Mechanical Implications of Pneumatic Neck Vertebrae in Sauropod Dinosaurs

Electronic supplementary material (ESM) to

Mechanical implications of pneumatic neck vertebrae in sauropod dinosaurs

Daniela Schwarz-Wings1 & 2, Christian A. Meyer2, Eberhard Frey3, Hans-Rudolf Manz-Steiner4, Ralf Schumacher5

1Museum für Naturkunde Berlin, Invalidenstrasse. 43, D-10115 Berlin, Germany. E-mail:

2Naturhistorisches Museum Basel, Augustinergasse 2, CH-4001 Basel, Switzerland.

3Staatliches Museum für Naturkunde Karlsruhe, Erbprinzenstrasse 13, D-76133 Karlsruhe, Germany.

4Fachhochschule Nordwestschweiz, Hochschule für Technik, Gründenstrasse 40, CH-4132 Muttenz. 5Fachhochschule Nordwestschweiz, Hochschule für Life Sciences, Gründenstrasse 40, CH-4132 Muttenz.

The Electronic supplementary material (ESM) contains additional information about the methods used for the reconstruction of soft-tissues and calculations of weight reduction in sauropod vertebrae, as well as an overview about the methods, software and material used to obtain the FE-data from the vertebrae.

1. Methods

2. Details on FEA

3. Supplementary figure

4. Supplementary references

1. Methods

1.1. Soft-tissue reconstructions. For soft-tissue reconstructions, topographical similarities of tissue attachment sites were used in the context of an Extant-Phylogenetic-Bracket (EPB) approach (Bryant & Russell 1992; Carrano & Hutchinson 2002; Witmer 1995; Witmer 1997). Criteria used for recognising osteological correlates of pneumatic structures in sauropod vertebrae followed the work of Britt (1993), O’Connor (2003; 2004; 2006), Wedel (2005; 2000) and Witmer (1990; 1997). Soft-tissue reconstructions for the studied specimens have been published in (Schwarz & Fritsch 2006) and (Schwarz et al. 2007).

1.2. Calculation of weight reduction. We used the tomographic images to quantify how much of the bone material in a vertebra was replaced by air-filled space. From each vertebra, ten transverse cross-sections were chosen and surrounded by an “ideal vertebra” outline, using the software ImageJ. The total amount of pixel covered by pneumatic structures was subtracted from the total amount of pixel of the “ideal vertebra” outline, and an average value was formed from the ten cross-sections for each vertebra. Transformed into percentages, this value gives a minimum estimate of how much space in a vertebra was occupied by pneumatic structures, and, therefore of how much of the bone material was resorbed. This procedure differs from the method of determining the Air Space Proportion (ASP) of Wedel(Wedel 2005), in that it also includes the neural arch and thus involves measuring the entire vertebra. We always used several cross-sections to calculate an average value, because individual values vary strongly throughout a given vertebra:

These results can be supplemented by those given by Wedel(Wedel 2005), which include more than one cross-section, for the cervical vertebrae of Apatosaurus (51%), Tornieria (“Barosaurus”, 60%), Camarasaurus (50%) and Sauroposeidon (79%). Weight would have further decreased when taking into account large external pneumatic diverticula, however, uncertainties in the reconstructed extent of these diverticula (Schwarz & Frey 2008) prevent such changes from being accurately quantifiable.

Museum abbreviations: MB.R. – Museum für Naturkunde Berlin/Germany, Collection of fossil Reptilia; MB E – Museum für Naturkunde Berlin/Germany, old field number for specimens; SMA – Sauriermuseum Aathal/ Switzerland.

2. Details on FEA

2.1. Material used for FEA. The 4th cervical vertebra of Brachiosaurus brancai (MB.R.2180.25, SI 70) from the Late Jurassic Tendaguru beds in Tanzania was selected to produce a FE model for a loading situation in the neck of a large sauropod (neck length 8.6m) with cervical vertebrae possessing a pair of cervical ribs about 50 % longer than the vertebral body. The vertebra was slightly transversely compressed. The cervical rib was not preserved in the original and therefore was added to the model as a simple rod.

A mid-cervical vertebra of Diplodocus (SMA L25-3) from the Late Jurassic Howe Quarry in the Morrison Formation, USA, was selected to model a loading situation in the neck of a another large sauropod (neck length ca. 7 m), but with cervical ribs being just a little longer than the adjacent vertebra. This rib configuration is probably not typical for diplodocids, in which at least Diplodocus carnegi and Apatosaurus spp.are known to have short cervical ribs.

2.2. Model Creation. The 4th cervical vertebra of Brachiosaurus brancai was scanned in the Clinic for Small Pets of the Free University of Berlin, using a high-resolution Multislice-CT scanner (GE Healthcare Light Speed advantage QXi) (for details, see Schwarz & Fritsch 2006). The vertebra of Diplodocus was scanned with a Multidetector CT-scanner (Sensation 16, Siemens, Erlangen; Germany) (for details, see Schwarz et al. 2007). The CT data (volume model) were converted into a surface model, represented by small triangulated facets, the so-called STL-format (software: Mimics 9.11). Deformation on each of the two vertebrae (compression, breakage, distortion) was removed by manual retrodeformation, first with Geomagic® Studio and second using Phantom® haptic device in FreeForm® Modeling Plus. The resulting vertebrae represented a 3D model of the idealized undistorted vertebra.

In a second step, a copy of the ideal vertebral models was combined with the original CT data in Mimics 9.11. Because of the diagenetic distortion and partially collapsed pneumatic system, the latter could not be separated as a whole, and the pneumatic cavities were inscribed manually into each of the more than 900 single images of the CT stack. These images were combined and converted in Geomagic® Studio to produce a new volume reconstruction of the cavity system. Employing FreeForm® Modeling Plus again, the cavity model was smoothed and remaining holes were filled, resulting in an idealized and undistorted cavity system.

In a third step, the cavity system was re-converted into STL format and together with the ideal vertebra imported to Magics RP. Applying now a Boolean Operation in Magics RP, the cavity system was subducted from the vertebra, which resulted in a surface (STL) model replicating both the external vertebral surface, and its (simplified) internal cavity system. Finally, both vertebral models were meshed (i.e., broken up into the finite elements connected by nodes) by the FEA software I-DEAS, creating a 3D FE model of each, consisting of linear tetrahedrons with a total of 4000 nodes.

2.3. Material properties, boundary constraints. The material properties of the sauropod bone were based on the mechanical properties of the bone of fast-growing large mammals, because these properties have been successfully applied to other FE analyses of dinosaur bones under the assumption that similar histology results in similar material properties(Rayfield 2007; Rayfield et al. 2001; Snively & Russell 2002). The specific values of bovine haversian bone were used: Young’s modulus 10 GPa, shear modulus 3.6 GPa, Poisson-Ratio 0.4, density 1.895(Rayfield et al. 2001). For reasons of simplicity, isotropy was assumed for the vertebral bone, regarding it (as in most investigations of structural biomechanics) as a linearly elastic material based on its elastic properties in response to physiologically normal loads. Ligaments and muscles were modelled as spring elements. The vertebrae were set to boundary constraints, which prevented all possible modes of rigid body motion. Recent reconstructions of sauropod neck muscles and ligaments(Schwarz et al. 2007; Wedel & Sanders 2002) were used for defining the points where main loads were applied to the vertebrae (Fig. 1). Calculations by Henderson(Henderson 2006) were used for mass estimations of the neck. Although these values do not represent an exact reconstruction of the neck weight, they are also not expected to be irregularly low or high. The weights were similar for both vertebrae, because the 4th cervical vertebra of Brachiosaurus was estimated to weigh roughly the same as the selected mid-cervical vertebra of Diplodocus. The neck weight was inserted as the resulting momentum in terms of a couple of forces.

3. Supplementary figure

Supplementary figure 1 a) Von-Mises comparative stress in the FE models during extension of the neck, Brachiosaurus vertebra model without cervical rib. b) Von-Mises comparative stress during lateral flexion in the model of the Diplodocus vertebra. Flexed side: high stress occurs in the diapophyseal region and along the cervical rib, c) same vertebra, extended side: cervical rib and parapophyseal region of vertebra are loaded, d) same vertebra, combined cross-sections.

4. Supplementary references

Britt, B. B. 1993 Pneumatic postcranial bones in dinosaurs and other archosaurs. PhD thesis. University of Calgary, Alberta 383 p.

Bryant, H. N. & Russell, A. P. 1992 The role of phylogenetic analysis in the inference of unpreserved attributes of extinct taxa. Philosophical Transactions of the Royal Society of London, B 337, 405-418.

Carrano, M. T. & Hutchinson, J. R. 2002 Pelvic and hindlimb musculature of Tyrannosaurus rex (Dinosauria: Theropoda). Journal of Morphology 253, 207-228.

Henderson, D. M. 2006 Burly gaits: centers of mass, stability, and the trackways of sauropod dinosaurs. Journal of Vertebrate Paleontology 26, 907-921.

O`Connor, M. P. 2003 Pulmonary pneumaticity in extant birds and extinct archosaurs. Stony Brook University, Stony Brook. 304 p.

O`Connor, M. P. 2004 Pulmonary pneumaticity in the postcranial skeleton of extant aves: a case study examining Anseriformes. Journal of Morphology 261, 141-161.

O'Connor, M. P. 2006 Postcranial pneumaticity: An evaluation of soft-tissue influences on the postcranial skeleton and the reconstruction of pulmonary anatomy in archosaurs. Journal of Morphology 267, 1199-1226. (doi:

10.1002/jmor.10470)

Rayfield, E. J. 2007 Finite Element Analysis and understanding the biomechanics and evolution of living and fossil organisms. Annual Review of Earth and Planetary Sciences 35, 541-576.

Rayfield, E. J., Norman, D. B., Horner, C. C., Horner, J. R., Smith, P. M., Thomason, J. J. & Upchurch, P. 2001 Cranial design and function in a large theropod dinosaur. Nature 409, 1033-1037.

Schwarz, D. & Frey, E. 2008 Is there an option for a pneumatic stabilization of sauropod necks? - An experimental and anatomical approach. Palaeontologia Electronica 11, 17A:26p.

Schwarz, D., Frey, E. & Meyer, C. A. 2007 Pneumaticity and soft-tissue reconstructions in the neck of diplodocid and dicraeosaurid sauropods. Acta Palaeontologica Polonica 52, 167-188.

Schwarz, D. & Fritsch, G. 2006 Pneumatic structures in the cervical vertebrae of the Late Jurassic (Kimmerigian-Tithonian) Tendaguru sauropods Brachiosaurus brancai and Dicraeosaurus. Eclogae Geol. Helv. 99, 65-78.

Snively, E. & Russell, A. P. 2002 The Tyrannosaurid Metatarsus: Bone Strain and inferred Ligament Function. Senckenbergiana lethaea 82, 35-42.

Wedel, M. J. 2005 Postcranial skeletal pneumaticity in sauropods and its implications for mass estimates. In The Sauropods: Evolution and Paleobiology (ed. K. A. Curry Rogers & J. A. Wilson), pp. 201-228. Berkeley: University of California Press.

Wedel, M. J., Cifelli, R. I. & Sanders, R. K. 2000 Osteology, paleobiology, and relationships of the sauropod dinosaur Sauroposeidon. Acta Palaeontologica Polonica 45, 343-388.

Wedel, M. J. & Sanders, R. K. 2002 Osteological correlates of cervical musculature in Aves and Sauropoda (Dinosauria: Saurischia), with comments on the cervical ribs of Apatosaurus. PaleoBios 22, 1-6.

Witmer, L. M. 1990 The craniofacial air sac system of mesozoic birds (Aves). Zoological Journal of the Linnean Society 100, 327-378.

Witmer, L. M. 1995 The Extant Phylogenetic Bracket and the importance of reconstructing soft tissues in fossils. In Functional Morphology in Vertebrate Paleontology (ed. J. Thomason), pp. 19-33. Cambridge: Cambridge University Press.

Witmer, L. M. 1997 The evolution of the antorbital cavity in archosaurs: a study in soft-tissue reconstruction in the fossil record with analysis of the function of pneumaticity. J. Vert. Paleontol., Mem. 3, 1-73.

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