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

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maintained. An angle of 2 degrees proved adequate for authentic surface contours with a minimum number of elements. The resulting meshes (Figure 4.3) consisted of 3237 tetrahedral elements for MT 11,2226 for MT III, and 31 01 for MT IV. These were converted to AVS and xgobi visualization formats and MARC input format by the program extract-tetra, written by Dr. Phiilips. MARCMENTAT is a set of finite element processing and user interface software, held under kense by the <strong>University</strong> of Calgary Human Performance Lab (HPL). The MARC format files were transferred via FTP to the server at the HPL. Calculated forces, material properties, and boundary conditions were applied in MENTAT, and MARC camed out the construction and solution of finite element equations. RESULTS 1. The metatarsus normal to the substrate Figures 4.5 and 4.6 show the pattern of compressive strain energy in the G. libratus metatarsus model. Figure 4.4 is a contour plot of compressive strain. The simplest visualization option, showing contour lines of strain along element sides, proved to be the most informative. Two salient patterns emerge from the results: 1 ) Artifacts of the tetrahedral meshing technique are easily differentiable from informative results; 2) Regions of high strain correlate with proposed distal ligament positions and the proximal gracile portion of MT III. These points are now examined in tum.
1) Informative strain results versus mesh artifacts. Figure 4+4 overlies strain results from the first analysis on the surface of the finite element model. The faded gray lines are edges of visible element faces, and the purple Iines represent concentrations of compressive (2-axis) strain. Near the proximal and distal ends of the bone, several purple Iines show strain at particularly long element edges that are perpendicular to the compressive stress (one is pinpointed by the green line in the figure). Because these edges are long and have a subhorizontal orientation, they act as long moment arms for the compressive loading. This results in artifactual strain on the elements. In contrast, strain is also evident along element edges that are short and vertically oriented (Figure 4.4, located by red lines), providing moment arms of negligible to zero length for stresses along the z axis. The small size of elements in these regions provides high resolution for strain resuits. The magnitude of strain (close to 0.2 mm) is more significant when the element edges are nearly parallel with the compressive ground-reaction force, because bone is strongly resistant to such loadings. Conversely, the same apparent magnitude of strain at long, horizontal element edges indicates that in vivo strain was less extensive in these regions, and that indicated çtrain along subvertical edges is more biologically informative. The distribution of significant strain results is now delineated. 2. Strain distribution. Under both ioading regimes with the metatarsus normal to the substrate, the regions of greatest bone strain occur along the distal articular surfaces between metatarsais, and along the proximally narrow portion
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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
Page 167: Figure 3.5. MT II (left element) an
Page 171: Figure 3.7. Osteological correlates
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Page 179: Figure 3.1 1 ae. The metatarsal rec
Page 187: Figure 3.13. Ligament contribution
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Page 202 and 203: A FORCE INPUTS AND MATERIAL PROPERT
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Page 228: Figure 4.3. Finite element mesh of
Page 232: Figure 4.5. Strain distribution in
Page 236 and 237: CHAPTER 5: Mechanical and evolution
Page 238 and 239: y distal intermetatarsal ligaments,
Page 240 and 241: Probable fundion of the tyrannosaur
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Figure 5.2. Phylogeny of the Therop
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Bock W.J. and von Wahlert G. Evolut
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Cume P.J. 1997. Theropoda. In: Fari
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Grenard S. 1991. Handbook of Alliga
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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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