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Finite element analysis (FEA) is a powerful tool to characterize the functional behaviour of bone. Here we use this technique to study the metacarpal arrangement of the Asian elephant. The objective of this work is to search for valid criteria that distinguish the known natural arrangement among a variety of configurations, including some fictitious ones. FEA yields significant statistical differences within the three arrangements tested. Our calculations suggest that the median value of stress (von Mises) could be a discriminant criterion, at least in graviportal taxa. Such a method could thus be applied to other graviportal organisms such as sauropod dinosaurs.

L’analyse par éléments finis (FEA) est un outil puissant permettant de caractériser le comportement fonctionnel de l’os. Nous proposons ici d’utiliser cette technique pour étudier l’arrangement métacarpien de l’éléphant d’Asie, dans le but de mettre en évidence un critère valide permettant de caractériser l’arrangement naturel connu parmi plusieurs possibilités, dont certaines fictives. L’analyse en éléments finis réalisée ici révèle des différences statistiques significatives entre trois arrangements testés, et suggère que la valeur médiane de stress (von Mises) pourrait être un critère discriminant, au moins chez les taxons graviporteurs. Une telle méthode pourrait donc être appliquée à d’autres organismes graviporteurs tels que les dinosaures sauropodes.

Even if several complete skeletons of extinct taxa are known, the possible arrangements of the preserved bones, especially their limbs, can remain ambiguous in absence of discernible articular facet. Therefore, the reconstruction of their body and posture are highly debatable. For example, the lesser degree of ossification of articular facets in dinosaurs leads to a debate on their stance and gait (

In this context, it becomes fundamental to search for appropriate criteria that could allow testing and verification of the reconstructions of extinct animals. We believe this is possible because different bone arrangements necessarily lead to different stress patterns (

Improvement of computing performance of finite element analysis (FEA) now makes it possible to use this as a virtual experimental platform to analyze diverse bone arrangements. By allowing the calculation of the stress distribution in virtually loaded bones, FEA makes it possible today to go farther in the understanding of the functional behaviour of skeletal elements (

The purpose of the present study is to investigate parameters provided by FEA on how the metacarpal arrangement of an Asian elephant,

The metacarpus used in the present study is from a fresh limb of

We performed FEA in order to examine stress distributions within the elephant metacarpus with the software

the models are aligned with the general coordinate system. Each metacarpal remains as single objects, which are only connected at the proximal end by multiple rigid links. These rigid links coerce even distribution of force within the connected nodes, therefore simulating the wrist joint as a solid, static carpal assemblage (

a natural arrangement (EN,

an “open” arrangement (E1,

a slightly more “tubular” arrangement (E2,

in absence of data from elephant bone, material properties are taken from published values (^{3}; elastic modulus (

the load applied, 13,750 N per limb, is calculated from an estimation of 5.6 ton weight. This value represents a high estimation for adult elephants. We average an Asian elephant of 5 tons, with a specimen of exceptional size such as the naturalized elephant ‘Siam’ at the Muséum national d’histoire naturelle (6–7 tons). Despite the fact that the autopod used for the study was smaller (sub-adult specimen), we intended to push the limits of the structure, taking into account that the limbs do not only overcome body weight, but also dynamic loading during locomotion which amplifies the forces. Nevertheless, our model is linear static, and so it is a function between load and material property, which will show similar stress distributions independent of magnitudes (

loading is applied normal to the joint surface (

in order to contrast the different metacarpal arrangements, comparative statistics were performed using von Mises stress values obtained for each brick element from FEA. The values were exported from STRAUS7 software (v2.3, 2004) and statistical analyses were performed with R GUI software (v2.4.0, free licence) and a specific module of analysis programmed by one of the authors (K. Moreno). Only the values of ‘bricks’ from the metacarpal diaphyses are taken. This precaution allows us to avoid the artefacts introduced in the model at both the loaded and the constrained surfaces, which are the proximal and distal epiphyses, respectively. Descriptive statistics were used to provide statistical summaries (boxplots) of the stress distribution in models. Boxplot allows to depict groups of numerical data through their five-number summaries (

The analyses of the three models reveal large differences between stress patterns of the natural metacarpal arrangement (

‘Global’ approach (see above). The Wilcoxon tests revealed that observed differences between the three metacarpal arrangements were highly significant: E1 vs. E2 (V = 5759770658, ^{−16}), E1 vs. EN (V = 11501993517, ^{−16}) and E2 vs. EN (V = 11610895239, ^{−16}). This data suggests that the comparison between metacarpal arrangements shows a lower median (SGmed) stress in natural configuration than in both fictitious configurations (

‘Individual’ approach (see above). More precisely, the analysis of stress level in individual metacarpals permits to establish a “stress profile” for each model (

Our results confirm that the stress pattern cannot be solely referred to the morphology of the metacarpals, which remains unaltered, but it is a function of the metacarpal arrangement. A significant increase in the median level of stress is observed in the metacarpus when the natural arrangement is modified (E1, E2). Therefore the median appears as a potential good indicator of the most likely ‘natural’ metacarpal arrangement among the available possibilities. Similarly, the reduction of the interquartile range around a higher median in the fictitious configurations E1 and E2 suggests an increase of zones at higher stress. On the other hand, an increasing interquartile range around a lower median in the natural metacarpal arrangement suggests that the bone is globally maintained at a lesser level of stress. However, the higher maximum intensity in this arrangement also suggests the presence of larger stressed zones, highly localized in the metacarpus.

Visualization of stress pattern and stress profile of the natural metacarpal arrangement allow us to specify the localization of these zones (

the higher level of stress in McI and V, positioned posteriorly to McII-IV, suggests a redistribution of the stress in the posterior part of the metacarpus;

these zones are clearly identified at mid-diaphysis and may correspond to regions presenting a higher risk of fracture. In real conditions, the presence of a well developed footpad might help overcome this problem redistributing the forces, probably by unloading the highly stressed posterior elements of the metacarpus (McI, McIV). However, FEA tests were not performed in this respect.

Interestingly, we can establish a parallel between these results and those of precedent studies about the structure of elephant autopods. Elephants have a cartilaginous medial element localized in the manus and pes footpad acting as a ‘sixth digit’ (

Our results indicate that it is possible to recognize the natural metacarpal arrangement of the extant Asian elephant among three different configurations by finding the stress distribution with the lowest median. Consequently, it is conceivable to use the same parameter to determine the most likely ‘natural’ metacarpal arrangement in extinct graviportal taxa where reconstitutions are debated such as sauropod dinosaurs.

High stress found in most posterior metacarpals of the Asian elephant can be linked with the presence of footpad and predigit. However, in absence of data on the exact influence of these elements (and other soft and connective tissues) on the stress distribution, our model can only reveal a rough stress pattern. However, this rough pattern is comparatively useful because in extinct taxa the soft tissues are usually not preserved. Nevertheless, our approach is potentially more informative in graviportal taxa whose footpad is absent, as in derived sauropods (

The authors thank John Hutchinson for his invaluable assistance in obtaining the CT scan data. This study was performed at the 3D platform of the Department “Histoire de la terre”, UMR7207 CR2P CNRS “Centre de recherche sur la paléobiodiversité et les paléoenvironnements”, Muséum National d’histoire naturelle. We thank Gaël Clément, Didier Geffard-Kuriyama and Philippe Taquet for the invitation to publish in this special volume. Helpful comments of three anonymous reviewers greatly improved the manuscript.

Finite element model of the metacarpals of

Modèle en éléments finis des métacarpes d’

The three metacarpal arrangements of

Les trois arrangements métacarpiens d’

Descriptive statistics from von Mises stress values for each metacarpal arrangement of

Statistiques descriptives à partir des valeurs de stress de von Mises pour chaque arrangement métacarpien d’

Descriptive statistics (boxplot) from von Mises stress values (MPa). Mc: metacarpal; Min.: lower stress value; Med.: median stress value; Max.: highest stress value; Q1 and Q3, first and third quartile, respectively. Only stress values from metacarpal diaphyses’ ‘bricks’ are taken, in order to avoid methodological artefacts (see text for details).

Statistiques descriptives (