μm and an average spacing of 366 μm (see Tables 2 and4). VOIs include an average Conn.D of 19 trabeculae/mm 3 and an average Tb.N of 2 trabeculae/mm. The average BS/TV is 2.45 mm -1 and the average DA is 0.66. In squamates (Figure 3), BV/TV shows a wide range of variation (from 0.083 in Basiliscus to 0.3 in Heloderma) and the average BV/TV is 0.22.

In Testudines, trabeculae of the proximal humeral metaphysis have an average length of 314 μm, an average thickness of 182 μm and an average spacing of 325 μm (see Tables 2 and4). VOIs include an average Conn.D of 67 trabeculae/mm 3 and an average Tb.N of 2.80 trabeculae/mm. The average BS/TV is 3.25 mm -1 and the average DA is 0.59. In turtles (Figure 4), BV/TV shows two well-distinct categories (Kruskal-Wallis chi-squared = 5, p-value = .02535) and the average BV/TV is 0.39.

| Phylogenetic signal

Pagel's lambda for each parameter are presented in Table 5. A significant phylogenetic signal is present for the parameter "BV/TV" (Pagel's T A B L E 6 Allometry in the proximal humeral metaphysis. Trabecular parameters scaling against TV (Total volume) for all reptiles, only squamates and only turtles. The two variables were log-transformed. a iso represents the expected scaling exponent under isometry, a obs the observed scaling exponent, CI 95% represents the confidence intervals to 95% of the observed slope (a obs ) and Allo, the corresponding allometry (-for negative allometry, 0 for isometry and + for positive allometry) λ = 0.705; p-value < .03, see mapping in Supporting Information, file 4). BV/TV shows a wide variation in squamates (from 0.083 to 0.300, Figure 3). In contrast, this parameter is separated into two welldistinct categories in turtles (from 0.294 to 0.304 and from 0.416 to 0.479, Figure 4). Other parameters do not show any significant phylogenetic signal.

| Structural scaling of trabeculae

To test the allometries of trabecular parameters in reptiles (all specimens, only Squamata and only Testudines), we calculated the slope (a obs ), the confidence intervals to 95% of the slope, the coefficient of determination (R 2 ) and p-value of the regressions of each trabecular parameter against the size proxy TV (Table 6, Supporting Information, file 5).

| Lifestyles

While the classic LDA allows to accurately separate the different lifestyles (85-100% of the taxa are closer to the center of gravity of their own lifestyle), using a leave-one-out cross-validation procedure strongly decreases the performance of the discriminant analysis (well-predicted lifestyle: 40-75%, Table 7, Supporting Information, files 6 and 8). The analysis of residuals rather than raw data does not necessarily give a better discrimination. The removal of the correlated variables (BS/TV and Tb.Sp) enables a better discrimination, contrary to the exclusion of BV/TV (Figure 5). Using the PCA scores for the individuals, a better class-separation is found for the analysis with raw data, but not with size-corrected data.

Gathering lifestyles into two groups enables a better discrimination with a LDA using CV (not in the case of a LDA without CV). Gathering lifestyles into three groups (Figure 6) gives a better discrimination (or the same discrimination in the case of a LDA without CV on size-corrected data).

Using CV, the best separation (60%) of the five lifestyles is maximized in the LDA on the raw data with the removal of two correlated variables (Table 7 and Figure 5). In the Figure 5, morphological spaces of different lifestyles do not overlap. Reducing into three groups of lifestyles, we obtained the highest discrimination of 70% with CV and no overlaps of the lifestyles (Figure 6).

To summarize all these linear discriminant analyses (Supporting Information, file 6), we have a poor prediction of lifestyles with CV for aquatic (well-predicted lifestyle to 8.33%), fossorial (34.6%) and climbing lifestyles (25%) and a well-predicted lifestyle in amphibious (79.17%) and terrestrial lifestyles (66.67%). Specimens from lifestyles with too few specimens failed to be correctly recognized. Among them, turtles that are not amphibious (Centrochelys, Caretta, Chelus) led to the worst predictions (less than 17%). The amphibious group with specimens from all main clades is generally subject to good prediction (79.17%). No test could be performed to compare DA in squamates according to the lifestyles due to a small number of included taxa. Nevertheless, the amphibious Amblyrhynchus shows a higher DA value (0.841) than the terrestrial squamates (from 0.497 to 0.699).

| DISCUSSION

| Phylogenetic signal

BV/TV is the only trabecular parameter that yields a significant Pagel's lambda (0.705, p-value = .003), and it is significantly lower in squamates than in the crocodylian-turtle clade. We propose a physiological explanation related to the limb bone extremities about this phenomenon. Turtles and crocodylians develop cartilaginous limb bone extremities without secondary ossification centers [START_REF] Haines | The evolution of epiphyses and of endochondral bone[END_REF]. In contrast, squamates show secondary ossification centers, which strengthen the limb bone extremities [START_REF] Haines | The evolution of epiphyses and of endochondral bone[END_REF].

In squamates, the wide range of BV/TV variation could be linked to the various locomotor postures (Figure 3). [START_REF] Ruddock | Social structure of the lizard, Cordylus giganteus[END_REF], but this posture could be only practiced during this behavior. The sampled specimen of Heloderma has the highest BV/TV value and both sprawling postures seem to be used depending on the individuals. Amblyrhynchus has a high BV/TV value (0.27), which might be associated with the high compactness values especially found in its fore limb [START_REF] Hugi | Life history and skeletal adaptations in the Galapagos marine iguana (Amblyrhynchus cristatus) as reconstructed with bone histological data-A comparative study of iguanines[END_REF]. A higher compactness in fore limb bones counteracts lung buoyancy and facilitates diving and long-lasting underwater stays [START_REF] De Ricqlès | Bone histology, heterochronies and the return of tetrapods to life in water: Where are we?[END_REF][START_REF] Hugi | Life history and skeletal adaptations in the Galapagos marine iguana (Amblyrhynchus cristatus) as reconstructed with bone histological data-A comparative study of iguanines[END_REF].

In contrast, BV/TV shows two well-distinct categories in turtles (Figure 4).

| Structural scaling of trabeculae

Allometric scaling of trabecular architecture has been analyzed in different bones (femur, humerus, lumbar, and thoracic vertebrae) in various taxa of mammals and birds. Thus, we could compare the observed scaling (a obs ) of the regression between different trabecular parameters and their size proxies (which is always a length or the body mass)

from others studies with an expected scaling under isometry (a iso ).

Average branch length (Av.Br.Len) scales with a significant negative allometry in squamates and in turtles. This parameter has rarely been used in other studies focused on allometries to our knowledge, but it was significantly correlated to body size in the fore limb epiphyses of extant xenarthrans [START_REF] Amson | Trabecular architecture in the forelimb epiphyses of extant xenarthrans (Mammalia)[END_REF].

Trabecular thickness (Tb.Th) and spacing (Tb.Sp) scales with a significant negative allometry in squamates and in turtles. This same significant allometry was also widely found in mammals (Barak, Lieberman, & Hublin, 2013;[START_REF] Cotter | Trabecular microarchitecture of hominoid thoracic vertebrae[END_REF][START_REF] Doube | Trabecular bone scales allometrically in mammals and birds[END_REF][START_REF] Fajardo | Lumbar vertebral body bone microstructural scaling in small to medium-sized strepsirhines[END_REF][START_REF] Ryan | Trabecular bone microstructure scales allometrically in the primate humerus and femur[END_REF] and in birds [START_REF] Doube | Trabecular bone scales allometrically in mammals and birds[END_REF].

Bone surface density (BS/TV) scales with isometry in squamates and in turtles, while it has shown positive allometry in mammalian and avian femora (see Table 1 in [START_REF] Doube | Trabecular bone scales allometrically in mammals and birds[END_REF].

Bone volume fraction (BV/TV) shows no dependence with size in squamates and in turtles. BV/TV was also reported to be independent of body size in mammals, through various sampled bones in a wide variety of taxa (Barak, Lieberman, & Hublin, 2013), but also in more restricted samplings: in thoracic vertebrae of hominoids [START_REF] Cotter | Trabecular microarchitecture of hominoid thoracic vertebrae[END_REF] or in fore limb epiphyses of xenarthrans [START_REF] Amson | Trabecular architecture in the forelimb epiphyses of extant xenarthrans (Mammalia)[END_REF]. However, other analyses have found that BV/TV had a positive allometry in the femoral epiphyses of mammals and birds [START_REF] Doube | Trabecular bone scales allometrically in mammals and birds[END_REF], in the lumbar vertebrae of strepsirrhine primates [START_REF] Fajardo | Lumbar vertebral body bone microstructural scaling in small to medium-sized strepsirhines[END_REF], in the humeral and femoral heads of primates [START_REF] Ryan | Trabecular bone microstructure scales allometrically in the primate humerus and femur[END_REF] and in the femoral heads of sciuromorphs [START_REF] Mielke | Trabecular architecture in the sciuromorph femoral head: Allometry and functional adaptation[END_REF]. For BV/TV, isometry or positive allometry do not seem to be associated to a particular bone (both present in vertebrae and limbs bones) or clade (both present throughout mammals), but this parameter might be correlated to other characteristics, such as locomotor postures.

Connectivity density (Conn.D) scales with significant positive allometry in squamates and in turtles. This parameter has also shown a same significant allometry in mammals (Barak, Lieberman, & Hublin, 2013;[START_REF] Doube | Trabecular bone scales allometrically in mammals and birds[END_REF][START_REF] Fajardo | Lumbar vertebral body bone microstructural scaling in small to medium-sized strepsirhines[END_REF][START_REF] Ryan | Trabecular bone microstructure scales allometrically in the primate humerus and femur[END_REF] and in birds [START_REF] Doube | Trabecular bone scales allometrically in mammals and birds[END_REF].

The degree of anisotropy (DA) shows no correlation with size in squamates and in turtles, like in the thoracic vertebrae of hominoids [START_REF] Cotter | Trabecular microarchitecture of hominoid thoracic vertebrae[END_REF]. In mammals, DA has shown a negative allometry in epiphyses: in the femora of many clades of mammals (see Table 1 in [START_REF] Doube | Trabecular bone scales allometrically in mammals and birds[END_REF], in the femoral heads of sciuromorphs [START_REF] Mielke | Trabecular architecture in the sciuromorph femoral head: Allometry and functional adaptation[END_REF], in the humeral and femoral heads of primates [START_REF] Ryan | Trabecular bone microstructure scales allometrically in the primate humerus and femur[END_REF] and in various VOIs of mammals (Barak, Lieberman, & Hublin, 2013). In birds, DA has shown a negative allometry in the femoral condyle, but a positive allometry in the femoral head [START_REF] Doube | Trabecular bone scales allometrically in mammals and birds[END_REF]. It is unexpected that DA shows a negative allometry in mammals and avian epiphyses, but no correlation with size in nonavian reptiles metaphyses (this could be linked to the different location of the sampled VOI).

Trabecular number (Tb.N) scales with a positive allometry in squamates and in turtles. This parameter has shown a significant positive allometry in mammals (Barak, Lieberman, & Hublin, 2013;[START_REF] Cotter | Trabecular microarchitecture of hominoid thoracic vertebrae[END_REF][START_REF] Fajardo | Lumbar vertebral body bone microstructural scaling in small to medium-sized strepsirhines[END_REF][START_REF] Ryan | Trabecular bone microstructure scales allometrically in the primate humerus and femur[END_REF].

To summarize, within amniotes, BS/TV, BV/TV, and DA have different allometric (or isometric) scalings depending on the VOI location and the sampled clade. In contrast, the positive allometries (Tb.Th, Tb.Sp) and negative allometries (Conn.D, Tb.N) seems to be relatively conserved in mammals, birds, turtles and squamates. We can suppose that these allometric scalings, previously emphasized in mammals and birds, could be generalized to amniotes. Additional studies in other clades like crocodylians and sphenodontians, but also lissamphibians, will be necessary to confirm this statement.

| Lifestyles

The exclusion of BV/TV (which showed a significant phylogenetic signal) for the parameters included in the LDA leads to a decrease of the discriminating power. Within reptiles, BV/TV seems to be a complex trabecular parameter correlated to the phylogeny, but also to lifestyles and locomotor postures (see above). Conversely, BS/TV and Tb.Sp, which are highly correlated to other parameters, show no link to the phylogeny or the lifestyle. In our study, the coordinates of the individuals from principal component axes does not give better discrimination. Gathering lifestyles into two or three groups is a good compromise to obtain a clearer separation (65-75%) because the probability of misidentifications of CV decreases. Nevertheless, on the raw data, the analysis with three groups of lifestyles yields a better discrimination than the analysis with two groups. These results are encouraging: morphological spaces of lifestyle rarely overlapped, even if predictions with CV reached 70%. Nevertheless, it seems important to notice that more specimens should be added in the poorly represented lifestyles, especially aquatic and climber. As highlighted in this study, considering multiple architectural parameters together can prove more informative in elucidating lifestyles than by studying a single variable in isolation. This result had also been found by other studies in the case of locomotor behavior in primates (Amson & Nyakatura, 2018;[START_REF] Hébert | Comparative threedimensional structure of the trabecular bone in the talus of primates and its relationship to ankle joint loads generated during locomotion[END_REF][START_REF] Ryan | Unique suites of trabecular bone features characterize locomotor behavior in human and non-human anthropoid primates[END_REF][START_REF] Scherf | A comparison of proximal humeral cancellous bone of great apes and humans[END_REF].

| Degree of anisotropy versus lifestyle

We compared the degree of anisotropy according to the lifestyle.

Comparing all the specimens, there is no clear distinction of lifestyles.

Indeed, the small size of some squamates implies that the corresponding VOI only comprise a few trabeculae (as in Smaug or Basiliscus). Large specimens would give more reliable results in the analysis of the degree of anisotropy.

Using only specimens with more than 50 trabeculae, we obtain a poor separation of lifestyles. Amphibious specimens show a wide range of variation of DA, because this group consists of three distantly related clades. Indeed, this variation is lower in turtles. Aquatic specimens tend to have distant values of DA, and the fossorial specimen a low DA. However, the small sample size makes any further interpretation difficult to draw.

In turtles, the degree of anisotropy tends to be higher in amphibious taxa than in the fossorial Centrochelys. In large squamates, there is a similar gradient with a higher degree of anisotropy in the amphibious Amblyrhynchus than in terrestrial relatives. We hypothesized that terrestrial tetrapods may have a more defined orientation of their tra-

| Potential limitations

Some possible limitations should be noted for this study. First, the scan resolution can induce possible bias because some trabecular parameters are sensitive to this acquisition parameter [START_REF] Isaksson | Structural parameters of normal and osteoporotic human trabecular bone are affected differently by microCT image resolution[END_REF][START_REF] Sode | Resolution dependence of the non-metric trabecular structure indices[END_REF]. For instance, the relative resolution (i.e., mean trabecular thickness/voxel size, see [START_REF] Sode | Resolution dependence of the non-metric trabecular structure indices[END_REF], Kivell et al., 2011) ranges between 1.53 in Chelus and 20.53 in Centrochelys.

Conversely, we only could sample one specimen per species and hence did not take into account the intraspecific variation, which has been highlighted in several trabecular parameters, like the degree of anisotropy [START_REF] Ryan | Angular orientation of trabecular bone in the femoral head and its relationship to hip joint loads in leaping primates[END_REF]. However, the addition of additional specimens will certainly improve the models. Moreover, we scanned the left or right humerus depending on the availability, which could be another bias, but we do not think that the results are influenced by the humerus laterality.

Moreover, the placement of volumes of interest may create a bias in the results. We extracted VOIs from the proximal metaphysis, at the location where the pectoral process was the most developed, in order to compare homologous areas between the sampled specimens and to avoid the presence of epiphyseal plates in squamates. The regions directly adjacent to the articular condyles, directly exposed to mechanical loadings, may show stronger lifestyle discrimination. However, in our case, these regions could not be sampled in squamates because of their epiphyseal plates.

The choice of a VOI of maximal size, rather than a scaled VOI, can be also bias the trabecular parameters. However, most of the studied parameters (bone volume fraction, trabecular thickness, number, and spacing) were not influenced by VOI size in other studies [START_REF] Kivell | Methodological considerations for analyzing trabecular architecture: An example from the primate hand[END_REF][START_REF] Lazenby | Scaling VOI size in 3D μCT studies of trabecular bone: A test of the oversampling hypothesis[END_REF]. In contrast, degree of anisotropy could be more sensitive to VOI size change, when studying a more heterogeneous structure [START_REF] Kivell | Methodological considerations for analyzing trabecular architecture: An example from the primate hand[END_REF][START_REF] Lazenby | Scaling VOI size in 3D μCT studies of trabecular bone: A test of the oversampling hypothesis[END_REF]. Furthermore, VOIs are not scaled and do not have the same size for all specimens:

the extracted volume can be small in some specimens (e.g., 0.433 mm 3 in Kinosternon) or large in other ones (e.g., 1,268.667 mm 3 in Caretta). Moreover, a larger pectoral process, related to the anatomy or the lifestyle of a small animal, could give a larger VOI and potentially change the allometric scaling of trabecular parameters.

Our choice of VOI selection could skew the results, but to our knowledge, it was the only procedure that facilitated sampling of enough trabeculae from small specimens (of which the metaphyses include only few trabeculae).

Using TV as a proxy for body size could be another limitation. We could not use other size proxies like humeral length or minimal diaphyseal circumference, because the sampled specimens have a wide variety of morphologies.

Finally, we also tried to take into account potential phylogenetic effects thanks to the use of pFDA and the measure of Pagel's lambda for each trabecular parameter. However, the fact that our sampling is uneven could involve a strong phylogenetic bias.

| Conclusion

This study is the first to present 3D-trabecular architecture of the humeral proximal metaphysis in various clades of extant reptiles (Crocodylia, Squamata, and Testudines) through a μCT-scan dataset.

Thanks to the analyses of trabecular parameters, we are able to highlight allometries, most of which were also found in mammals and birds. These parameters do not show a significant phylogenetic signal, except for the bone volume fraction (BV/TV), which can be strongly correlated to the epiphysation degree. The various linear discriminant analyses show that lifestyle discrimination seems possible. We also find a tendency for the degree of anisotropy to differ between terrestrial and amphibious lifestyles, but further analyses including greater sampling will be required to confirm this statement.

Moreover, this study provides other useful data to perform further trabecular anisotropy analyses concerned with lifestyle signals. It is preferable to focus at the rank order rather than larger clades, where the anisotropic signals could be mixed. Furthermore, larger specimens should be studied in order to recover a reliable degree of anisotropy. It would not be surprising if other studies also recover a gradient in the trabecular anisotropy values among lifestyles (rather than a clear discrimination), because lifestyles often describe a continuum from strictly terrestrial to strictly aquatic ones. In the same way that some studies were able to predict locomotor behavior of extinct primates (Ryan & Ketcham, 2002b), studies on relationships between lifestyle and trabecular architecture could help to determine accurately the lifestyle of other extinct tetrapods (see e.g., Amson & Nyakatura, 2018).

  terminal taxa covariance compared to the covariance expected under a Brownian motion given the topology and the branch lengths. A value of 0 means the phylogenetic independence of the terminal taxa, while a value of 1 means that the values are in direct proportion to their shared evolutionary history. With the contMap and phenogram functions of the "phytools" package[START_REF] Revell | Phytools: An R package for phylogenetic comparative biology (and other things)[END_REF], we represented the evolution of the BV/TV continuous trait on the tree of reptiles (see mapping in Supporting Information, file 4). Distribution of this trait is also represented with phenograms for squamates (Figure3) and turtles (Figure4). Structural scaling of trabeculae: All variables were log-transformed and allometry was investigated with linear regression of each parameter against the body size proxy, TV. In Mielke et al. (2018), the F I G U R E 2 Selection of volume of interest (VOI). (a) 3D reconstruction (ventral view) of the proximal epiphysis and metaphysis of the humerus of Tiliqua scincoides (MNHN-ZA-AC-1898-285). (b, c and d) transverse sections in the proximal metaphysis of humerus of Centrochelys sulcata (MNHN-ZA-AC-1974-68), Varanus salvator (MNHN-ZA-AC-1977-4) and Crocodylus niloticus (MNHN-ZA-AC-2005-71), respectively. The red circle represents the place of extraction of VOI, at the location where the pectoral process is the most developed. Scale bars = 2 mm [Color figure can be viewed at wileyonlinelibrary.com]

F

  I G U R E 3 Phenogram of squamates defined by the BV/TV parameter. Locomotor postures are indicated on the right part F I G U R E 4 Phenogram of turtles defined by the BV/TV parameter. Locomotor postures are indicated on the right part Testudines and in Squamata. For all of these comparisons, we performed the following protocol. As involved specimens change for each comparison, we checked the normality of the distribution of DA, the homogeneity of variance and we compared lifestyles with an ANOVA, a Student's t-test or a Kruskal-Wallis rank sum test (see above for test conditions). Before performing Bartlett's test or a comparison test, we removed lifestyles containing only one specimen from the analysis.

  Av.Br.Len, Tb.Th, and Tb.Sp show a significant negative allometric scaling in reptiles generally, but also in squamates and turtles. Larger reptiles have shorter, thinner, and more densely packed trabeculae than expected under geometric scaling. Conn.D and Tb.N show a significant positive allometric scaling in reptiles generally, in squamates and in turtles. Larger reptiles have more trabeculae per volume unit than expected under geometric scaling. BS/TV, BV/TV, and DA show no significant allometric scaling in reptiles, squamates, and turtles. Larger reptiles do not have more trabecular bone per unit of volume or more (or less) aligned trabeculae.

F

  I G U R E 5 LDA on the raw data with removal of two correlated variables (BS/TV and Tb.Sp). The analysis is performed on the five groups of lifestyle: Aquatic (filled triangle point-up), amphibious (filled circle), climbing (filled triangle point-down), fossorial (filled square), and terrestrial (filled diamond) F I G U R E 6 LDA on the size-corrected data. The analysis is performed on three lifestyle groups: Aquatic (filled triangle point-up), amphibious (filled circle) and a ground category, which brings together climbing (filled triangle point-down), fossorial (filled square) and terrestrial (filled diamond) lifestyles. The categories corresponding to five-lifestyle scheme (see text) are nevertheless indicated For the comparison of the DA, the ANOVA suggests that there is no significant differences among the lifestyles (Shapiro-Wilk test: W = 0.95501, p-value = .4495; Bartlett's test: K 2 = 2.1955, p-value = .6998; ANOVA: p-value = .999). The same conclusion is reached when specimens for which VOIs with less than 50 trabeculae and lifestyles with less than two specimens are excluded (Shapiro-Wilk test: W = 0.93941, p-value = .4108; Bartlett's test: K 2 = 1.0333, p-value = .5965; ANOVA: p-value = .925). Amphibious specimens show the widest range of variation of DA (from 0.448 to 0.841); aquatic specimens have two different values of DA (0.444 and 0.779), while the fossorial specimen shows a low DA (0.445); terrestrial specimens have an intermediate DA (from 0.497 to 0.699). For the comparison between DA in Testudines, there is no significant difference between the amphibious and aquatic lifestyles (Shapiro-Wilk test: W = 0.93398, p-value = .553; Bartlett's test: K 2 = 5.4335, p-value = .01975; Kruskal-Wallis chi-squared: t = 0, p-value = 1). Aquatics turtles have two distant values (0.444 and 0.779). Values of DA are intermediate with a limited range in amphibious turtles (from 0.574 to 0.662), but higher than the one of the fossorial Centrochelys (0.445).

  Squamates with the lowest BV/TV values (Basiliscus, Tupinambis and Varanus) are able to practice occasional bipedalism. Squamates that use a "raised" sprawling posture (Trioceros, Varanus, Tupinambis and Basiliscus) have low BV/TV values (0.083-0.224). Uromastyx and Tiliqua, with higher BV/TV values (0.231 and 0.246 respectively) show a "belly-dragging" sprawling posture. The three other squamates (Smaug, Heloderma, and Amblyrhynchus) have unclear locomotor postures. Smaug has a high BV/TV value (0.264): it can raise itself off the ground by extending its legs during display

Table 3

 3

, for Squamata and Testudines in Table

4

, see Fiji Macro in Supporting Information, file 3). These parameters were often used by others authors, except for average branch length (Av.Br.Len, only measured by

[START_REF] Amson | Trabecular architecture in the forelimb epiphyses of extant xenarthrans (Mammalia)[END_REF]

. Thickness (Tb.Th) and Av.Br.Len are expressed in mm; bone surface (BS) in mm 2 ; bone volume (BV) in mm 3 ; connectivity (Conn) is approximately the number of trabeculae in the VOI; connectivity density (Conn.D) in number/mm 3 ; number (Tb.N) in number/mm. Degree of anisotropy (DA) has no unit, its scale ranges from 0 (trabeculae have no preferential orientation) to 1 (trabeculae are perfectly aligned). As the DA algorithm is a heuristic, we ran it 10 times for each VOI and averaged the obtained values. Two other trabecular parameters, spacing (Tb.Sp) in mm and the total volume of VOI (TV) in mm 3 , could not be correctly measured from a spherical VOI by BoneJ, which requires a cuboid stack (the option "use ROI Manager" was not used). We therefore devised a custom script to calculated them. After VOI extraction with CTAn and thresholding with BoneJ, we obtained a spherical VOI of trabecular bone (bone in white, void in black) inside a cubic stack with black background. If one would measure Tb.Sp of this

  T A B L E 3 Means of raw measurements for each lifestyle Lifestyle Av.Br.Len (mm) Tb.Th (mm) Tb.Sp (mm) Conn.D (number/mm 3 ) BS/TV (mm -1 ) BV/TV (no unit) DA (no unit) Tb.N (mm -1 ) Means of raw measurements in Squamata and in Testudines (standard deviation in brackets)

	Aquatic	0.463	0.235	0.466	13	1.50	0.37		0.61	1.93
	Amphibious 0.270	0.169	0.313	66	3.69	0.38		0.64	2.74
	Terrestrial	0.255	0.116	0.388	19	2.23	0.21		0.63	2.05
	Fossorial	0.330	0.190	0.386	15	2.08	0.32		0.63	1.98
	Climbing	0.163	0.083	0.326	26	2.21	0.15		0.62	1.80
	Note: See Table 2 for abbreviations.
	T A B L E 4 Clade	Av.Br.Len (mm)	Tb.Th (mm)		Tb.Sp (mm)	Conn.D (number/mm 3 )	BS/TV (mm -1 )	BV/TV (no unit)	DA (no unit)	Tb.N (mm -1 )
	Squamata	0.238 (0.073)	0.115 (0.038)	0.366 (0.106)	19 (11.5)	2.45 (1.84)	0.22 (0.06)	0.66 (0.11)	2.0 (0.76)
	Testudines	0.314 (0.174)	0.182 (0.102)	0.325 (0.190)	67 (78)	3.25 (2.75)	0.39 (0.07)	0.59 (0.11)	2.8 (1.54)
	Note: See Table 2 for abbreviations.
	T A B L E 5 Pagel's lambda and associated p-values for each
	trabecular parameter
		Pagel's lambda		Lambda p-value
	Av.Br.Len	0.000			1.000
	Tb.Th	0.140			0.524
	Tb.Sp	0.000			1.000
	BS/TV	0.000			1.000
	Conn.D	0.166			0.486
	BV/TV	0.705			0.003
	DA	0.001			0.996
	Tb.N	0.000			1.000

Note: See Table

2

for abbreviations. Significant results are in bold (p-value <.05).

  See Table2for abbreviations of trabecular parameters. List of different linear discriminant analyses (LDA). More details in the material and methods section. Percentages correspond to the correct predictions of the LDAs (i.e., number of correctly classified specimens divided by the number of specimens)

			All			Squamata			Testudines
	Parameters a iso	a obs	CI 95%	Allo a obs	CI 95%	Allo a obs	CI 95%	Allo
	Av.Br.Len	0.33	0.1796	0.1482; 0.2109	-	0.1691	0.1119; 0.2264	-	0.1935	0.1348; 0.2521	-
	Tb.Th	0.33	0.2031	0.1601; 0.2460	-	0.1637	0.0767; 0.2506	-	0.1985	0.1351; 0.2618	-
	Tb.Sp	0.33	0.1363	0.0776; 0.1951	-	0.1514	0.0666; 0.2362	-	0.1839	0.1660; 0.2018	-
	BS/TV	-0.33 -0.335	-0.5091; -0.1609	0	-0.4104	-0.8267; 0.0058	0	-0.4503	-0.6214; -0.2792	0
	BV/TV	0	0.06044 -0.0268; 0.1477	0	0.02427 -0.1574; 0.2059	0	-0.007963 -0.0799; 0.0640	0
	Conn.D	-1	-0.3436	-0.5046; -0.1826	+	-0.2892	-0.4639; -0.1145	+	-0.5066	-0.6742; -0.3390	+
	DA	0	-0.03439 -0.0743; 0.0056	0	0.0038	-0.0829; 0.0905	0	-0.04601	-0.0969; 0.0049	0
	Tb.N	-0.33 -0.1426	-0.2200; -0.0652	+	-0.1394	-0.2871; 0.0083	+	-0.2064	-0.2683; -0.1446	+
	Note: Linear discriminant analyzes			Raw data no CV	Raw data with CV		Size-corrected data no CV	Size-corrected data with CV
	Basic					95%	45%		95%	50%
	BV/TV removal				95%	40%		90%	45%
	Two correlated variables (BS/TV + Tb.Sp) removal		95%	60%		85%	55%
	On PCA scores				100%	55%		95%	50%
	Two groups: Water and ground			90%	65%		95%	75%
	Three groups: Aquatic, amphibious and ground		100%	70%		95%	70%

T A B L E 7

  Turtles with lowest BV/TV values (0.294-0.304) have high swimming abilities (Caretta, Kinosternon, and Mauremys).

	A significant
	reduction of body mass would improve locomotor performance of
	aquatic animals, especially their acceleration abilities and maneuver-
	ability (de Ricqlès & de Buffrénil, 2001). Turtles with highest BV/TV
	values (0.416-0.479) walk on land (Centrochelys) or at the bottom of
	lakes (Pelusios, Cyclanorbis, Chelus, and Emys). As in the marine iguana
	Amblyrhynchus, heavier bones may act as ballast and allow the animal
	to stay immersed on the bottom (de Ricqlès & de Buffrénil, 2001).

ACKNOWLEDGMENTS

We thank the PhD program "Interface pour le Vivant (IPV)" for research funding, the German Research Council (DFG AM 517/1-1) which funded Eli Amson and the Action Thématique du Muséum (ATM) for CT-scan funding. We also acknowledge Maïté Adam, Marta Bellato and Patricia Wils (UMS 2700 OMSI, AST-RX) for the CTscanning procedure. We also want to thank Natacha Catz and Audrey Pofis for their invaluable help in this project. We want to thank Salvador Bailon for the access to the collection of comparative anatomy and Michel Laurin for the loan of the humerus of Amblyrhynchus cristatus. Finally, we thank the two anonymous reviewers for their particularly useful comments.

AUTHOR CONTRIBUTIONS

MP, QG and DG conceived the study. MP, DG and QG conceived the methodology for image processing. MP acquired and analyzed the raw data, and drafted the manuscript. EA drafted the Fiji script. All authors performed the analyses. All authors reviewed the manuscript and gave their final approval.

SUPPORTING INFORMATION

Additional supporting information may be found online in the Supporting Information section at the end of this article.