Finite-element analysis of biting behavior and bone … et al_2005_The...Finite-Element Analysis of Biting Behavior and Bone Stress in the Facial Skeletons of Bats ELIZABETH R. DUMONT,1*

Finite-Element Analysis of BitingBehavior and Bone Stress in the

Facial Skeletons of BatsELIZABETH R. DUMONT,1* JUSTIN PICCIRILLO,2 AND IAN R. GROSSE2

1Department of Biology, University of Massachusetts, Amherst, Massachusetts2Department of Mechanical and Industrial Engineering, University of

Massachusetts, Amherst, Massachusetts

ABSTRACTThe wide range of dietary niches filled by modern mammals is reflected

in morphological diversity of the feeding apparatus. Despite volumes of dataon the biomechanics of feeding, the extent to which the shape of mammalskulls reflects stresses generated by feeding is still unknown. In addition tothe feeding apparatus, the skull accommodates the structural needs of thesensory systems and brain. We turned to bats as a model system forseparating optimization for masticatory loads from optimization for otherfunctions. Because the energetic cost of flight increases with body mass, itis reasonable to suggest that bats have experienced selective pressure overevolutionary time to minimize mass. Therefore, the skulls of bats are likelyto be optimized to meet functional demands. We investigate the hypothesisthat there is a biomechanical link between biting style and craniofacialmorphology by combining biting behavior and bite force data gathered inthe field with finite-element (FE) analysis. Our FE experiments comparedpatterns of stress in the craniofacial skeletons within and between twospecies of bats (Artibeus jamaicensis and Cynopterus brachyotis) underroutine and atypical loading conditions. For both species, routine loadingproduced low stresses in most of the skull. However, the skull of Artibeuswas most resistant to loads applied via its typical biting style, suggesting amechanical link between routine loading and skull form. The same was nottrue of Cynopterus, where factors other than feeding appear to have had amore significant impact on craniofacial morphology.© 2005 Wiley-Liss, Inc.

Key words: biting behavior; bone stress; adaptation; finite-ele-ment analysis; Chiroptera

Mammal evolution is largely a story of the expansion ofdietary niches from an insect-eating ancestor to includefoods ranging from meat and bone to plankton. This di-versity is clearly reflected in the morphology of the cranio-facial skeleton. The association between skull structureand diet across distantly related mammals suggests thatskull shape underwent selection over evolutionary time asnew dietary niches were explored. Many excellent labora-tory-based studies of feeding have provided a wealth ofdetailed information about the biomechanical behavior ofbones and muscles under controlled experimental condi-tions. Building on this knowledge, morphologists are be-ginning to venture into the field to investigate how natu-ral behaviors interact with morphology to define howanimals function within their native environments. By

combining data gathered in the laboratory with behaviorand performance data from the field, modern comparative

Grant sponsor: the National Science Foundation; Grant num-ber: IBN 9905404.

*Correspondence to: Elizabeth R. Dumont, Department of Bi-ology, University of Massachusetts, Morrill Science Center, 611North Pleasant Street, Amherst, MA 01003. Fax: 413-545-3243.E-mail: [email protected]

Received 12 January 2005; Accepted 13 January 2005DOI 10.1002/ar.a.20165Published online 3 March 2005 in Wiley InterScience(www.interscience.wiley.com).

THE ANATOMICAL RECORD PART A 283A:319–330 (2005)

© 2005 WILEY-LISS, INC.

morphologists hope to discover the links between mor-phology and behavior and gain greater insight into theevolution of functional diversity.

One defining characteristic of mammals is the distinc-tive structure of their jaws and teeth. All mammals havea single paired lower jaw bone and most possess severaltypes of complex teeth that occupy different functionalregions of the mouth. In keeping with this complexity,field-based behavioral studies demonstrate that mammalsuse several different combinations of teeth when they bitefood items (Van Valkenburgh, 1996; Dumont, 1999; Du-mont and O’Neal, 2004). These biting styles can includeteeth from one or both sides of the mouth and teeth fromvarious locations along the tooth row. Importantly, eachbiting style loads the facial skeleton in a different way.Unilateral (one-sided) bites apply predominantly torsionalloads, bilateral (two-sided) bites apply predominantlybending loads, and the location of a bite along the toothrow affects bite force (Dumont and Herrel, 2003). Fieldstudies demonstrate that most species of carnivores andfruit bats studied thus far use characteristic biting stylesthat are statistically distinct even in the face of variationamong individuals (Van Valkenburgh, 1996; Dumont,1999; Dumont and O’Neal, 2004). In other words, thecraniofacial skeletons of different species are often ex-posed to different loading regimes.

In this study, we addressed the hypothesis that there isa biomechanical link between biting style and craniofacialmorphology by comparing patterns of stress in the cranio-facial skeletons of two fruit bats (Artibeus jamaicensis andCynopterus brachyotis) under normal and atypical loadingregimes. Within each species, we compared stresses gen-erated under the expected range of bite forces for eachbiting style (based on population statistics) as well asunder a constant bite force. If craniofacial morphology isoptimized for the most common biting styles, we predictthat the skulls of these bats will be most resistant to loadsapplied through their preferred loading regime. We alsocompared the relative strength of Artibeus andCynopterus under different loading conditions. This al-lowed us to investigate how these distantly related batsovercome the mechanical challenge of being small animalsthat eat hard fruits.

Evidence that morphology is optimized or tuned forpreferred loading regimes would suggest that loads im-posed by feeding played a role in the evolution of cranio-facial morphology. Alternatively, the lack of an associationbetween craniofacial morphology and biting behaviorwould support the contention that the craniofacial skele-

ton is not optimized solely for feeding (Hylander et al.,1991; Hylander and Johnson, 1997) and must be a com-promise between conflicting functional demands.

To evaluate our hypothesis, we needed a method thatwould allow us to assess the impact of bite force over largeregions of the skull and facial skeleton simultaneously.We also needed to be able to conduct experiments in whichall loading variables could be manipulated very accu-rately. Traditional in vivo experimental methods, usingstrain gauges, for example, allow data to be collected fromonly a few small areas at a time and it is virtually impos-sible to control loading conditions precisely in live ani-mals. Moreover, in very small animals such as bats, thesurgical placement of strain gages likely would interferewith normal feeding. To overcome these limitations, weturned to finite-element analysis (FEA). FEA was devel-oped to visualize and quantify stress and strain distribu-tions across entire mechanical components due to knownand controllable loading conditions (see Richmond et al.,2005, this issue). Because of these qualities, FEA was agood alternative to traditional in vivo experimental tech-niques.

MATERIALS AND METHODSComparative Sample and Experimental Design

Artibeus jamaicensis (family Phyllostomidae) andCynopterus brachyotis (family Pteropodidae) represent in-dependent lineages of fruit bat in the New and Old Worldtropics. We selected these species because of their conver-gence in ecological niche and body size. Although Artibeusand Cynopterus are relatively small, on average 42 and44 g, respectively, both frequently include figs and otherhard fruits in their diets (Fleming, 1988; Tan et al., 1998;Gianini and Kalko, 2004). They face similar mechanicalchallenges during feeding, but Artibeus and Cynopterusroutinely employ significantly different biting styles (Ta-ble 1).

Artibeus exhibits a significant difference in biting stylewhen eating soft and hard fruits (Dumont, 1999) andresponds to the mechanical challenge of breaking aparthard fruit by switching to unilateral molar bites. Whilehigher forces are produced during unilateral molar biting(Table 2), this loading regime primarily twists the facialskeleton dorsally on the working side. In contrast to Arti-beus, there is no statistical difference in the combinationof biting styles used by Cynopterus during soft- and hard-fruit feeding. Cynopterus consistently emphasizes bilat-eral biting, which applies primarily bending loads to therostrum.

TABLE 1. Proportions of biting styles used by Artibeus jamaicensis and Cynopterusbrachyotis when feeding on soft and hard fruits*

Unilateralcanine

Bilateralcanine

Unilateralmolar

Bilateralmolar n

Hard fruitArtibeus jamaicensisa 0 9.3 80 10.7 3Cynopterus brachyotis 7.98 39.33 7.15 45.58 3

Soft FruitArtibeus jamaicensisa 29.1 39.7 19.1 11.3 3Cynopterus brachyotis 0 61.67 2.76 35.56 4

*Mean percentages of biting styles and the number of individuals sampled (n) are reported. Each individual was representedby a series of at least 20 bites.aDumont (1999).

320 DUMONT ET AL.

Based on these biting behavior data, we conducted fi-nite-element (FE) experiments to investigate the hypoth-esis that the skulls of Artibeus and Cynopterus are moreresistant to loads imposed by their typical biting behav-iors than by loads imposed by atypical biting behaviors.First, we modeled the effects of each species’ typical bitingbehavior during hard-fruit feeding by loading each modeliteratively until known average bite forces were gener-ated. Second, we use the same procedure to model atypicalbiting behaviors in each species. Third, we compared theresponse of each model to atypical and typical loading byapplying the same bite force at each of the two bite points.This allowed us specifically to assess the role of craniofa-cial structure in dissipating loads applied at differentlocations. Finally, to assess the effects of geometry andloading condition on patterns of stress transmission, eachmodel was loaded with a bite force of 22.5 N (the averagebite force for Artibeus in unilateral molar biting) undereach loading regime. Overall, these experiments providedtwo independent tests of the association between bitingbehavior and stress in the craniofacial skeleton: one inArtibeus and another in Cynopterus.

In contrast to engineered products, it is important toconsider the impact of individual variation when modelingorganisms. Although our models were constructed andloaded with data from full-grown adult bats, it is possiblethat the specimens we modeled did not represent averagemorphologies or produce average bite forces. Ideally, onewould assess individual variation by constructing modelsfrom a series of individuals with known bite forces. Be-cause that is not feasible given current modeling tech-niques, we addressed the issue of variation more simply byapplying bite forces to our models at magnitudes rangingfrom the mean to the mean plus two standard deviations.

FE ModelingThe first step in a successful FEA is to generate a

sufficiently accurate geometric model of the structure ofinterest. For engineered structures, this is often astraightforward process in which structures are built bydeveloping a parametrically controlled model (i.e., input-ting structures with predefined sizes and shapes). Thehighly irregular shape of biological structures and thefrequent need to build models from imported data greatlycomplicates the process of generating FE models.

To build FE models of the skulls of Artibeus andCynopterus, we acquired 3D stereolithography (STL)-for-matted surfaces representing the geometry of each skullfrom the University of Texas High-Resolution ComputedTomography Facility at Austin, Texas. These files weregenerated from stacks of 2D micro-CT scans with a spatialresolution of 0.019 mm.

The STL format consists of a tessellated surface meshcomposed of three-noded triangular elements. These tri-

angles may be considered first-order representations ofreal-world geometries in that while element vertices re-side on true surfaces, the STL surfaces are planar inter-polations between vertices. As with any similar represen-tation of second- or higher-order real-world surfaces, asthe quantity of elements and vertices increase, their over-all geometric precision increases. This is particularly im-portant in the case of structures with complex and organicgeometries, where accurate geometric representationmust be weighed against the information-handling capa-bility of computer hardware.

The initial STL surfaces contained approximately500,000 triangular elements, which were too large to su-perimpose directly into an FE model. Even if there werefewer elements, the quality of the elements and meshwere unsuitable for FE modeling because of unevenlyskewed internal angles and location mismatch of adjacentnodes. In addition, numerous geometric errors existed inthe initial STL surface representation due to spuriouspixels captured by the pixel thresholding method, inad-vertently omitted pixels in desired regions, and fine-graingeometries in certain sections of the skulls. Comparativesize differentials and geometric complexity led to furtherdifficulties in generating a representative model.

Based on our experience in modeling, we took thesefactors into consideration while refining the STL modelusing Raindrop’s Geomagic Studio, a rapid prototypingsoftware tool. For example, we decided that the thinness,complex geometry, and load-bearing capacity of nasal con-chae provided justification for simplifying this region. Wealso corrected artificial holes, surface irregularities, andextraneous geometry that resulted from the digital recon-struction process. Fortunately, the skulls of these adultbats did not have visible sutures and could be modeledaccurately as a continuous bony structure that varies inthickness. Once the overall surface geometry of each skullwas resolved to represent a fully enclosed, “water-tight”volume, a new STL surface mesh was generated and ex-ported.

The next step in the process was to import the water-tight STL surface mesh into an FEA tool. For our FEmeshing and analysis, we employed Strand7 (G�D Com-puting, Sydney, Australia). Within Strand7, we were ableto use the STL surface representation as a geometric basisfor automatically generating an FE mesh of three-nodedtriangular plate elements. The main differences betweenthis mesh and the imported STL surface representationwere significantly less distortion (i.e., improved triangularshapes) and the use of adaptive element sizes (i.e., smallerelements in areas of complex geometry and larger ele-ments in areas of less geometric complexity) (Fig. 1).

Once the FEA tool automatically generated a plate ele-ment surface mesh, interactive editing of the mesh wasrequired to resolve a handful of meshing errors, such as

TABLE 2. Means and standard deviations of bite forces (in Newtons) during unilateral canine, bilateralcanine, and unilateral molar biting for Artibeus jamaicensis and Cynopterus brachyotis*

Unilateralcanine n

Bilateralcanine n

Unilateralmolar n

Artibeus jamaicensis 9.49 � 2.74 10 18.8 � 5.56 19 22.5 � 10.95 24Cynopterus brachyotis 11.5 � 1.19 10 11.4 � 3.17 5 14.0 � 2.23 10

*Data from Dumont and Herrel (2003) and Aguirre et al. (2002).

321BITING BEHAVIOR AND STRESS DISTRIBUTION

the existence of free (i.e., unattached) plate element edges.Using the refined plate element surface mesh, the Strand7automatic tetrahedral mesher created a volumetric meshof 10-noded tetrahedrals. At the end of this step, all plateelements were removed from the FE model, leaving only avolumetric mesh that defined the geometry of the skull(Fig. 1). The completed Artibeus model contained 251,96810-noded tetrahedral elements, 399,806 nodes, and ap-proximately 1.2 million degrees of freedom. Due to im-proved grading of the mesh, the Cynopterus model hadfewer elements (138,037), nodes (235,097), and degrees offreedom (approximately 700,000). Overall, very little de-tail was lost between the initial STL files and the 10-noded tetrahedral models.

Ten-noded tetrahedrals are quadratic elements inwhich the displacement field may vary quadratically overeach element volume, and thus the stress and strain mayvary linearly over each element volume. In contrast, four-noded tetrahedrals are linear elements, admitting a lineardisplacement field and constant stress and strain fieldsover each element volume. Thus, for a given element size,10-noded tetrahedral elements are more accurate for mod-eling complex stress and strain distributions compared to4-noded tetrahedral elements. Of course, four-noded ele-ments require less computational resources. Sufficientlyrefined models, however, should converge to identical re-sults for both 4- and 10-noded meshes. We compared anal-yses using 4- and 10-noded tetrahedral versions of our bat

Fig. 2. Finite-element model of Artibeus jamaicensis illustrating theapplied muscle forces (arrows) and kinematic constraints (crosses) forthe bilateral canine load case. In addition to the constraints at the caninetips, a single node in the center of each temporomandibular joint (notvisible from this perspective) was constrained in the x-, y-, and z-planes.Note that the same muscle forces illustrated here were also applied tothe other side of the skull.

Fig. 1. Comparison between STL surface representations and 10-noded finite-element models forArtibeus jamaicensis (top) and Cynopterus brachyotis (bottom). STL representations are on the left andfinite-element models on the right.

322 DUMONT ET AL.

models and found that mean stress values were within10%. This difference is minimal and indicates that both ofour models are robust. Ultimately, we elected to use the10-noded models because of their increased accuracy.

Material Properties, Constraints, and LoadingConditions

The second requirement for successful FE analyses is arealistic estimate of the material properties of the struc-ture being modeled. Perhaps not surprisingly, there are nodata summarizing Young’s modulus or Poisson’s ratio forthe very thin and highly curved bones of bat skulls. How-ever, comparative studies of the stiffness and yieldstrength of cortical bone suggest that material propertiesare relatively constant over a wide taxonomic range(Erickson et al., 2002). Based on these comparative data,we assigned our models average values of Young’s modu-lus (E � 2 � 1010 Pa) and Poisson’s ratio (� � 0.3) basedon mammalian bone.

Many studies have documented that bone is anisotropicand that its material properties vary regionally (Turnerand Burr, 2003). However, for modeling simplicity anddue to the lack of reference data, we assumed in thisanalysis that the bone of bat skulls is homogeneous andisotropic. We suspect that regional variation in materialproperties may be less of an issue for bat skulls than forthe skulls of larger mammals because bat skulls are al-most completely composed of exceptionally thin corticalbone. The facial skeletons of larger mammals contain sig-nificantly more cancellous bone and cortical bone of vary-ing thickness. On the other hand, because all bone inves-tigated thus far is anisotropic, we also suspect that thesame is true of the bone of bat skulls. Because we assumethat bat skull bone is homogeneous and isotropic, theabsolute stress values obtained from our analyses must beinterpreted cautiously. However, it is important to empha-size that assuming the material properties of Artibeus andCynopterus skulls are similar, we can compare the relativemagnitude and distribution of stress in the two specieswith a great deal of confidence.

The third requirement for successful FE modeling is toapply realistic forces and constraints to the model. Wemodeled the forces exerted on the skull by the masseterand temporalis muscles by applying loads to three nodesrepresenting the region of each muscle attachment (Fig.2). The load vectors applied to nodes approximated thedirection of muscle fibers and the proportion of total forcegenerated by masseter and temporalis was based on mus-cle mass data from closely related species (Artibeus litu-ratus and Nyctimene robinsoni) (Storch, 1968). We mod-eled the relative contribution of temporalis:masseter tojaw adduction as 80:20 in Artibeus and 56:44 inCynopterus. The pterygoid muscles are very small in bothspecies; we did not model their forces.

We followed the methods outlined by Strait et al. (2002,2005, this issue) for applying constraints to the model. Tomodel reaction forces at the temporomandibular joint(TMJ), a single node at each TMJ was constrained againstdisplacement. This effectively created an axis of rotationfor the skull due to the application of the muscle forces. Toprevent this rigid body motion and induce elastic defor-mation in the skull due to biting forces, nodes on the tipsof the appropriate teeth were constrained against dis-placement (i.e., displacements in the x-, y-, and z-planeswere set equal to 0). For bilateral canine biting, a single

node on the tip of each of the canine was fully constrained.For unilateral canine biting and unilateral molar biting, asingle node on the tip of the appropriate tooth was fullyconstrained. Note that the displacement constraints weimposed at the bite point(s) and at the TMJs prevented allpossible modes of rigid body motion, including rotationsabout any axis. It should be emphasized that solid ele-ments, such as the linear or quadratic tetrahedrals, do nothave rotational degrees of freedom. Hence, to preventrigid body rotation in an FE model composed of solidelements, sufficient displacement constraints must be im-posed at nodes to prevent rigid body rotation about anyaxis. This requires careful attention to the kinematics ofthe system in order to specify constraints sufficient toprevent rigid body motion while not overconstraining thesystem. Too many constraints may produce unrealisticstresses and strains due to Poisson’s effect.

Each analysis of a biting behavior was completed in twosteps. Initially, an arbitrary total amount of muscle force,FT, was divided between the masseter and temporalismuscles based on muscle mass proportions. All muscleswere assumed to act simultaneously and all dynamic ortransient effects were neglected. Once the analysis prob-lem was solved, the reaction forces at the constrainedtooth (or teeth for the bilateral canine case) necessary forsystem static equilibrium were determined. This reactionforce, FR

n, was then compared to experimental in vivo biteforce measured for the bat species, Fexp. Since the com-puted reaction force is in direct proportion to the totalapplied muscle load, the required total amount of muscleforce, (FT)new, necessary to yield the experimentally mea-sured bite force is given simply by

(FT)new � �Fexp

FRn� FT

In the second step of the analysis, the computed totalamount of muscle force, (FT)new, was distributed amongthe masseter and temporalis muscles based on musclemass portions. The solution of this second analysis prob-lem yielded the deformation of the bat skull, strains, andstresses for a particular feeding behavior that resulted inreaction force(s) at the constrained tooth (teeth) that iden-tically matched voluntary bite force values collected in thefield (Table 2) (Aguirre et al., 2002; Dumont and Herrel,2003). Essentially, known bite forces values were used tocalculate the muscle forces required to maintain staticequilibrium in the analysis.

It is important to note that our bite force measurementtechnique provided a bite force that was essentially nor-mal (perpendicular) to the palate of the bat. Therefore, inthe above equation, the reaction force, FR

n, was obtained bytaking the projection of the total reaction force vector atthe tooth node (or nodes) in the direction normal to thepalate, i.e., the dot product between the nodal reactionforce vector and the unit normal to the palate, n̂:

FRn � �F� R�n̂�

The unit normal to the palate, n̂, was computed usingthe coordinates of finite-element nodes residing on thepalate and vector algebra.

323BITING BEHAVIOR AND STRESS DISTRIBUTION

Assessing StressAny discussion of stress and strain must address the

nature of stress and strain as second-order tensors. Con-sider three mutually orthogonal planes at a material pointwith each unit outward normal to the plane aligned with

a coordinate axis of a Cartesian x-y-z coordinate system.In a general state of stress, there are six components ofstress (and strain) that act on these planes: three compo-nents normal to these planes (�x, �y, and �z) and threetangential or shear components (�xy, �xz, and �yz). How-

Fig. 3. Von Mises stress during unilateral molar biting (right) and bilateral canine biting (left) in Artibeusjamaicensis. Views of the craniofacial skeleton include frontal view (A), three-quarters lateral view of the rightside (B), and the palate (C).

324 DUMONT ET AL.

ever, at any material point, there is a rotation of thiscoordinate system and its associated orthogonal planesthat will maximize the normal component of stress whileat the same time eliminate all the shear stress compo-nents acting on the newly oriented planes. This is calledthe principal state of stress with the coordinate axis de-fining this orientation of planes designated as 1, 2, and 3.The normal stress components acting on the planes de-fined by the 1, 2, and 3 directions are called principalstresses and are designated as �1, �2, and �3.

Bone, like most biological materials, is elastic and failsunder a ductile model of fracture (Nalla et al., 2003).Therefore, we chose to report a type of stress, the VonMises stress, which is a good predictor of failure underductile fracture. The failure of ductile materials most of-ten occurs due to distortion. The Von Mises stress (�v) is ascalar function of the principal stresses �1, �2, and �3 thatdirectly measures how the state of stress at any pointdistorts the material:

�v � �12 ((�1 � �2)2 � (�1 � �3)2 � (�2 � �3)2)�

12

In fact, the square of the Von Mises stress is directlyproportional to the strain energy of distortion. Further,the difference between any two principal stresses is equalto twice the maximum shear stress that acts on a planeparallel to the other principal stress. Hence, the VonMises stress is related to the maximum shear stressesfound on three orthogonal planes. Ductile failure is pre-dicted when the Von Mises stress reaches the yieldstrength of the material.

For each species and loading condition, we plotted thevolume of the skull that was stressed at values rangingfrom 0 to an upper limit imposed by singularities in theexperimental results. This range included stress data for98–99% of model volume for both models and loadingconditions. Using this range, we also calculated meanstress (adjusted for volume differences among individualfinite elements). We estimated the upper limit of stressconservatively as the minimum stress value at which thesingularities caused by point loads on the zygomatic archcoalesced. These singularities are certainly artifacts ofmodeling muscle forces with point loads. Unfortunately,they make it impossible to identify the highest stressesproduced in the models with any degree of certainty. How-ever, maximum stress may be of more biological impor-tance than mean stress since it reflects the occasional,perhaps dangerously high load that an animal may en-counter. In order to compare maximum stresses betweenloading conditions and models, we focused on maximumstress values in the palate, a region that was not affectedby our use of point loads and in which we could easilyidentify local stress maxima.

RESULTSBiting in Artibeus jamaicensis

Artibeus focuses on unilateral molar biting during hard-fruit feeding and uses bilateral canine biting much lessfrequently (Table 1). There are significant differences inthe patterns of stress under these two loading conditions(Fig. 3). The superior surface of the rostrum experiencesthe highest stress during bilateral canine loading (Fig.

3A). Likewise, the medial surface of the orbit, infratem-poral fossa, and rostrum experience the highest strainsduring unilateral molar loading (Fig. 3B). The most dra-matic differences between loading regimes are seen in thepalate (Fig. 3C). Stress is widely distributed through thepalate and is concentrated in the pterygoid plates duringbilateral canine biting. In contrast, unilateral molar bitingproduces much lower and more localized stresses. Theseobservations are supported by quantitative differences be-tween the two loading regimes (Fig. 4).

At average bite forces, both mean stress and maximumstress in the palate are lowest during unilateral molarloading, despite the fact that bite force is higher. Thediscrepancy between unilateral and bilateral loading ismuch larger when bite forces were increased by two stan-dard deviations. Bite force is 67% higher in unilateralmolar biting, but maximum stress in the palate is lowerand mean stress is very similar to the values generatedunder bilateral canine biting. At two standard deviationsabove mean bite force, maximum stress in the palatereaches 51 and 60 MPa in unilateral molar and bilateralcanine loading, respectively. To evaluate the relativestrength of the Artibeus model in unilateral molar andbilateral canine loading, a bite force of 22.5 N was appliedto both loading conditions (Fig. 5). Mean stress was 45%greater and maximum stress in the palate was 58%greater under bilateral canine loading.

Biting in Cynopterus brachyotisCynopterus frequently uses bilateral canine biting dur-

ing feeding; unilateral molar biting is rare. Contour plots

Fig. 4. The volume of the skull stressed (% volume) plotted againststress during biting (stress, in MPa) in Artibeus jamaicensis. Graphsillustrate stress under mean bite forces (top) and bite forces that are twostandard deviations above the mean (bottom). Unilateral molar bites areon the left and bilateral canine bites on the right; 98–99% of total skullvolume is plotted on each graph.

325BITING BEHAVIOR AND STRESS DISTRIBUTION

illustrate that the distribution and intensity of stress dif-fered subtly between the two loading conditions (Fig. 6).During bilateral canine biting, stress in the palate wasmore evenly distributed and lower than during unilateralmolar loading. Bilateral canine biting also resulted inlower and less extensive stress along the inferior marginof the orbit. More minor differences between the effects ofthe two biting styles can be logically traced to the loadingconditions, namely, higher stresses occurred above themolar tooth during unilateral molar loading and along thesuperior surface of the rostrum in bilateral canine loading.The apparent similarities between the two loading re-gimes were supported by quantitative data (Fig. 7).

At average bite forces, unilateral molar loading resultedin slightly higher mean stress as well as 16% greatermaximum stress in the palate. When bite force was in-creased by two standard deviations, mean stress valuesremained within 10% of one another and maximum stressin the palate was nearly identical under the two loadingconditions (49 and 48 MPa). To compare the strength ofthe Cynopterus model under the two loading conditions, abite force of 22.5 N was applied under both unilateralmolar and bilateral canine biting (Fig. 5). Mean stress was15% greater under bilateral canine loading but the maxi-mum stress in the palate was again nearly identical be-tween the two cases.

Biting in Artibeus jamaicensis vs. Cynopterusbrachyotis

Given an equal bite force of 22.5 N, the Artibeus modelencountered lower mean stress and lower maximumstress in the palate than did the Cynopterus model (Fig.5). The difference between the two species was greatest

during unilateral molar biting, where average stressesin Cynopterus were 66% higher than in Artibeus andmaximum stress in the palate of Cynopterus was morethan twice that seen in Artibeus.

DISCUSSION

Our initial prediction was that the skulls of these batsare most resistant to loads applied through their preferredloading regime. We tested this prediction in two ways. Byinvestigating mean and maximum stresses under a pre-dicted range of normal bite forces, we modeled how theskulls transmit loads under an expected range of loadingconditions associated with feeding. Under these condi-tions, our prediction was largely supported by maximumpalate stress data. At average bite forces, maximum stressin the palate was highest under the atypical loading con-dition in both species (i.e., bilateral canine loading inArtibeus and unilateral molar loading in Cynopterus).This relationship held for Artibeus when bite forces wereincreased by two standard deviations. In contrast, maxi-mum stress in the palate of Cynopterus was essentiallyequal under the higher loads. Mean stress appears to beless informative in that it varied little between loadingregimes except in Artibeus, where mean stress was muchhigher during bilateral canine with average bite forces.Perhaps it is not surprising that mean stress is less infor-mative than maximum stress values as infrequent largeloads are more likely to result in structural failure thanaverage loads (Alexander, 1997).

On a purely structural level, we also evaluated theability of each model to resist loads during unilateralmolar and bilateral canine biting by applying the sameforce (22.5 N) through both loading conditions. At thesame bite force, a stronger structure will be less stressed.In other words, a much higher load would be required tostress that structure to its ultimate yield point. Artibeuswas strongest against unilateral molar loading as evi-denced by the lower mean and maximum palate stresses.This is reflected in living animals, where unilateral molarbite forces are larger and more variable than bilateralcanine bite forces. Cynopterus was also stronger in unilat-eral canine biting but, in contrast to Artibeus, the differ-ence between the two loading regimes was extremelysmall. Again, this is reflected in the behavior of livinganimals in which the forces generated in unilateral molarand bilateral canine biting are very similar. As in Arti-beus, bite force in Cynopterus is most variable under thepreferred, in this case bilateral canine, biting style.

These data help to explain why Artibeus focuses onunilateral molar bites when it is confronted with a hardfood item. The skull of Artibeus is strongest against uni-lateral molar loading and therefore, Artibeus can generatethe largest bite forces during unilateral molar biting. It isless clear why Cynopterus emphasizes bilateral caninebiting. One possibility is that it is associated with themorphology of its teeth. Although Cynopterus can gener-ate slightly higher (by 0.8 N) bite forces during forcefulunilateral molar biting, its canine teeth are much sharperthan its molars (data not shown). Therefore, the caninesmay be more effective at concentrating available forces onsmall areas of contact with food items and thereby initiatecracks (Lucas, 1979; Lucas and Luke, 1984; Evans andSanson, 1998). Whether the combination of bite force andsharp teeth renders bilateral canine biting in Cynopterus

Fig. 5. The volume of the skull stressed (% volume) plotted againststress during biting (stress, in MPa) in Artibeus jamaicensis (top) andCynopterus brachyotis (bottom) at a bite force of 22.5 N. Unilateral molarbites are on the left and bilateral canine bites on the right.

326 DUMONT ET AL.

more effective in breaking apart hard food items thanunilateral molar biting is an interesting prospect that willrequire further experimentation.

To take our comparisons further, we removed the effectof bite force and focused on the consequences that bonegeometry and patterns of muscle loading could have ondifferences between Artibeus and Cynopterus (Fig. 7). The

skull of Artibeus is much stronger than the skull ofCynopterus under both biting styles and dramaticallystronger in unilateral molar biting. Cynopterus, on theother hand, consistently experiences higher stresses andis more evenly stressed than Artibeus.

Differences in geometry probably account for the factthat stress in the facial skeleton of Artibeus is frequently

Fig. 6. Von Mises stress during unilateral molar biting (right) and bilateral canine biting (left) in Cynopterus brachyotis. Views of the craniofacialskeleton include frontal view (A), three-quarters lateral view of the right side (B), and the palate (C).

327BITING BEHAVIOR AND STRESS DISTRIBUTION

transmitted through the anterior portion of the rostrum,while stress in Cynopterus is transmitted more posteriorlythrough the maxilla near the root of the zygomatic arch.The shorter, more rounded palate and a sloped rostrum ofArtibeus may provide a better pathway for stress trans-mission than the longer and more squared rostrum ofCynopterus. Likewise, the wider and more substantialzygomatic arches of Cynopterus, in combination with alonger palate, may provide the predominant load trans-mission pathway.

In addition to skull geometry, the ratio of temporalis tomasseter muscles may have had a significant impact onthe patterns of stress generated within the two models. Inour model, jaw adduction in Artibeus is dominated by thetemporalis muscle (80% of total force), which focused highforces on the lateral wall of the skull in both loadingconditions. In contrast, we assigned the masseter musclein Cynopterus two times more force than in Artibeus (44%vs. 20% of total force). The larger masseter loads may beresponsible for the high stresses seen in the zygomaticarches of Cynopterus under both loading regimes. In bothspecies, focal areas of extremely high stress occurredwhere the point loads representing muscles were applied,and these modeling artifacts were excluded from quanti-tative analyses. It is important to point out, however, thatareas of high stress away from the load application pointswere not affected by this idealization due to Saint-Ve-nant’s principle (Cook and Young, 1985). Therefore, mostof the stress in the two models is unaffected by the pointload artifacts. Another aspect of muscle biology that mayhave impact the stress distributions we saw was our as-sumption that the jaw adductors fire simultaneously and

contribute in accordance with (an estimate of) their rela-tive strength. Teasing apart the roles of bone geometry,relative muscle size, and muscle firing sequences on pat-terns of stress could provide insights into the kinds ofevolutionary changes that are most likely to affect skullfunction.

From an evolutionary perspective, one of the most in-triguing questions to arise from this study is why Artibeusand Cynopterus represent such different solutions to thechallenge of being a small mammal that eats hard foods.Both species are short-faced members of their respectivelineages and they are approximately the same size. De-spite these convergences in ecology, skull shape, and bodysize, their skulls appear to dissipate bite forces in verydifferent ways. Artibeus exhibits a greater than expecteddifference in strength between unilateral molar and bilat-eral canine biting. Given the relatively long palate ofCynopterus, the strength of the two biting behaviors ismore equal than would be expected. In addition, the skullof Artibeus is stronger than the skull of Cynopterus de-spite the fact that the two species are similar in size.Without a broader comparative sample, it is impossible todetermine whether one or both species is specialized (Ar-tibeus for strong unilateral molar biting, Cynopterus forstrong bilateral canine biting) or whether each one simplyepitomizes the typical condition of most bats within itsrespective clade.

Although we have established that Artibeus andCynopterus are very different, an interesting similaritybetween them is the concentration of stresses/strains onthe palate and pterygoid plates. Theoretical analyses ofcraniofacial biomechanics have suggested that both re-gions transmit masticatory stress (Cartmill, 1977; Thoma-son and Russell, 1986; Covey and Greaves, 1994). Thepalate and pterygoid plates demonstrate a good exampleof the utility of FE analysis. Models of palate and ptery-goid plate function have not been verified in vivo in smallmammals because the placement of strain gages is bothtechnically difficult and likely to interfere with normalfeeding behaviors. In this case, FE analyses offered aglimpse of the stress states of regions that are otherwisedifficult to access and suggests that in vivo investigationsof the palate may yield interesting results. Whether theseresults are accurate depends, of course, on the quality ofour FE models, the authenticity of our loading conditions,and our assumptions about the physical properties of batskull bone.

Given the current lack of data on the physical propertiesof bat skull bone, it is impossible to determine the effect ofthe stresses generated under our predicted range of biteforce values. Stresses could be either approaching theultimate strength of the bone, just high enough to stimu-late bone remodeling (and thus avoid fatigue fracture), orso low as to have no impact on bone remodeling andmaintenance. Behavioral studies do illustrate that thesebats engage in long periods of biting and chewing andsuggest that repetitive loading may be an issue for theseanimals (Dumont, 1999; unpublished data from thisstudy). It is also interesting to note that if our stressvalues are reasonably accurate, then the palate ap-proaches the ultimate strength of cortical bone in shearwith a safety factor of approximately 2.8 during strongbiting. In the case of Artibeus during bilateral caninebiting, the safety factor may drop to 2.3. [These estimatesassume an ultimate stress in shear for bone of 70 MPa

Fig. 7. The volume of the skull stressed (% volume) plotted againststress during biting (stress, in MPa) in Cynopterus brachyotis. Graphsillustrate stress under mean bite forces (top) and bite forces that are twostandard deviations above the mean (bottom). Unilateral molar bites areon the left and bilateral canine bites on the right; 98–99% of total skullvolume is plotted on each graph.

328 DUMONT ET AL.

(Nordin and Frankel, 2001), which translates into 140MPa on the Von Mises stress scale.] While these aretantalizing observations, both experimental strain dataand bone material properties data are absolutely essentialbefore safety factors in bat skulls can be investigatedrigorously.

These data do, however, demonstrate that the batskull does not constitute what engineers term a fullystressed design. Man-made products that are optimizedto bear routine loads while being as lightweight aspossible experience high uniform stresses under normalloading conditions. These finite-element analyses ofbats are in agreement with experimental studies ofother mammals that demonstrate strong strain gradi-ents in the facial skeleton (Ravosa et al., 2000; Herringet al., 2001; Ross, 2001). These data add further supportto the conclusion that the skulls of mammals are notoptimized solely for feeding (Hylander et al., 1991; Hy-lander and Johnson, 1997), but must represent a com-promise between competing functional demands. Nev-ertheless, it also appears that feeding behavior (i.e.,loading regime) is strongly associated with craniofacialform.

The only way to validate FE models is to compare theresults to in vivo/in vitro analyses of bone strain. Todate, there are no data on bone strain in the skulls ofbats. However, two lines of evidence suggest that ouranalyses were meaningful. First, both models re-sponded to loading conditions in ways that could bepredicted from in vivo studies. Predominantly bendingloads (bilateral canine biting) resulted in more or lesssymmetrical stresses on the superior surface of the ros-trum and on the palate. In contrast, predominantlytorsional loads (unilateral molar biting) produced moreasymmetrical stresses on the rostrum and palate thatare topographically consistent with in vivo assessmentsof shear. Second, our microstrain values were in a rangethat is reasonable based on in vivo analyses of strain inthe facial skeletons of other mammals. Again, the accu-racy of absolute stress values generated by our analysesis unknown because they have not been validatedthrough in vivo experimentation. However, our modelswere geometrically accurate and, assuming that ourloading conditions, material properties assignments,and constraints were reasonable approximations of re-ality, the patterns of stress distribution in Artibeus andCynopterus are comparable. The differences betweenthese patterns appear to highlight fundamental func-tional differences between the skulls of the two species.

In sum, this study demonstrates a clear associationbetween feeding ecology, biting behavior, and craniofa-cial form in Artibeus jamaicensis. Hard fruits are bittenprimarily with unilateral molar bites, where the highestbite forces are produced by virtue of the great strengthof the skull against loading regime. The relationshipamong feeding ecology, biting behavior, and craniofacialform is not so clear in Cynopterus brachyotis, althoughits skull is stronger than expected under its preferredbilateral canine loading regime. Whether this approxi-mates equality in bite force and skull strength underunilateral molar and bilateral canine biting representsa derived condition must await data from a broad rangeof pteropodid species. While this analysis affirms theconclusion that craniofacial form is surely a result ofmany competing functional demands, it does illustrates

a clear association between stresses generated duringfeeding and the resistance of the skull to those stresses.If bite force is a performance variable that ultimatelyimpacts fitness, then it is entirely possible that selectionfor increased bite force could drive evolutionary changesin craniofacial morphology and/or feeding behavior.

ACKNOWLEDGMENTSWe thank the staff of the University of Texas High-

Resolution Computed Tomography Facility for their helpand patience as we developed their protocol for transform-ing CT scans into finite-element models. We also thankNancy Simmons of the American Museum of Natural His-tory for access to STL files of Cynopterus brachyotis, andthe anonymous reviewers of this manuscript for theirmany helpful suggestions. We extend special thanks toCallum Ross for inviting them to participate in this sym-posium and providing the opportunity to exchange ideaswith so many excellent colleagues.

LITERATURE CITEDAguirre LF, Herrel A, van Damme R, Matthysen E. 2002. Ecomor-

phological analysis of trophic niche partitioning in a tropical savan-nah bat community. Proc Royal Soc Lond Ser B Biol Sci 269:1271–1278.

Alexander RM. 1997. A theory of mixed chains applied to safetyfactors in biological systems. J Theor Biol 184:247–252.

Cartmill M. 1977. Daubentonia, Dactylopsila, woodpeckers and klino-rhynchy. In: Martin RD, Doyle GA, Walker AC, editors. Prosimianbiology. London: Duckworth. p 655–670.

Cook RD, Young WC. 1985. Advanced mechanics of materials. NewYork: Macmillan.

Covey DSG, Greaves WS. 1994. Jaw dimensions and torsion resis-tance during canine biting in the Carnivora. Can J Zool 72:1055–1060.

Dumont ER. 1999. The effect of food hardness on feeding behaviour infrugivorous bats (Phyllostomidae): an experimental study. J ZoolLond 248:219–229.

Dumont ER, Herrel A. 2003. The effects of gape angle and bite pointon bite force in bats. J Exp Biol 206:2117–2123.

Dumont ER, O’Neal R. 2004. Food hardness and feeding behavior inOld World fruit bats (Pteropodidae). J Mammal 85:8–14.

Erickson GM, Cantanese J, Keaveny TM. 2002. Evolution of thebiomechanical material properties of the femur. Anat Rec 268:115–124.

Evans AR, Sanson GD. 1998. The effect of tooth shape on the break-down of insects. J Zool 246:391–400.

Fleming TH. 1988. The short-tailed fruit bat. Chicago: University ofChicago Press.

Gianini NP, Kalko KV. 2004. Trophic structure in a large assemblageof phyllostomid bats in Panama. Oikos 105:209–220.

Herring SW, Rafferty KL, Liu ZJ, Marshall CD. 2001. Jaw musclesand the skull in mammals: the biomechanics of mastication. CompBiochem Physiol A Mol Integrat Physiol 131:207–219.

Hylander WL, Picq PG, Johnson KR. 1991. Masticatory stress hypoth-eses and the supraorbital region of primates. Am J Phys Anthropol86:1–36.

Hylander WL, Johnson KR. 1997. In vivo bone strain patterns in thezygomatic arch of macaques and the significance of these patternsfor functional interpretations of craniofacial form. Am J Phys An-thropol 102:203–232.

Lucas PW. 1979. The dental-dietary adaptations of mammals. NuesJahrbuch Geol Palaontol 8:486–512.

Lucas PW, Luke DA. 1984. Chewing it over: basic principles of foodbreakdown. In: Chivers DJ, Wood BA, Bilsborough A, editors. Foodacquisition and processing in primates. New York: Plenum Press. p283–301.

Nalla RK, Kinney JH, Ritchie RO. 2003. Mechanistic failure criteriafor the failure of human cortical bone. Nat Mater 2:164–168.

329BITING BEHAVIOR AND STRESS DISTRIBUTION

Nordin M, Frankel VH. 2001. Basic biomechanics of the musculoskel-etal system, 3rd ed. Philadalphia: Lippincott Williams and Eilkins.

Ravosa MJ, Johnson KR, Hylander WL. 2000. Strain in the galagofacial skull. J Morphol 245:51–66.

Richmond BG, Wright B, Grosse IR, Dechow PC, Ross CF, SpencerMA, Strait DS. 2005. Finite Element Analysis in Functional Mor-phology. Anat Rec 283A:259–274.

Ross CF. 2001. In vivo function of the craniofacial haft: the interor-bital “pillar.” Am J Phys Anthropol 116:108–139.

Strait DS, Wang O, Dechow PC, Ross CF, Richmond BG, Spencer MA,Patel BA. 2005. Modeling elastic properties in finite-elementanalysis: how much precision is needed to produce an accuratemodel? Anat Rec 283A:275–287.

Storch G. 1968. Funktionsmorphologische Untersuchungen an derKaumuskulatur und an kerrelierten schadelstrukturen der chirop-

teren. Abhandlungen Senckenbergischen Naturforschenden Gesell-schaft 51:1–92.

Strait D, Richmond B, Ross CF, Spencer M. 2002. Finite-elementanalysis of a macaque skull: applications for functional morphology.Am J Phys Anthropol 34(Suppl):149.

Tan KH, Zubaid A, Kunz TH. 1998. Food habits of Cynopterusbrachyotis (Muller) (Chiroptera: Pteropodidae) in peninsular Ma-laysia. J Tropic Ecol 14:299–307.

Thomason JJ, Russell AP. 1986. Mechanical factors in the evolution ofthe mammalian secondary palate: a theoretical analysis. J Morphol189:199–213.

Turner CH, Burr DB. 2003. Basic biomechanical measurements ofbone: a tutorial. Bone 14:595–608.

Van Valkenburgh B. 1996. Feeding behavior in free-ranging largeAfrican carnivores. J Mammal 77:240–254.

330 DUMONT ET AL.