Palaeontologia Electronica palaeo-electronica.org Multibody dynamics model of head and neck function in Allosaurus (Dinosauria, Theropoda) Eric Snively, John R. Cotton, Ryan Ridgely, and Lawrence M. Witmer ABSTRACT We present a multibody dynamics model of the feeding apparatus of the large Jurassic theropod dinosaur Allosaurus that enables testing of hypotheses about the animal’s feeding behavior and about how anatomical parameters influence function. We created CT- and anatomical-inference-based models of bone, soft tissue, and air spaces which we use to provide inertial properties for musculoskeletal dynamics. Esti- mates of bone density have a surprisingly large effect on head inertial properties, and trachea diameter strongly affects moments of inertia of neck segments for dorsoventral movements. The ventrally-placed insertion of m. longissimus capitis superficialis in Allosaurus imparted over twice the ventroflexive accelerations of a proxy control inser- tion lateral to the occipital condyle, the latter being its position in nearly all other thero- pods. A feeding style that involved defleshing a carcass by avian-raptor-like retraction of the head in Allosaurus is more probable than is lateroflexive shake-feeding, such as that seen in crocodilians and inferred for tyrannosaurids. Eric Snively. Department of Mechanical Engineering, Russ College of Engineering, 249 Stocker Center, Ohio University, Athens, OH 45701, USA [email protected] John R. Cotton. Department of Mechanical Engineering, Russ College of Engineering, 249 Stocker Center, Ohio University, Athens, OH 45701, USA [email protected] Ryan Ridgely. Department of Biomedical Sciences, Heritage College of Osteopathic Medicine, Ohio University, Athens, OH 45701, USA [email protected] Lawrence M. Witmer. Department of Biomedical Sciences, Heritage College of Osteopathic Medicine, Ohio University, Athens, OH 45701, USA [email protected] Keywords: Dinosauria; biomechanics; feeding; multibody dynamics; muscle PE Article Number: 16.2.11A Copyright: Palaeontological Association May 2013 Submission: 18 July 2012. Acceptance: 21 January 2013 Snively, Eric, Cotton, John R., Ridgely, Ryan, and Witmer, Lawrence M. 2013. Multibody dynamics model of head and neck function in Allosaurus (Dinosauria, Theropoda), Palaeontologia Electronica Vol. 16, Issue 2; 11A 29p; palaeo-electronica.org/content/2013/389-allosaurus-feeding SNIVELY ET AL: ALLOSAURUS FEEDING INTRODUCTION Bates and Falkingham (2012) bridged extant and fossil dynamics with simulations of biting in Allosaurus Musculoskeletal Anatomy humans, Alligator, Tyrannosaurus, and Allosaurus. Allosaurus was the most common dinosaurian Their dynamic simulations found higher bite forces predator in its ecosystems during the Late Jurassic in Allosaurus than expected from previous static of North America (154–148 Ma; Foster, 2007). analyses based on finite element reaction forces There are at least two species of Allosaurus (Rayfield et al., 2001). Bates and Falkingham’s (Chure, 2000; Loewen, 2009). These and other (2012) analyses showed the versatility of multibody taxa in Allosauroidea had ball-and-socket joints dynamics methods, adapting the free program between their opisthocoelous vertebral centra GaitSym which is normally applied to simulate (Madsen, 1976; Holtz et al., 2004; Brusatte and locomotion (Sellers et al., 2009; http://www.animal- Sereno, 2007), suggesting a highly mobile neck. simulation.org). This morphology contrasts with tyrannosaurid Feeding Apparatus Dynamics of Allosaurus: theropods of similar size to allosauroids, such as Goals and Hypotheses Tyrannosaurus rex, in which the centra have amphiplatyan (flat) intervertebral joints (Brochu, Using multibody dynamics, we can simulate 2003). Allosaurus crania have ventrolaterally head and neck motions in Allosaurus with ranges sweeping paroccipital processes, with unusual of parameter values, enabling us to estimate iner- muscle attachments that suggest powerful ventrof- tial properties and accelerations of its head and lexion of the head (Bakker, 1998[2000]; Rayfield et neck and circumscribe possible feeding behavior. al., 2001; Snively and Russell, 2007a; Carrano et There are three potential benefits to this approach. al., 2012). Computer modeling of range of motion First, we can quantify the functional morphology and musculoskeletal dynamics enables testing of behind the ecological success of a widespread and hypotheses related to Allosaurus feeding, and will long-lasting carnivorous taxon. Second, lessons guide more elaborate investigations of anatomy from constructing the multibody dynamics model and feeding in this apex predator. will establish its effectiveness and methods of best use for comparative studies of other taxa, including Multibody Dynamics of Head and Neck Motion large Morrison theropods such as Ceratosaurus Dynamics of head and neck motion have that partitioned predatory niches with Allosaurus precedent in studies of humans and other extant (Foster, 2007). Finally, we can address explicit animals. Dynamic simulations of head and neck hypotheses about neck function that are difficult to function in humans (Delp and Loan, 1995; Vasa- test by other means. vada et al., 1998, 2008a, b; van Lopik and Acar, Neck muscles of large theropods varied in 2007; Marin et al., 2010) enable non-invasive, morphology, relative size, and functional capability. exploratory analyses with precise control over input Snively and Russell (2007a) presented measure- variables. Analogous benefits apply to simulations ment and statistical evidence that Allosaurus had of extinct animals, for which in vivo study is impos- smaller dorsiflexors than adult tyrannosaurids of sible and most parameter values are unknown. equivalent size. Conversely, Snively (2006) estab- Non-human models of head-neck function have lished morphometrically that allosauroids had concentrated on feeding in reptiles. For example, larger ventroflexive moment arms than did tyranno- Moazen et al. (2008a) simulated dynamics of biting saurids, and that Allosaurus’s insertion of m. lon- in the lizard Uromastix, incorporating complex gissimus capitis superficialis may have further aspects of muscle force production, and validation increased ventroflexive torque. The effect of this with experimental data, as inputs for finite element insertion on ventroflexive angular accelerations analysis of bite stress. Curtis et al. (2010a,b) con- has yet to be quantified. structed a model of the tuatara Sphenodon (includ- By comparing angular accelerations, we test ing neck muscles) to examine the effects of muscle the hypothesis that unusual muscle attachments activation levels on bite force and neuromuscular below the level of the occipital condyle of Allosau- control. Modeled bite forces were lower than the rus conferred more rapid ventroflexion than if the forces that the tuataras exerted experimentally muscle inserted in the same coronal plane as the (Curtis et al., 2010b). Moazen, Curtis, and col- condyle. Such a lateral insertion is present in leagues used the software MSC Adams (MSC nearly all other theropods. Misplacing it here in Software, Santa Ana, California, USA; see Appen- Allosaurus serves as a control, enabling us to com- dix 1) for their simulations. pare ventroflexive accelerations in the “real” mor- 2 PALAEO-ELECTRONICA.ORG S11 S9 S8 S7 S6 S5 S3 S1 C1 C2-1 C3 C4 C5 C6 C7 C8 C9 S10 S4 S2 E2 E1 anterior, nasal airways antorbital middle ear oropharyngeal trachea suborbital diverticula diverticula cavity FIGURE 1. Lateral and dorsal profiles of Allosaurus (MOR 693) used for 3D reconstructions. Air spaces are color coded as transparent objects; colors may appear darker where the rendering of the bone is darker. Lines labeled as C represent cervical (neck) segments associated with respective cervical vertebrae, as S represent divisions of the skull and head. E=ear, C=cervical, S=skull. Specific landmarks: E1 and E2, intermediate segments of the middle ear cavity. C2-1, posterior of these vertebrae and the skull, except the retroarticular process. S1, top of parietals. S2, anterior edge of visible jaw muscles. S3, pos- terior edge of orbit. S4, posterior edge of lacrimal. S5, anterior edge of lacrimal’s jugal ramus, posterior edge of antor- bital sinus. S8, anterior extent of antorbital sinus. S10, anterior extent of bony nostril. phology and a proxy basal condition. Greater ness Memorial Hospital (Athens, Ohio). Chure ventroflexive acceleration would have behavioral (2000), Loewen (2009), and Chure and Loewen consequences for Allosaurus, perhaps enabling (unpublished data) have reviewed the specimen’s rapid downward strikes (Bakker, 1998[2000]; Ray- species taxonomy. Here we defer to upcoming field et al., 2001) and augmented bite force by publications by these authors and refer to the ani- slower motions (Antón et al., 2003), compared with mal simply as Allosaurus, omitting the species des- ecological contemporaries such as Torvosaurus ignation. To calculate mass, centers of mass and Ceratosaurus (Foster, 2007). (COM), and mass moments of inertia (I), the head and neck geometries of Allosaurus (including major MATERIALS AND METHODS air spaces) were modeled in Solid Edge (Siemens PLM, Köln, Germany) as a series of lofted elliptical Bone and Soft Tissue Geometry frusta. For non-elliptical cross sections, we derived The Allosaurus skull specimen used is a cast equations to obtain I for any super-elliptical frusta of Museum of the Rockies (MOR) 693, scanned at (Appendix 2) with the same radii as the Solid Edge a