(PDF) Palatal Biomechanics and Its Significance for Cranial ... · Palatal Biomechanics and Its Significance for Cranial Kinesis in Tyrannosaurus rex IAN N. COST ,1* KEVIN M. MIDDLETON,1 - DOKUMEN.TIPS (2023)

Palatal Biomechanics and ItsSignificance for Cranial Kinesis

in Tyrannosaurus rexIAN N. COST ,1* KEVIN M. MIDDLETON,1 KALEBC. SELLERS,1

MICHAEL SCOTT ECHOLS,2 LAWRENCE M. WITMER,3 JULIAN L. DAVIS,4ANDCASEY M. HOLLIDAY 1

1Department of Pathology and Anatomical Sciences, University ofMissouri, Columbia,Missouri

2Echols Veterinary Services, Salt Lake City, Utah3Department ofBiomedical Sciences, Heritage College of Osteopathic Medicine,Ohio

University, Athens, Ohio4Department of Engineering, Universityof Southern Indiana, Evansville, Indiana

ABSTRACTThe extinct nonavian dinosaur Tyrannosaurus rex,considered one of

the hardest biting animals ever, is often hypothesized to haveexhibitedcranial kinesis, or, mobility of cranial joints relativeto the braincase. Cra-nial kinesis in T. rex is a biomechanicalparadox in that forcefully bitingtetrapods usually possess rigidskulls instead of skulls with movable joints.We tested thebiomechanical performance of a tyrannosaur skull using aseries ofstatic positions mimicking possible excursions of the palatetoevaluate Postural Kinetic Competency in Tyrannosaurus. Afunctionalextant phylogenetic bracket was employed using taxa,which exhibit mea-surable palatal excursions: Psittacus erithacus(fore–aft movement) andGekko gecko (mediolateral movement). Staticfinite element models ofPsittacus, Gekko, and Tyrannosaurus wereconstructed and tested with dif-ferent palatal postures usinganatomically informed material properties,loaded with muscle forcesderived from dissection, phylogenetic bracketing,and a sensitivityanalysis of muscle architecture and tested in orthalbitingsimulations using element strain as a proxy for modelperformance. Extantspecies models showed lower strains in naturallyoccurring postures com-pared to alternatives. We found thatfore–aft and neutral models of Tyran-nosaurus experienced loweroverall strains than mediolaterally shiftedmodels. Protractormuscles dampened palatal strains, while occipital con-straintsincreased strains about palatocranial joints compared to jawjoint

This article includes AR WOW Videos. Videos 1–6 can beviewed athttps://players.brightcove.net/656326989001/mrOxISgynX_default/index.html?videoId=6058428214001.Videos7–12 can be viewed athttps://players.brightcove.net/656326989001/mrOxISgynX_default/index.html?videoId=6058434297001.Videos 13–18 can be viewed athttps://players.brightcove.net/656326989001/mrOxISgynX_default/index.html?videoId=6058438903001.

Abbreviations: FAM = fore–aft movement; FEA = finite ele-mentanalysis; FEM = finite element model; FM = muscle force;lf = fiberlength; mAMEM = m. adductor mandibulae externusmedialis; mAMEP = m.adductor mandibulae externus profundus;mAMES = m. adductormandibulae externus superficialis; mAMP= m. adductor mandibulaeposterior; mDM = m. depressor man-dibulae; mEM = m.ethmomandibularis; MLM = mediolateralmovement; mLPT = m. levatorpterygoideus; mPM =m. pseudomasseter; mPPT = m. protractorpterygoideus; mPSTp =m. pseudotemporalis profundus; mPSTs = m.pseudotemporalis

superficialis; mPTd = m. pterygoideus dorsalis; mPTv =m.pterygoideus ventralis; PCSA = physiological cross-sectionalarea;PKC = postural kinetic competency; VM = muscle volume; θ =pen-nation angle; με =microstrainGrant sponsor: Division of EarthSciences; Grant number:

EAR-163753; Grant sponsor: Division of IntegrativeOrganismalSystems; Grant numbers: IBN-0407735, IBN-9601174,IOB-0343744, IOB-0517257, IOS 1457319, IOS-1050154,IOS-1456503,IOS-1457319.*Correspondence to: Ian N. Cost, Departmentof Pathology and

Anatomical Sciences, University of Missouri, Columbia, MOE-mail:[emailprotected] 26 June 2018; Revised 13 April2019; Accepted 22

April 2019.DOI: 10.1002/ar.24219

Published online 00 Month 2019 in Wiley OnlineLibrary(wileyonlinelibrary.com).

THE ANATOMICAL RECORD (2019)

© 2019 WILEY PERIODICALS, INC.

https://orcid.org/0000-0002-5087-6823https://orcid.org/0000-0001-8210-8434https://players.brightcove.net/656326989001/mrOxISgynX_default/index.html?videoId=6058428214001https://players.brightcove.net/656326989001/mrOxISgynX_default/index.html?videoId=6058428214001https://players.brightcove.net/656326989001/mrOxISgynX_default/index.html?videoId=6058434297001https://players.brightcove.net/656326989001/mrOxISgynX_default/index.html?videoId=6058434297001https://players.brightcove.net/656326989001/mrOxISgynX_default/index.html?videoId=6058434297001https://players.brightcove.net/656326989001/mrOxISgynX_default/index.html?videoId=6058438903001https://players.brightcove.net/656326989001/mrOxISgynX_default/index.html?videoId=6058438903001https://players.brightcove.net/656326989001/mrOxISgynX_default/index.html?videoId=6058438903001mailto:[emailprotected]

constraints. These loading behaviors suggest that even smallexcursionscan strain elements beyond structural failure. Thus,these postural tests ofkinesis, along with the robusticity of othercranial features, suggest thatthe skull of Tyrannosaurus wasfunctionally akinetic. Anat Rec, 00:000–000, 2019. © 2019 WileyPeriodicals, Inc.

Key words: cranial kinesis; jaw muscles; skull;Tyrannosaurus;bird; lizard; finite element model

Vertebrate feeding adaptations resulted in a diversity ofcranialstructures and functions, many of which led tochanges in palatalfunctional morphology. Despite thesemodifications, many reptilesmaintain a series of linkagesbetween the palate and braincase thatoften permit cranialkinesis. Cranial kinesis manifests as aspectrum of palatalmotions among lineages (Versluys, 1910; Bock,1964, 1999;Zusi, 1984, 1993; Gussekloo, 2000; Holliday andWitmer,2007). Because many of the joints linking the palate tothebraincase remain unfused, the skulls of many extinct spe-cies ofdinosaurs, crocodylomorphs, and other fossil reptileshave also beenhypothesized to have had various forms ofcranial kinesis (Rayfield,2005a; Holliday and Witmer,2007). For example, Tyrannosaurus rex,which hasplesiomorphic, ball and socket-shaped palatobasal andoticjoints, has been hypothesized by different authors tohavepossessed one of several forms of cranial kinesis (Molnar,1998;Rayfield, 2004; Larsson, 2008). A functional paradoxremains: why domature individuals of one of the world’smost forceful biting,osteophagus animals (Gignac andErickson, 2017) ever known maintainflexible joints whenthe hardest biting taxa of other terrestriallineages(e.g., crocodile, tiger, and hyena; Erickson et al., 2003;Wroeet al., 2005; Tseng and Binder, 2010) suture theircranialelements to form rigid skulls?

Kinetic competency of Tyrannosaurus has beenexplored previouslyand interpretations and methodsvary. Osborn (1912) first remarkedon the seeminglymobile nature of particular condylar joints butsuggestedthe surrounding bones limited any particular movement.Alsociting the condylar otic joint between the quadrateand squamosal,Molnar (1991, 1998) instead inferredlimited streptostyly (rotationof the quadrate about theotic joint) in Tyrannosaurus. Rayfield(2004), 2005a, b)inferred numerous sutural and condylar jointswithin thepalate and face of Allosaurus, Tyrannosaurus, andothertheropods to be capable of movement following finite ele-mentanalysis (FEA) of patterns of stresses. Larsson(2008) extendeddiscussion of Tyrannosaurus kinesis andstreptostyly with newdetails on the condylar nature ofthe palatobasal joint. Conversely,Holliday and Witmer(2007) described Tyrannosaurus and manynonaviandinosaurs as being partially kinetically competent,mean-ing that these taxa possess patent otic and palatobasaljointsas well as protractor musculature necessary tomediate powered(driven by muscle force rather thanbeing passive) kinesis. However,these taxa lack permis-sive linkages in the skull that would enablegross move-ments of the palate or face. Regardless, thesehypotheseshave yet to be fully tested in a phylogeneticfunctionalcontext using 3D modeling techniques.

Permissive linkages in lizards and birds result fromtheelimination of bones comprising the postorbital and

temporal bars, development of craniofacial hinge joints(flex-ion zones), and the elimination of the epipterygoid inbirds.These morphological changes manifest differently in thesetwoclades. Species of lizards exhibit a diversity of oftencoupledkinetic behaviors including, but not limited tostreptostyly,mediolateral motion (MLM) at the palatobasaljoint, and mesokinesis(flexion of the facial skeleton aboutthe frontoparietal joint;Rieppel, 1978; Smith and Hylander,1985; Herrel et al., 2000;Metzger, 2002, Evans, 2003). Manyspecies of birds, including ducks,parrots, and many neo-avians also employ streptostyly andprokinesis (elevation ofthe beak at the craniofacial hinge) as wellas concomitantfore–aft motion (FAM) about the palatobasal joint(Hofer,1950; Burton, 1974a, 1974b; Hoese and Westneat, 1996;Boutand Zweers, 2001; Dawson et al., 2011). Although thepalatobasaljoint and likely other palatocranial joints areunsutured, they lackmobility in many species of lepidosaurs(Metzger, 2002; Curtis etal., 2010; Jones et al., 2011), birds(Zusi, 1993; Gussekloo, 2005),and nonavian dinosaurs(Holliday and Witmer, 2007).

We use two species of extant, kinetically competent rep-tiles,tokay geckos (Gekko gecko), and grey parrots (Psittacuserithacus),to model, frame, and test hypotheses of function inthe extinctreptile species T. rex. Tokay geckos eliminated theupper and lowertemporal bars of their skulls, have large jawmuscles relative totheir body size, strut-like pterygoid andepipterygoid bones, andpalates connected to the brain-case through synchondrodial(cartilaginous without asynovial cavity) otic and diarthrodial(cartilaginous witha synovial cavity) palatobasal joints (Rieppel,1984;Herrel et al., 2007; Payne et al., 2011; Mezzasalma etal.,2014; Daza et al., 2015). Herrel et al. (1999, 2000)andMontuelle and Williams (2015) found Gekko to exhibitacombination of mediolateral and fore–aft streptostyly,long axisrotation of the palate, and bending of the palateabout hypokinetic(palatine-pterygoid suture) joints andthe mesokinetic hinge.Because the long axis rotation ofthe palate requires it to alsoswing mediolaterally, wemodeled the palate accordingly in amediolateral move-ment, as internal palatal element kinematicsremainsundescribed.

Grey parrots lack upper temporal bars and epipterygoids,havestrut-like lower temporal bars, pterygoids, and quad-rates, andarticulate the palate to the braincase viadiarthrodial otic andanalogous “palatobasal” joints betweenthe palate and parasphenoidrostrum (Bailleul and Holliday,unpublished data). Parrots employprokinesis (Zusi, 1967) inwhich FAM of the palate occurs at theotic and palatobasaljoints to elevate the beak about thecraniofacial hinge. Thesemovements are facilitated by largeprotractor and adductormuscles (Hofer, 1949, 1950), including theneomorphicpsittacid pseudomasseter and ethmomandibularismuscles(Tokita, 2003, 2004; Carril et al., 2015).

COST ET AL.2

Given previous research (Molnar, 1991, 1998; Carr,1999;Rayfield, 2004, 2005a; Snively et al., 2006; Molnar,2008;Holliday, 2009; Bates and Falkingham, 2012; GignacandErickson, 2017), we know enough about Tyrannosaurus cra-nialanatomy to rigorously explore hypotheses of cranialbehavior andfunction and examine the kinetic capacity ofthese forcefully bitingancient predators. The skulls ofTyrannosaurus and many othernonavian theropod dino-saurs maintain both upper and lower temporalbars,epipterygoids, dorsoventrally thin palatal elements, androbustscarf joints between elements of the dermatocraniumand palate(Molnar, 1991, 1998; Carr, 1999; Snively et al.,2006), all of whichare features considered to limit cranialmobility (Holliday andWitmer, 2007). Regardless, Molnar(1991), Rayfield (2005a), andLarsson (2008) hypothesizedFAM via streptostyly in Tyrannosaurusbased on the balland socket-shaped (i.e., condylar) otic andpalatobasal joints.These joints are spanned by large adductormuscles laterally(Molnar, 2008; Holliday, 2009; Bates andFalkingham, 2012;Gignac and Erickson, 2017) as well as large,tendinous pro-tractor muscles medially (Holliday and Witmer,2007;Holliday, 2009). Here we test the performance ofTyranno-saurus finite element models (FEMs) compared to thoseofknown, kinetically competent Gekko and Psittacusmodels.Accurately modeled jaw muscle loads and jointarticulationswere integrated into each model in akinetic (neutral),MLM(MLM of the palate about the otic and palatobasal joints),andFAM (FAM about the otic and palatobasal joints pos-tures). Strainsof the models were analyzed qualitativelyand quantitatively todetermine the optimal and most likelyposture of the Tyrannosauruspalate. A better understand-ing of the loading environment of theskull and kinetic com-petency of extinct dinosaur species like T.rex illuminatesvertebrate adaptations for feeding, the evolutionarydevelop-ment of cranial joints, and the origins of avian-stylecranialkinesis from nonavian theropod dinosaurs.

METHODS

Finite element modeling is a common approach used toevaluatebiomechanical performance of dinosaur skulls(Rayfield, 2004; Moazenet al., 2009; Lautenschlager et al.,2013; Lautenschlager, 2015).Although many studies employmodels of taxa for specific instancesof feeding behaviors,few explore changes in gape and otherexcursions of cranialelements during feeding cycles (e.g., Moazenet al., 2008;Lautenschlager, 2015). Similarly, here we test theperfor-mance of several different kinetic postures across asampleof taxa. The heads of P. erithacus (MUVC AV042) and

G. gecko (MUVC LI044) were scanned in a SiemensINVEON SPECT/CT(VA Biomolecular Imaging Center,Columbia, MO) with voxel sizes of63.4 and 92.1 μm, respec-tively. A 1/6-scale model of T. rex (BHI3033) was scanned ina General Electric LightSpeed Ultra MultisliceCT scanner(voxel size of 625 μm, 120 kV, 170 mA,OhioHealthO’Bleness Memorial Hospital, Athens, OH). CT dataweresegmented in Avizo Lite 9 (FEI Company, Hillsboro, OR).

Bones of the palate and the rostrum (in Gekko andPsittacus) weresegmented separately from bones of the neu-rocranium anddermatocranium in each model, allowing forpostures to be modified(See Table 1 for segmented ele-ments). Stereolithographical models(STL files) were gener-ated from segmentation and were cleaned andrepositionedin anatomical postures of hypothesized kinesis inGeomagic(3D Systems, Rock Hills, SC). Skeletal elements werejoinedtogether prior to construction as FEMs. FEMs werecon-structed in Strand7 (Strand7 Pty. Ltd., Sydney, Australia)usingfour point tetrahedral elements. Joints between thepalate andbraincase, and kinetic hinges in Gekko andPsittacus, were thenbroken to simulate mobile joints. Con-nections between the now openelements were linked to oneanother with beams assigned theproperties of joint mate-rials. Beam number within the joint areaswas dependent onthe size of the articular surfaces of bones formingthe joints.

Postural kinetic competency (PKC) models were con-structed usingthe BoneLoad workflow (Grosse et al., 2007;Davis et al., 2010;Sellers et al., 2017, Fig. 1). BoneLoaddistrib-utes theestimatedmuscle forces in each posturalmodel acrossthe attachmentsites of muscles which are in turn used to loadthe model. Jointmaterials were modeled using links andbeams to emulate differentarticular tissuematerial properties(e.g., suture/ligament, hyalinecartage, bone). This approachdiffers from other models thatincluded ligamentous connec-tions modeled as continuous layers ofbrick elements with dif-ferent material properties to emulatecranial sutures (Moazenet al., 2009; Reed et al., 2011; Curtis etal., 2013; Jones et al.,2017). In general, the models built hereusing linkages aremore yielding than previous models. Greaterflexibility in ourmodeled joints should allow for betterdissipation of forces inbiologically accurate biomechanicalenvironments than fullyfusedFEMs (e.g.,Moazen et al., 2009; Joneset al., 2011).

Modelswere built in three positions, which approximatedif-ferent kinetic motions: akinesis (hereafter referred to astheneutral posture), FAM, and MLM. Each model was con-structed toexhibit a neutral posture by opening the mandibleto a 20-degreesgape without shifting either the quadrate orpalate. A postureresulting from FAM (prokinesis

TABLE 1. Segmented skeletal elements, constructed joints, andmobile elements represented in each taxon inthis study

Taxon Elements segmented Joints modeledMobile elementsin finalmodel

Gekko Palatine, pterygoid, rostrum, quadrate,mandible,neuro/dermatocranium

Palatobasal, otic,frontoparietal hinge

Rostrum, palatine, pterygoid,epipterygoid, quadrate

Tyrannosaurus Palatine, pterygoid, rostrum,epipterygoid,ectopterygoid, vomer, quadrate,mandible,neuro/dermatocranium

Palatobasal, otic Pterygoid, epipterygoid,ectopterygoid,quadrate

Psittacus Palatine, pterygoid, jugal, rostrum,quadrate,mandible, neuro/dermatocranium

Palatobasal, otic,craniofacial hinge

Rostrum, palatine, pterygoid,quadrate, jugal

Mobile elements are defined as elements of the palate that arecapable of moving as a result of being joined to the cranium byjointand sutural materials only in the finite element model. Theseentities are consistent across postures within each taxon.

BIOMECHANICS AND CRANIAL KINESIS IN T. REX 3

Fig. 1. Postural Kinetic Competency modeling workflow followedin this study. Microcomputed Tomography data (A) are segmented tobuild 3Dmodels by segmenting individual bones (or bony segments;e.g., beak, braincase) as separate elements (B). 3D models arereconstructed in kineticpostures with individual elementsrealistically articulated (C). The resulting models are importedinto Strand7 as stereolithographical files and aremeshed using4-node tetrahedra (D). Meshed models are prepared for finiteelement analysis (FEA) by mapping muscles on the surfaceandeliminating tetrahedra in joint areas (E1). Beams are attachedto the facing sides of joint surfaces and are given materialproperties reflectingcapsular or sutural ligaments (E2). Theresulting finite element model is loaded using distributed muscleforces via the BoneLoad MATLAB programand Strand7 FEA software(F).

COST ET AL.4

+ streptostyly), and a posture resulting from MLM(streptostyly +hypokinesis + mesokinesis) created by initiallyshifting thequadrate at the otic joint 5-degrees rostrocaudallyand 5-degreesmedially (Fig. 2). Previous studies detectedquadrate rotationsbetween 5 and 10-degrees in extanttaxa (Hoese and Westneat, 1996;Herrel et al., 1999; Metzger,2002; Montuelle and Williams, 2015;Claes et al., 2016). Amovement of 5-degrees, therefore, is aconservative estimate ofstreptostylic quadratemovement.

To model soft-tissue attachment sites, models were impo-rted toStrand7 and material properties assigned to specificregions of themodels. All models were assigned isotropicmaterials duringconstruction and identical bone properties(E = 13.65 GPasensuRayfield, 2011; ν = 0.3). Articulated pal-atobasal and oticjoints, the frontoparietal joint, and the

craniofacial hinge were built by eliminating bricks in thejointspace and linking portions of the model to one anotherusingstructural beams attached to the facing sides ofthe joints. Otherpotentially mobile joints, such as theepipterygoid-pterygoid in thegecko, or the quadrate-quadratojugal joint and palatine-maxillaryjoint in the par-rot, were left fused to focus on strains atprimary locations ofkinesis in the palate and quadrate. Joints werereconstructedin Psittacus and Gekko using beam propertiessimulating ratcranial sutures (E = 2.35 MPa, ν = 0.3; Chien et al.,2008).Tyrannosaurus joints were reconstructed using beamproper-ties simulating canine patellar tendon (E = 4.57 MPa,ν =0.3; Haut et al., 1992). Joint materials of different-sizedanimalswere used in an attempt to mimic joints of closerphysiological sizein the taxa of interest. Sensitivity analysis

Fig. 2. Comparisons of postures using overlays of each of thethree models: Left, Gekko gecko; Middle, Tyrannosaurus rex; Right,Psittacuserithacus showing postural change in left lateral (A) andventral (B) views and in rostral (C), lateral, (D), and ventral (E)views showing overlaidpostural configurations used to model kineticcompetency. Postures are overlaid using the jaw joint as the originof the axes. Neutral models arerepresented in gray, FAM models inorange, and MLM models in blue. Angles of rotation/translation atthe otic joint are shown using color-codedangle measurements in (A)and (B).

BIOMECHANICS AND CRANIAL KINESIS IN T. REX 5

was conducted using the sutural materials of the Tyranno-saurusmodel in Psittacus to determine the role these valuesmay haveplayed in the analysis.

Muscle attachment sites were mapped onto models usinginformationfrom dissection, observation, and the literature(Hofer, 1950;Abdala and Moro, 1996; Herrel et al., 1999;

Fig. 3. Mapped attachments of jaw muscles used to load finiteelement models of (A) Gekko gecko; (B) Psittacus erithacus, and(C)Tyrannosaurus rex in Top: left oblique; Middle: left lateral;and Bottom: ventral views for each taxon. Muscle map colors followsame palate andhypotheses of homology as Holliday (2009).

COST ET AL.6

Tokita, 2004; Holliday, 2009; Carril et al., 2015; Fig. 3).Ana-tomical details for muscle fiber length and pennation offibersrelative to central axes were measured in Gekko andPsittacus andcompared to the literature (e.g., Herrel et al.,1999; Hieronymus,2006; Carril et al., 2015; Table 2) to esti-mate physiologicalcross-sectional area (PCSA) using equa-tion (1) (Sacks and Roy,1982):

PCSA=VMlf

× cos θð Þ, ð1Þ

where VM is the muscle volume, lf is the fiber length, andθ isthe pennation angle of the muscle.

The pennation angles of Tyrannosaurus jawmuscles wereestimatedto fall within known pennation angles of alligator,bird, and lizardjawmuscles based on visible osteological cor-relates suggestive oftendon attachments as well as coarsephylogenetic bracketing. Hence,muscles with pennateextant homologs and informative osteologicalcorrelateswere conservatively modeled as more pennate thanothermuscles. For example, m. adductor mandibulaeexternusprofundus, which is the large muscle that attaches tothedorsotemporal fossa and is relatively pennate in mostverte-brates, was modeled with 20-degrees pennation angle,whereasm. adductor mandibulae posterior, which attachesto the body of thequadrate, was modeled as being largelyparallel fibered (5-degreespennation angle) given the lack ofclear tendinous scars on thequadrate in Tyrannosaurus andits relatively simple architecture inbirds, non-crocodyliformsuchians (Holliday and Witmer, 2009), andarchosaur out-groups (e.g., lizards; Haas, 1973; Holliday andWitmer,2007; Holliday, 2009). All muscles were modeled to havefiberlengths that were two-third the length of the muscleitself, whichis also generally conservative across vertebrates(Bates andFalkingham, 2018).

To further justify our phylogenetically bracketed esti-mates ofjaw muscle architecture in Tyrannosaurus, wedeveloped a sensitivityanalysis to explore the effects of fiberlength and pennation onPCSA. Because fiber length andpennation angle are the physiologicalparameters that mod-ulate the force predicted from anatomicalcross-sectionalarea for a given muscular geometry, PCSA and, byexten-sion, muscle force is a function of fiber length andpennationalone. In theory, pennation can vary from 0-degreesasymp-totically to 90-degrees, and fiber length can vary from1asymptotically to 0. To explore the parameter space of pen-nationand fiber length, we calculated the PCSA of each jawmuscle ofTyrannosaurus for 100 values of pennation rang-ing from 0 to89.1-degrees and 100 values of fiber lengthranging from 0.01 to 1,for a total of 10,000 combinations permuscle. This range capturesthe full potential range of thefactors that contribute to PCSA inTyrannosaurus.

Muscle volume, fiber architecture (Table 2), andmuscleattachment centroids were then used to calculate 3Dresul-tants of jaw muscles as well as ultimately distributedloadson the FEM sensu Sellers et al. (2017) using equation (2):

FM=PCSA×Tspecific, ð2Þ

where Tspecific is specific tension (Porro et al., 2011), andFMis muscle force. The resultant muscle force and muscleattachmentcentroids serve as muscle parameter input inthe BoneLoad workflow.Models were all constrained atbilateral, caudal bite points. Allmodels are constrained bysingle nodes at the mandibular condyle ofthe quadrate in

TABLE

2.Musc

lepar

ameter

suse

dto

estimat

ephys

iologica

lcr

oss-se

ctional

area

san

djaw

musc

leforc

euse

din

finiteelem

entmod

els

mAMES

mAMEM

mAMEP

mAMP

mPSTs

mPSTp

mPTd

mPTv

mPPT

mEM

mPM

mLPT

mDM

Fiber leng

th(cm)

Gekko

1.3

1.1

0.8

1.3

0.8

0.8

0.8

0.4

0.8

1T.rex

4652

5728

5541

3228

106

25Psittac

us

1.6

1.5

0.3

1.4

1.2

1.0

1.0

1.6

2.1

0.7

Pen

nation

angle(θ)

Gekko

200

50

015

155

55

T.rex

00

015

1010

1015

150

5Psittac

us

2020

06.66

14.54

4.09

02.57

05.52

Muscle

volume(cm

3)

Gekko

0.44

50.18

00.46

30.14

10.12

80.09

30.39

10.07

20.02

80.06

6T.rex

20,971

17,729

11,914

37,120

7,79

22,66

840

,106

8,56

22,18

754

58,98

1Psittac

us

1.07

0.07

00.00

60.02

62.63

1.54

0.03

60.09

81.24

0.08

4Force

(N)

Gekko

9.25

4.58

16.84

3.11

4.28

3.44

13.77

4.49

1.12

1.96

T.rex

3,34

39,84

16,63

539

,859

4,20

91,86

534

,816

8,82

05,48

93,18

010

,206

Psittac

us

21.17

13.41

6.90

6.20

63.11

47.38

11.38

19.99

17.59

35.37

Abb

reviations:

mAMES,m.ad

ductor

man

dibu

laeex

tern

ussu

perfi

cialis;mAMEM,m.ad

ductor

man

dibu

laeex

tern

usmed

ialis;

mAMEP,m.ad

ductor

man

dibu

lae

extern

uspr

ofund

us;

mAMP,m.ad

ductor

man

dibu

laepo

sterior;

mDM,m.de

pressorman

dibu

lae;

mEM,m.ethm

oman

dibu

laris;

mPM,m.ps

eudo

mas

seter;

mPSTs,

m.ps

eudo

tempo

ralissu

perfi

cialis;mPSTp,

m.ps

eudo

tempo

ralispr

ofun

dus;

mPTd,

m.pteryg

oide

usdo

rsalis;mPTv,

m.p

terygo

ideu

sve

ntralis;

mPPT,m.pr

otractor

pteryg

oide

us;m

LPT,m

.lev

ator

pteryg

oide

us.

BIOMECHANICS AND CRANIAL KINESIS IN T. REX 7

all planes of movement and at a series of occipital attach-mentsnear the approximate center of muscle attachments,sensu Snively andRussell (2007). Muscles were activatedsimultaneously at maximalforce in each model similar tothe methods used by Bates andFalkingham (2012) to esti-mate the bite force of Tyrannosaurus.Muscle activation pat-terns were also addressed during post hoctesting. Straindata were analyzed across the cranium and withinskeletalelements to describe kinetic competency and thelikelihoodof kinetic postures in the analyzed taxa.Tetrahedral(“brick”) strains were sampled in specific regions ofthe skel-etal elements of the palate. Surface tetrahedrals inregionsof interest were selected as pools to sample fromwhichincluded anterior, middle, and caudal portions of thepala-tine and pterygoid bones. The quadrate was sampled inotic,middle, and ventral regions because this bone isorientedperpendicularly to the palatine and pterygoid bones.Theregions were then subsampled randomly using a randomnumbergenerator (built inMicrosoft Excel) to assign 50 rowsof data to beincluded in the quantitative analyses.

We expected neutral posture models to exhibit a baselevel ofstrain in the palatal elements. Postural kinetic com-petenciesexhibiting strain in the palates higher than theneutral posturemodels represent less likely loading condi-tions. Conversely,models exhibiting strain in the palateslower than the neutral PKCswere considered acceptable,more likely, anatomical configurations.Although the localeffects of strain on bone tissue growth andresorption arecomplicated (e.g., Frost, 1987; Martin, 2000; HerringandOchareon, 2005), Curtis et al. (2011), using FEA for bonestrain,as we are here, hypothesized that cranial elements inSphenodon andother vertebrates assumed shapes that werebest adapted to theiraverage loading environments as ameans of optimizing strain acrossthe entire skull. Thus,although higher and lower strains are notfundamentally“bad” or “good,” we can expect behaviors such as jointexcur-sions that elicit exceptionally higher strains in elementstobe less optimal than other behaviors. We define structuralfailurein our models as strains that exceed 6,000 micro-strain (με)because this value is contained within ranges ofthe estimatedstrain of bone failure (e.g., Reilly and Currey,1999; Campbell etal., 2016).

RESULTSMuscle and Bite Forces in Extant Species

Modeled Psittacus bite force (61.78N [rostral biteposi-tion]–96.44N [caudal bite position]) was greater thanthe16.74N reported for Monk Parakeets (Myiopsittamonachus)estimated using PCSA by Carril et al. (2015) asexpectedgiven that the skull of P. erithacus is about twiceaslarge. Bite forces in our Gekko models (11.27N [rostralbiteposition]–18.53N [caudal bite position]) were nearranges reportedby both Anderson et al. (2008; 10.1N–19.1N) and Herrel et al.(2007; 10.78N–16.97N) usingbite force meters.

Sensitivity Analysis of Muscle Forces inTyrannosaurus

The distribution of PCSA values of our sensitivity analysisoftheoretical muscle architecture is represented using aheatmap (Fig.4). Although pennation angle and fiber lengthare the two parameterson which PCSA depends, there is afunctional relationship betweenpennation and fiber length in

which fiber length has a stronger effect on PCSA than pen-nationangle. For example, when we hold fiber length con-stant (anyhorizontal line on Fig. 4), larger values ofPCSA are associatedwith low pennation angle, and thelargest value was 64 times thesmallest value (approxi-mately equal to cos−1 (89.1-degrees)). Whenwe hold pen-nation angle constant (any vertical line on Fig. 4),largervalues of PCSA are associated with shorter fiber length,andthe largest value was 100 times larger than thesmallest value(equal to 0.01−1). This and the construc-tion of the PCSA equationshow that the effect of fiberlength is greater than that ofpennation angle on PCSA(sensu Gans and De Vree, 1987).

Upon this heatmap (Fig. 4), we project the regression lineofBates and Falkingham (2018), which compiled over 1,000measuredvertebrate muscles, along with plots of Bates andFalkingham’s(2012), Gignac and Erickson’s (2017), and ourphylogeneticallybracketed Tyrannosaurus muscle architec-ture data. Bates andFalkingham’s (2012) muscle force esti-mates used combinations ofpennation angles of 0–20-degreesand fiber lengths of 0.1–0.4 timesmuscle length (i.e., 1/10–2/5times muscle length), which resultedin forces below theregression line, thus corresponding to higherforces. Gignacand Erickson (2017) modeled muscles with 0-degreespen-nation and a fiber length equal tomuscle length, thecombina-tion of which yields the lowest possible PCSA. ThePCSAestimates in Tyrannosaurus from the present study fall closetothe regression line of all known vertebrate PCSAs publi-shed byBates and Falkingham (2018), suggesting that thevalues we used areclose to predictions from extant taxa andour bite force estimatesare reasonable.

Fig. 4. The relationship between fiber length, pennation angle,andforce in muscle physiology and its application toreconstructingfunction in fossil taxa using recent case studies.PCSA is a function ofpennation angle and fiber length and is mappedas a heatmap withcontour lines. We replotted the regression linefrom Bates andFalkingham, 2018 (labeled “B&F 2018”) showing theclassic predictionthat increasing pennation in order to accommodateshorter musclefibers increases PCSA. PCSA values from recentstudies, Gignac andErickson, 2017 (labeled “G&E 2017”) andBates and Falkingham, 2018,of Tyrannosaurus cranial biomechanicsare also plotted to showsimilarities in approaches.

COST ET AL.8

Bite forces in our Tyrannosaurus model (35,365N–63,492N)extensively overlap with the range reported byBates and Falkingham(2012; 18,065N–57,158N) and areabout twice the magnitude predictedby Gignac andErickson (2017; 8,526–34,522N). These differencesbetweenour results and those of Gignac and Erickson (2017)arelikely due to our inclusion of pennate jaw muscles,whereas thelatter authors modeled all jaw muscles asparallel fibered.

Analyses of Strain Patterns

Strain differences were found among the Gekko modelswith respectto the bones, sampling region, and posture.The neutral Gekko model(Fig. 5A; Supporting InformationVideos 1–6:https://players.brightcove.net/656326989001/mrOxISgynX_default/index.html?videoId=6058428214001)exhibitedhigher strains in the pterygoid than those in thequadrate or thepalatine. The ventral portion of theepipterygoid was extremelystrained around the joint withthe pterygoid, which may be anartifact of the modelingprocess wherein the epipterygoid andpterygoid werefused together. The body of the pterygoid, however,isstrained across its length, representing a higherstrainconcentration than in any of the other elements of thepal-ate (Fig. 5A). The FAM Gekko model reveals high strainsin thequadrate, and pterygoid suggesting that this is notan optimalposture (Fig. 5B). However, the MLM Gekkomodel (Fig. 5C) exhibitslow strains in the elements of thepalate, suggesting that the MLMmodel is a more optimalposture, along with the neutral posture. Theotic processretains slightly higher strains than the other portionsofthe quadrate in the MLM model. The pterygoid still pos-sesseslocalized higher strains (Fig. 5C), though these arelower comparedto the pterygoid in the FAM model(Fig. 5B).

The MLM model of Gekko (Fig. 6) possessed lowermedian strainvalues (1,731 με) than those of neutral(2,277 με) or FAM (2,714 με)postures (Table 3). The low-est strain values of Gekko are found inthe palatines.However, strains were lowest in different portions ofthepalatine in each of the postural models of Gekko. The ven-tralportion of the quadrate was most strained in theFAM Gekko model(6,322 με) and least strained in theneutral posture (1,767 με).Median strain values of wholeelements are shown for all taxa inTable 4. The otic andmiddle regions of the quadrate possessedidentical strainprofiles in all three postures, despite differencesin rota-tion at the otic joint. Similarly, the pterygoid exhibitedaconserved pattern of caudal to rostral strain decreaseacross allmodels. The caudal to rostral pattern isobserved in the FAM posturein the palatines; however,this is reversed in the neutral posture.In the MLM pos-ture, the rostral region of the palatine wassubjected tomore strain than the middle region but the caudalregionwas subjected to the highest strain.

The Psittacus models also experienced differing strainsin thebones, sampling region, and between postures. Inthe neutralPsittacus model (Fig. 5D; Supporting Informa-tion Videos 7–12:https://players.brightcove.net/656326989001/mrOxISgynX_default/index.html?videoId=6058434297001),the quadrate and pterygoid experienced highstrain relative to otherparts of the cranium (Fig. 5D).The palatine, postorbital process,and the interorbital

septum experienced low strains in this posture despiteserving asmuscle attachment sites (Fig. 5D). The FAMPsittacus model revealedhigh strains on the rostralaspects of many of the kinetic palatalelements (Fig. 5E).In the MLM Psittacus model (Fig. 5F), strainsare notice-ably higher at the otic process of the quadrate, thepost-orbital process, and the middle of the palatine comparedto theFAM model (Fig. 5D). Strain in the pterygoid isrelatively uniformthroughout the bone compared to thatseen in the palatine.

In Psittacus (Fig. 7), the MLM model exhibited higheroverallmedian strain of the palate (753 με) than neutral(619 με) or FAM(543 με) models (Table 3). Strain values ofthe FAMmodel were thelowest, as expected by observationsof feeding behaviors. The MLMmodel possessed higheroverall strains in the palatine andpterygoid, maintainingthe same trend as the other Psittacuspostures. Pterygoidstrains in the MLM model increased from themiddle andcaudal regions to the rostral region whereas in theneutralmodel strain steadily decreased moving rostrally. IntheFAMmodel, peak strains were found in the caudal region ofthepterygoid, however, the middle region appeared to pos-sessdecreased strain. The strain again increased in the ros-tralsampling region. In all three postures strain decreasedfrom caudalto rostral in the palatines. The otic process ofthe quadratepossessed the highest strain values across allpostural models ofPsittacus.

Strain differences found among theTyrannosaurusmodel’sbones,sampling regions, and between postures werehighlighted by areas ofstructural failure. The neutral Tyran-nosaurusmodel (Fig. 5;Supporting InformationVideos13–18:https://players.brightcove.net/656326989001/mrOxISgynX_default/index.html?videoId=6058438903001)exhibited lowstrain throughout the palate with the exception ofmodelingartifacts at joints of the palate. The caudal portion ofthe pter-ygoid was weakly strained whereas the body of thequadrateexperienced higher strains in the neutral posture (Fig.5G).The palatine and pterygoid exhibited higher strains acrosstheirrostral bodies and the quadrate showed high strainvalues acrosspterygoid and otic processes (Fig. 5G). Thejoints of the FAMTyrannosaurus model (Fig. 5H) wereincreasingly strained,particularly at isthmuses and articula-tions with the cranium.Lower overall strain was foundthroughout the FAM model, but areasof failure remainedprevalent across the palate (Fig. 5H). Thepalatine of theFAMmodel exhibited lower overall strain than theother ele-ments in the palate (Fig. 5H). The MLM Tyrannosaurusmodelfound the otic joint to be highly strained, and the bod-ies of thequadrate, pterygoid, and palatine bones to all behighly strained(Fig. 5I). High strains also propagatedthroughout the facialskeleton in the MLM model (Fig. 5I).Failures in the MLM model wereobserved throughout thepterygoid and the dorsal ridge of thequadrate body (Fig. 5I).Across the Tyrannosaurus models, the lowertemporal barexperiences high strains near the quadratojugal-jugalsuturethat approach or exceed levels of structural failure(Fig.5G–I).

Tyrannosaurus (Fig. 8) exhibited different quantitativestrainprofiles across the three postural models. The MLMmodel exhibitedthe highest median strain values (1,768 με) ofthe three posturalmodels (neutral 1,542 με; FAM 1259 με; seeTable 3). Across allthree postures, the quadrate was similarlystrained overall, thoughthe middle region was more variable(Fig. 8). The middle region ofinterest was subjected to morestrain than the ventral or oticregions in all postures, but

BIOMECHANICS AND CRANIAL KINESIS IN T. REX 9

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Fig. 5. Heat maps depicting Von Mises strains in Gekko gecko(A–C), Psittacus erithacus (D–F), and Tyrannosaurus rex (G–I) inLeft, Neutral;Middle, FAM; and Right, MLM postures of each taxon.Models are shown in left oblique (top), left lateral (middle), andventral (bottom) views. Heatmaps show strains in postural modelswith all muscles fired simultaneously. Areas of high strain appearin warmer colors; white areas are beyondthe scales presented withthe models. Cooler colors depict areas of low strain concentration.Bones of the left lateral dermatocranium (i.e., portionsof themaxilla, jugal, lacrimal, postorbital, and quadratojugal bones)have been removed on heat maps of T. rex to show details of thepalate,although all bones were in place for the analysis.

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especially in the MLM posture (Fig. 8). The neutralpostureexhibited similar ventral and otic strains (1,540 and 1,459με,respectively); however, the otic strains were noticeablyhigherin both the MLM and FAM models (1,980 and 2,029με,respectively). The pterygoid in the MLM posture ofTyran-nosaurus was subjected to greater strain than eithertheneutral or FAM postures. The rostral region of the ptery-goidwas subjected to the least strain by large margins in

both the neutral and MLM models. The most appreciabledifferencebetween models, however, can be seen withinthe caudal portions ofthe three models (Fig. 8). A slightincrease was observed frommiddle to rostral in the FAMmodel. In all three postures, thepalatine exhibited thehighest median strains in the rostral portionwith similarstrain patterns in the caudal and middle aspects aswell.The caudal portion of the palatine was subjected to low

Fig. 6. Strains of regions of interest in the palatal elementsof Gekko gecko. Regions of interest and scatter plots showingindividual samplepoints as well as median strains (color-coded bysampling region) are represented. Otic, middle, and ventral regionscorrespond to sampling of thequadrate whereas rostral, middle, andcaudal regions correspond to sampling areas of the palatine andpterygoid. Each sampling region consists of50 tetrahedra sampledrandomly from the surface of the skeletal element. Horizontal linesrepresenting the median value of the neutral posture areshown inred in each region of the palatal bones to facilitate comparisonacross postures.

BIOMECHANICS AND CRANIAL KINESIS IN T. REX 11

median and overall strains in all three models, but thisisespecially so in the FAMmodel (Fig. 8).

DISCUSSIONTyrannosaurus Was Functionally Akinetic

By incorporating cranial joint articular tissues, distrib-utedmuscle loads, and posture analysis to infer cranialperformance inT. rex, we have gained a nuanced under-standing of the biomechanicsof the skull. We accuratelyestimated the biomechanical environmentof Gekko andPsittacus using PKC methods and achievedlifelikeresults prior to modeling T. rex. Rotation of thequadrate

5-degrees rostrocaudally and mediolaterally was suffi-cient toaffect the rostral elements of the palate and thefacial skeletonsuch that lifelike fore–aft and MLMs werereflected in the models ofboth extant taxa. Functionallyacceptable ranges of strain wereobserved in models ofFAM in Psittacus and MLM in Gekko. Equallyimportant,MLM in Psittacus and FAM in Gekko resulted in failuresatjoints, within individual bones, and across the palate.Thus, theloading behavior of the Tyrannosaurus modelalso performs withacceptable accuracy with respect tothe anatomical potential of theanimal. Using these find-ings, we conclude that Tyrannosaurus wasfunctionallyakinetic. Although hypotheses of fore–aft palatalmotionin Tyrannosaurus are more supported compared to thoseofmediolateral palatal motion, the linkages surroundingthe otic jointimpede fore–aft excursions of the quadrate,and the loading that thepalate and craniofacial skeletonexperience during bites suggestspowered, fore–aft kine-sis is extremely unlikely. Like paleognaths(Gussekloo,2005), many iguanians and other lepidosaurs (Jonesetal., 2017), many dinosaurs (Holliday and Witmer,2007), stemcrocodylomorphs (Pol et al., 2013), andnumerous diapsid species,including Tyrannosaurus,remain akinetic despite possessingunsutured otic andpalatobasal joints.

Cranial kinesis in Tyrannosaurus has been debatedsince shortlyafter the initial description of the taxon.Osborn (1912) recognizedthe morphological limitations ofkinesis in Tyrannosaurus, initiallydescribing the oticjoint as immobilized by the pterygoid,quadratojugal, andsquamosal via sutures between the quadrate andsur-rounding bones. Osborn’s description of the otic jointwasrefuted by Molnar (1991) who recognized that, althoughthe oticjoint was surrounded by sutured elements, thejoint itself wassmooth and saddle shaped which in turnled to subsequent functionalanalyses of otic joint kinesisby Molnar (1991, 1998), Rayfield(2005a), and Larsson(2008). Larsson (2008) supported inferences ofpropalinal(fore–aft) movement of the Tyrannosaurus palate,statingthat movement was possible due to osteologicalanatomy,kinetically competent joints throughout the palate,andstreptostylic movement of the quadrate. Molnar (1991,1998)described streptostylic movement as well, statingthat the oticjoint could allow for “swings in several direc-tions” (1991, p.163) and was capable of resisting forces inmultiple directions.Although streptostyly and propalinalpalatal movements, as a result,appear reasonable in adisarticulated specimen, the rigidity of thefacial skeleton,congruency of the otic joint, and the similaritiesbetweenthe neutral and FAM models suggest that any movementof thepalate was incidental and potentially injurious toTyrannosaurus.Moreover, the craniofacial skeleton ofadult tyrannosaurs hasnumerous bony features that defytranslational movements of thepalate including the fol-lowing: rigid, unbendable bones, asecondary palate builtby massive, co-sutured maxillae, and heavilyinterdigi-tated sutural and scarf joints like thefrontonasal,circummaxillary, and temporal joints (Carr, 1999;Snivelyet al., 2006). These lines of evidence all suggestTyranno-saurus was functionally akinetic, despitepossessingunsutured otic and palatobasal joints (Figs. 9 and10).

TABLE 3. Median strain of entire palate by model

Taxon Posture Median Strain

Gekko gecko Neutral 2,277.36MLM 1,731.44FAM 2,714.28

Tyrannosaurus rex Neutral 1,542.46MLM 1,768.37FAM 1,259.19

Psittacus erithacus Neutral 619.13MLM 753.24FAM 543.55

Quadrate, pterygoid, and palatine regions of interest aretakeninto account in these medians. Abbreviations: FAM,fore–aftmovement; MLM, mediolateral movement.

TABLE 4. Median strain of palate elements organizedby posturefor each taxon

Taxon Bone Posture Median Strain

Gekko gecko Palatine Neutral 1,346.01Pterygoid Neutral2,822.19Quadrate Neutral 2,516.53Palatine MLM 620.17Pterygoid MLM1,731.44Quadrate MLM 4,094.59Palatine FAM 2,300.19Pterygoid FAM2,759.20Quadrate FAM 4,341.22

Tyrannosaurus rex Palatine Neutral 995.86Pterygoid Neutral1,993.55Quadrate Neutral 1,540.88Palatine MLM 1,024.31Pterygoid MLM2,348.10Quadrate MLM 1,980.55Palatine FAM 534.07Pterygoid FAM1,259.19Quadrate FAM 2,029.88

Psittacus erithacus Palatine Neutral 326.41Pterygoid Neutral1,121.62Quadrate Neutral 412.29Palatine MLM 753.24Pterygoid MLM884.82Quadrate MLM 258.73Palatine FAM 455.94Pterygoid FAM587.26Quadrate FAM 210.53

Multiple regions of interest are taken into account indeter-mining the median values of each bone (quadrate,pterygoid,and palatine). Abbreviations: FAM, fore–aft movement;MLM,mediolateral movement.

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Challenges to Modeling Kinesis and CranialFunction

Despite advances over previous modeling approaches, ourprocesshas several important sources of error and uncer-tainty, includingtissue material properties, joint postureand range of motion, andjaw muscle activation patterns.

We also acknowledge that taphonomic issues and recon-structionof fossils lead to potential sources of error inmodeling extincttaxa as described by Hedrick et al.(2019). Material properties ofnon-osseous tissues arenot well described outside of mammals andare unknownfor large, extinct theropod dinosaurs. Wang et al.(2012;

Fig. 7. Strains of regions of interest in the palatal elementsof Psittacus erithacus. Regions of interest and scatter plotsshowing individual samplepoints as well as median strains(color-coded by sampling region) are represented. Otic, middle, andventral regions correspond to sampling of thequadrate whereasRostral, middle, and caudal regions correspond to sampling areas ofthe palatine and pterygoid. Each sampling region consistsof 50tetrahedra sampled randomly from the surface of the skeletalelement. Horizontal lines representing the median value of theneutral postureare shown in red in each region of the palatal bonesto facilitate comparison across postures.

BIOMECHANICS AND CRANIAL KINESIS IN T. REX 13

testing of various material properties), Lautenschlager(2013;testing of beaks, teeth, and bone), and Cuff et al.(2015;validation study) all explored the impact of vari-ous materialproperties in mammal, dinosaur, and birdFEMs. We used these studiesto inform our assignmentsof skeletal and articular properties tomodels, bearing inmind that Strait et al. (2005) noted that elasticproper-ties have small impacts on model performance. We

therefore constructed our joints with separate materialsfor thelarge cranium of Tyrannosaurus (canine patellartendon) and thesmaller crania of Psittacus and Gekko (ratcranial suture). Althoughsutural areas and joints weremodeled in other studies (e.g., Moazenet al., 2009; Joneset al., 2011, 2017; Porro et al., 2011) as FEMelementsassigned the properties of sutural or joint materials,thismethod retains a tightly packed area of the model which

Fig. 8. Strains of regions of interest in the palatal elementsof Tyrannosaurus rex. Regions of interest and scatter plots showingindividual samplepoints as well as median strains (color-coded bysampling region) are represented. Otic, middle, and ventral regionscorrespond to sampling of thequadrate whereas Rostral, middle, andcaudal regions correspond to sampling areas of the palatine andpterygoid. Each sampling region consistsof 50 tetrahedra sampledrandomly from the surface of the skeletal element. Horizontal linesrepresenting the median value of the neutral postureare shown inred in each region of the palatal bones to facilitate comparisonacross postures.

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would instead be occupied by more flexible material all-owingfor more deformation in sutures and joints involvedin cranialkinesis; cranial sutures not associated with kine-sis are lessflexible. We consider our method of creating

open spaces within the joint capsules of the model and join-ingthese portions using flexible beams to more accuratelysimulatemalleable soft tissue by permitting more realisticdeformation atjoints; however, further studies are needed

Fig. 9. Comparison of neutral postures of Tyrannosaurus rex andPsittacus erithacus in left rostrolateral view showing effects ofprotractor muscleactivation, constraints, and sutural materials onthe behavior of models. Jaw joint constraints with activated (A)and deactivated (B) protractormuscles reveal few differences instrains in the model. Occipital constraints with activated (C) anddeactivated (D) protractor muscles revealsignificant differences instrain distribution in the palate. Regions of models with hatchingrepresent areas that have been cut away to allow forbettervisualizations of internal structures. Psittacus erithacus ispresented to show differences between using rodent suturalproperties (E) andcanine sutural properties (F). Rodent suturalproperties were used in Psittacus and Gekko and canine suturalproperties were used inTyrannosaurus. Sutural properties wereconsidered based on taxon size.

BIOMECHANICS AND CRANIAL KINESIS IN T. REX 15

to validate these findings. Node anomalies at jointarticula-tions are a result of this joint construction, but donotchange the overall strain patterns of the model withfusedjoints.

Static postures in our models are merely moments in acoordinatedseries of motions during feeding bouts.Although we only testedthree specific instances of whatcould be a dynamically changingjoint articulation, recentstudies of ball and socket joints suggestthat despite theirseemingly flexible ranges of motion, they do notnecessarilyperform this way (e.g., Manafzadeh and Padian,2018).Moazen et al. (2008) suggested that the temporal ligamentsinUromastyx stabilized the quadrate during feeding. Anal-ogously,Manafzadeh and Padian (2018) found that only10% of possiblepostures were valid once capsular liga-ments were included in theball and socket-shaped articula-tion. Indeed, Tyrannosaurusquadrates possess enlargedtuberosities on the medial portion of theotic process thatbear the features of attachments for largecapsular liga-ments and complementary ligamentous scars adorn thelat-eral portion of the otic joint. Likewise, the palatobasaljointis highly congruent with a labrum of pterygoid bonenearlyencompassing the basipterygoid condyle, furthersuggestingpronounced capsular ligaments. Thus, bony jointmorphol-ogy (Holliday and Witmer, 2007), loading, andposturalanalysis suggest that a miniscule, and likelybiologicallyinsignificant, envelope of motion was available for the6-barlinkage system of the robustly built Tyrannosauruspalate,which spans pairs of highly congruent palatobasal, otic,andcraniofacial joints compared to the relatively freelymoving birdhip joints. Finally, despite slight vagaries inthe articulation ofour model and that of the original BHI3033 mount (e.g., palatobasalarticulations, epipterygoid-pterygoid joint), these morphologiesstill likely fall withinthe possible natural variation of the T.rex population mak-ing our results biologically realistic andsimilar to other

studies of posture and range of motion (e.g., Gatesy etal.,2010; Mallison, 2010; Claes et al., 2017; Olsen et al.,2017).

We modeled jaw muscles as contracting synchronouslyat maximalforce even though it was likely that, as hasbeen shown in otherdiapsids, there is variation in the fir-ing sequence and magnitudeof cranial musculature(Busbey, 1989; Nuijens et al., 1997; Herrelet al., 1999;van der Meij and Bout, 2008; Vinyard et al., 2008;Perryand Prufrock, 2018). Protractor and adductor musclesshowvariation in activation pattern during the feedingcycle, and theloads these muscles impart appear to helpstabilize the cranialjoints (Cundall, 1983; Herrel et al.,1999; Holliday and Witmer,2007). Moreover, the orienta-tion and osteological correlates ofthe m. protractorpterygoideus indicate that it was highlytendinous, likelypennate, and oriented dorsoventrally andmediolaterally(Holliday, 2009). This architecture suggests m.protractorpterygoideus had very limited excursion, and, atbest,held the palate against the braincase, restrainingitsmovements and filling a largely postural role.

Finally, to further understand the role of muscle loadsandconstraints on the model, we conducted post hoc testswith neutralTyrannosaurus models using occipital con-straints as well asdifferential activation of the protractormuscles. Constraints onthe occipital surface of the skullwere modeled to mimic cervicalmuscle loads imparted dur-ing inertial feeding mechanisms (Snivelyand Russell, 2007;Snively et al., 2014) as well as to free the jawjoint from arti-ficial constraints. Additionally, protractormuscles were tog-gled on and off in the neutral T. rex model totest for theireffect on palatal strains. Protractor muscles werefound tonot alter the distribution and range of strains in thepalatesuggesting they may not be functionally important, andevenmay be potentially vestigial. Conversely, occipitalcon-straints shifted and diminished the strains experienced bythequadrate and pterygoid, but increased strains experi-enced by theepipterygoid as it was cantilevered by itslaterosphenoidattachment. Regardless, the low strainsexperienced by the braincasein the neutral and FAMmodels in all tests indicate that althoughthe palate wasincapable of movement, it was capable of dissipatinghighstrains away from the braincase, thus insulating theneuro-sensory capsules of the head (Holliday and Witmer, 2007).

CONCLUSIONS

This study presents a unique method of exploring Tyran-nosauruscranial kinesis that incorporates anatomically dis-tinct,distributed muscle loadings, reconstructions of jointtissues,varying postures of cranial elements, and ultimatelyanalysis ofcranial performance using finite element model-ing. Its newapproaches differ from previous inferences ofmuscle architecture(Gignac and Erickson, 2017), joint func-tion (Molnar, 1991;Rayfield, 2004, 2005a, b), and joint kine-matics (Larsson, 2008).The findings presented here offer anuanced, integrative approach totesting biomechanicalhypotheses of cranial function in extant aswell as extinctvertebrate species. Not only are these methodsapplicable totesting a priori assumptions about kinematics andfunctionin living animals, but they also offer a detailed approachtotesting behavioral and functional hypotheses in animals thatareimpossible to explore using in vivo approaches. Fewmodeling studiesincorporate multiple lines of evidence, suchas multiple postures,joint tissues, and distributed muscleloadings in such diversespecies, and here we illustrate how

Fig. 10. Illustration of Tyrannosaurus skull in left lateral(top) andventral (bottom) views with key functional characteristicsof the feedingapparatus. Numerous features of the skull ofTyrannosaurus suggest itwas not capable of substantial cranialkinesis.

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powerful these inferential approaches can be usingTyranno-saurus as a case study. These approaches found inferencesofgross cranial mobility in Tyrannosaurus to be unsupportedand thatTyrannosaurus was functionally akinetic.

ACKNOWLEDGEMENTS

We thank the University of Missouri Biomolecular Imag-ing Centerand OhioHealth O’Bleness Hospital (Athens,Ohio) for scanningspecimens. We thank Juliann Tea,Emily Rayfield, Anthony Herrel,Marc Jones, and EricSnively for providing advice and assistanceduring thedevelopment of this study. We thank Peter Larson attheBlack Hills Institute and Art Anderson at Virtual Sur-faces forpermission to use the 3D model of BHI 3033. Wethank Emily Rayfield,Marc Jones, and Brandon Hedrickfor comments that improved thismanuscript’s clarity andcontent. Finally, we thank Brandon Hedrickand PeterDodson for inviting us to the special issue. Modelsarepublically hosted on Open Science Framework:BirdNet:https://osf.io/e3v7u/.

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BIOMECHANICS AND CRANIAL KINESIS IN T. REX 19

Palatal Biomechanics and Its Significance for Cranial Kinesis inTyrannosaurus rexMETHODSRESULTSMuscle and Bite Forces in ExtantSpeciesSensitivity Analysis of Muscle Forces inTyrannosaurusAnalyses of Strain Patterns

DISCUSSIONTyrannosaurus Was Functionally AkineticChallenges toModeling Kinesis and Cranial Function

CONCLUSIONSACKNOWLEDGEMENTSLiterature Cited