Figure 1.
Relative surface densities of cranial bone in Stegoceras validum (UA 2).
External densities of the cranium of Stegoceras validum, in dorsal (A), ventral (B), lateral (C, D), anterior (E) and posterior (F) views. Note high densities of cranial ornamentation, and numerous neurovascular canals (correlates of a keratinous pad) exiting onto the cranial roof.
Figure 2.
Internal densities of bone in Stegoceras validum (UA 2).
Transverse CT sections from anterior (A) to posterior (F) through the cranium of Stegoceras validum (UA 2) seen in anterior oblique view. Inset CT reconstruction in lateral view (top) depicts section positions. Density and thickness of cortical bone increase towards the apex of the dome from the periphery, anteroposteriorly (B–D) and medially (C, D). Trabeculae radiate roughly perpencidular to the dome's outer surface, evident in the low-density (blue) region posterior to the orbit (B–E). Note that density of superficial bone may be inflated by beam hardening, but a dense, deep compact layer is definitively present. Dense compact bone (Hounsfield values of approximately 2000) surrounds presumed vascular traces, forming tubes that empty onto the dome surface; three of these are visible in D and E. These tubular structures recall struts within artiodactyl cranial sinuses.
Figure 3.
Surface densities of cranial bone in the duiker Cephalophus leucogaster (AMNH 52802).
External cranial densities of the white-bellied duiker, in dorsal, ventral (A, B), right and left lateral (C, D), and anterior and posterior (E, F) views. Duikers collide with a rounded dome formed by thick frontals (the frontals are not fused, as in Stegoceras). The color scale is in Hounsfield units, centered at 1334 (water = 0). The horn sheaths are rendered as slightly transparent, to emphasize high densities of the horn cores; compare with the musk oxen (Figures 4, 5, 6).
Figure 4.
Densities of the frontal dome of Cephalophus leucogaster (AMNH 52802) in transverse section.
A section through the posterior portion of the orbit and anterior region of the endocranial cavity (A, B) shows dense and diffuse trabecular bone (C) between bands of compact bone. Regions of compact bone are thinner than in Stegoceras, and larger trabeculae appear more robust (compare with Figure 2). The density color scale is the same as in Figure 3.
Figure 5.
Comparison of sagittal-section densities in crania of Stegoceras validum (UA 2) and Cephalophus leucogaster (AMNH 52802).
A, B, C. Sagittal sections through the cranium of Stegoceras validum, at positions shown in the dorsal view (top). D, E, F. Sections through the cranium of Cephalophus leucogaster, at positions shown in the dorsal inset (top). Note similar stratification of compact and cancellous layers in F, through the middle of the duiker's lobate dome, and B, through the center of the pachycephalosaur's dome. ec = endocranial cavity.
Figure 6.
Comparison of dome structure in Stegoceras (UA 2), the duiker Cephalophus (AMNH 52802), and bighorn sheep Ovis canadensis (UCMZ).
Midsagittal sections through the crania of Stegoceras validum, duiker Cephalophus leucogaster, and a bighorn sheep Ovis canadensis reveal similar dome structure. A. In the Stegoceras specimen, compact bone (z1 and z3: zones 1 and 3: [7]) occurs deep and superficial to a cancellous region (z2: zone 2: [7]). Moderately dense compact bone shows as a green band at the base of zone 3 (white line); note cancellous bone (blue) above the line in the anterior portion of this zone. B. Cephalophus. C. Similar stratification is evident in the sectioned Ovis cranium, with nearly identical zones of cancellous and compact bone broken by a ventral sinus.
Figure 7.
External cranial bone and horn densities in the adult musk ox (Ovibos moschatus: UCMZ M 1978.1.92).
Densities of the cranium and horn sheaths in adult Ovibos moschatus, in dorsal (A), ventral (B), lateral (C, D), anterior (E) and posterior (F) views. Note bone higher bone densities than in the juvenile specimen (Figure 5), and the expanded keratin pads over the parietals.
Figure 8.
Internal densities of horn and bone in adult musk ox (Ovibos moschatus UCMZ M 1978.1.92).
CT sections through the cranium of juvenile Ovibos moschatus. Dorsal and lateral CT renders show section position. A.–C. Right, mid-, and left sagittal sections show thick regions of trabeculae above the endocranial cavity, with a superficial layer of dense cortical bone over the apex of the brain (B). The most extensive cancellous bone occurs beneath the apeces of the horn sheaths, in line with the occipital condyles. A network of struts connects frontal and maxillary sinus regions (A and C). D.–F. Transverse sections from anterior to posterior show decreasing instances of struts and increasing cancellae as the horn sheaths become taller, and dense bone of the skull roof beneath the sheaths. Note the extent of trabecular bone between the sheaths and occipital condyles, in line with forces of head-butting impacts. Abbreviations: ec = endocranial cavity, fs = frontal sinus, ms = maxillary sinus, ps = parietal sinus.
Figure 9.
External densities of horn and bone in juvenile musk ox (UCMZ 1979.60).
Densities of the cranium and horn sheaths in juvenile Ovibos moschatus, in dorsal (A), ventral (B), lateral (C, D), anterior (E) and posterior (F) views. Note higher densities anterior to the bases of the horns, and higher density of horn keratin than much of the cranial bone. The horns' keratin has yet to develop into a large pad above the parietals. Enamel densities are high and clipped out using this color scale.
Table 1.
Taxa and specimens examined, and forces applied for FEA.
Figure 10.
Cranial densities in Giraffa (TMM M 6815, UCMZ 1976.33), the peccary Tayassu (UCMZ 1975.279), and pachycephalosaur Prenocephale (GI SPS, field number PJC2004.8).
CT sections through crania of comparative taxa, with slices mapped onto lateral renders of crania. A. Giraffa camelopardalis male (TMM M6815), transverse section through the region of a median ossicone. B. Oblique transverse section of Giraffa camelopardalis (UCMZ 1976.33) through the posterior ossicones. C. Enlargement of B focusing on the ossicones. The layering of densities in the giraffe ossicones resembles that in the dome of Stegoceras validum (Figure 6). D. Transverse section through the cranium of Tayassu tajacu, showing a non-cancellous skull roof over cranial sinuses. D. Section through the cranium of the pachycephalosaur Prenocephale prenes (GI SPS). Despite mineral inclusions (localized red and yellow areas) and CT artifacts, the scan shows dense superficial and cancellous deep regions within the dome. Abbreviations: ec = endocranial cavity, fs = frontal sinus, lo = lateral ossicone; mo = median ossicone; ps = parietal sinus.
Figure 11.
Cranial densities in the pronghorn (Antilocapra, UCMZ M 1989.61), elk (Cervus UCMZ M 1986.54), and llama (Lama, UCMZ M 1987.5).
CT sections through artiodactyl crania, with insets depicting section locations on lateral CT reconstructions. A. Transverse section through the pronghorns and anterior braincase of Antilocapra americana, showing dense bone (bright red) where the pronghorns meet the skull roof but no cranial sinuses. B. Oblique section through the posterior cranium of Antilocapra americana. The lack of cranial sinuses is similar in both depicted regions. C. Transverse section through the cranium of Cervus canadensis reveals cancellous bone at the antler bases. D. Section through the cranium of Lama glama reveals a thin skull roof. These specimens' morphologies contrast with extensive cancellous bone and/or sinuses above the endocranium in head-striking artiodactyls Ovibos and Giraffa, and the pachycephalosaurs Stegoceras and Prenocephale. Abbreviation: ec = endocranial cavity.
Figure 12.
Stress and strain in the dome of Stegoceras validum (UA 2).
A. Von Mises stresses (indicating closeness to yield) in a mid-sagittal section through the cranium of the pachycephalosaur Stegoceras validum. The highest stress within cancellous regions of the dome about 1 MPa, indicating a safety factor of 8–10 at the tested force. Stresses in compact bone surrounding the brain peak at 5 MPa, for a safety factor of 20–30. Constraints inflate stress artificially at the basal tubera and occipital condyle, and basicrainial and braincase stresses would be lower than depicted here. B. Von Mises stress and strain at 29 samples of a vertical transect through the dome. Strains are expressed in terms of safety factor: ultimate bone strain (0.6%) divided by the actual strain. Log10 values are used, because cortical safety factors approach 100 in some regions.
Figure 13.
Effects of keratinous pad shape on head-butting stresses of Stegoceras validum (UA 2).
For all simulations impact force is 1360 N, and stresses are von Mises values. The range and peak visible stress are noted in the color scales. A. Dorsal view of cranium. Force is distributed across a large surface area as a large keratin pad is deformed upon impact. Peak stress at the impact site is 6 MPa, and modal stress is 3 MPa. B and C. More concentrated impacts, simulating a thinner layer of keratin. D. Ventral view of stresses in impact C, showing occipital condyle (oc) and muscular constraints (mc). The detail level of this model (2 million elements) increases chances of artificially high stress at near-singularities, such as when force is applied to the edges of neurovascular canals.
Figure 14.
External views of finite element stress in the duiker Cephalophus leucogaster (AMNH 52802).
Von Mises stresses of a 1360 N impact are depicted in lateral (A), dorsal (B), and ventral (C) views. Note artificial clipping occurs at the constraints. Higher stress occur at the impacts and around the brain than in Stegoceras (Figure 12), for the same collision force. The histogram depicts color coding for stress magnitudes, and the proportion of elements experiencing given levels of von Mises stress.
Figure 15.
Internal stresses in the cranium of the duiker Cephalophus leucogaster (AMNH 52802).
Internal von Mises stresses are evident in posteroventral oblique (A) and lateral (B) views, through sections shown in respective insets. Impact stress diminishes from superficial to deep (B), but greater stresses occur at on the internal surface of the braincase than in Stegoceras. The histogram reflects the relative number of elements at different stress magnitudes.
Figure 16.
Finite element stresses in the musk ox Ovibos moschatus (UCMZ M 1978.1.92).
Von Mises stresses for Ovibos moschatus, in anterior oblique, posterior oblique, and dorsal view (A–C). D. Ventral view into the braincase (sectioned at the plane shown in A), showing high stress posteriorly. The highest stresses occur at the site of impact and (artificially) at muscular constraints (D); note the different color scale for stresses. E. Sagittal section (location marked in C) shows higher stresses channeled away from the endocranial cavity, in line with the posteroventrally directed impact force.
Figure 17.
Finite element results of two head-strike simulations in the giraffe (UCMZ 1976.33).
Von Mises stresses in Giraffa camelopardalis, with the cranium in dorsal A, B) and oblique (C, D) views. A′ is a ventral view of a coronally-sectioned cranium (at the plane in D), looking up into the endocranial cavity. A, A′, and C depict vertical impacts through the median ossicone and frontal sinus. Note comparatively high stresses at the posterior muscular constraint and substantial stress in the endocranial cavity compared with Ovibos (Figure 11 D), yet more localized stress than in Antilocapra (Figure 13). Peak stresses are lower when the force is spread over all three ossicones (B and D), suggesting that such impacts are more favorable to the animals.
Figure 18.
Head-strike stresses in the pronghorn (UCMZ M 1989.61).
Stresses in Antilocapra americana, primarily from mediolateral bending (A–C) and consolidated as von Mises stress (D, E). C is a ventral view of the cranium sectioned in the plane shown in A. Relatively high tensile stresses occur at the base of the pronghorn cores (A, B) and roofing the endocranial cavity (C), where CT reveals dense compact bone (Figure 8).
Figure 19.
Simulated head-strike stresses in the llama (UCMZ M 1987.5).
Von Mises stress from a simulated head impact in Lama glama, an artiodactyl that does not fight in this manner. A. Dorsal and B. ventral endocranial views depict higher stresses that occur at yield in cancellous bone orthogonal to the impact.
Figure 20.
Strengths of behavior-morphology correlations for selected taxa.
Correlate disruption values from Table 3, for incorrectly assigned behaviors in modern taxa and for Stegoceras validum when hypothesized as not head-butting. ∑ correlations values on the left indicate how much incorrect assignment perturbs the original correlations, and the scale on the right indicates how well the animals' morphology fits their “correct" behavior. The pachycephalosaur Stegoceras has a strong affinity with its hypothesized head-butting behavior, while the giraffe's lower score indicates ambiguous correlations between its morphology and behavior.
Table 2.
Possible categories and classes for recursive partition analysis.
Table 3.
Correlate disruption of recursive partitioning for selected taxa.
Figure 21.
Finite element models with CT-based stiffness values.
Elastic modulus indexed to CT Hounsfield values in (A) Stegoceras validum (UA 2), (B) Ovibos moschatus, and (C) Antilocapra americana. Moduli were assigned manually for Stegoceras, because CT beam hardening inflated some densities and fossilization obscured others. Modulus assignment for bone was automated in Ovibos and Antilocapra, and the pad in Ovibos assigned the modulus of alpha keratin.