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

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detemined by using the photographic method described above, with the metatarsals held at a 50 degree angle. Area proportions are 0.406 for MT III, and 0.297 for MT II and MT IV. Using equation (8), the resulting forces on the metatarsals at 50 degrees are therefore: F~m1=(37873 N)(0.297)=11248 N F~m~(37873 N)(0.406)=15376 N F~~-nv=(37873 N)(0.297)=11248 N. The force on the distal end of MT III, with it inclined at 50 degrees, is the important value for this analysis. The vector wmponents of this force (Figure 4.2) were calculated; these components were input along the z and y ordinate axes in the finite element program. It was assumed that the proximal end of MT III was held rigid by its articulations with MT II and MT IV. With boundary conditions set to zero displacement or rotation at the proximal end of the MT Ill, the finite eiement program calculated bending moments acting on the metatarsal, in arder ta arrive at the resulting strains. 2. Mafenal properfies Finite element modeling can incorporate material properties of objects with non-homogeneous intemal structure, such as bones with cortical and trabecular wnstituents, as well as stnicturally homogeneous objects such as ligaments. CT scans revealed that dense cortical bone is predominant in the G. libratus metatarsus. Cancellous bone is restricted to narrow bands near the phalangeal and rnesotarsal articular surfaces, and to srnall regions near the proximal and distal extremities of the medulary cavities. Unfortunately, the size and shape of
elements in the finite element rnesh precluded precise regional distinctions between cortical and cancellous bone. Therefore material properties for cortical bone were applied to the entire model. Values for elastic modulus and Poisson's ratio were taken from the literature (Table 4.1). B. PREPROCESSING FOR FEA: MODELING AND MESH GENERATION Preprocessing of data for finite element study involved constructing a 30 model from CT data, and creating a finite element continuum mesh within that model. Creation of the model entailed the use of several software packages at the <strong>University</strong> of Calgary Visualization Center, with corresponding iterations of data manipulation. The sequence of methodologies involved data transfer and preparation, wrve identification and stacking, and mesh generation. 7. Data transfer Raw data from CT scans of Gorgosaurus libratus (see Chapter 3) were extracted from DAT tape at the Alpha Cluster Supercomputing Center at the <strong>University</strong> of Calgary. These were transferred via FTP to Apple Power Macintosh G4 and IBM UNlX cornputers in the Visualization Center. The headers of the image files (including specirnen and CT technique setting information) were excised. The resulting 300 images measured 512x512 pixels each, and showed cross sections through the metatarsus in transverse planes. These images were saved in uncompressed TIF format with Macintosh byte order, and were written to a CD-ROM.
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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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Page 159: Figure 3.1. Schematic representatio
Page 163: Figure 3.3. CT reconstruction of ri
Page 167: Figure 3.5. MT II (left element) an
Page 171: Figure 3.7. Osteological correlates
Page 175: Figure 3.9. Osteological correlates
Page 179: 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 198 and 199: The practicality of the finite elem
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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
Page 206 and 207: The preceding loading regime entait
Page 210 and 211: 2. Preparation of data for contour
Page 212 and 213: . - Elastic modulus (GP4 Ex EY Ez P
Page 214 and 215: conversion. Volume-to-nuages facili
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Page 220 and 221: anterodorsal rotation of the distal
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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
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
Page 242 and 243: Ornitholestes, and camosaurs) incre
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Page 248 and 249: face of the skull met part of the m
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dromaeosaurids], and a dade compris
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arctometatarsalian forrns. The conv
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Proximal intermetatarsal ligaments
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witti a surfeit of potentially supp
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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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