What's inside a sauropod limb? First three‐dimensional investigation of the limb long bone microanatomy of a sauropod dinosaur, Nigersaurus taqueti (Neosauropoda, Rebbachisauridae), and implications for the weight‐bearing function

Various terrestrial tetrapods convergently evolved to gigantism (large body sizes and masses), the most extreme case being sauropod dinosaurs. Heavy weight‐bearing taxa often show external morphological features related to this condition, but also adequacy in their limb bone inner structure: a spongiosa filling the medullary area and a rather thick cortex varying greatly in thickness along the shaft. However, the microanatomical variation in such taxa remains poorly known, especially between different limb elements. We highlight for the first time the three‐dimensional microstructure of the six limb long bone types of a sauropod dinosaur, Nigersaurus taqueti. Sampling several specimens of different sizes, we explored within‐bone, between‐bones, and size‐related variations. If a spongiosa fills the medullary area of all bones, the cortex is rather thin and varies only slightly in thickness along the shaft. Zeugopod bones appear more compact than stylopod ones, whereas no particular differences between serially homologous bones are found. Nigersaurus' pattern appears much less extreme than that in heavy terrestrial taxa such as rhinoceroses, but is partly similar to observations in elephants and in two‐dimensional sauropod data. Thus, microanatomy may have not been the predominant feature for weight‐bearing in sauropods. External features, such as columnarity (shared with elephants) and postcranial pneumaticity, may have played a major role for this function, thus relaxing pressures on microanatomy. Also, sauropods may have been lighter than expected for a given size. Our study calls for further three‐dimensional investigations, eventually yielding a framework characterizing more precisely how sauropod gigantism may have been possible.

T E R R E S T R I A L gigantism appeared several times in the evolutionary history of tetrapods, such as in large proboscideans, rhinocerotoids, dicynodonts, ornithischians, theropods and sauropods (Alexander 1998;Sander & Clauss 2008;Sulej & Nied zwiedzki 2019;Hutchinson 2021), reaching a multi-tonne body mass. These forms, often said to be 'graviportal', show morphological features in their limb bones related to the support of a heavy weight, such as straightened and/or robust bones, depending on the taxon, but also proximal elements proportionately longer than distal ones (Gregory 1912;Osborn 1929;Coombs 1978;Hildebrand 1982;Carrano 2001Carrano , 2005Christiansen 2007;Mallet et al. 2019;Hutchinson 2021;Lefebvre et al. 2022).
Their microanatomy (i.e. the inner architecture constituting the bone) also shows adequacy with a heavy-weight support role, since heavy quadrupedal taxa tend to show an increase in compactness, with a medullary area filled by a spongiosa often associated with a thickening of the cortex (Wall 1983;Houssaye et al. 2016;Nganvongpanit et al. 2017 fig. 1). Those trends are also found, maybe to a lesser extent, in gigantic bipeds such as large theropods, with a thickening of the cortex and sometimes a spongiosa partly filling the shaft (see Fabbri et al. 2022, extended data figs 1, 2, 8, 10). Microanatomical features associated to heavy-weight bearing are thought to be related to resistance to compressive loading, avoiding crushing fractures by improving energy absorption when the limb impacts the ground (Oxnard 1990;Augat & Schorlemmer 2006;Houssaye et al. 2016Houssaye et al. , 2021. This condition contrasts with more lightly built terrestrial tetrapods that show a tubular organization with an open medullary cavity, with spongious bone restricted to the metaphyses and epiphyses (Wall 1983 fig. 2;Oxnard 1990;Canoville & Laurin 2010;Houssaye et al. 2018).
However, little is known about microanatomical patterns in sauropod limb bones, notably due to their large size rendering them hardly available for appropriate sampling. Many studies have focused on the histology (i.e. the study of the nature of osseous tissues), especially of limb bones, to address questions about sauropod growth patterns and metabolism (e.g. de Ricql es 1983;Curry 1999;Sander 2000;Klein & Sander 2008;Mitchell & Sander 2014;Curry Rogers et al. 2016;Cerda et al. 2017;Cerda. 2022), insular dwarfism (e.g. Sander et al. 2006Stein et al. 2010), exceptional preservation of cartilage (e.g. Schwarz et al. 2007) and palaeopathology (e.g. Gonz alez et al. 2017;Jentgen-Ceschino et al. 2020). For this purpose, partial cross-sections and core-drillings (Sander 2000), more easily obtainable for such large specimens, were sufficient, whereas microanatomical studies, which address the distribution of the osseous tissues in the bone, rather require complete cross-sections. Particular interest has also been cast on the microanatomy and histology of other postcranial elements, especially regarding axial pneumaticity (e.g. Wedel 2003Wedel , 2005  Although studies have investigated or illustrated one or several entire transverse sections of sauropod stylopod and zeugopod bones (Hatcher 1901;Ostrom & McIntosh 1966;de Ricql es 1983;Rimblot-Baly et al. 1995;Galton 2005;Wings et al. 2007;Ye et al. 2007;Woodward & Lehman 2009;Company 2011;Sander et al. 2011;Klein et al. 2012b;Hedrick et al. 2014;Mitchell & Sander 2014;Curry Rogers et al. 2016;Ghilardi et al. 2016;Houssaye et al. 2016;Curry Rogers & Kulik 2018;Gonz alez et al. 2020) and could be of interest for studying microanatomy, this gives an incomplete and poorly intercomparable overview of the sauropod limb long bones' inner structure. Microanatomy indeed varies for the same bone between various specimens of a same species, but also between the different bones of a single individual (Currey & Alexander 1985;Laurin et al. 2011 Intra-individual skeletal variations can reflect paramount biomechanical implications. Indeed, differences in cortical and trabecular features may be the response to differential mechanical stresses experienced by limb bones, during locomotion and even during standing at rest (Currey & Alexander 1985;Oxnard 1990;Amson & Kolb 2016;Houssaye et al. 2016). They can reflect size (and mass)-related differences of forces involved in biomechanical stressful events, such as foot impact (Warner et al. 2013), and variability in loading experienced during locomotion (Willie et al. 2020), although this signal may be mixed with those associated with jointly active pressures, such as mass saving (Currey & Alexander 1985;Amson & Kolb 2016). However, this intra-individual variation has scarcely been documented, given the difficulty in making longitudinal sections (e.g. Wall 1983), but is now increasingly investigated with the advent of x-ray microtomography, allowing the creation of virtual sections of a digitized bone (e.g. Nakajima et al. 2014;Houssaye & Botton-Divet 2018;Amson 2021). To our knowledge, Curry Rogers et al. (2016) provided the first illustration of sauropod longitudinal sections of stylopodial (humerus, femur), zeugopodial (tibiae, fibulae) and autopodial (metacarpal III, metatarsal I) elements of a perinate specimen of the titanosaur Rapetosaurus krausei. However, this study focused on the histology and growth pattern of this sauropod, and hence did not describe the bone microanatomy.
Here we provide the first three-dimensional microanatomical investigation of a sauropod, using the rebbachisaurid sauropod Nigersaurus taqueti (Sereno et al. 1999(Sereno et al. , 2007. By studying for the first time the six types of limb long bone of several individuals varying in size, we aim to determine the microanatomical pattern occurring in this sauropod. This will highlight: (1) intra-bone; (2)between-bones; and (3) size-related variations; thus allowing a discussion of limb long bone microanatomical adaptation to biomechanical constraints in this taxon.
Given the outcomes of previous studies made on heavy-weight bearing taxa (Wall 1983;Houssaye et al. 2016), we expect to find in all Nigersaurus limb long bones a marked thickening of the cortex along the shaft, and a spongiosa filling the medullary area. Since the body centre of mass is inferred to be posteriorly placed in most diplodocoid sauropods (Henderson 2006), we may also expect to find a substantial difference in the microanatomical pattern between forelimb and hindlimb bones (i.e. hindlimb microanatomy bulkier than forelimb one). Consistently with Amson & Kolb (2016) who suggested less pressure related to mass saving on zeugopod bones than on stylopod bones, which hence probably reflect more pressure related to biomechanical stresses for the zeugopods, we expect to find a more robust pattern in the radius and ulna compared to the humerus, and in the tibia and fibula with respect to the femur.

Material
We studied 13 limb bones (four humeri, two radii, one ulna, two femora, two tibiae and two fibulae; see Table 1) referred to the sauropod Nigersaurus. This elephant-sized sauropod (Sereno et al. 2007) is known from several bones representing several specimens of various sizes, collected in Aptian-Albian deposits of Gadoufaoua, Elhraz Formation, Niger (Taquet 1976). Although initially diagnosed as a 'dicraeosaurid titanosaur' (Taquet 1976), this material was later attributed as a diplodocoid belonging to the more recently erected Rebbachisauridae family, within the species Nigersaurus taqueti (Sereno et al. 1999). Moreover, this material was compared to the type and referred material of Nigersaurus taqueti (Sereno et al. 1999(Sereno et al. , 2007, examined at first hand by one of us (RA). The bones sampled here were selected for their completeness, the quality of their preservation, and with the concern to cover the largest possible size range available (sampling the largest and smallest individuals available when possible; Table 1). Three bones from a single forelimb belong with certainty to the same individual (MNHN.F.GDF242), and two hindlimb zeugopod are reasonably associated to the same individual (MNHN.F. GDF2094 & 2095. These specimens are housed in the palaeontological collections of the Mus eum national d'Histoire naturelle, Paris, France (MNHN).

Methods
Bones were scanned with high-resolution computed tomography (GEphoenix|X-ray v|tome|xs 240) at the AST-RX platform (UMS 2700) of the MNHN; reconstructions were performed using datox/res software. Image visualizations and virtual sections were performed using VGStudioMax v.2.2 (Volume Graphics Inc., Heidelberg, Germany). The resolution of the scans depended of the size of the specimens (the larger the specimen, the larger the resolution). Virtual sections were made in the coronal and sagittal planes crossing the middle of the shaft with the bones oriented so that the midshaft region is vertical. In addition, virtual transverse sections were made at midshaft, permitting analogous comparisons with transverse sections widely encountered in the literature as made in the reference plane, and another at the estimated position of the GC, where the cortex is the thickest, in order to produce biologically homologous sections, since bone microanatomy can strongly vary along the shaft, and since the GC is rarely at midshaft (Nakajima et al. 2014; Houssaye & Pr evoteau 2020). In these transverse sections, we measured the proportion of the total cross-sectional area occupied by the cortex. It estimates quantitatively the overall cortical thickness of the section. This cortical extension index (CEI) is a ratio calculated as follows: CEI = 1 -((Medullary area)/(Sectional area)). Area measurements were performed using the polyline and measurement tools in the software ImageJ v.1.53a (Schneider et al. 2012). Due to the incompleteness of some sections, this measurement was based on the plaster-reconstructed parts of the bones when they occur, since they appeared to follow the whole geometry of the original bone, without extrapolations. When these reconstructions were missing, a straight line was traced to estimate the missing portion. As the delineation between the cortex and the spongiosa is sometimes unclear, all CEI estimations were taken three times and averaged to account for any potential measurement error. The maximum length (ML) was virtually measured on 3D models of the bones using the Meshlab software (Cignoni et al. 2008). Illustrated virtual sections were luminosityinverted and, when relevant, manually contrast-adjusted using Inkscape software.

Humerus
In the sampled humeri, the medullary area is totally filled by a spongiosa made of thin and numerous osseous trabeculae ( Fig. 1A-F). The GC is located slightly below the midshaft level ( Fig. 1A-C). The cortex is rather thin, even near the GC, where it is slightly thicker. The CEI slightly differs between the smallest (about 50% in MNHN.F.GDF2097; Table 1; Fig. 1D) and the largest (around 60%, in MNHN.F.GDF243 & 2045; Table 1; Fig. 1E) specimens, whatever the type of transverse section observed.

Radius
In the sampled radii, the medullary area is relatively smaller and thus the cortex relatively thicker in the shaft region than in the humerus, and is totally filled by a spongiosa (Fig. 1G-H, J-K). The osseous trabeculae are thin and numerous as in the humerus, but the density of the spongiosa diminishes towards the core of the shaft. The GC is located around midshaft (MNHN.F.GDF242.2; Fig. 1H), though its precise position is unclear since the associated localized thickening of the cortex is rather gradual. Transversally the cortex is thicker anterolaterally and posteromedially (MNHN.F.GDF2057, Fig. 1J; unclear in MNHN.F.GDF242.2 due to poor preservation). The CEI ranges between 73% and 77% (Table 1).

Ulna
In the sampled ulna ( Fig. 1I, L), the bone microanatomy is similar to that of the radius. The GC is located around midshaft (Fig. 1I). The cortical thickening around the GC is more acutely marked than in the humerus and the radius. At the GC, the cortex is thicker posteriorly than mediolaterally (Fig. 1I, L; CEI is estimated around 73%; Table 1). Due to incompleteness, it is not possible to know if the cortex is anteriorly as thick as posteriorly.

Femur
The osseous trabeculae of the sampled femora are thin and numerous ( Fig. 2A-B, D-E). The spongiosa is present in the majority of the medullary area of the smallest specimen (MNHN.F.GDF75; Fig. 2A, D). It is, however, not totally clear if the medullary area of the smallest specimen was entirely filled in the midshaft region, due to taphonomic alterations. The spongiosa totally fills the medullary area in the largest specimen (MNHN.F.GDF327; Fig. 2B, E), with no medullary cavity. The GC is slightly below the midshaft in the smallest specimen (MNHN.F.GDF75; Fig. 2A) and around the midshaft in the largest specimen (Fig. 2B). In the smallest specimen ( Fig. 2A), the structures at midshaft and near the GC are similar, and the cortical thickness is roughly homogeneous along the sections. The CEI in the small  specimen is lower (between 52% and 55%, Table 1; Fig. 2D) than in the large specimen (CEI estimated around 59%; Table 1; Fig. 2E).

Tibia
In the sampled tibiae, the osseous trabeculae are thin and numerous (Fig. 2C, F, G, J). In the small specimen (MNHN.F.GDF2094; Fig. 2C, F), trabecular density is lower in the core of the medullary area especially above the GC. The trabecular density is homogeneous along the shaft in the large specimen (MNHN.F.GDF244; Fig. 2G, J). The GC is located below the midshaft (Fig. 2C, G). The spongiosa is slightly denser in this region in the large specimen than in the small one. The cortex is proportionally thicker than in the humerus and the femur, with a CEI around 64-70%, whichever section or specimen is considered (Table 1; Fig. 2F, J). The cortical thickening around the GC is as marked as in the ulna. The cortex is proportionally thicker posteriorly, especially in the largest specimen (Fig. 2G).

Fibula
In the sampled fibulae (Fig. 2H, I, K, L), the bone microanatomy is similar as in the tibiae, with a trabecular density lower in the core (in the small specimen MNHN.F.GDF2095; Fig. 2H, K) to homogeneous (in the large specimen MNHN.F.GDF2055; Fig. 2I, L) in the medullary area. The osseous trabeculae are thin and numerous. The GC is located below the midshaft (Fig. 2H, I). The CEI in the large specimen is thicker (77-80%;

Microanatomical pattern in Nigersaurus
The limb long bone microanatomy of Nigersaurus is characterized by a rather thin cortex and a spongiosa partially to totally filling the medullary area. The CEI of Nigersaurus stylopod bones varies between 50% and 60%. These values are relatively low when compared with other large terrestrial animals (CEI ranges from 43% in a juvenile Apatosaurus to 93% in the black rhinoceros Diceros bicornis; see Table 1 & Table S1). The extension of the spongiosa in the shaft is observed in many other terrestrial heavy-weight bearing taxa (proboscideans, rhinoceroses, sauropods; see Variation between bones. As expected, the zeugopod bones of Nigersaurus are more compact than the stylopod ones (Table 1) showed a highly consistent intraspecific trend in nonflying amniotes, with zeugopod bones almost always showing larger cortical occupation of the total diameter of the shaft than stylopod bones. This suggests that our observation is relatively ubiquitous in terrestrial animals, and is probably not linked to a heavy-weight bearing specialization. Thus, zeugopod microanatomy may generally be more constrained than stylopod microanatomy by weight-bearing biomechanical pressures in any terrestrial taxa. However, contrary to our expectations, no differences were found in the microanatomical pattern between forelimb and hindlimb serially homologous bones that could have reflected hindlimb elements bearing more weight than anterior ones.
Size-related variation. Two patterns related to the size of the specimens are observed: first, larger humeri, femora and fibulae tend to have a thicker cortex than smaller ones, and second, the trabecular density tends to increase in larger tibiae and fibulae. These two observations constitute a very plausible ontogenetic (i.e. growth) variation in Nigersaurus. However, a rather large intraspecific size variability at the same ontogenetic stage can occur in some sauropod taxa (Klein & Sander 2008;Mitchell & Sander 2014). In our study, since the magnitude of size variation in the sampled humeri, femora, tibiae and fibulae is large (c. 2 in each type of bone), we may reasonably favour the hypothesis that, for each type of those bones, at least the smallest and largest individuals correspond to two different ontogenetic stages (although alternative hypotheses such as sexual dimorphism (see discussion in Klein & Sander 2008) cannot be ruled out with our data). Functionally, these two observed size-related trends may be associated with the increase in body mass occurring during postnatal growth, and therefore would reflect an increase in the role of weight support at least in the hindlimb during this period. Such size-related variation might also occur in radii and ulnae, for which only one complete bone was available. Size-related cortical thickening is also found in flightless birds, and is probably associated with the regular bone growth through ontogeny (Canoville et al. 2022). This pattern is also found in two small ornithischian taxa (i.e. femur of Dysalotosaurus, Heinrich et al. 1993; tibia and fibula of Jeholosaurus, Han et al. 2020), which could suggest that this pattern is widespread at least among dinosaurs. The microanatomical data presented in this study highlight a very robust profile in the fibula, contrasting with the reduced presence of the fibula in a large number of terrestrial amniotes. This could indicate that this bone had a predominant role along with the tibia in order to support the body mass in Nigersaurus. However, the similar thickening observed in the small ornithischian Jeholosaurus (Han et al. 2020) may imply that this trend is widespread among non-avian dinosaurs, hence not particularly characteristic of heavy taxa. Size-related increase in trabecular density might also occur in humeri and femora, since the precise density of the smallest specimens is unclear due to preservation.

Implications for the weight-bearing function in sauropods
Our results suggest that Nigersaurus shows some features expected to occur in association with a heavy-weight bearing biology, namely the presence of a spongiosa and a longitudinal cortical thickening along the shaft. However, this latter feature is only weakly marked, and the cortex is rather thin, compared to extant heavy mammals, notably rhinoceroses (see Wall 1983  A fairly high degree of microanatomical variability seems to be present across sauropod species, as suggested by transverse cross sections found in the literature. As in Nigersaurus, some other sauropods show a rather thin cortex, such as in the humeri of a small-sized Ampelosaurus individual and a juvenile specimen of Apatosaurus (see Houssaye et al. 2016). In contrast, the femur of a dwarf sauropod, Magyarosaurus (see Mitchell & Sander 2014), shows a very compact profile with a thick cortex. More surprisingly, a medullary cavity is found in the femora of very large taxa such as Diplodocus (see Hatcher 1901) and Alamosaurus (see Woodward & Lehman 2009), as well as in dwarf taxa such as Europasaurus and Magyarosaurus (see Mitchell & Sander 2014) suggesting that the presence of this feature may be not related to size. Assuming no taphonomic alterations, this overall variability seemingly poorly related to size is surprising, occurring as it does across a sample representing all the major locomotor groups (Carrano 2005) within sauropods. This appears particularly inadequate with the assumed extreme biomechanical pressures that should have counter-selected such variability when associated with a multi-tonne body mass. This trend also seems inconsistent with the evolution in sauropodomorph dinosaurs of the filling of the medullary area by spongious bone, which, since it co-occurs with the emergence of Sauropoda (sensu Salgado et al. 1997;Cerda et al. 2017), appears to be strongly related to the evolution of their gigantism. Cerda et al. 2017 pointed out that such spongious bone infilling may have been retained in smaller and tardive sauropods through phylogenetic inertia. The evolution of this condition is perhaps even more complex since several sauropods of different sizes appear to display a medullary cavity partly or totally devoid of spongiosa. While the acquisition of a spongiosa filling the medullary area appears to be both biomechanically advantageous for weight-bearing (Oxnard 1990;Houssaye et al. 2016Houssaye et al. , 2021 and correlated with the emergence of the bauplan characterizing sauropods (see Lefebvre et al. 2022), this feature does not appear to be a sine qua non condition for the evolution of extremely large forms, such as Alamosaurus (see Woodward & Lehman 2009). Therefore, the present study highlights the fact that the role of weight-bearing in Nigersaurus, as well as in a large number of the other sauropods examined here, probably depended less on microanatomy than in some other heavy-weight bearing extant mammals, such as rhinoceroses (Wall 1983;Houssaye et al. 2016 et al. 2007). As postcranial pneumaticity participated to decrease constraints related to weight-bearing function, the evolution of this parameter probably had a critical influence on the evolution of limb long bone structure. These two hypotheses should be tested through a larger exploration of limb bone microanatomy in massive terrestrial taxa. Although our study constitutes to our knowledge the largest documentation of the microanatomical pattern of entire limb long bones for a sauropod, the absolute size of our sample remains limited. Threedimensional patterns seen in such large taxa are still extremely poorly documented, and our study calls for others to better delineate the evolutionary trends of microanatomical features in relation to heavy weight support. An integrative focus should be made on both columnar (sauropods, elephants) and non-columnar (e.g. rhinoceroses, heavy ornithischians) taxa, ideally in a quantitative and phylogenetically-informed framework. Notably, a more exhaustive documentation of microanatomical diversity of sauropods should highlight the extent to which our conclusions can be generalized to the whole diversity within this clade.
Our results suggest that the degree of gigantism observed in extant terrestrial tetrapods (i.e. only represented by mammals) might not be fully analogous to the extreme condition seen in sauropods. The specificities related to their evolutionary history (particularly their cartilaginous epiphyses and well-developed pneumaticity) need to be taken into account to accurately infer how they evolved, perhaps by also addressing how the morphological traits of extant archosaurs scale with increasing size and increasing biomechanical pressures.

CONCLUSION
The present study corresponds to the first threedimensional investigation of the limb long bone microanatomy of a sauropod. The examination of Nigersaurus' longitudinal and transverse virtual sections permitted us to highlight a spongiosa partially or totally filling the medullary area, a trait classically associated with the support of a heavy body mass, and whose density appeared to vary with size in the tibia and the fibula. However, contrary to expectations, a rather thin cortex was found, only varying weakly in thickness along the shaft, contrasting with usually thick and abruptly varying cortices seen in heavy taxa. The cortex in zeugopod bones is proportionally thicker than in the stylopod ones, congruently with the literature, whereas no strong difference distinguishes the forelimb and the hindlimb serial homologues, despite the unequal distribution of the centre of mass (and, therefore, biomechanical constraints) in most sauropods. Cortical thickening in Nigersaurus is thus far from the degree expected, based on previous studies on heavy taxa. Complete cross-sections from the literature suggest a high variability in cortical thickening and presence of spongiosa in the shaft across sauropod taxa (i.e. far beyond the pattern observed in Nigersaurus), which does not appear to be related to size. Our results suggest that the microanatomical structure in sauropod limb bones was not subject to drastic selective pressures imposed by heavy weight-bearing. Instead, the columnar limb architecture, as well as some other external features, such as the presence of a fleshy pad and cartilaginous epiphyses may have been sufficient to support heavy weight, hence relaxing biomechanical pressures on microanatomy. This observation may also suggest that the mass increase in sauropods was lower than expected in relation to size increase, rejoining the conclusions of studies on postcranial pneumaticity, and tending to support the lowest body mass estimations made for sauropod taxa. More specifically, the pattern seen in Nigersaurus limb long bones is congruent with the lightened condition of the rest of its skeleton. The trends highlighted in this study would benefit from a more exhaustive exploration of microanatomical variability within sauropods, but also of other heavy terrestrial tetrapods, which will help us to better understand the evolution of limb bone microanatomy in relation to weight-bearing and to gigantism.
Acknowledgements. We warmly thank Marta Bellato for performing the scans and reconstructions at the AST-RX platform (UMS 2700, MNHN). We also thank Vincent Pern egre, Damien Olivier, Sandra Daillie, and Maxime Peretta for providing help and access to the MNHN collections, Cyril Etienne and Guillaume Hou ee for discussion on their preliminary work on rhinoceroses and tapirs, and K evin Le Verger and Pierre Lamarche for their logistic help for this study. We also thank Ignacio Cerda (Museo Carlos Ameghino, Cipolletti, Argentina) and an anonymous reviewer for their constructive comments that improved the quality of this manuscript, as well as Stephan Lautenschlager (University of Birmingham, Birmingham, UK) for his scientific editorial work, and Sally Thomas (Technical Editor and Publications Officer, The Palaeontological Association, UK) for the technical review, editorial work and comments. This work was funded by the European Research Council and is part of the GRAVIBONE project (ERC-2016-STG-715300).