Rowe Andre Thesis.Pdf (1.335Mb)
UNIVERSITY OF WISCONSIN-LA CROSSE
Graduate Studies
BIOMECHANICS OF JUVENILE TYRANNOSAURID MANDIBLES AND THEIR
IMPLICATIONS FOR BITE FUNCTION
A Manuscript Style Thesis Submitted in Partial Fulfillment of the Requirements for the
Degree of Master of Science
Andre Jordan Rowe
College of Science and Health
Biology
May, 2019
ABSTRACT
Rowe, A. R. Biomechanics of juvenile tyrannosaurid mandibles and their implications for bite function. MS in Biology, May 2019, 54pp. (E, Snively)
The tyrannosaurids are among the most iconic dinosaurs described by science. Biomechanical data such as bite force allow for comparative analyses between established tyrannosaurid genera. The results of this study are used to infer mandible (lower jaw) strength at different growth stages, bases on estimates of jaw muscle forces the animals exerted. We found that mandibles of small/subadult tyrannosaurs experiences lower stress overall because muscle forces were relatively lower, but that mandibles experienced greater mandible stresses at decreasing sizes when specimen muscle force or surface area is normalized. Strain on post-dentary ligaments decreases stress and strain in the posterior dentary and where teeth impacted food. Tension from the lateral insertion of the looping m. (musculus) pterygoideus ventralis increases compressive stress on the angular but decreases anterior bending stress on the mandible. Lowered mid-mandible bending stresses are consistent with ultra-robust teeth and high anterior bite force in adult Tyrannosaurus rex. The results may be indicative of separate lifestyles and feeding mechanics between juvenile and adult tyrannosaurids. Juvenile tyrannosaurs were probably incapable of the bone-crunching bite of mature individuals and hunted smaller prey, while adult tyrannosaurs fed on larger prey items which they were better able to subdue.
iii ACKNOWLEDGMENTS
I would like to thank Lawrence Witmer (Ohio University) and Heather Rockford
(O’Bleness Memorial Hospital, Athens, OH) for scans and loans of both Tarbosarus bataar and the juvenile Tyrannosaurus rex “Jane” (BMRP 2002.4.1). I would also like to
thank Ryan Ridgely (Ohio University) for the Jane surface, Jeff Parker (WPL) for the
Raptorex kriegsteini (LH PV18) scan, Brian Cooley for the “Sue” sculpture (Ohio
University), and Prathiba Bali (University of Calgary) for the adult Tyrannosaurus rex
“Sue” (FMNH PR 2081) scan. Additionally, thanks to Gail Gillis for engineering support
and Kaitlyn Nichols for muscle reconstructions.
iv TABLE OF CONTENTS
PAGE
LIST OF TABLES ...... vi
LIST OF FIGURES ...... vii
INTRODUCTION ...... 1
Hypotheses and Rationale ...... 3
Criteria for Testing Hypotheses and Interpreting Relative Stresses ...... 3
METHODS ...... 8
Finite Element Modeling ...... 16
RESULTS ...... 20
DISCUSSION ...... 31
Paleoecology ...... 33
Skull Strength Adaptations and the Secondary Palate in Theropods ...... 37
FUTURE WORK ...... 40
REFERENCES ...... 42
v LIST OF TABLES TABLE PAGE
1. Tyrannosaurid specimens tested in Strand7...... 12
2. Muscle force components for the adult T. rex...... 13
3. Muscle force components for the juvenile T. rex...... 13
4. Muscle force components for Raptorex...... 14
5. Muscle force components for Tabrosaurus...... 14
6. Properties applied to dinosaur jaw models (Porro et al. 2011) ...... 15
vi LIST OF FIGURES
FIGURE PAGE
1. Skeletons of the four tyrannosaurid specimens tested...... 6
2. Muscle insertions for Tarbosaurus...... 10
3. Tarbosaurus mandible with constraints placed...... 18
4. Adult Tyrannosaurus rex mandible with von Mises stresses...... 19
5. Raptorex mandible with von Mises stress results...... 21
6. T. rex demonstrating effects of m. pterygoideus ventralis insertion...... 23
7. Brick strain results for juvenile Tyrannosaurus rex...... 24
8. Strain at juvenile T. rex teeth with and without ligaments...... 25
9. Stress comparison in juvenile T. rex with and without ligaments...... 26
10. Adult T. rex analysis with extruded beam elements...... 27
11. Tarbosaurus von Mises stress results...... 28
12. Comparison of all tyrannosaurid mandibles...... 30
13. Various herbivorous dinosaurs that coexisted with T. rex...... 34
14. Various herbivorous dinosaurs that coexisted with Tarbosaurus...... 36
15. Comparison between a spinosaurid and tyrannosaurid...... 38
vii INTRODUCTION
The clade Tyrannosauridae is comprised of some of the largest terrestrial animals
to have ever lived, including the famous North American predator Tyrannosaurus rex
(Osborn, 1905), its Mongolian counterpart Tarbosaurus bataar (Maleev 1955) and the
Chinese Zhuchengtyrannus magnus (Hone et al. 2011). They are characterized by their
large heads, fused nasal bones (Snively et al. 2006), spring-loaded feet (Coombs 1978;
Holtz 1994, 1995; Snively and Russell 2002, 2003; Snively et al. 2004) and robust teeth
(Osborn 1906; Molnar 1991; Farlow et al. 1991). Tyrannosaurids are a group of
dinosaurs belonging to Saurischia—one of two major divisions of dinosaurs based on special articulations in the dorsal or central vertebrae, an elongated neck, hollow air sac chambers in the neck vertebrae, reduced first digit, and enlarged thumb claws (Holtz
2004). From there they lie within Theropoda, which includes all of the carnivorous dinosaurs. They are a relatively derived group of theropod dinosaurs being more closely related to birds than to other large theropods such as allosauroids and spinosaurids
(Brusatte et al. 2010). Tyrannosaurs overall are a long-lived group that originated by the
Middle Jurassic, nearly 165 million years ago.
The primary purpose of this study is to determine the mandibular biomechanical capabilities of several tyrannosaurid genera, and how bite capabilities changed with growth. Biomechanics is the study of the structure and function of the mechanical aspects of biological systems, including locomotion and kinesiology. In extinct animals, we can
1 infer topics such as bite force or body movements using fossilized bones. Finite element analysis (FEA) is a non-invasive modelling technique that allows for calculations of stresses exerted by living and extinct animals. It is commonly used in construction and architecture to test weaknesses of bridges and buildings, as it can analyze any solid structures. In recent decades it has been used in zoology and paleontology mostly to study the crania or upper part of the skull of both living and extinct animals.
Rayfield (2005) used the technique to study sutures and bite performance in the crania of the carnivorous dinosaur Allosaurus fragilis. FEA has been previously used to study the mandibles of other animals, such as mammal chewing biomechanics (Zhou et al. 2019) and crocodilian strain response to biting and twisting loads (Walmsley et al.
2013). Mandibles of the horned dinosaur Centrosaurus analyzed in FEA revealed their chewing mechanics (Bell et al. 2009); besides this, there have not been many 3D analyses for dinosaur mandibles. This study is among the first to analyze 3D carnivorous dinosaur mandibles in FEA and to test for changes in biting capability as dinosaurs mature.
Discoveries of several nearly complete tyrannosaurid skeletons in recent decades make the group of macropredators a great candidate for CT-scanning and finite element analysis, as tyrannosaur ontogeny is relatively well-understood and skull material is readily available for analysis.
Four tyrannosaur specimens across different ontogenetic stages were tested: juvenile Tyrannosaurus rex, adult Tyrannosaurus rex, Raptorex kriegsteini, and
Tarbosaurus bataar (Fig. 1). Differences in age allows us to better understand changes in stresses the animals experienced as they matured and how they were able to cope with higher stresses at maturity. Stress is a physical quantity that expresses the internal forces
2 that neighboring particles of a material exert on each other, while strain is the measure of
the deformation of the material.
Hypotheses and Rationale
We tested two main hypotheses with results from simulated stress and strain in the mandibles. (1) Larger tyrannosaurid mandibles experienced absolutely lower peak stress, because they became more robust (deeper and wider relative to length) as the animals grew (Currie 2003). (2) At equalized mandible lengths, younger tyrannosaurids experienced greater stress and strain relative to the adults, suggesting relatively lower bite forces consistent with proportionally slender jaws. Setting mandible lengths to be equal in length enables us to compare adaptations for bite performance: at the same body size, a deeper mandible with lower stress would indicate the ability to deliver a more forceful bite. Two of our specimens enable a natural experiment for hypothesis 2. The
Tarbosaurus and juvenile Tyrannosaurus rex mandibles are of roughly equal length (71 cm); however, the Tarbosaurus mandible is wider and deeper, suggesting greater resistance to equivalent forces and the potential to handle greater bite force.
Criteria for Testing Hypotheses and Interpreting Relative Stresses
As explained in detail below, we primarily compared mandible strengths with von
Mises stress, a value which accurately predicts how close ductile (slightly deformable/non-brittle) materials like bone are to breaking or permanent deformation.
Mandibles with lower von Mises stress were judged to be stronger under the imposed bite
simulations, as lower stresses indicate less susceptibility to breakage or deformation. If
both mandibles have von Mises stress far below failure levels, is there informative
adaptive significance between experienced stress, for example 40 mega pascals (about
3 25% of failure stress), and zero stress (T. Greiner personal communication 2019)?
Relative stresses are informative because bone remodels under applied loading regimes,
and relative experienced stresses therefore likely reflect active bone adaptation to loading
from actual behavior. Furthermore, lower relative stress can reflect momentarily
excessive construction (Gans 1979), the overhead capability for rare life-or-death situations where loading is exceptionally great.
As with most such biomechanical studies in vertebrate paleontology, small sample sizes constrain statistical testing due to the rarity of fossilization, and unknowns about fossil preservation constrain our confidence in specific point stresses and especially strain values (Rayfield 2007). Overall stress distribution and magnitudes, however, depend on mandible shape, size, and force loading, which are well-constrained in our specimens on their jaw hinges and teeth which impacted food. We therefore use primarily visual, color-indexed comparison of stress magnitudes (Rayfield 2007) and strain magnitudes, which reveal overall magnitudes and distribution of stress and strain on specific points in the mandibles tested. Our evaluation of these hypotheses is predictive for future statistical comparisons including phylogenetic and developmental influences
(Snively et al. 2019), possible with sample sizes of at least 10 per compared group
(Snively et al. 2019).
In addition to testing these hypotheses, we are interested in further implications for feeding at different ontogenetic stages in tyrannosaurs and the evolution of their jaw muscles. Certain muscles may have been particularly important for facilitating unique feeding strategies employed by tyrannosaurs—we are interested in which muscles, and how they aided in feeding or distribution of stresses. Adult tyrannosaurids are noted for
4 their “puncture-pull” biting technique in which they splintered bone (Carr and
Williamson 2004); muscles that impart high bite force without over-stressing bones and ligaments of the mandible would facilitate such a feeding strategy.
The recently described tyrannosaur Raptorex kriegsteini from Asia is important as a representative small juvenile tyrannosaurid. Raptorex was less than 2 m long yet exhibits all major tyrannosaurid functional specializations in the skull and skeleton, including a diminutive forelimb. Little is known about the specimen; its biting performance and hunting behavior have yet to researched. Raptorex was described as a small adult approximately 5 to 6 years old from lower Cretaceous Yixian Formation of China (Sereno et al. 2009, Li et al. 1994). However, the specimen is most likely a 3-year- old juvenile of much later, extensively studied tyrannosaurs (Fowler et al. 2011), such as Tarbosaurus bataar from the upper Cretaceous Nemegt Formation of Mongolia (Maleev 1965, 1974; Hurum and Currie 2000; Hurum and Sabath 2003; Saveliev and Alifanov 2007, Tsuihiji et al. 2011). Comparisons between the Raptorex specimen and an adult Tarbosaurus may reveal stress and strain patterns reminiscent of those in the juvenile and adult Tyrannosaurus rex specimens.
5
Figure 1. Skeletons of the four tyrannosaurid specimens tested. Clockwise from above
left: adult Tyrannosaurus rex “Sue” (FMNH PR 2081) (Field Museum of Natural
History, Chicago, IL; photo by the Field Museum), juvenile Tyrannosaurus rex
“Jane” (BMRP 2002.4.1) (Burpee Museum of Natural History; photo by A.
Rowe), adult Tarbosaurus bataar (Dinosaurium exhibition, Prague, Czech
Republic; photo by R. Holiš) and Raptorex kriegsteini skeletal reconstruction (LH
PV18) (Long Hao Institute of Geology and Paleontology, Hohhot, Inner
Mongolia, China; photo by P. Sereno).
6 In a juvenile Tyrannosaurus rex at a later ontogenetic stage, we tested for the function of post-dentary ligaments, behind the mandible's tooth-bearing bone.
Comparative analyses with and without these ligaments can reveal their effect on stress and strain the animals experienced when biting. (Time constraints precluded analysis of ligament effects in more than one specimen.)
7 METHODS
A virtual 3D solid model, divided into many smaller shapes called elements, is
used to study the mechanical behavior of tyrannosaurid lower jaws by means of finite
element analysis (FEA). FEA is a popular mathematical tool in biomechanics to evaluate
the strain and stress state within a solid, given its material properties, and under the
actions of appropriate loads and constraints that represent a particular functional or
behavioral scenario (Maiorino et al. 2015). FEA enables us to reconstruct stress and
strain within the skeleton and allows us to explore questions of how that skeleton
functioned and why evolution shaped it in a particular manner (Rayfield 2007). Its
noninvasiveness and applicability to extinct taxa has caused a surge in popularity amongst vertebrate paleontologists.
A mandible model of the single Raptorex kriegsteini specimen, two
Tyrannosaurus rex specimens, and single adult or subadult Tarbosaurus specimen are
analyzed using a combination of Avizo and Strand7 software (Table 1). Avizo is a software application which enables interactive visualization and computation on 3D data sets; we use it to model our 3D dinosaur mandibles and make them as realistic as possible before importing them Strand7, the software application that runs the finite element analyses. We resample our CT data in Avizo to reduce pixilation for a smoother, more realistic model and apply densities to the dinosaur mandibles. We enter in a range of densities in the CT scan to capture bone and teeth of the object and make a surface. We
8 reduce the triangle count and remesh the model to make surface triangles as equilateral as
possible for realistic results in Strand7: 15 times taller than wide is adequate. We then
import the model into Strand7, the finite element analysis software, which allows us to
analyze stresses and strains of the tyrannosaurid mandibles.
Our reconstructions of dinosaur jaw muscles are derived from Holliday (2009)
and Gignac and Erickson (2017) (Fig. 2). Muscle force is proportional to cross-sectional area multiplied by a force/area that muscles produce in adult T. rex (31.5 N/cm2: Gignac
and Erickson 2017) and is scalable linearly to cross-sectional area of muscles between
tyrannosaur species. The physiological cross-section and corresponding physiological
cross-sectional area (PCSA) are orthogonal to the long direction of all fibers in the
muscle. If all fibers in the muscle were arranged in parallel, the PCSA would equal their
total cross-sectional area (Zatsiorsky and Prilutsky 2012). Fiber lengths of 0.35 times that
of each muscle's length are incorporated from Bates and Falkingham (2012, 2018). We
multiplied estimated forces from Gignac and Erickson (2017) by 1/0.35 to obtain forces
corrected for this adjustment to PSCA.
9 Figure 2. Muscle insertions where nodes were mapped for Tarbosaurus bataar model in
Strand7 based on Holliday 2009 and Gignac and Erickson 2017. Nodes were
mapped in identical areas for all four tyrannosaurid models tested while
accounting for mandible size and shape variation. Full muscle names are indicated
in Table 2.
10 Gignac and Erickson (2017) scaled muscle forces of adult Tyrannosaurus rex
specimen FMNH PR 2081 from those estimated for a reconstruction of another adult,
BHI 3033. Muscle forces of the juvenile Tyrannosaurus rex are scaled relative to the
force values from FMNH PR 2081, and muscle cross-sectional areas and forces of LH
PV18 (Raptorex) are scaled via the subtemporal fenestra method (Sakamoto 2006); the
subtemporal fenestra is where the jaw muscles pass through in a typical reptile mandible.
Because the method uses an area, forces are scaled from the juvenile T. rex to Raptorex
(Raptorex length/juvenile T. rex length)2. We apply the same muscle forces from the juvenile Tyrannosaurus rex to Tarbosaurus because the mandibles are the same length.
We trigonometrically calculated muscle force components (Table 2-5) by measuring distances and angles from origin to insertion in our own models and after
Gignac and Erickson (2017). To transfer these components into Strand7's coordinate system and with the jaws slightly open, we used coordinate frame rotation methods from
Gilbert et al. (2016). Frame rotation reorients each muscle vector from the specimen’s original coordinate system into the Strand7 coordinate system. We first determine muscle lines of pull and force components from musculoskeletal reconstructions and rotate these vectors by reorienting the model. Rotations are often necessary because models vary from the original CT scanned orientation which may be lying on their side, upside down, slightly tilted up or sideways.
11 Table 1. Tyrannosaurid specimens tested in Strand7. Genera, museum catalog numbers,
and mandible lengths are listed. (Museum abbreviations: FNMH, Field Museum
of Natural History, Chicago, IL; BMRP, Burpee Museum Rockford Paleontology,
Rockford, IL; LH, Long Hao Institute of Geology and Paleontology, Hohhot,
Inner Mongolia, China.)
Specimen name Specimen Mandible number length (cm)
Adult Tyrannosaurus rex FMNH PR 127.5 2081
Juvenile Tyrannosaurus rex BMRP 70.3 2002.4.1
Raptorex kriegsteini LH PV18 29
Tarbosaurus bataar N/A 71
12 Table 2. Muscle force components in Newtons for the adult Tyrannosaurus rex FMNH PR 2081 model. The left side of the jaw was
tested. (Muscle abbreviations: mames, Musculus adductor mandibulae externus superficialis; mamem, M. adductor
mandibulae externus medialis; mamep, M. adductor mandibulae externus profundus; mamp, M. adductor mandibulae
posterior; mps, M. pseudotemporalis complex; mint, M. intramandibularis; mptd, M. pterygoideus dorsalis; mptv, M.
pterygoideus ventralis.)
Left mandible rotation about y axis = -6 º mames mamem mamep mamp mps mint mptd mptv x component 12963.79 4871.56 12212.41 10211.07 10152.18 6491.49 2640.76 40916.35 y component -603.86 -127.53 481.84 696.25 3030.57 -1500.35 374.41 14928.06 z component 4145.24 1284.74 86.61 2578.99 3139.31 3533.01 2735.86 -15531.11
Table 3. Muscle force components for the juvenile Tyrannosaurus rex BMRP 2002.4.1 model. The left side of the jaw was tested.
Muscle abbreviations as in Table 2.
Left mandible rotation mames mamem mamep mamp mps mint mptd mptv about y axis = 7.81 º x component -1101.66 -411.63 -1025.92 -861.81 -1042.63 -564.23 -240.76 -3229.78 y component 31.82 5.52 -67.78 -67.09 -263.13 105.27 -46.71 -1102.39 z component 231.99 64.16 86.61 118.91 150.19 243.39 199.07 -1722.26
13
Table 4. Muscle force components for Raptorex kriegsteini (LH PV18) model. Both sides of the jaw were tested.
Right mandible rotation about y axis = 6.51 º mames mamem mamep mamp mps mint mptd mptv x component -29.41 -8.13 -10.75 -14.83 -18.23 -31.06 -25.021 -220.81 y component 139.26 52.04 129.69 108.94 131.79 71.33 30.43 408.26 z component -3.36 -0.51 8.81 8.82 33.68 -12.60 6.47 134.37 Left mandible rotation about y axis = -6.51 º mames mamem mamep mamp mps mint mptd mptv x component 29.41 8.12 10.75 14.83 18.23 31.06 25.02 220.81 y component 139.26 52.03 129.68 108.94 131.79 71.32 30.43 408.26 z component -3.36 -0.51 8.81 8.82 33.68 -12.60 6.48 134.38
Table 5. Muscle force components for Tarbosaurus bataar model. Both sides of the jaw were tested.
Right mandible rotation mames mamen mamep mamp mps mint mptd mptv about y axis = 7.81 º x component -1101.66 -411.62 -1025.92 -861.80 -1042.63 -564.23 -240.75 -3229.78 y component 31.82 5.53 -67.77 -67.09 -263.13 105.27 -46.71 -1102.37 z component 231.99 64.17 86.60 118.90 150.20 243.39 199.07 -1722.26 Left mandible rotation mames mamen mamep mamp mps mint mptd mptv about y axis = -7.81 º x component 1101.66 411.62 1025.92 861.80 1042.63 564.23 240.75 3229.78 y component 31.82 5.53 -67.77 -67.09 -263.13 105.27 -46.71 -1102.37 z component 231.99 64.17 86.60 118.90 150.20 243.39 199.07 -1722.26
14 We apply tissue material properties of alligators as a proxy, given the close evolutionary relationship between dinosaurs and crocodilians (Porro et al. 2011; Table 6).
Strand7 allows for various material properties to represent the structure of the solid object analyzed; these properties vary based on bone, teeth, or ligaments. The elastic modulus is a quantity that measures an object's resistance to being deformed elastically when a stress is applied to it, shear modulus describes the material's response to shearing stresses, and
Poisson's ratio is the ratio of the proportional decrease in a lateral measurement to the proportional increase in length in a sample of material that is elastically stretched.
Table 6. Properties applied to dinosaur jaw models based on alligator data (Porro et al.
2011).
Elastic Shear modulus modulus Poisson's Material Orientation (GPa) (GPa) ratio Bone x 8.1 y 9.26 z 19.71 xy 3.17 0.38 xy 4.45 0.08 yz 5.51 0.15 Teeth (BMRP 2002.4.1) All 21 N/A 0.31 Ligaments (BMRP 2002.4.1) All 0.1 N/A 0.3
15 In juvenile Tyrannosaurus BMRP 2002.54.1 we applied separate properties for
bone, dentine (which makes up most of the teeth of reptiles), and ligaments. Bone is
represented in blue, dentine in green, and ligament in yellow to easily distinguish the
contrasting properties. In the other three tyrannosaur models, we use the same properties
for bone throughout.
Finite Element Modeling
We begin in the Avizo software by importing data from a CT scan obtained from analyzing the fossil bone in a CT-scanning machine, cropping the data to the dimensions of the object we want, and resampling the CT data to reduce pixilation for a smoother,
more realistic model. We then select a range of densities in the CT scan to capture bone
and teeth of the object and make a surface. We then reduce the triangle count and remesh
the model to make surface triangles as equilateral as possible for realistic results in FEA
(15 times taller than wide is adequate). The surface editor tests the model surface for
intersecting triangles, closedness, and aspect ratio of triangles. We use another surface
editor function ("prepare generate tetra grid") to fix remaining high aspect ratio surface
triangles and generate a "solid" tetrahedral volume mesh from the surface for FEA. We
may choose to make surface and volume meshes of multiple sizes—larger models are
more accurate but take longer to solve. We still keep the largest mesh so we can run
convergence analyzes of the smaller meshes; we want the most accurate results for the
minimal solving time by comparing smaller meshes with the largest mesh in Strand7.
We can now import the mesh model into Strand7, go to brick or solid object
properties and assign appropriate material properties to the tetrahedral model: elastic
modulus and Poisson’s ratio. An elastic modulus is a quantity that measures an object’s
16 resistance to being deformed elastically when a stress is applied to it. The elastic modulus
of an object is defined as the slope of its stress–strain curve (stress/strain) in the elastic
deformation region (Askeland and Phulé 2006), when it can spring back to its original shape. Poisson's ratio describes the resistance of a material to distort under mechanical
load rather than to alter in volume (Greaves et al. 2011) and is the quotient of transverse
strain (bulging under compression or thinning under tension) and longitudinal strain from
applied loads. We then assign constraints to restrict free body motion, typically near the
hinges of the jaw in mandible-related tests (Fig. 3). We select nodes in the areas where
forces are being tested and divide the total estimated muscle forces by the total number of
nodes selected. For several analyses of FMNH PR 2081 (“Sue”), research associate Gail
Gillis simulated a food object with bone properties in contact with the teeth. This
arrangement is more realistic for stress at points of constraint, which a necessary artifice
of FEA. Gillis extruded beam elements from nodes of contact (the originally constrained
nodes) and constrained the beams at their other ends. The beams were assigned stiffness
of compact bone (Table 6).
17 Figure 3. Lateral view of Tarbosaurus mandible with constraints placed at the anterior
teeth and jaw hinges. Constraints are placed to simulate teeth making contact with
flesh and bone during feeding. No nodes for muscle attachment have been
selected.
Once we are satisfied with our constraint placement based on tooth positions, beam placement, and node placement based on Holliday 2009 and Gignac and Erickson
2017 muscle reconstructions, we perform FE analyses under linear static assumptions, with unchanging loads and material properties. We first examine resulting von Mises stress, which is a good indicator of how close a structure is to breaking. These are drawn as contours with a user-specified range of colors on the model to indicate where stresses experienced are least and most significant (Fig. 4).
18 Figure 4. Completed FEA on adult Tyrannosaurus rex “Sue” (FMNH PR 2081) mandible
demonstrating a range of stresses, with blue and green denoting the lowest
amount of stresses experienced and red and white displaying the highest.
Constraints are placed at anterior teeth and hinges of the jaw. Linear static
analyses were performed on all tyrannosaurid specimens in Strand7.
19 RESULTS
Smaller/subadult tyrannosaurs experienced greater mandible stresses when
mandible length and surface area are equalized by adjusting their sizes in Avizo and
Strand7, but they experienced lower absolute stresses when compared to the adult forms.
At equal mandible lengths, Raptorex would experience 6.05 times the bending stresses
relative to “Sue,” and 1.84 times the stresses of “Jane.” Raptorex experienced the overall
lowest peak von Mises stresses of all the tyrannosaurs (Fig. 5). Juvenile tyrannosaur
“Jane” would have experienced 3.29 times the compressive and tensile bending stresses
relative to the adult tyrannosaur “Sue."
We have found that tension from the lateral insertion of the looping m. (musculus)
pterygoideus ventralis muscle is linked to increasing compressive stresses on the angular,
a large bone near the posterior of the mandible, but it serves to decrease anterior bending
stresses on the mandible (Fig. 6). The lowered mid-mandible bending stresses are
consistent with the highly robust and conical teeth on the anterior of the tyrannosaur jaw,
where, usually, they may have applied their highest impact bite forces. Crocodilians
experience the inverse situation: they possess robust teeth near the posterior end of their
mandible where they apply their highest bite forces (Erickson et al. 2012).
From our work on the juvenile Tyrannosaurus rex, we have found that strain on
post-dentary ligament, or fibrous muscle insertions posterior to the teeth, decreases stress and strain in the posterior and where teeth impacted their food (Fig. 7, 8). Additionally,
20 these ligament insertions reduce overall stresses at the teeth and on the mandible by roughly 10 MPa, creating a more realistic scenario when the animal was biting down
(Fig. 9).
Figure 5. von Mises stress, the measurement of how close a structure is to breaking, for
Raptorex kriegsteini (LH PV18) in lateral view (top) and dorsal view (bottom).
Units are in mega pascals (MPa). Constraints are placed at the fifth and sixth
tooth and the hinges of the jaw.
21 von Mises stress, which is a good predictor of failure under ductile fracture, or fracture characterized by large amounts of plastic deformation, commonly occurs in bone. It is a function of principal stresses in σ1, σ2, and σ3, or the three different dimensions, that measures how stress distorts a material. Failure of ductile material is
estimated when von Mises stress equals the yield strength of the material in uniaxial
tension (Rayfield 2007). Despite greater stress than in juveniles, the adult mandible
maintains safety factors, or expressions of how much stronger the system is than it needs
to be for an intended load, of 3-4 relative to ultimate stress. Research associate Gail
Gillis’ analyses of the adult Tyrannosaurus rex with the simulated food object reduced
stresses at points of contact to less than 200 MPa, versus almost 800 MPa when the
contact points served as constraints (Fig. 10).
22 Figure 6. Adult Tyrannosaurus rex “Sue” in lateral view and dorsal view, demonstrating
the effects of the m. pterygoideus ventralis with and without the muscle insertion.
Constraints are placed at the anterior teeth and hinges of the jaw. Units are in
mega pascals (MPa). Note the increased stress on the angular but decreased stress
throughout the mandible in the model simulating the looping medial pteygoideus
ventralis insertion.
23 Figure 7. Lateral view of brick strain results from a simulated bite in the juvenile
Tyrannosaurus rex “Jane” (BMRP 2002.54.1) mandible. Strain is not expressed in
units as it is the ratio between the extension and original length of the material.
Note regions of high strain on ligaments where the bones come together. The red
lines with small arrowheads represent muscle forces. Constraints are placed at the
seventh and eighth tooth and the hinges of the jaw.
24 Figure 8. Juvenile Tyrannosaurus rex “Jane” mandible in lateral view without ligaments
(top) and with ligaments (bottom), illustrating differences in strain at the teeth.
Strain is a measure of deformation in a structure; ligaments or fibrous connective
tissues were integral to reducing this deformation when teeth came into contact
with food.
25 Figure 9. Juvenile Tyrannosaurus rex “Jane” (BMR mandible in lateral view without
ligaments (top) and with ligaments (bottom), illustrating differences in stress at
the teeth and mandible. In addition to reducing strain at the teeth, ligaments
reduced stress in the mandible overall. Units are in mega pascals (MPa).
26 Figure 10. Research associate Gail Gillis’ adult Tyrannosaurus rex analysis which
simulated a food object with bone properties in contact with the teeth. Gillis
extruded beam elements from nodes of contact and constrained the beams at their
other ends. This reduced stress at the teeth relative to analyzes which lacked the
extruded beam elements. Units are in mega pascals (MPa).
27 The Tarbosaurus specimen experiences more pronounced stresses on the m. adductor mandibular posterioris (mamp) and m. pterygoideus ventralis (mptv) of roughly
5-15 MPa but less overall stress on the angular relative to other tyrannosaurs tested (Fig.
11). The Tarbosaurus jaw is notable for its widely set mandibles and asymmetry, but it is almost identical in length to the juvenile T. rex specimen tested.
Figure 11. von Mises stress test results on the Tarbosaurus specimen in lateral view (top)
and dorsal view (bottom). Units are in mega pascals (MPa). Constraints are placed
at the sixth tooth and hinges of the jaw. Note the asymmetry of the mandible,
resulting in disproportionate von Mises stresses on each side of the mandible.
28 Stresses are also notable on the m. pseudotemporalis profundus (mamep) located near the posterior teeth, achieving between 25-30 MPa in adult Tyrannosaurus rex (Fig.
12).
29 Figure 12. Lateral mandible views (from top to bottom) of Raptorex kriegsteini, juvenile
T. rex, Tarbosaurus, and adult T. rex, illustrating differences in jaw morphology
and von Mises stresses during ontogeny. Units are in mega pascals (MPa). Note
the transition from the slenderer mandible of the juvenile tyrannosaur relative to
the angular, deeply-set mandible of the adult tyrannosaur.
30 DISCUSSION
A profile of how changes in ontogeny result in different mandible stresses and strain is presented here. Our results indicate that predatory lifestyles of juvenile and adult tyrannosaurids may have differed significantly. These data may correlate with proposed ontogenetic growth series that have been constructed (Currie 2003; Carr and Williamson
2004): elongate and gracile skulls of juveniles become deeper, more robust, and more heavily ornamented. These adult features are integral to the novel tyrannosaurid “bone- crunching” puncture-pull feeding, suggesting it was only employed by larger, older individuals; this idea may be further supported by the adults experiencing lesser stresses compared to juvenile forms at equalized mandible lengths. While adult tyrannosaurs were likely experiencing more significant stresses near the mid-mandible relative to the other tyrannosaurs, they were better equipped to deal with those stresses due to mandible size.
Stresses on the mid-mandible are lessened but increased near the mandible hinge by the pterygoideus ventralis insertion which presents a trade-off for the animal. While a risk to the jaw hinge is costly and teeth can be replaced, teeth are still immediately necessary for prey acquisition, feeding, and combat. Tyrannosaur remains with broken or fractured jaw hinges have yet to be found, suggesting that this stress distribution along the mandible was more beneficial to the animal in the long term.
31 Additionally, research associate Gail Gillis’ realistic analysis with simulated bone biting reduces artificially high stress at the originally constrained nodes. However, the resulting stress (180 MPa) is far beyond the shear strength of the afflicted bone (about less than 100 MPa), while remaining lower than (but close to) the compressive strength of dentine that makes up most of the teeth (197 MPa: Chun et al. 2014). This high stress is consistent with enormous tooth-tip pressures calculated for adult T. rex, splintering of prey bone under catastrophic failure (seen in fossils and simulated experimentally:
Erickson et al. 1996; Gignac and Erickson 2017), and even with occasional breakage seen in tyrannosaurid teeth still within the jaw.
32 Paleoecology
Subadult tyrannosaurids experienced relatively low von Mises stresses compared to the mature individuals; this suggests that subadults tyrannosaurids were feeding on smaller, potentially more agile prey, while the bone-crunching bite employed by mature individuals was reserved for large, less mobile prey, such as hadrosaurids. Hadrosauridae consisted of the large, herbivorous duck-billed dinosaurs such as Edmontosaurus (Fig.
13) which possess ample evidence for active predation from tyrannosaurs (Carpenter
1997; Hone and Watabe 2010; Rothschild and DePalma 2013).
Our FEA data indicate that younger individuals were active predators, somewhat akin to dromaeosaurs such as Deinonychus (Ostrom 1970). Dromaeosaurs were a group of theropod dinosaurs distinguished from tyrannosaurs by their well-developed slashing talon on their second pedal digit (toe), a stiffened tail which possibly functioned as a dynamic stabilizer, and large grasping manus (hands). Tyrannosaurids are noted for their surprising agility, including the Raptorex specimen (Snively et al. 2019); this may be ideal for tracking down and ambushing prey. Tyrannosaurs were speculated to have maintained a walking speed of 4.5–8.0 km/h, exceeding that of potential prey (Currie
1983; Persons and Currie 2014).
33 Figure 13. Skeletons of five herbivorous dinosaur genera that coexisted with
Tyrannosaurus rex in Maastrichtian North America based on fossil material
recovered. Clockwise from above left: bird-like caenagnathid Anzu (Carnegie
Museum of Natural History, Pittsburgh, PA; photo by E. Snively), adult
hadrosaurid Edmontosaurus (Dinosaur Resource Center, CO; photo by A. Rowe),
adult ceratopsian Triceratops (Burpee Museum of Natural History, Rockford, IL;
photo by A. Rowe), armored anykylosaur Scolosaurus (Royal Tyrrell Museum,
Drumheller, Alberta; photo by Alan and Flora Botting), and long-necked
sauropod Alamosaurus (Perot Museum of Nature and Science, Dallas, TX; photo
by E. Snively).
Late-stage juvenile tyrannosaurids at a near-identical age to the juvenile
Tyrannosaurus rex in our study were likely feeding on large prey despite lacking the bone-crunching adult bite (Peterson and Daus 2019). While biomechanically capable of puncturing bone during feeding, and doing so without the large, blunt dental crowns of adult, this was likely a postmortem feeding trace. Ventral bite traces on the hadrosaurid
34 vertebrae suggest that the tyrannosaur was feeding after the haemal complexes or blood
vessels and most of the superficial hypaxial muscles ("core" muscles on the tail) and m.
caudofemoralis longus (tail muscle) had been removed. Hadrosaurs grew exceptionally
fast, perhaps minimizing predation pressure from younger tyrannosaurs (Cooper et al.
2008). The crushing bite of adult and perhaps late-stage juvenile tyrannosaurids was likely useful for dispatching adult hadrosaurs and other large herbivores (Fig. 13, 14).
Prey items for adult tyrannosaurids likely included the large, herbivorous ceratopsians. The ceratopsians were a group of dinosaurs renowned for their imposing facial horns and large frills. Tyrannosaurus and Triceratops coexisted in Maastrichtian
North America and are popularly depicted being engaged in combat. Various frill pathologies and cranial lesions have been attributed to predation from Tyrannosaurus rex
(Happ 2008); these pathologies may be as extreme as horns being bitten off almost entirely (Hone and Rauhut 2010).
The potential diet of large Mongolian predators like Tarbosaurus consisted of large sauropods and hadrosaurids (Owocki et al. 2019; Fig. 14). The Nemegt Basin of
Southern Mongolia offers a wealth of fossil material for isotopic study of paleoenvironments. Stable isotopes of oxygen and carbon are notable in paleontological work as they can aid in diet reconstructions and paleoecology. Tooth enamel carbonate along the growth axes of five Tarbosaurus bataar teeth have aided in identification of seasonal climatic variations and imply the presence of a woodland ecosystem dominated by large herbivores. Tooth drag and puncture marks attributed to Tarbosaurus have been reported from bones of the hadrosaurine Saurolophus (Hone and Watabe 2010; Fig. 14) and the sauropod Opisthocoelicaudia (Borsuk-Białynicka 1977; Fig. 14). These data
35 combined with carbon isotope signatures and FEA data imply that Tarbosaurus was an
apex predator in the Late Cretaceous of the Gobi region.
Figure 14. Skeletons of five herbivorous dinosaur genera that coexisted with
Tarbosaurus bataar in Maastrichtian Mongolia based on fossil material
recovered. Clockwise from above left: horned ceratopsian Protoceratops (Field
Museum, Chicago, IL; photo by E. Snively), hadrosaurid Saurolophus (Gifu,
Japan; photo by Y. Tamai), long-clawed theropod therizinosaur Nothronychus
(Utah Museum of Natural History, Salt Lake City, UT; photo by E. Snively),
long-necked sauropod Opisthocoelicaudia (Museum of Evolution of Polish
Academy of Sciences; photo by A. Grycuk) and a small, agile oviraptorid (Field
Museum, Chicago, IL; photo by E. Snively). Note that Nothronychus did not
originate in Mongolia but therizinosaur material has been recovered there.
In Maastrichtian (72.1-66 million years old) North America, Tyrannosaurus rex was considered the apex tyrannosaurid; skin pathologies (Rothschild and DePalma 2013), healed prey vertebrae containing teeth (DePalma et al. 2013), and coprolite or fossil feces
36 analyses (Chin et al. 1998) indicate an active predatory lifestyle. The extent of active predation in Tyrannosaurus has remained a contentious topic for decades (Horner 1994,
1997; Holtz 2008). Bone regrowth in herbivorous dinosaurs (Carpenter 1997) seems to verify the active predatory hypothesis; herbivorous dinosaurs may have escaped the attacking predator and later died elsewhere. Our FEA data along with the deep-set jaws of adult Tyrannosaurus rex indicates a powerful, locking bite was delivered by the animal; however, there remains the possibility of potential prey escaping from non-fatal wounds that afflicted the tail or other appendages.
Skull Strength Adaptations and the Secondary Palate in Theropods
Tyrannosaurs are notable for their possession of a substantial ossified secondary palate that most other large-bodied theropods lacked (Holtz 1998, 2000, 2003, 2004). A typical large theropod skull would be relatively strong in vertical compressive loads but lack solid support to resist torsional or twisting loads (Snively et al. 2006). The solid bony palate of tyrannosaurs formed by medial extensions of the maxillae and premaxillae and the diamond-shaped anterior end of the vomer would allow for greater resistance to torsional loads (Holtz 2008). Our FEA findings further validate the animal’s powerful bite and demonstrates a biting potential that few other large theropods could achieve.
Spinosaurs, another large theropod group notable for their elongated neural spines which supported sails or humps of skin, also possessed a similar bony secondary palate
(Taquet and Russell 1998; Sereno et al. 1998; Fig. 15). The spinosaurs possessed a much narrower rostrum more akin to those of crocodilians; they are hypothesized to have used
37 it in capturing fish. Rayfield et al. (2007) and Cuff and Rayfield (2013) concluded that alligator crania greatly outperform those of spinosaurs in bending and torsion resistances
Figure 15. Skull of the early Cretaceous spinosaurid Suchomimus of Niger (top) (Science
Museum of Minnesota; photo by E. Snively), compared with adult Tyrannosaurus
rex “Stan” (bottom) (University of Wisconsin Geology Museum; photo by E.
Snively).
38 when size is accounted for. This suggests that some large theropod dinosaurs achieved
adequate resistance to different feeding loads through their large size rather than merely
the morphology of their mandibles.
The pliosaurs, a group of four-flippered marine reptiles from the early Jurassic to
Late Cretaceous, also possessed long, low crania and mandibles similar to those of spinosaurs. The absolute size of their nearly 2-meter skulls sufficiently resisted bending and torsion, despite a jaw morphology unsuited to resisting those feeding loads
(McHenry 2009; Foffa et al. 2014).
Instances of spinosaur teeth imbedded in scavenged remains (Buffetaut et al.
2004) and spinosaur predation of large herbivorous dinosaurs are rare (Charig and Milner
1997). The biomechanical evidence suggests that tyrannosaurs were relatively more active terrestrial hunters who utilized their wide-set jaws, load-resistant mandibles, and secondary palate primarily for pursuing and capturing large prey, while spinosaurs utilized their mandibles primarily for fishing and opportunistic scavenging.
In conclusion, tyrannosaurids possessed a rigid, bone-crunching bite that other predatory dinosaurs of the Mesozoic era lacked, despite similarities of some in the secondary palate. Their wide-set jaws and stress-resistant biting allowed them to easily subdue prey and swallow chunks of flesh and bone. Their biting capabilities, massive size, and surprising agility likely made them the apex predators in their ecosystems.
39 FUTURE WORK
This study centered on the mandibles of tyrannosaurids at varying ontogenetic stages. Finite element modeling of the cranium of the tyrannosaurids tested is achievable and can further reveal stresses and strain occurring elsewhere in the tyrannosaur head during feeding. We can then test the hypothesis that the m. pterygoidus ventralis was also reducing stresses elsewhere on the cranium of the animal rather than simply the mandible.
FEA comparisons will be informative about skull function in adult tyrannosaurids with differing morphology. There is the possibility of investigating stress and strain in other tyrannosaurids such as adult Tyrannosaurus rex “Scotty” (RSM P2523.8) or
Alioramus altai (Brusatte et al. 2009), a Maastrichtian tyrannosaurid from China. RSM
P2523.8 is notable for its overall massive size and robust skull comparable to “Sue.”
Alioramus possesses a more gracile and slender body plan and mandibles, more akin to
Raptorex and other subadult tyrannosaurids. FEA is a relatively new technique in the field of vertebrate paleontology and there remains a wealth of fossil material that has yet to be tested for biomechanical capabilities. Based on current data from our own FEA work, we can test the hypothesis that larger tyrannosaurids such as RSM P2523.8 were better able to withstand higher stresses relative to the slenderer jaws of other adult tyrannosaurids such as Alioramus. Given that we often do not examine absolute numbers in FEA studies, for future comparisons we can sample homologous points in the dinosaur
40 mandibles (Gilbert et al. 2016) and use numerical methods to compare stresses and
strains across 2D regionals of bones (Snively et al. 2010).
Within jaws of given tyrannosaurs, we can investigate stress and strain as they bit at different points in their jaws. Constraints simulate the contact points for teeth as they bit down on prey and faced resistance from flesh and bone. Our FE analyses on the four tyrannosaurid mandibles presented here are focused on the anterior teeth, which likely first made contact with flesh. Assigning these constraints only to the posterior teeth could yield entirely different stress and strain results; given the significance of anterior teeth in tyrannosaur feeding, we could test the hypothesis that the smaller and less robust posterior teeth would break and deform under similar loads placed on the anterior teeth in our study, validating the necessity of large, robust anterior teeth in the clade for purposes of efficient feeding.
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