A Comparison of the Jaw Mechanics in Hadrosaurid and Ceratopsid Dinosaurs Using Finite Element Analysis

Authors


Abstract

Hadrosaurid and ceratopsid dentaries display traits that suggest divergent functions toward broadly similar diets of fibrous plants. Computed tomographic scans of dentaries of a lambeosaurine and a centrosaurine (Centrosaurus aptertus) were used to compare feeding function of these animals using finite element analysis (FEA). In the hadrosaur, mediolateral expansion of the dentary and elongation of the coronoid process of the surangular were optimally developed to withstand torsion associated with transverse-isognathous jaw occlusion. FEA results strongly suggest longitudinal rotation of the hadrosaurid mandible. Mediolaterally compressed mandibles and FEA stress for the ceratopsid are in compliance with purely isognathous jaw adduction, although palinal retraction during the powerstroke cannot be ruled out. The ceratopsid dentary is further reinforced by a longitudinal ridge on the lateral surface of that element. Surface texture indicating Sharpey's fibers within the ceratopsid coronoid process suggests greater bite force than in lambeosaurines. These findings corroborate previous interpretations and suggest complementary or alternative kinematics to maxillary pleurokinesis in hadrosaurs. Anat Rec, 292:1338–1351, 2009. © 2009 Wiley-Liss, Inc.

Hadrosaurian and ceratopsid dinosaurs were the most common and diverse megaherbivores in Laurasia during the Late Cretaceous, comprising up to 50% and 25% of the fauna, respectively (Dodson, 1983; Brinkman, 1990; Ryan and Evans, 2005). Strong evidence exists for an Asian origin for both clades and subsequent radiation into North America (Godefroit et al., 2004, 2008; You and Dodson, 2004; Chinnery-Allgeier and Kirkland, 2007); however, dispersal into Gondwana also occurred, where they formed relatively minor components of the ecosystem (Rich et al., 1988; Rich and Vickers-Rich, 1989; Coria, 1999).

Hadrosaurs and ceratopsids share a suite of morphological and ecological characters that suggest potential competition for resources (Table 1). Both were large [over 6 tonnes for some ceratopsids; 13 (Paul, 1997) to 16 tonnes (Dodson et al., 2004) for the hadrosaur Shantungosaurus], rapid-growing, and occasionally gregarious herbivores common in both lowland and inland (including xeric) environments. Coprolites, preserved stomach contents, and phytoliths confirm hadrosaurs browsed on leaves, twigs, and even decomposing wood (Krauss, 2001; Chin, 2007; Tweet et al., 2008). Evidence from phytoliths suggests that ceratopsids may have fed more on cycads than hadrosaurs (Krauss, 2001). Both groups were environmentally sensitive, exhibiting pronounced regionalization in regards to marine influence and latitudinal gradients (Russell and Chamney, 1967; Lehman, 2001; Ryan and Evans, 2005; Sampson and Loewen, 2007). In fact, high-resolution biostratigraphy of hadrosaur-ceratopsian distribution reveals that diversity of these groups was not as high in any given formation as previously thought. Instead, species were subject to rapid turnover (replacement) and accommodated oscillations of the paleoshoreline to remain in their preferred habitats (Russell and Chamney, 1967). Although certain taxa appear predisposed to forming large herds of up to 300 individuals, they do not appear to have undertaken long-distance seasonal migrations (Fiorillo and Gangloff, 2001; Bell and Snively, 2008); short migrations between lowland and highland communities were perhaps more likely (Brinkman et al., 1998; Bell and Snively, 2008).

Table 1. Similarities between hadrosaurid and ceratopsid mandibles
Teeth form a continuous shearing/grinding surface
Teeth extend caudal to the coronoid process
Teeth arranged in vertical “families” forming a dental battery
Coronoid process extends dorsal to the occlusal surface
Diastema present
Diastemic portion of dentary ventrally and medially deflected
Edentulous predentary covered in life by a keratinous sheath
Quadrate-articular joint ventrally deflected relative to occlusal surface
Postdentary elements project caudal to the coronoid process

Hadrosaurs and ceratopsids possess highly derived and efficient dental batteries, a feature that has received considerable attention in the literature (Ostrom, 1961, 1964; Weishampel, 1983, 1984; Norman and Weishampel, 1985; Weishampel and Horner, 1990; Dodson et al., 2004). A suite of additional morphological similarities between the mandibles of ceratopsids and hadrosaurs (Table 1) imply similar feeding techniques and competition for resources. We review their mandibular anatomy and masticatory hypotheses later. Despite their overall similarities common to cerapodan dinosaurs, mandibles of most hadrosaurs appear to be more gracile than those of ceratopsids; yet, the latter have a narrower occlusal surface. These variances suggest the benefit of detailed comparisons of feeding function in these dinosaurs. To test for operational differences in dentaries of ceratopsid and hadrosaurid dinosaurs, qualitative states of jaw muscle insertions were compared, macroscopic histological composition of the jaws were surveyed via computed tomographic (CT) scans, and computerized models derived from CT scans were tested using finite element analysis (FEA).

ANATOMICAL REVIEW OF HADROSAUR AND CERATOPSID LOWER JAW

The Hadrosaur Mandible

Osteology and myology.

The hadrosaur predentary is a U-shaped element that formed the broad oral margin associated with the duck-bill morphology in this group. The oral margin becomes increasingly denticulate throughout ontogeny and was covered in life by a ramphotheca (Sternberg, 1935). The predentary loosely encloses the symphysis of the dentary, a connection that was held together by ligaments that rapidly decayed after death. Symphyseal suture interdigitation is only weakly developed providing limited surface area for ligament attachment (Herring, 1972).

The dentary appears relatively gracile compared with that of ceratopsids. The rostral portion is edentulous and deflected ventrally and medially where it contacts its mate. The length of this region and degree of deflection appear to be species-specific and may be quite pronounced in some taxa (Prieto-Marquez et al., 2006). The laterally set coronoid process extends dorsally from the caudal margin of the dentary and curves medially. Its distal terminus becomes slightly expanded rostrocaudally for attachment of muscle (M). adductor mandibulae externus profundus and M. pseudotemporalis. Compared with ceratopsids, hadrosaurian muscle insertions are considerably less developed; however, distinct regions are noticeable. Nearly the entire length of the caudal border of the coronoid process forms a discrete and prominent ridge, interpretable by this morphology (Benjamin et al., 2002) and its location as the tendon insertion for M. adductor mandibulae externus profundus. The insertion of M. pseudotemporalis is a semioval region along the rostrolateral surface of the coronoid process and pits presumably formed from the insertion of Sharpey's fiber bundles (Benjamin et al., 1986) occur on this surface. M. adductor mandibulae externus medialis inserted into a caudolaterally expressed tuberosity on the coronoid “shaft.” Slight horizontal ridges indicate gradational fibrous insertions along the length of the “shaft.” Medial inflection of the coronoid aligns the apex of that process directly over the tooth row. A deep Meckelian fossa exists medial to the coronoid process into which part of the surangular is set. An elongate flange of the surangular (the coronoid process of the surangular: Horner, 1992) rests along the lateral wall of the Meckelian fossa. M. adductor mandibulae posterior also inserted here. The loosely arranged postdentary bones (surangular, articular, angular, and splenial) form a discrete process that is ventrally offset relative to the occlusal surface and extends caudally from the dentary. Inserted onto the lateral and medial surfaces of this process were M. adductor mandibulae externus superficialis and M. pterygoideus dorsalis, respectively. The quadrate condyle fits into an open cotyle between the articular and surangular to form the jaw joint. Teeth are arranged in vertical families of three to five teeth in each alveolus and there may be as many as 60 alveoli in an adult dentary (Horner et al., 2004), which extend caudal to the coronoid process. The occlusal surface of the teeth is inclined medially and is slightly concave ventromedially.

Masticatory mechanism.

The extraordinary dental adaptations of hadrosaurs have long been recognized although considerable debate has persisted about their function (Ostrom, 1961; Weishampel, 1983, 1984; Norman and Weishampel, 1985). Weishampel (1983, 1984) and Norman and Weishampel (1985) proposed that hadrosaurs combined isognathous occlusion with external rotation of the maxillae, providing a transverse component to the power stroke. This rotation would have been achieved singularly in hadrosaurs by novel premaxilla-maxilla, lacrimal-prefrontal, jugal-postorbital, and quadrate-squamosal articulations, which divided the skull into a naso-cranial and maxillary-facial unit (Norman and Weishampel, 1985; Rybczynski et al., 2008). External rotation was achieved mechanically during elevation of the mandibles, which forced the maxillary unit to flex outward. This condition appears plesiomorphic for Hadrosauridae (Head, 1998). Other forms of transverse-isognathous occlusion are found in more primitive ornithopods (heterodontosaurids, hypsilophodonts, and iguanodonts); however, the transverse component is achieved by bowing of the mandible in heterodontosaurids and pleurokinesis in the latter two groups (Weishampel, 1984).

Rybczynski et al. (2008) tested the hypothesis of pleurokinesis in the hadrosaur Edmontosaurus and secondarily in Corythosaurus. Moderate pleurokinetic movements would cause large secondary displacements of bones ultimately linked to the maxilla causing possible destabilizing disarticulation unless specialized joint capsules and muscle action damped the motion (Rybczynski et al., 2008). Extensive pleurokinetic mastication was therefore unlikely in Edmontosaurus, but remains to be tested in other hadrosaurs.

The quadrate-articular joint in hadrosaurs is ventrally offset from the tooth row. This innovation permitted synchronous occlusion of the entire tooth rows of respective upper and lower jaws, as in modern mammals (Pough et al., 2005).

The ceratopsid mandible

Osteology and myology.

The ceratopsid predentary is a single penta-radiate element that caps the symphyses of the dentaries. Proximally, it may be divided into pairs of caudodorsal and caudoventral processes that neatly enclose the dentary symphysis. The caudoventral processes are slender and fingerlike compared with the more robust caudodorsal processes. A single medial process extends just dorsal to the caudoventral processes where it maintains separation between the two dentary bones. The rostral end of the predentary forms a triangular prism that is recurved dorsally. The entire rostral and ventrolateral surfaces of the predentary are intricately sculpted by foramina and grooves for the passage of blood vessels that presumably supplied a keratinous ramphotheca (Dodson et al., 2004).

The dentary is the only tooth-bearing element in the ceratopsid mandible and consists of a roughly rectangular body and a laterally displaced coronoid process. The dentaries meet at the symphysis, which is only slightly ventrally deflected in derived ceratopsians. The symphyseal junction possesses well-developed, elongate ridges that interdigitate with the opposing dentary. Evidence for ligaments in this region is indicated by several large, parallel ridges with a roughened, pitted texture on an avascular surface (Benjamin et al., 2002). The number of alveoli increases during ontogeny and up to 40 tooth positions may be present in the largest taxa (e.g., Triceratops; Dodson et al., 2004). Three to four teeth may occupy a single tooth position; however, a maximum of two teeth per position were active at any time. A tooth column may be up to half the depth of the dentary. The teeth form a continuous shearing surface that is vertical and extends caudal to the coronoid process. A short diastema occurs between the rostral-most tooth and the predentary–dentary contact. The coronoid process arises from the lateral surface of the dentary where it is extremely robust, becoming expanded and more plate-like dorsally to form the attachment region of the major jaw muscles (M. adductor mandibulae externus profundus, M. pseudotemporalis: Rybczynski et al., 2008). Three unique regions of tendon insertions are evident on the lateral surface of the expanded dorsal terminus of the coronoid process. Insertion of M. adductor mandibulae externus profundus is situated on the dorsocaudal border of the coronoid process. Superficially there are randomly oriented, highly spiculate textures indicative of fibrocartilaginous tendon insertions (Shaw and Benjamin, 2007). This texture grades into the second region that covers approximately 75% of the lateral surface of the coronoid process and is distinguished from the former region by exhibiting sharp, parallel ridges oriented approximately 60° from the long axis of the dentary body. The third insertion region (corresponding to M. pseudotemporalis) occurs along the rostral wing of the coronoid process and is typified by randomly oriented rugose textures grading into the parallel ridges on the lateral coronoid surface. Each of these regions are avascular and the bone surfaces show pitting where tendon fibers inserted into the cortical bone surface (Benjamin et al., 2006). Tendon insertion textures are also present along the ridge that attaches the shaft of the coronoid process to the body of the dentary. The insertion site for M. adductor mandibulae externus medialis, which occurs along this ridge is oriented in the same direction as the insertion sites on the coronoid process. Inferring from the amount of developed rugosity, the insertion for M. adductor mandibulae externus profundus produced the greatest force (Thomopoulos et al., 2003) and muscle contraction would have resulted in caudodorsally directed adduction of the mandible (Ostrom, 1964).

Caudally, the deep Meckelian fossa is surrounded by the expanded base of the coronoid process, laterally, and the caudal extension of the tooth row, medially. Together, the surangular, angular, splenial, and articular form a robust process projecting caudally from the dentary, although the surangular is reduced (Dodson et al., 2004) relative to hadrosaurs. The entire retroarticular process is short and broad compared with hadrosaurs but is likewise ventrally displaced from the tooth row.

Masticatory mechanism.

In contrast to hadrosaurs, ceratopsids possessed no correlates of cranial kinesis; however, like hadrosaurs, the quadrate-articular joint is ventrally offset from the tooth row permitting synchronous occlusion of the jaws. Wear surfaces in the teeth are vertical, indicating purely isognathous occlusion (Ostrom, 1964). Ostrom (1964) described in detail the shearing mechanism in the ceratopsid jaw, which is virtually unique to this group. The dentition of ceratopsids performed like scissors with no apparent grinding or crushing ability, a technique usually attributed to carnivory. Although vertical shear plays a relatively minor role in occlusion in modern herbivores (Ostrom, 1964), contemporary herbivorous communities are dominated by mammals, which have the unique ability to transversely mobilize the dentaries. Dental microwear, however, in Triceratops and Chasmosaurus shows bi- and poly-modal scoring on worn tooth enamel, which could only have occurred during an asymmetrical palinal retraction following vertical occlusion of the jaws (Varriale, 2004). Therefore, it seems likely that ceratopsids employed both vertical and palinal components to the powerstroke.

MATERIALS AND METHODS

CT Scanning and Interpretation

All specimens used in this study are housed at the University of Alberta Laboratory of Vertebrate Palaeontology (UALVP), Edmonton, Alberta. CT scans were made of an isolated Lambeosaurinae indet. dentary and articulated mandibles of Centrosaurus apertus (Table 2), on a GE Lightspeed CT scanner (Canada Diagnostics Centre, Calgary, Alberta), at 1 mm effective thickness. Postdentary elements were sculpted in plasticine, based on comparisons with other specimens (e.g., UALVP16248, UALVP49067) and the published literature (Ostrom, 1964; Horner, 1992; Rybczynski et al., 2008). The resulting data were examined in three orthogonal planes, and reconstructed as volumetric and surface models, using OsiriX, Amira 4 (Mercury Computer Systems), and Mimics (Materialise Inc.). Internal morphology and gross-scale density variance were evaluated with a greyscale look-up table. We used the full color, NIH table in OsiriX to discriminate finely between density values, across the entire range resolvable by the scanner. Anatomical abbreviations are given in Table 3.

Table 2. Specimens used in this study
Museum no.TaxonFormationDentary length (mm)Length of tooth row (mm)Coronoid height from base of dentary (mm)
UALVP41Centrosaurus apertusDinosaur Park435305200
UALVP11734Lambeosaurinae indet.Dinosaur Park465275205
Table 3. List of Abbreviations
Anatomical abbreviations
DnDentine
ElEnamel
CaBCancellous bone
CBCortical bone
M. amemAdductor mandibulae externus medialis
M. amesAdductor mandibulae externus superficialis
M. amepAdductor mandibulae externus profundus
M. ptvPterygoideus ventralis
M. ptdPterygoideus dorsalis.

Finite Element Analysis: 3D Models

Model geometry.

 We produced 2D and 3D finite element models of CT scanned specimens. For each 3D model, DICOM CT data were imported into Mimics (Materialise Inc.) and thresholded to the density range of mineralized vertebrate tissues. We refined this “mask” for 3D modeling by removing artifacts and filling cavities, using the multislice edit tool in Mimics. Computed surface models assisted with identifying artifacts that were difficult to observe in individual slices. We created hexahedral meshes in Mimics and after applying material properties (see later) exported the mesh in Nastran format into Strand7® Pty. Ltd.

Material properties.

For all models, we assumed isotropic properties for bone resisting forces axially instead of radially. The latter are a realistic possibility with masticatory loads, but applying isotropic properties for all specimens imposed precise control for testing our comparative hypotheses. Artifacts from CT beam hardening often prevented certain assignment of material properties based on Hounsfield density values (Wroe, 2007). We therefore created two models per specimen: one with uniform bone properties and another with modified properties derived from Hounsfield units (HU).

Because compact bone predominated in all specimens, in the uniform model, we assumed properties of compact bone subject to Haversian reworking by repeated feeding loads (Rayfield et al., 2001; elastic modulus E = 2e10, Poisson's ratio [orthogonal versus axial strain] ν = 0.34, density ρ = 1,850 kg/m3). These properties and those for tooth dentine and enamel were applied to appropriate regions of the model in Strand7. (Precise regions for these material properties were assigned to 2D section models, as described later.)

We applied Hounsfield-derived properties in Mimics for export into Strand7, using methods similar to those of Arbour and Snively (this volume). The program determined HU densities for all voxels and divided them into 18 ranges. Using data from Hellmich et al. (2008), we derived a simple relationship between elastic modulus (E) and HU density (ρH.U.):

equation image

Mimics applied varying elastic moduli and density from this equation and our assigned uniform Poisson's ratio (ν = 0.34) to each voxel. We assigned properties of the uniform model to areas of zero density (artifacts of imperfections in the specimen) and to the reconstructed postdentary regions.

Forces and constraints.

In adduction, the mandibles of both ceratopsids and hadrosaurs behaved as a class three lever, where the force (i.e., contraction of the primary masticatory muscles) is applied between the fulcrum (i.e., the articular-quadrate articulation) and the point of resistance (food reaction force at the tooth row). For adductor muscles in this study (Fig. 1) we followed reconstructions by Ostrom (1961, 1964), Dodson (1996), Holliday and Witmer (2007), and Rybczynski et al. (2008). Adduction forces corresponding of M. pterygoideus ventralis were omitted from our analyses. This muscle loops ventrally around the lower jaw, introducing uncertainties in its lateral cross-section and force generating capability. We interpreted the function of M. pterygoideus as contribution to momentary constraint and stabilization of the jaw joint, although in life it had adductive and protractive actions.

Figure 1.

Muscle insertions on a typical hadrosaur (A–C) and ceratopsid jaw (D–F) based on reconstructions by Ostrom (1961, 1964), Dodson (1996), Holliday and Witmer (2007), and Rybczynski et al. (2008). (C, F) Close-ups of the coronoid processes of the hadrosaur and ceratopsid, respectively, in lateral view. Note the caudally-inclined striations, indicative of Sharpey's fibers, are well-developed in the ceratopsian coronoid process but lacking in that of the hadrosaur. Abbreviations as in Table 3. Scale bar = 1 cm.

For other muscles in the hadrosaur, we applied methods of Snively and Russell (2007) and Rayfield et al. (2001) to derive muscle forces from cross-section, specific tension, and lines of muscle pull. Because we lacked data on muscle dimensions in ceratopsids, we scaled estimates of their force from the ratio of the specimen's insertion area on the coronoid process versus that of the hadrosaur. Using lever mechanics we calculated food reaction forces at the predentary-dentary contact [referred to herein as “rostral-load” (RL); necessary because our hadrosaur specimen lacked a predentary] and at the midpoionts of the dental batteries [referred to hereafter as “mid-load” (ML)] in both specimens (Fig. 2). These points were selected to test the cropping capacity of the predentary (without having to consider potentially misleading ligamentous strength) and the primary chewing/shearing surface along the tooth row, respectively. We constrained the models on the dorsal surface of the articular (the site of the jaw articulation) to prevent rigid body motion and allow the models to deform.

Figure 2.

Finite element models of the (A) hadrosaur and (B) ceratopsid jaws were constrained at the articulation surface with the quadrate (X). Each model was subjected to two analyses: a rostral load at the predentary-dentary contact and a mid load on the primary masticatory surface. Food reaction forces are in parentheses.

FINITE ELEMENT ANALYSIS: 2D MODELS

Quasi-2D models (Rayfield, 2004) were created to replicate transverse sections through the jaws. Following methods of Snively and Cox (2008), we traced transverse CT sections from the midpoint of each tooth row, viewed with the NIH color palette to determine densities. The traces included the overall transverse section and regions corresponding to different tissues (dentine, enamel, compact, and cancellous bone) evident from CT density data and the gross cross-sectional anatomy. We imported the combined traces for each section into COMSOL Multiphysics®, and applied tissue material properties to respective regions. We constrained the sections ventrally and applied mid-battery food reaction forces calculated for the 3D models of the specimens.

We visualized 2D results with the von Mises yield criterion, to evaluate relative proximity to yield within the structure, and as a reflection of strain energy density (Farke et al., 2008). Von Mises was appropriate because bone has high collagen content and is ductile under moderate, gradually applied loads. However, it is not useful for visualizing types of stress because von Mises is a summation of principal components of stress and not a characterizable force/area. We therefore also plotted shear stress for the 2D cross sections, to test hypotheses of extensive “grinding” shear in the lambeosaurine versus “chopping” shear in the Centrosaurus.

RESULTS

Internal Anatomy of Ceratopsid Mandibles

Taphonomic artifacts are evident throughout the bone elements, but this has resulted in minimal loss of information and does not obscure the internal structure of the bone. However, metal fragments within the bone have created artifacts that are especially noticeable within the caudal-most regions of the dentary, making bone density interpretations difficult.

Predentary.

The ceratopsid predentary grades from highly vascularized bone rostrally to a region of predominantly dense cortical bone caudally. Rostrally, the dorsally recurved triangular prism is suffused with secondary and tertiary vascular traces from primary vascular canals (Fig. 3A). Internal vascular canals permeate the entire region and exit rostrolaterally and rostroventrally to supply the bone-ramphotheca junction. Despite relatively dense vascularization of this region there are no vascular foramina along the rostrodorsal tip of the predentary or in the dorsal, bilaterally scalloped region caudal to the tip. The surface of this margin is subaeroate in texture having the appearance of a finely vesicular surface that has been eroded or scoured.

Figure 3.

Computed tomographic imaging of Centrosaurus apertus (UALVP41) mandibles, indexed by longitudinal slice position in the scan. A: (Slice 44) cross-section of the rostral-most tip of the predentary showing highly vascularized, dense subaeroate bone. Vascular canals perforate the entire region and exit as foramina rostroventrally to supply the bone-ramphotheca junction. B: (Slice 107) cross-section of the rostromedial portion of the predentary showing more typical distributions of cortical bone at the margins of the element and cancellous bone infilling the central corpus. Dense bone is most noticeable along the lateral borders and especially within the ventral apex (arrow). Vascular traces are present and exit along the ventrolateral surfaces. C: (Slice 223) cross-section of the caudomedial portion of the predentary showing neurovascular canals within each caudodorsal process (arrow). Increased cortical bone thickness is expressed along the dorsolateral surface of the scalloped region. D: (Slice 242) cross-section of the caudal portion of the predentary showing cortical and dense cancellous bone distribution. Dense bone is situated primarily within the ventral-most regions of the predentary. E: (Slice 313) cross-section of the rostral-most portion of the dentary enclosed by the predentary processes. Bilateral neurovascular canals extend throughout the dorsal region of the body, and exit rostrally. The dentary symphysis exhibits interdigitation (arrow). F: (Slice 367) cross-section of the rostral edentulous dentary body. Cortical and dense cancellous bone remains concentrated along the borders of the body, especially within the ventral region. A second neurovascular canal lies ventral to the rostral canal (arrows). The second canal exits the bone rostrally onto the ventrolateral surface. G: (Slice 653) cross-section of the medial dentary body, showing tooth morphology. A large neurovascular canal travels from the caudal dentary and exits laterally (arrow). The surangular fossa is noticeable caudoventrally. H: (Slice 739) cross-section through the coronoid process. CT artifacts obscure comparative cortical bone density, but a cavity of cancellous bone is evident dorsally within the coronoid process. Length of dentary = 435mm.

Progressing caudally, cortical bone becomes increasingly concentrated along the ventrolateral borders and cancellous bone of decreasing trabecular density grades into the central corpus (Fig. 3B). The majority of cortical bone occurs ventral to the internal cancellous region. A primary rostromedially directed neurovascular canal is present within each of the caudodorsal processes of the predentary and terminates rostrally as a series of finely branching secondary vessels (Fig. 3C). The primary canal also gives rise to the multitude of secondary vessels that radiate rostrolaterally.

The thickness of cortical bone continues to increase caudally within the scalloped, dorsolateral borders of the predentary. There is a substantial increase in cancellous bone density within the ventral apex of the element at the predentary–dentary juncture (Fig. 3D). Cortical bone in this region is well defined and variously grades into dense cancellous bone toward the interior of the corpus. Except for the dorsal-most portions of the caudodorsal processes that exhibit cancellous centers, the remainder of the caudodorsal processes and the caudoventral processes are primarily composed of cortical bone.

Dentary.

The dentary is composed of variously distributed regions of cortical and cancellous bone throughout the entire rectangular-shaped body and laterally projecting coronoid process.

Cortical and dense cancellous bone remain concentrated along the ventrolateral borders of the dentary (Fig. 3E–G). Bilateral neurovascular canals extend virtually the entire length of the dentary. They originate on the dorsal portion of the Meckelian fossa extending rostrally, finally exiting at the mandibular symphysis. These canals are continuous with those described within the caudal region of the predentary. This canal gives rise to several, secondary neurovascular canals; the first two of which diverge rostrolaterally, immediately rostral to the origin and exit rostral to the base of the coronoid. A secondary neurovascular canal of similar diameter to the primary canal diverges ventrally from the latter at about the fourth alveolus. This canal exits the bone rostrally along the ventro-lateral surface just caudal to the mandibular symphysis.

Progressing caudally toward the first alveolus, cortical and dense cancellous bone increases along the lateral and ventral borders of the bone. A horizontal line of at least 22 similarly sized, evenly spaced neurovascular foramina enters the dentary body along the medial surface and extends the length of the tooth row (Fig. 3G).

In the caudal-most region of the dentary, dense bone appears concentrated along the medial border of the body; however, this is most likely an artifact caused by metal pins placed in the bone for mounted display. Dense cancellous bone infills the interior of the body. Beam hardening artifacts obscure bone density distribution within the coronoid process (Fig. 3H); however, large, sparsely trabeculated regions are evident within the main body of the dentary and within the coronoid process. It is uncertain if or how the spicules and striations on the lateral surface of the coronoid processes are supported internally.

3D finite element results.

ML analyses of the ceratopsid jaw produced low stresses concentrated along the leading edge of the coronoid process (Fig. 4A–C). Tensile stresses were transmitted from the coronoid process to the rostroventral edge of the dentary along the longitudinal ridge on the lateral surface of this bone. Compression on the caudal edge of the coronoid process was related to tension along its leading edge caused by the direction of pull from M. adductor mandibulae externus profundus and M. pseudotemporalis (Fig. 4A). Results along the base of the coronoid process on its caudal aspect were more complex but appear to represent tension along the surangular-dentary union (Fig. 4C). Compression related to joint reaction forces were low and localized to the joint surface; stress levels remained relatively low in the entire postdentary region. Higher relative stresses on the right mandible compared with the left side are probably related to asymmetry in the specimen as already noted.

Figure 4.

Three-dimensional finite element analysis results of Centrosaurus jaw (UALVP41) in lateral (A, D, G), rostral oblique (B, E, H), and caudal oblique (C, F, I) views. (A–C) mid-tooth row load; (D–F) rostral load; and (G–I) unloaded surface render. Note the propagation of stresses from the base of the coronoid along the longitudinal ridge on the lateral wall of the dentary.

When forces were applied more rostrally to the dentary, a notable increase in tensile stress was incurred along the longitudinal ridge on the lateral wall of the dentary (Fig. 4D,E). Minor compression was also observed on the ventral margin of the dentary directly ventral to the coronoid process. Stresses on the postdentary elements remained consistent with results for our ML analysis.

A control analysis, using uniform material properties, produced identical results to the aforementioned tests indicating stress patterns behaved independently of material properties.

2D finite element results.

Reactive stresses in the ceratopsid dentary were very low. Unsurprisingly, von Mises index magnitudes peaked at the point of force application (i.e., the tip of the tooth crown) but were rapidly dissipated by the enamel, preventing transmission of stresses into the dentine. Shear plots corroborated this result (Fig. 5).

Figure 5.

Two-dimensional finite element analysis results for Centrosaurus apertus jaw. A: Cross-section of the dorsal portion of the right dentary in rostral view, showing compressive and tensile shear stresses concentrated at the tip of a tooth. B: Food reaction force was applied to the tip of the tooth crown (arrow) in compliance with an isognathous, shearing bite. Enamel damped forces transmitted into the dentine. Note the columnar cross-sectional profile of the dentary compared with that of the hadrosaur, and low von Mises quantities indicating low proximity to yield. C: Lateral view of the right mandible. The solid line identifies the location of the cross-section (slice 603).

Hadrosaur Mandible

Internal anatomy of the dentary.

Bone density along the dentary UA11734 is remarkably uniform for much of its length. The rostral edentulous portion is typified by a thin outer layer of dense cortical bone infilled by cancellous bone (Fig. 6F). Cortical bone increases in thickness caudally in the ventral half of this region whereas the dorsal half remains largely cancellous (Fig. 6E). The exit foramen for a primary neurovascular canal is clearly visible on the ventrolateral margin of the rostral edentulous portion of the dentary (Fig. 6F). It is traceable caudally to a position ventral to the tenth alveolus. The canal maintains a trajectory parallel to the tooth row despite the medial curvature of the rostral dentary. Cortical bone reaches its greatest thickness along the ventral, ventromedial, and ventrolateral margins of the dentary for the entire length of the tooth row (Fig. 6C). Only a thin layer of cortical bone persists on the dorsolateral dentary wall. Spongy cancellous bone dominates the body of the element, becoming more dense (but not cortical) where it grades into alveolar bone. A center of less dense cancellous bone extends through the middle third of the tooth row length to about the base of the coronoid process.

Figure 6.

Computed tomographic images of an unidentified hadrosaur dentary (UALVP11734) in rostral view, indexed by longitudinal slice position in the scan. A: (Slice 249) cross-section through the coronoid process and the Meckelian fossa. Hardening artifacts are apparent as sub-parallel streaks throughout the slice. B: (Slice 316) cross-section rostral to the base of the coronoid process. Cortical bone is restricted to the lateral wall of the dentary. The dark, pulp centre of three teeth can be seen medially. C: (Slice 490) cross-section through the middle of the tooth row. Dense cancellous bone is visible as a white band extending dorsoventrally through the middle of the slice. Note that it does not appear as dense as cortical bone on the lateral and ventral perimeters. A mental foramen can be seen ventromedially perforating the outer wall but does not penetrate deep into the alveolar region. D: (Slice 600) cross-section through the rostral tooth row showing mediolateral compression of the dentary. Cortical and cancellous bone is distributed in subequal proportions in this region. E: (Slice 718) cross-section through the edentulous portion of the dentary showing a thin perimeter of cortical bone. Cancellous bone dominates the central and dorsal regions. F: (Slice 810) cross-section through the symphyseal region showing a preponderance of cancellous bone. The arrows indicate the primary neurovascular canal. Length of dentary = 465 mm.

The large primary neurovascular canal is traceable through the entire length of the dentary (Fig. 6A–F, arrows). It begins as an ovoid foramen that opens through the Meckelian fossa and continues rostrally lateral to the base of the tooth row through the body of the dentary, finally exiting through a large foramen on the ventral surface of the edentulous rostral portion (Fig. 6F). A short diverticulum arises dorsally from the main canal close to the rostral exit foramina and terminates abruptly. Numerous smaller neurovascular pathways branch rostrodorsally, rostrolaterally, or rostroventrally from the primary neurovascular canal and exit on the lateral wall of the dentary.

Mental foramina on the medial surface of the dentary correspond with the base of individual alveoli but do not appear to penetrate deeper (i.e., lateral to the alveoli) into the jaw (Fig. 6C).

Hardening artifacts make interpretation of bone densities through the coronoid region more difficult. The flared dorsal end of the coronoid process appears to be strongly reinforced with cortical bone on all sides with only a small amount of cancellous bone infilling the centre. The shaft is made up principally of cancellous bone with a thick layer of cortical bone on the lateral wall, although it is possible that scanning “noise” may have contributed to the apparent density of this region (Fig. 6A).

3D finite element results.

 ML finite element analyses of the hadrosaur jaw caused notable torsion in the postdentary bones. Laterally, high tensile stresses were highest at the surangular-dentary contact and a concomitant peak in compressive forces immediately caudal to this point at about the articular-surangular contact (Fig. 7A). Compression and tension were relatively lower on the medial surfaces of these bones (Fig. 7D). The coronoid process also experienced considerable tension along its rostral border and associated compression caudally although stress in these areas was more localized. Food reaction forces on the occlusal surface resulted in minor compression of the tooth row.

Figure 7.

Three dimensional finite element analysis results for the hadrosaur dentary (UALVP11734) in lateral (A, E, I), rostral oblique (B, F, J), and caudal oblique (C, G, K), and medial (D, H, L) views. (A–D) mid-tooth row load; (E–H) rostral load; and (I–L) unloaded surface render. Note the reversed order of compression/tension between medial (A) and lateral views (D) showing torsion of this region.

In the RL analysis, food reaction forces resulted in tensile and compressive stresses on the coronoid process comparable with our ML analysis; however, stresses on the postdentary elements were negligible compared with the ML analysis (Fig. 7E–H).

A control analysis using uniform material properties demonstrated stress patterns that were independent of material properties.

2D finite element results.

At the loading point, von Mises magnitudes and shear stress were preferentially directed along the lateral surface of the tooth crown. Enamel on the medial surface readily resisted loading causing a peak in shear stress in the dentine along the occlusal surface of the tooth. A zone of low stress persisted ventral to this point before dissipating completely. A second, smaller anomaly on the ventral jaw margin is an artifact of constraint parameters in the 2D model and should be disregarded. Stress levels and von Mises magnitudes were negligible throughout the remainder of the cross-section, indicating that the applied force did not strongly tax the jaw in this region (Fig. 8).

Figure 8.

Two-dimensional finite element analysis results for the hadrosaur dentary (UALVP11734). A: Rostral view of a cross-section through the dorsal portion of the dentary showing a region of high-compressive shear (yellow to blue) along the occlusal surface. B: Dorsoventral food reaction forces were applied to the dorsolaterally facing occlusal surface (arrow), corresponding to the region of high shear stress in A. Note also the elliptical cross-sectional shape of the dentary and low von Mises quantities (and proximity to yield) throughout the structure. C: Lateral view of UALVP11734. Solid line identifies the position of the cross-section (slice 511).

DISCUSSION

Mechanical Implications of Results for Hadrosaur and Ceratopsid Mastication

Adduction forces on the ceratopsid jaw, related to the action of M. adductor mandibulae externus profundus and M. pseudotemporalis, placed considerable stress on the coronoid process. Nevertheless, these stresses, identified by finite element modeling of the jaws during isognathous occlusion, were accommodated by several morphological adaptations. The longitudinal ridge on the lateral surface of each dentary apparently buttressed the coronoid process against caudal bending. The role of this buttress was particularly critical during rostral loading; stresses on the coronoid process were propagated along this ridge rather than remaining concentrated in the coronoid process, thereby reducing the risk of breakage along the shaft of the coronoid process. The presence of Sharpey's fibers on the expanded dorsal terminus of the coronoid process is similarly indicative of high tension and powerful muscular contraction (Benjamin et al., 2002; Snively and Russell, 2002, 2003). Sharpey's fibers are indicated by the raised, parallel striations on the muscle insertion point for M. adductor mandibulae externus profundus and M. pseudotemporalis (Fig. 1F). The caudally-inclined striations (approximately 60° from the long axis of the dentary body) on the ceratopsid jaw also correspond to the direction of muscle pull conferring maximum strength to this region (Benjamin et al., 2002). Sharpey's fibers were not identified on the hadrosaur jaw indicating comparatively weaker muscular contraction of the major jaw adductor muscles (Fig. 1C; Benjamin et al., 2002).

In contrast to the ceratopsid jaw, joint reaction forces produced torsion in the postdentary elements of the hadrosaur. Force vectors on the right mandible demonstrate anticyclonic (counter clockwise) twisting of these bones when viewed caudally (Fig. 9) implying rotation of the mandible around its longitudinal axis. These vectors correspond to the path of M. pterygoideus ventralis, which inserts on the caudolateral surface of the surangular and wraps medially under the surangular, extending rostrodorsally to its origin on the pterygoid (Rybczynski et al., 2008). This muscle would have played an important role in the stabilization of the jaw, counteracting longitudinal rotation of the mandible, and antagonizing contractions of M. adductor mandibulae externus medialis. To prevent injury, the bones in the postdentary complex may have been mobile around the jaw joint and kinetic, although this hypothesis remains to be tested. The loose union between the predentary and dentary would have permitted such movement (Herring, 1972) and longitudinal rotation of the dentary, as in heterodontosaurids (Weishampel, 1984), is most likely to have occurred. This is contrasted by the snug mortice and tenon joint between the predentary and dentary in ceratopsids, which prevented longitudinal rotation that would have had deleterious effects on the scissor-like configuration of the upper and lower jaws. Ridges along the dentary symphysis increased the available surface area for ligament tissues thus fixing the articulation of right and left mandibles (Herring, 1972). Force vectors in the ceratopsid jaw confirm major stresses were directed around a simple hinge between the articular and quadrate (Fig. 10). The absence of torsion in this region and throughout the rest of the jaw (see later) is consistent with purely isognathous occlusion and a lack of a transverse component to the powerstroke. However, palinal retraction of the mandibles (Varriale, 2004) cannot be ruled out. We acknowledge that the robustness of postdentary region of UALVP11734 may be artificially high as we were not able to successfully recreate sutures between the constituent elements. Therefore, our results may suggest lower-than-expected stresses in this region. More accurate modeling that recognizes the discrete elements in this region should produce an even clearer picture of torsion in the postdentary complex (Rafferty and Herring, 1999; Rayfield, 2005).

Figure 9.

Stress vectors in the postdentary elements of the hadrosaur jaw (UALVP11734). Stress vectors (small arrows) show anticyclonic twisting of the entire postdentary region (large arrow) associated with transverse-isognathous occlusion. Stress vectors match the path of M. pterygoideus ventralis suggesting this muscle helped stabilize the jaw joint and rotate the jaw back into position. Boxed area on the hadrosaur mandible (inset) demarcates the enlarged image.

Figure 10.

Stress vectors in the postdentary elements of Centrosaurus apertus (UALVP41). Stress vectors (arrows) show a divergent pattern on the ventral surface of the postdentary complex ventral to the jaw joint. Vectors indicate a simple hinge-like motion of the jaws and the absence of torsion. Boxed area on the ceratopsid mandible (inset) identifies the enlarged image.

Tensile forces in the hadrosaur peaked along the surangular-dentary union, particularly between the coronoid process of the surangular and the dentary itself. This would have had the effect of separating these bones. The enlarged coronoid process on the hadrosaur surangular (sensu; Horner, 1992) was likely an adaptation for dampening these stresses by increasing the surface area for ligamentous attachment between these elements (Herring, 1972). This is supported by the relatively low torsional stresses experienced by the ceratopsian in those same bones and by the concomitantly shorter coronoid process on the surangular. Moreover, mediolateral expansion of the dentary presents an ovoid profile in cross-section conducive to torsion resistance (Snively et al., 2006; McHenry et al., 2006; Fig. 8). This is contrasted by the more columnar cross-sectional profile in the ceratopsian jaw in line with an isognathous power stroke (Ostrom, 1964) and corresponding dorsoventrally directed tooth reaction forces. These shapes faithfully reflect standard engineering principles, which state that cylindrical beams are optimally designed to resist torsion. In fact, a cylindrical beam will resist nearly twice the torsion of a rectangular beam (aspect ratio = 5:1) of the same cross-sectional area (McHenry et al., 2006).

Finite element modeling of lambeosaurine and centrosaurine mandibles comply with previously inferred masticatory methods (Ostrom, 1964, Weishampel 1983, 1984, Norman and Weishampel, 1985). The complex transverse-isognathous occlusion in the hadrosaur jaw resulted in mediolaterally directed food reaction forces and high shear across the occlusal surface. Concurrently, the hadrosaur mandible underwent considerable torsional stresses both along the tooth row and in the postdentary bones. Longitudinal rotation of the dentary, as in heterodontosaurids (Weishampel, 1984), is tenable but remains to be tested. Mediolateral widening of the dentary presents an elliptical cross-sectional profile optimally adapted to resisting torsion (McHenry et al., 2006). The elongate coronoid process of the surangular is similarly suited to cope with tension along the lateral surangular-dentary contact.

Ceratopsids possessed relatively more robust jaws than hadrosaurs. The narrow, rectangular jaw cross-section is well-adapted to resist dorsoventrally directed food reaction forces incurred during purely isognathous occlusion but is incompatible with strong transverse components to the power stroke. The jaws were additionally strengthened by the presence of Sharpey's fibers at the insertion point for M. adductor mandibulae externus profundus and M. pseudotemporalis and by a longitudinal ridge of bone on the lateral surface of the dentary.

As common faunal components in Late Cretaceous Laurasian terrestrial ecosystems, hadrosaurs, and ceratopsians were potential competitors for resources, particularly fodder. Finite element analyses reveal a suite of unique modifications to the mandibles that permitted the coexistence of these groups. The robust ceratopsid mandible was capable of producing powerful isognathous powerstrokes designed for shearing tough vegetation but was unable to further process its food by mastication alone. Although hadrosaurs possessed a relatively weaker bite force, their torque-adapted jaws were suited for processing more fibrous vegetation associated with transverse-isognathous occlusion.

Acknowledgements

Canada Diagnostic Centres (Calgary) are gratefully acknowledged for CT scanning of the specimens. Don Henderson, Francois Therrien, and Brandon Strilisky (Royal Tyrrell Museum of Palaeontology) provided access to specimens. The authors thank Victoria Arbour and Philip Currie for discussion, and Anne Delvaux, Michael Lawrenchuk, and Jia Li for technical support. This manuscript greatly benefited from insightful reviews by Peter Dodson and two anonymous reviewers. Finally, the authors thank Peter Dodson for the opportunity to contribute to this volume.

Ancillary