THE UNIVERSITY OF CALGARY Eric Snively A ... - Ohio University

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CHAPTER 5: Mechanical and evolutionary integration of the tyrannosaurid arctometatarsus Chapter 1 introduced the bones and ligaments of the arctometatarsus as an integrated subsystem of the tyrannosaurid phenotype, and intewening sections tested hypotheses that this unusual morphology suggests. This chapter explores the implications of putative metatarsus function for tyrannosaurids and other theropods. The first section discusses the utility of the finite element method for assessing combined functions of bones and elastic connective organs, with the loading regime of the arctometatarsus presented as a salient example. Subsequently, the chapter consolidates findings on theropod MT III variation and biomechanics, and discusses the ramifications of these hypotheses in the context of phylogenetic distribution, biological role, and selective utility of the arctometatarsus. FlNlTE ELEMENT ANALYSE AND <strong>THE</strong> FUNCTIONAL INTERPLAY <strong>OF</strong> BONES AND LIGAMENTS Lessons for applying the finite element method to palaeontology The finite element results (Chapter 4) point to the promise and limitations of the method for the study of kinematics of extinct animals. The rigor of any finite element analysis is proportional to the quality of the model. Uninformative results do not anse from deficiencies of the method, but rather from unrefined structural representations. Yet cornputer models of only moderate resolution, such as those employed in this study, can yield data useful for testing functional hypotheses when initial kinematic conditions and material properties are realistic.
The analyses of the Gorgosaurus Iibratus metatarsus (Chapter 4) suggest three lessons for Mure palaeontological applications of the finite element method: 1. Prirnary data from fossils take precedence over other considerations in the execution of a realistic model and analysis. The G. libratus metatarsus investigated in this study was remarkably well-preserved and undistorted. This ensured that digitized and stacked cross sections from CT scans replicated the metatarsus of the living animal with a high degree of fidelity. In addition, proper density settings for the CT scans easily resolved the medullary cavities, even where they were filled in with matrix. 2. Finite element analysis can be informative using meshes of moderate resolution, but meshes with larger numbers of elements are both desirable and practical. Generally, a mesh with more elements will result in a more realistic assessrnent of strain distribution, because the elements are smaller. Short lengths of element edges potentially present shorter moment arms for impinging stresses. In a mesh of a 50 cm bon8 consisting of 2200 elements, the large size of some tetrahedral edges resulted in identifiable artiiacts (see Results, Chapter 4). These undesirable results are avoidable. The proœssing power of modem computers allows for rapid solution of stiffness matrix equations, even with very large file sizes (represented by large numbers of elements). The construction and solution of equations for a tetrahedral mesh of the combined metatarsus, with approximately 8000 elements, took less than one minute. 3. Strain results fram static analyses of bones c;tn elucidate the funcüon of associated ligaments. If the tyrannosaurid MT III was not suspended elastically
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THE UNIVERSITY OF CALGARY Functiona
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Many figures in this thesis use col
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ACKNOWLEûGEM ENTS Many friends and
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Approval page Acknowledgements Tabi
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CONCLUDING COMMENTS Figures for Cha
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CHAPTER 5: Mechanical and phylogene
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LIST OF FIGURES Figure 1 .l. Phylog
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Figure 3.6. Osteological correlates
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AMNH GI HMN IVPP MOR NMC OMNH PIN P
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and constructional morphology revea
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1985, Bryant and Seymour 1990). If
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surfaces of a Tyrannosaurus rex spe
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3. Troodontidae (Figure 1.2): Trwdo
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Hypothesized functions of the tyran
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1. Atomization (Chapters 2 and 3).
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Figure 1.1. P hylogenetic diagram o
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Figure 1.2. Phylogenetic diagram of
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Figure 1 .S. Skeletal restorations
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did not quantify the degree of prox
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qualitative debate over arctometata
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This hypothesis focuses on tyrannos
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Table 2.1. Theropod and Plafeosauru
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specimens in the figures reflects a
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were not attempted. While this limi
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Chapter 3). 1 now address variation
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- Ç6'P 1 68'€tr 1 L'OC 99'66 L'9
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Table 2.3: Log-transformed values f
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experiences a sharp laterally indin
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ecause it can be cursorily dassifie
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arctometatarsalian specimens, the l
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) Shaf€ and region of proximal ar
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a) Ginglymus. Figure 2.14 shows the
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) Shaft and region of proximal arti
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measurements of width pV2S%TU-DE an
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Table 2.4b Variancelmeasurement eac
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the largest sum of linear measureme
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Table 2.5: Specimen statistics Herr
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and Sinraptor dongi specimens. With
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In addition, a hook like proximal a
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oth physical narrowing and elongati
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1s the MT 111 shape segregation fun
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tyrannosaurids, ornithomimid, and t
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proximal constriction, white EImisa
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Figure 2.2. Tyrannosaurid, trwdonti
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Figure 2.4. Dromaeosaurid and carno
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- Anterior (flexor) surface medial
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Figure 2.7. Left MT III of Tyrannos
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Figure 2.8. Left MT III of Gorgosau
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Figure 2.9. Left MT III of an omith
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Figure 2.10. Left metatarsus of Tmd
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Figure 2.1 1. Left MT III of Elmisa
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Figure 2.12. Right MT III of Deinon
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Figure 2.13. Left MT III of Allosau
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Figure 2.14. Left metatarsus of Sin
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Figure 2.15. Plots of MT Ill specir
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Figure 2.16. Plot of third metatars
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tv . ... . Ri. . . .
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Figure 2.19. Plot of third metatars
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CHAPTER 3: Tensile keystone model o
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dynamically transmitted Iommotor fo
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Table 3.1 . Metatarsi examined in t
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interrnetatarsal dynamics in these
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compelled analysis of movement evid
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Once prepared, TMP 94.1 2.602 and i
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Daspletosaurus tomsus (MOR 590), an
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2. Freedom of movement inferred fro
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Table 3.2. Surface areas of intemet
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phylogenetic bracketing Wtmer 1995)
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4) Forces from anterior displacerne
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e expected for tyrannosaurid interm
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The preceding discussion derives fr
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weapons sparring), and the arctomet
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Figure 3.1. Schematic representatio
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Figure 3.3. CT reconstruction of ri
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Figure 3.5. MT II (left element) an
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Figure 3.1 1 ae. The metatarsal rec
Page 187: Figure 3.13. Ligament contribution
Page 191 and 192: Figure 3.15. Anatorny of the equid
Page 193: Figure 3.16. Cornparison of loading
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Page 202 and 203: A FORCE INPUTS AND MATERIAL PROPERT
Page 204 and 205: Alexander et al. (1 979) rewrded a
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Page 224: Figure 4.1. Initial loads and bound
Page 228: Figure 4.3. Finite element mesh of
Page 232: Figure 4.5. Strain distribution in
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Page 240 and 241: Probable fundion of the tyrannosaur
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Page 262 and 263: Proximal intermetatarsal ligaments
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Page 267: Figure 5.2. Phylogeny of the Therop
Page 278 and 279: Bock W.J. and von Wahlert G. Evolut
Page 280 and 281: Cume P.J. 1997. Theropoda. In: Fari
Page 282 and 283: Grenard S. 1991. Handbook of Alliga
Page 284 and 285: Liem K.F. and Osse J.W.M. 1975. Bio
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Richtsmeier J.T. and Cheverud J.M.
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Woo S., Maynard J., Butler O. 1987.
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Different variables in a PCA will h
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THE UNIVERSITY OF CALGARY Eric Snively A ... - Ohio University

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