Charlotte A. Brassey

Minimum convex hull mass estimations of complete mounted skeletons

Body mass is a critical parameter used to constrain biomechanical and physiological traits of organisms. Volumetric methods are becoming more common as techniques for estimating the body masses of fossil vertebrates. However, they are often accused of excessive subjective input when estimating the thickness of missing soft tissue. Here, we demonstrate an alternative approach where a minimum convex hull is derived mathematically from the point cloud generated by laser-scanning mounted skeletons. This has the advantage of requiring minimal user intervention and is thus more objective and far quicker. We test this method on 14 relatively large-bodied mammalian skeletons and demonstrate that it consistently underestimates body mass by 21 per cent with minimal scatter around the regression line. We therefore suggest that it is a robust method of estimating body mass where a mounted skeletal reconstruction is available and demonstrate its usage to predict the body mass of one of the largest, relatively complete sauropod dinosaurs: Giraffatitan brancai (previously Brachiosaurus) as 23200 kg.

Finite element modelling versus classic beam theory: comparing methods for stress estimation in a morphologically diverse sample of vertebrate long bones

Classic beam theory is frequently used in biomechanics to model the stress behaviour of vertebrate long bones, particularly when creating intraspecific scaling models. Although methodologically straightforward, classic beam theory requires complex irregular bones to be approximated as slender beams, and the errors associated with simplifying complex organic structures to such an extent are unknown. Alternative approaches, such as finite element analysis (FEA), while much more time-consuming to perform, require no such assumptions. This study compares the results obtained using classic beam theory with those from FEA to quantify the beam theory errors and to provide recommendations about when a full FEA is essential for reasonable biomechanical predictions. High-resolution computed tomographic scans of eight vertebrate long bones were used to calculate diaphyseal stress owing to various loading regimes. Under compression, FEA values of minimum principal stress (σmin) were on average 142 per cent (±28% s.e.) larger than those predicted by beam theory, with deviation between the two models correlated to shaft curvature (two-tailed p = 0.03, r2 = 0.56). Under bending, FEA values of maximum principal stress (σmax) and beam theory values differed on average by 12 per cent (±4% s.e.), with deviation between the models significantly correlated to cross-sectional asymmetry at midshaft (two-tailed p = 0.02, r2 = 0.62). In torsion, assuming maximum stress values occurred at the location of minimum cortical thickness brought beam theory and FEA values closest in line, and in this case FEA values of τtorsion were on average 14 per cent (±5% s.e.) higher than beam theory. Therefore, FEA is the preferred modelling solution when estimates of absolute diaphyseal stress are required, although values calculated by beam theory for bending may be acceptable in some situations.

Downsizing a giant: re-evaluating Dreadnoughtus body mass

Estimates of body mass often represent the founding assumption on which biomechanical and macroevolutionary hypotheses are based. Recently, a scaling equation was applied to a newly discovered titanosaurian sauropod dinosaur (Dreadnoughtus), yielding a 59 300 kg body mass estimate for this animal. Herein, we use a modelling approach to examine the plausibility of this mass estimate for Dreadnoughtus. We find that 59 300 kg for Dreadnoughtus is highly implausible and demonstrate that masses above 40 000 kg require high body densities and expansions of soft tissue volume outside the skeleton several times greater than found in living quadrupedal mammals. Similar results from a small sample of other archosaurs suggests that lower-end mass estimates derived from scaling equations are most plausible for Dreadnoughtus, based on existing volumetric and density data from extant animals. Although volumetric models appear to more tightly constrain dinosaur body mass, there remains a clear need to further support these models with more exhaustive data from living animals. The relative and absolute discrepancies in mass predictions between volumetric models and scaling equations also indicate a need to systematically compare predictions across a wide size and taxonomic range to better inform studies of dinosaur body size.

Decoupled form and function in disparate herbivorous dinosaur clades

Convergent evolution, the acquisition of morphologically similar traits in unrelated taxa due to similar functional demands or environmental factors, is a common phenomenon in the animal kingdom. Consequently, the occurrence of similar form is used routinely to address fundamental questions in morphofunctional research and to infer function in fossils. However, such qualitative assessments can be misleading and it is essential to test form/function relationships quantitatively. The parallel occurrence of a suite of morphologically convergent craniodental characteristics in three herbivorous, phylogenetically disparate dinosaur clades (Sauropodomorpha, Ornithischia, Theropoda) provides an ideal test case. A combination of computational biomechanical models (Finite Element Analysis, Multibody Dynamics Analysis) demonstrate that despite a high degree of morphological similarity between representative taxa (Plateosaurus engelhardti, Stegosaurus stenops, Erlikosaurus andrewsi) from these clades, their biomechanical behaviours are notably different and difficult to predict on the basis of form alone. These functional differences likely reflect dietary specialisations, demonstrating the value of quantitative biomechanical approaches when evaluating form/function relationships in extinct taxa.

Scaling of Convex Hull Volume to Body Mass in Modern Primates, Non-Primate Mammals and Birds

The volumetric method of ‘convex hulling’ has recently been put forward as a mass prediction technique for fossil vertebrates. Convex hulling involves the calculation of minimum convex hull volumes (vol CH) from the complete mounted skeletons of modern museum specimens, which are subsequently regressed against body mass (M b) to derive predictive equations for extinct species. The convex hulling technique has recently been applied to estimate body mass in giant sauropods and fossil ratites, however the biomechanical signal contained within vol CH has remained unclear. Specifically, when vol CH scaling departs from isometry in a group of vertebrates, how might this be interpreted? Here we derive predictive equations for primates, non-primate mammals and birds and compare the scaling behaviour of M b to vol CH between groups. We find predictive equations to be characterised by extremely high correlation coefficients (r 2 = 0.97–0.99) and low mean percentage prediction error (11–20%). Results suggest non-primate mammals scale body mass to vol CH isometrically (b = 0.92, 95%CI = 0.85–1.00, p = 0.08). Birds scale body mass to vol CH with negative allometry (b = 0.81, 95%CI = 0.70–0.91, p = 0.011) and apparent density (vol CH/M b) therefore decreases with mass (r 2 = 0.36, p<0.05). In contrast, primates scale body mass to vol CH with positive allometry (b = 1.07, 95%CI = 1.01–1.12, p = 0.05) and apparent density therefore increases with size (r 2 = 0.46, p = 0.025). We interpret such departures from isometry in the context of the ‘missing mass’ of soft tissues that are excluded from the convex hulling process. We conclude that the convex hulling technique can be justifiably applied to the fossil record when a large proportion of the skeleton is preserved. However we emphasise the need for future studies to quantify interspecific variation in the distribution of soft tissues such as muscle, integument and body fat.

The role of cross-sectional geometry, curvature, and limb posture in maintaining equal safety factors: a computed tomography study

The limb bones of an elephant are considered to experience similar peak locomotory stresses as a shrew. “Safety factors” are maintained across the entire range of body masses through a combination of robusticity of long bones, postural variation, and modification of gait. The relative contributions of these variables remain uncertain. To test the role of shape change, we undertook X‐ray tomographic scans of the leg bones of 60 species of mammals and birds, and extracted geometric properties. The maximum resistible forces the bones could withstand before yield under compressive, bending, and torsional loads were calculated using standard engineering equations incorporating curvature. Positive allometric scaling of cross‐sectional properties with body mass was insufficient to prevent negative allometry of bending (Fb) and torsional maximum force (Ft) (and hence decreasing safety factors) in mammalian (femur Fb∞Mb0.76, Ft∞Mb0.80; tibia Fb∞Mb0.80, Ft∞Mb0.76) and avian hindlimbs (tibiotarsus Fb∞Mb0.88, Ft∞Mb0.89) with the exception of avian femoral Fb and Ft. The minimum angle from horizontal a bone must be held while maintaining a given safety factor under combined compressive and bending loads increases with Mb, with the exception of the avian femur. Postural erectness is shown as an effective means of achieving stress similarity in mammals. The scaling behavior of the avian femur is discussed in light of unusual posture and kinematics. Anat Rec, 296:395–413, 2013.

More than One Way of Being a Moa: Differences in Leg Bone Robustness Map Divergent Evolutionary Trajectories in Dinornithidae and Emeidae (Dinornithiformes)

The extinct moa of New Zealand included three families (Megalapterygidae; Dinornithidae; Emeidae) of flightless palaeognath bird, ranging in mass from <15 kg to >200 kg. They are perceived to have evolved extremely robust leg bones, yet current estimates of body mass have very wide confidence intervals. Without reliable estimators of mass, the extent to which dinornithid and emeid hindlimbs were more robust than modern species remains unclear. Using the convex hull volumetric-based method on CT-scanned skeletons, we estimate the mass of a female Dinornis robustus (Dinornithidae) at 196 kg (range 155–245 kg) and of a female Pachyornis australis (Emeidae) as 50 kg (range 33–68 kg). Finite element analysis of CT-scanned femora and tibiotarsi of two moa and six species of modern palaeognath showed that P. australis experienced the lowest values for stress under all loading conditions, confirming it to be highly robust. In contrast, stress values in the femur of D. robustus were similar to those of modern flightless birds, whereas the tibiotarsus experienced the highest level of stress of any palaeognath. We consider that these two families of Dinornithiformes diverged in their biomechanical responses to selection for robustness and mobility, and exaggerated hindlimb strength was not the only successful evolutionary pathway.

Investigating the running abilities of Tyrannosaurus rex using stress-constrained multibody dynamic analysis

The running ability of Tyrannosaurus rex has been intensively studied due to its relevance to interpretations of feeding behaviour and the biomechanics of scaling in giant predatory dinosaurs. Different studies using differing methodologies have produced a very wide range of top speed estimates and there is therefore a need to develop techniques that can improve these predictions. Here we present a new approach that combines two separate biomechanical techniques (multibody dynamic analysis and skeletal stress analysis) to demonstrate that true running gaits would probably lead to unacceptably high skeletal loads in T. rex. Combining these two approaches reduces the high-level of uncertainty in previous predictions associated with unknown soft tissue parameters in dinosaurs, and demonstrates that the relatively long limb segments of T. rex—long argued to indicate competent running ability—would actually have mechanically limited this species to walking gaits. Being limited to walking speeds contradicts arguments of high-speed pursuit predation for the largest bipedal dinosaurs like T. rex, and demonstrates the power of multiphysics approaches for locomotor reconstructions of extinct animals.

Convex-hull mass estimates of the dodo (Raphus cucullatus): application of a CT-based mass estimation technique

The external appearance of the dodo (Raphus cucullatus, Linnaeus, 1758) has been a source of considerable intrigue, as contemporaneous accounts or depictions are rare. The body mass of the dodo has been particularly contentious, with the flightless pigeon alternatively reconstructed as slim or fat depending upon the skeletal metric used as the basis for mass prediction. Resolving this dichotomy and obtaining a reliable estimate for mass is essential before future analyses regarding dodo life history, physiology or biomechanics can be conducted. Previous mass estimates of the dodo have relied upon predictive equations based upon hind limb dimensions of extant pigeons. Yet the hind limb proportions of dodo have been found to differ considerably from those of their modern relatives, particularly with regards to midshaft diameter. Therefore, application of predictive equations to unusually robust fossil skeletal elements may bias mass estimates. We present a whole-body computed tomography (CT) -based mass estimation technique for application to the dodo. We generate 3D volumetric renders of the articulated skeletons of 20 species of extant pigeons, and wrap minimum-fit ‘convex hulls’ around their bony extremities. Convex hull volume is subsequently regressed against mass to generate predictive models based upon whole skeletons. Our best-performing predictive model is characterized by high correlation coefficients and low mean squared error (a = − 2.31, b = 0.90, r2 = 0.97, MSE = 0.0046). When applied to articulated composite skeletons of the dodo (National Museums Scotland, NMS.Z.1993.13; Natural History Museum, NHMUK A.9040 and S/1988.50.1), we estimate eviscerated body masses of 8–10.8 kg. When accounting for missing soft tissues, this may equate to live masses of 10.6–14.3 kg. Mass predictions presented here overlap at the lower end of those previously published, and support recent suggestions of a relatively slim dodo. CT-based reconstructions provide a means of objectively estimating mass and body segment properties of extinct species using whole articulated skeletons.

The benefit of a tough skin: bullet holes, weathering and the preservation of heritage

Projectile damage to building stone is a widespread phenomenon. Sites damaged 100 years ago during the First World War still see daily use, while in a more contemporary setting numerous reports show the damage to buildings in Babylon, Mosul and Palmyra. While research has been carried out on the long-term effects of conflict such as fire damage, little is known about the protracted damage sustained through the impact of bullets, shrapnel and other metal projectiles outside of the field of engineering focused on ceramics and metals. To investigate alterations to mineral structure caused by projectile damage, impacts were created in medium-grained, well-compacted, mesoporous sandstone samples using 0.22 calibre lead bullets shot at a distance of 20 m. Half these samples were treated with a surface consolidant (Wacker OH 100), to mimic natural cementation of the rock surface. These samples were then tested for changes to surface hardness and moisture movement during temperature cycles of 15–65°C. Petrographic thin section analysis was carried out to investigate the micro-scale deformation associated with high-speed impact. The results surprisingly show that stress build-up behind pre-existing cementation of the surface, as found in heritage sites that have been exposed to moisture and temperature fluctuations for longer periods of time, can be alleviated with a bullet impact. However, fracture networks and alteration of the mineral matrices still form a weak point within the structure, even at a relatively low impact calibre. This initial study illustrates the need for geomorphologists, geologists, engineers and heritage specialists to work collectively to gain further insights into the long-term impact of higher calibre armed warfare on heritage deterioration.