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

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collective density of trabeculae (Kuhn et ai. 1989, Vahey et al. 1987). Haversian bone is somewhat weaker than pnmary bone, and on the microstnictural level different types of osteons Vary in matenal properties (Martin et al. 1998). These considerations of material and fundional properties must be regarded concurrently with possible loadings on the metatarsals of Gorgosaurus libratus. Fusion of the neural arches to the centra in the specimen TMP 94.12.602 (G. libratus) indicates that the animal was ai or near a fully adult age when it died (pers. obs.). For the purposes of modeling, the tissue properties of the metatarsus can be considerd those of a healthy, active adult animal. Because estimated loading regimes are inextricable from force inputs for biornechanical modeling, specific locomotor conditions are addressed in the Materials and Methods section. Putative loading regimes on the arctometatarsus derive from the energy transference model (Holtz 1994a), and from the tensile keystone model (Chapter 3). These models lead to the following kinematic hypotheses, which are testable with the finite element method: H(a): The energy transference hypothesis (Holtz 1994a): When the metatarsus was perpendicular to the substrate, stresses on ligaments would cause a transfer of loading from MT III to MTs Il and IV. H(b): The tensile keystone hypothesis: Ligament stresses within the arctometatarsus when the metapodium is at an acute angle to the substrate would cause MT II and MT IV to move posteromedially relative to the long axis of MT III.
Two analyses were fun in order to test these hypotheses, using the finite element method. The first investigation assumed loading regimes with the metatarsus normal to the substrate. The pattern of resulting strain energy would serve to identify areas where energy transference by ligaments would be most felicitous, and where the maintenance of safety factors would be most critical. This analysis, therefore, tested whether the position of ligaments postulated in Chapter 3 correlates with regions of high strain within the metatarsus, and aimed to reveal regions of osteological weakness that would potentially benefit from elastic energy transfer. With ligament position tested under the first finite element run, the second analysis incorporated a loading regime with the plantar surface of the metatarsus indined at 50 degrees to the substrate. The model of MT III was subjected to bending hads. This analysis was designed ta detemine if and where in MT III bending strains were likely to be damaging. if MT III was in danger of breaking under these loads, resistance of ligaments :O anterodorsal displacement of MT III, as postulated under the tensional keystone model, would serve to prevent this damage. MATERIALS AND METHODS As with other finite element analyses, this investigation requires four steps: assessment of the physical environment of the G. libratus metatarsus just after footfall; creation of a finite element model and mesh: solution of stiffness matrix equations to determine stresses and strains; and postprocessing for visualization and evaluation of results.
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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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Page 151 and 152: 4) Forces from anterior displacerne
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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
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 208 and 209: detemined by using the photographic
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
Page 216 and 217: maintained. An angle of 2 degrees p
Page 218 and 219: of MT III (Figure 4.4, pinpointed b
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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Alternately, a morphological novelt
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outgroup to ail theropods, and the
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convincingly evident in figures of
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parsimonious scenarios are outlined
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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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