Tyrannosaurus rex Osborn 1905

2. MATERIAL AND METHODS Specimens studied: AMNH 5027: American Museum of Natural History, New York; BHM 3033: Black Hills Museum, Hill City, South Dakota; MOR 555: Museum of the Rockies, Bozeman, Montana; SDSM 12047: South Dakota School of Mines, Rapid City, South Dakota; RTMP 81.6.1: Royal Tyrell Museum of Palaeontology, Drumheller, Canada. (a) Anatomical observations of sutural mobility Four facial sutures commonly appear patent and slightly mobile in T. rex skulls observed. These are the maxilla–jugal, postorbital–jugal, quadratojugal–jugal and postorbital–squam-osal contacts. Two of these sutures are not universally mobile: the quadratojugal–jugal suture is fused in some specimens (e.g. AMNH 5027) and movement at the postorbital–squamosal would be restricted by attachment of the superficial and possibly medial slips of the M. adductor mandibulae externus, which originate in part along the lateral supra-temporal fenestra margin. The remaining two sutures, namely the maxilla–jugal and postorbital–jugal contacts, remain patent in nearly all observed specimens, and are the main focus of this analysis. Patent, yet apparently immobile, sutures exist between many other cranial bones, and future analysis will attempt to elucidate the significance of these sutures. It should be noted that although the FEMs use a particularly loosely articulated skull (BHM 3033; figure 1) as a template, the following descriptions of cranial mobility are based on observations of numerous specimens (see above). (b) Jugal–postorbital contact The postorbital laps a smooth groove running down half the length of the anterior surface of the ascending process of the jugal (figure 2 a). Postorbital–jugal contact surfaces are variably rugose, with BHM 3033 bearing smooth articulation surfaces while ANMH 5027 and MOR 555 possess more rugose surfaces along the length of the contact. Furthermore, in AMNH 5027 and MOR 555, the anterior surface of the lower half of the ascending process bears a pronounced roughened region that marks the ventral extent of postorbital overlap. A depressed groove running along the posterior surface of the descending process of the postorbital marks the contact with the jugal. In all specimens observed and those documented in the literature (e.g. Brochu 2003) this contact is patent and potentially mobile, with the exception of MOR 008, in which the left jugalpostorbital contact is fused internally, probably as a result of the advanced age of this specimen (Molnar 1991). Additionally, minor interdigitations at the anterior edge of the postorbitaljugal suture in AMNH 5027 may have limited movement along the suture in this particular skull. Overlapping flanges at the postorbital–jugal contact surface generally prevent rotation in the transverse and parasagittal axis, but sliding of the jugal anteroventrally–posterodorsally against the postorbital is permitted (figure 2 a). (c) The maxilla–jugal contact The anterior portion of the jugal forks medially and laterally, ventral to its contact with the lacrimal. The medial fork laps on to the medial surface of the maxilla while the lateral fork further divides into a dorsal and ventral component, between which slots a narrow process of the maxilla (as noted by Molnar (1991)). Additionally the dorsal edge of an extended maxillary process laps the ventrolateral edge of the jugal along a posteriorly extended groove (figure 2 b). In none of the observed specimens was the maxilla–jugal contact fused. Dorsoventral and mediolateral movement plus rotation about the transverse and parasagittal axes is prevented by the interlocking mediolateral and dorsoventral articulations. The distinct anteroposterior orientation of all contacts suggest that slight anteroposterior sliding movement plus some limited rotation about the longitudinal axis of the jugal is permitted at this suture (figure 2 b). (d) Finite element modelling A two-dimensional (2D) FEM of a T. rex skull was created. A lateral-aspect photograph of BHM 3033 (Hell Creek Formation, South Dakota; figure 1 a) was digitized in SCION IMAGE (www.scioncorp.com). Outline x, y coordinates were imported into the Geostar geometry creator component of the COSMOSM FEA package (v. 2.0 for Unix; SRAC Corp. CA, USA and Cenit Ltd, UK). A series of 5 cm thick surfaces was created then ‘meshed’ to produce an interconnected grid of three-noded triangular FEs representing the lateral aspect of the cranium (figure 1 b). Each element was attributed the mechanical properties of bovine Haversian bone after Rayfield et al. (2001). The model represents a 2D section of the left aspect of the skull: the palate and braincase were not included. 2D models are used as a first approximation in orthopaedic biomechanical modelling, and using simple FEMs offers the potential to generate mechano-functional hypotheses (Carter et al. 1998), which may be further tested by digitally modifying future models. The 2D models presented here were constrained from moving about the lower temporal fenestra (figure 1 b) to focus upon the stress response of the rostrum, which as a more planar structure than the posterior skull is more appropriate for 2D modelling. Stress patterns posterior to the constraining surfaces, including the effect of condylar and muscular forces in the posterior skull, were not analysed and this region of the skull should therefore be ignored in relevant figures. Four structurally different FEMs were constructed by manipulating the base model: an initial ‘fused’ solid model with no mobile regions (figure 1 b) and three modified ‘mobile’ models showing differing degrees of intracranial mobility; a mobile post-orbital–jugal suture (figure 2 c), a mobile maxilla–jugal suture (figure 2 d), and a model with both a mobile maxilla–jugal and postorbital–jugal suture (not shown). The mobile FEMs (figure 2 c, d) were created by introducing breaks in the FE-mesh at the location of the appropriate suture in the actual skull. (e) Bite force magnitude and distribution Tyrannosaurus rex may have been capable of generating 13 400 N bite force at a single posterior tooth (Erickson et al. 1996). Using moment arm calculations to extrapolate this value rostrally along the tooth row, a total of 78 060 N was divided between biting teeth (therefore assuming 156 120 N bilaterally, less than, but approaching, values estimated by Meers (2002)). However, it may be argued that being first to contact a prey item, the large caniniform teeth received the majority of bite force (sensu Rayfield et al. 2001). In accordance with this suggestion, the two large caniniform teeth (figure 1 b) were allocated 13 000 N each, while the smaller incisiform and posterior maxillary teeth were allocated lesser values scaled to the size of the teeth. In this model a total of 31 000 N was applied. FEAs were performed to assess the stress response to this load in a fused or mobile skull. First, vertical dorsally directed bite forces representing the ‘puncture’ aspect of feeding were applied to the tooth tips in all four models and the corresponding stress and strain patterns were calculated. The analyses were then rerun applying instead a horizontally orientated, anteriorly directed bite force to represent the ‘pull’ tearing force, generated by the resistance of flesh and bone against the teeth during tugging and flesh-procuring behaviour (figure 1 b). Multiple tearing analyses applying moment-calculated forces, variable tooth-sizerelated forces and equal forces to all teeth were investigated. Because bite force was hypothetical but identical in related models, relative rather than absolute patterns of stress and strain could be assessed. 3. RESULTS Colour-coded stress distribution plots with superimposed stress vector orientation illustrate the pattern of stress and strain in the skull under biting and tearing loads (figures 3 and 4 and electronic Appendices A–C). By convention, tensile stresses and strains are allocated positive values, whereas compressive stresses and strains are assigned negative values. Principal stresses (P1 tensile; P3 compressive), shear stress in the sagittal (here XY) 2D plane, normal X, normal Y and sagittal XY shear strain were recorded (the software does not calculate principal strains). Principal stresses record peak compressive and tensile stresses when shear stress equals zero. Peak tensile, compressive and shear stresses and strains were recorded and treated as an indicator of skull ‘strength’: higher peak stresses mean that less force is needed to induce yielding, therefore the skull is weaker. Regardless of bite force magnitude (moment-arm versus ‘tooth-size’ forces), nearly identical patterns of stress and strain were produced in models of the same geometry (although absolute magnitudes differ). It can be assumed that the stress patterns figured here apply to either biting regime. (a) Stress in the fused-skull finite element model during biting and tearing Stress patterns in the vertical biting model (mimicking the ‘puncture’ phase of feeding) suggest that during biting, compressive stresses arc posterodorsally from the biting teeth through the maxilla and into the nasals and lacrimals (figure 3 a). Stress vectors trace this curvature then become longitudinally orientated in the posterior region of the nasals and dorsal body of the postorbital (figure 3 a). Peak tensile stresses are orientated longitudinally within the jugal and posterior maxilla, ventral to the lower temporal fenestra, orbit and antorbital fenestra (figure 3 b). Tension follows the ventral rim of the antorbital fenestra, leaving the main body of the maxilla dorsal to the tooth row relatively untensed (figure 3 b). Peak shear occurs in the nasals dorsal to the central antorbital fenestra and dorsal to the orbit (figure 3 c). When the biting simulation is altered to reflect pulling and tearing (hereafter known as the ‘tearing’ model), tensile vectors lose their anterodorsal component and trace the vent

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