Combined finite element and multibody dynamics analysis of biting in a Uromastyx hardwickii lizard skull

Evolution of the temporal skull openings in land vertebrates: A hypothetical framework on the basis of biomechanics

The complex constructions of land vertebrate skulls have inspired a number of functional analyses. In the present study, we provide a basic view on skull biomechanics and offer a framework for more general observations using advanced modeling approaches in the future. We concentrate our discussion on the cranial openings in the temporal skull region and work out two major, feeding-related factors that largely influence the shape of the skull. We argue that (1) the place where the most forceful biting is conducted and (2) the handling of resisting food (sideward movements) constitute the formation and shaping of either one or two temporal arcades surrounding these openings. Diversity in temporal skull anatomy among amniotes can be explained by specific modulations of these factors with different amounts of acting forces which inevitably lead to deposition or reduction of bone material. For example, forceful anterior bite favors an infratemporal bar, whereas forceful posterior bite favors formation of an upper temporal arcade. Transverse forces (inertia and resistance of seized objects) as well as neck posture also influence the shaping of the temporal region. Considering their individual skull morphotypes, we finally provide hypotheses on the feeding adaptation in a variety of major tetrapod groups. We did not consider ligaments, internal bone structure, or cranial kinesis in our considerations. Involving those in quantitative tests of our hypotheses, such as finite element system synthesis, will provide a comprehensive picture on cranial mechanics and evolution in the future.

Computational biomechanical modelling of the rabbit cranium during mastication

Although a functional relationship between bone structure and mastication has been shown in some regions of the rabbit skull, the biomechanics of the whole cranium during mastication have yet to be fully explored. In terms of cranial biomechanics, the rabbit is a particularly interesting species due to its uniquely fenestrated rostrum, the mechanical function of which is debated. In addition, the rabbit processes food through incisor and molar biting within a single bite cycle, and the potential influence of these bite modes on skull biomechanics remains unknown. This study combined the in silico methods of multi-body dynamics and finite element analysis to compute musculoskeletal forces associated with a range of incisor and molar biting, and to predict the associated strains. The results show that the majority of the cranium, including the fenestrated rostrum, transmits masticatory strains. The peak strains generated over all bites were found to be attributed to both incisor and molar biting. This could be a consequence of a skull shape adapted to promote an even strain distribution for a combination of infrequent incisor bites and cyclic molar bites. However, some regions, such as the supraorbital process, experienced low peak strain for all masticatory loads considered, suggesting such regions are not designed to resist masticatory forces.

Comparative cranial biomechanics in two lizard species: impact of variation in cranial design

Cranial morphology in lepidosaurs is highly disparate and characterised by the frequent loss or reduction of bony elements. In varanids and geckos, the loss of the postorbital bar is associated with changes in skull shape, but the mechanical principles underlying this variation remain poorly understood. Here, we sought to determine how the overall cranial architecture and the presence of the postorbital bar relate to the loading and deformation of the cranial bones during biting in lepidosaurs. Using computer-based simulation techniques, we compared cranial biomechanics in the varanid Varanus niloticus and the teiid Salvator merianae, two large, active foragers. The overall strain magnitude and distribution across the cranium were similar in the two species, despite lower strain gradients in V. niloticus. In S. merianae, the postorbital bar is important for resistance of the cranium to feeding loads. The postorbital ligament, which in varanids partially replaces the postorbital bar, does not affect bone strain. Our results suggest that the reduction of the postorbital bar impaired neither biting performance nor the structural resistance of the cranium to feeding loads in V. niloticus. Differences in bone strain between the two species might reflect demands imposed by feeding and non-feeding functions on cranial shape. Beyond variation in cranial bone strain related to species-specific morphological differences, our results reveal that similar mechanical behaviour is shared by lizards with distinct cranial shapes. Contrary to the situation in mammals, the morphology of the circumorbital region, calvaria and palate appears to be important for withstanding high feeding loads in these lizards.

Summary:In vivo measurements and computer-based simulations of the cranial mechanics of two large lizards indicate that similar mechanical behaviour is shared by lizards with distinct cranial architecture, and show the importance of the postorbital bar in resisting the feeding loads.

Biomechanics of juvenile tyrannosaurid mandibles and their implications for bite force: Evolutionary biology

The tyrannosaurids are among the most well-studied dinosaurs described by science, and analysis of their feeding biomechanics allows for comparison between established tyrannosaurid genera and across ontogeny. 3D finite element analysis (FEA) was used to model and quantify the mechanical properties of the mandibles (lower jaws) of three tyrannosaurine tyrannosaurids of different sizes. To increase evolutionary scope and context for 3D tyrannosaurine results, a broader sample of validated 2D mandible FEA enabled comparisons between ontogenetic stages of Tyrannosaurus rex and other large theropods. It was found that mandibles of small juvenile and large subadult tyrannosaurs experienced lower stress overall because muscle forces were relatively lower, but experienced greater simulated stresses at decreasing sizes when specimen muscle force is normalized. The strain on post-dentary ligaments decreases stress and strain in the posterior region of the dentary and where teeth impacted food. Tension from the lateral insertion of the looping m. ventral pterygoid muscle increases compressive stress on the angular but may decrease anterior bending stress on the mandible. Low mid-mandible bending stresses are congruent with ultra-robust teeth and high anterior bite force in adult T. rex. Mandible strength increases with size through ontogeny in T. rex and phylogenetically among other tyrannosaurids, in addition to that tyrannosaurid mandibles exceed the mandible strength of other theropods at equivalent ramus length. These results may indicate separate predatory strategies used by juvenile and mature tyrannosaurids; juvenile tyrannosaurids lacked the bone-crunching bite of adult specimens and hunted smaller prey, while adult tyrannosaurids fed on larger prey.

Kinematics and morphology: A comparison of 3D-patterns in the fifth pereiopod of swimming and non-swimming crab species (Malacostraca, Decapoda, Brachyura)

Swimming crabs of the taxon Portunoidea show specialized, paddle-shaped fifth pereiopods (P5), which play a role in these crabs' ability to swim. In this study, the morphology of the fifth pereiopod in swimming and non-swimming crabs was studied in detail and the mobility in the articulations between podomeres was calculated from reconstructed three-dimensional (3D)-models. This way, we aimed to provide new estimates of kinematic parameters, and to answer the question on a possible homology of the P5 within several portunoid clades. We measured and compared podomere length ratios, orientations of the joint axes, and modeled single range of motion (sROM) of each joint as well as the total range of motion (tROM) of all joints of the P5 as a whole. Seven Portunoidea species, four of them belonging to the P5-swimming crab morphotype (Liocarcinus depurator, Polybius henslowii, Callinectes sapidus, Portunus pelagicus) and three not belonging to this morphotype (Carcinus aestuarii, Portumnus latipes, and with uncertain status Carupa tenuipes) were compared with the non-portunoids Sternodromia monodi, Ranina ranina, Raninoides bouvieri, Eriocheir sinensis, Varuna litterata, Ashtoret lunaris, and Cancer pagurus. The study was carried out using a combination of microcomputer tomography (μCT)-techniques and 3D-reconstructions. The μCT-data were used to create surface models of the P5 in Amira, which were then 3D-animated and manipulated in Maya to qualitatively compare modeled kinematic parameters. Results show that the merus and carpus in swimming crabs are shorter than in non-swimming crabs, while sROM angles are generally larger. The tROM of all joints expressed as Euclidean distances is generally higher in the portunoids (except for Carcinus). Our comparison of the complete trajectory of the dactylus tip regarding all maximum joint positions of the studied species suggests that the P5-swimming leg might have evolved once in the Portunoidea and got lost afterward in certain clades.

Palatal Biomechanics and Its Significance for Cranial Kinesis in Tyrannosaurus rex

The extinct nonavian dinosaur Tyrannosaurus rex, considered one of the hardest biting animals ever, is often hypothesized to have exhibited cranial kinesis, or, mobility of cranial joints relative to the braincase. Cranial kinesis in T. rex is a biomechanical paradox in that forcefully biting tetrapods usually possess rigid skulls instead of skulls with movable joints. We tested the biomechanical performance of a tyrannosaur skull using a series of static positions mimicking possible excursions of the palate to evaluate Postural Kinetic Competency in Tyrannosaurus. A functional extant phylogenetic bracket was employed using taxa, which exhibit measurable palatal excursions: Psittacus erithacus (fore-aft movement) and Gekko gecko (mediolateral movement). Static finite element models of Psittacus, Gekko, and Tyrannosaurus were constructed and tested with different palatal postures using anatomically informed material properties, loaded with muscle forces derived from dissection, phylogenetic bracketing, and a sensitivity analysis of muscle architecture and tested in orthal biting simulations using element strain as a proxy for model performance. Extant species models showed lower strains in naturally occurring postures compared to alternatives. We found that fore-aft and neutral models of Tyrannosaurus experienced lower overall strains than mediolaterally shifted models. Protractor muscles dampened palatal strains, while occipital constraints increased strains about palatocranial joints compared to jaw joint constraints. These loading behaviors suggest that even small excursions can strain elements beyond structural failure. Thus, these postural tests of kinesis, along with the robusticity of other cranial features, suggest that the skull of Tyrannosaurus was functionally akinetic. Anat Rec, 303:999-1017, 2020. © 2019 Wiley Periodicals, Inc.

Ecomorphological diversification in squamates from conserved pattern of cranial integration

Factors intrinsic and extrinsic to organisms dictate the course of morphological evolution but are seldom considered together in comparative analyses. Among vertebrates, squamates (lizards and snakes) exhibit remarkable morphological and developmental variations that parallel their incredible ecological spectrum. However, this exceptional diversity also makes systematic quantification and analysis of their morphological evolution challenging. We present a squamate-wide, high-density morphometric analysis of the skull across 181 modern and extinct species to identify the primary drivers of their cranial evolution within a unified, quantitative framework. Diet and habitat preferences, but not reproductive mode, are major influences on skull-shape evolution across squamates, with fossorial and aquatic taxa exhibiting convergent and rapid changes in skull shape. In lizards, diet is associated with the shape of the rostrum, reflecting its use in grasping prey, whereas snakes show a correlation between diet and the shape of posterior skull bones important for gape widening. Similarly, we observe the highest rates of evolution and greatest disparity in regions associated with jaw musculature in lizards, whereas those forming the jaw articulation evolve faster in snakes. In addition, high-resolution ancestral cranial reconstructions from these data support a terrestrial, nonfossorial origin for snakes. Despite their disparate evolutionary trends, lizards and snakes unexpectedly share a common pattern of trait integration, with the highest correlations in the occiput, jaw articulation, and palate. We thus demonstrate that highly diverse phenotypes, exemplified by lizards and snakes, can and do arise from differential selection acting on conserved patterns of phenotypic integration.

Digital dissection of the head of the rock dove (Columba livia) using contrast-enhanced computed tomography

The rock dove (or common pigeon), Columba livia, is an important model organism in biological studies, including research focusing on head muscle anatomy, feeding kinematics, and cranial kinesis. However, no integrated computer-based biomechanical model of the pigeon head has yet been attempted. As an initial step towards achieving this goal, we present the first three-dimensional digital dissection of the pigeon head based on a contrast-enhanced computed tomographic dataset achieved using iodine potassium iodide as a staining agent. Our datasets enable us to visualize the skeletal and muscular anatomy, brain and cranial nerves, and major sense organs of the pigeon, including very small and fragile features, as well as maintaining the three-dimensional topology of anatomical structures. This work updates and supplements earlier anatomical work on this widely used laboratory organism. We resolve several key points of disagreement arising from previous descriptions of pigeon anatomy, including the precise arrangement of the external adductor muscles and their relationship to the posterior adductor. Examination of the eye muscles highlights differences between avian taxa and shows that pigeon eye muscles are more similar to those of a tinamou than they are to those of a house sparrow. Furthermore, we present our three-dimensional data as publicly accessible files for further research and education purposes. Digital dissection permits exceptional visualisation and will be a valuable resource for further investigations into the head anatomy of other bird species, as well as efforts to reconstruct soft tissues in fossil archosaurs.

Performance in three shell functions predicts the phenotypic distribution of hard-shelled turtles

Adaptive landscapes have served as fruitful guides to evolutionary research for nearly a century. Current methods guided by landscape frameworks mostly utilize evolutionary modeling (e.g., fitting data to Ornstein-Uhlenbeck models) to make inferences about adaptive peaks. Recent alternative methods utilize known relationships between phenotypes and functional performance to derive information about adaptive landscapes; this information can then help explain the distribution of species in phenotypic space and help infer the relative importance of various functions for guiding diversification. Here, data on performance for three turtle shell functions-strength, hydrodynamic efficiency, and self-righting ability-are used to develop a set of predicted performance optima in shell shape space. The distribution of performance optima shows significant similarity to the distribution of existing turtle species and helps explain the absence of shells in otherwise anomalously empty regions of morphospace. The method outperforms a modeling-based approach in inferring the location of reasonable adaptive peaks and in explaining the shape of the phenotypic distributions of turtle shells. Performance surface-based methods allow researchers to more directly connect functional performance with macroevolutionary diversification, and to explain the distribution of species (including presences and absences) across phenotypic space.

Warped finite element models predict whole shell failure in turtle shells

Finite element (FE) models have become increasingly popular in comparative biomechanical studies, with researchers continually developing methods such as 'warping' preexisting models to facilitate analyses. However, few studies have investigated how well FE models can predict biologically crucial whole-structure performance or whether 'warped' models can provide useful information about the mechanical behavior of actual specimens. This study addresses both of these issues through a validation of warped FE models of turtle shells. FE models for 40 turtle specimens were built using 3D landmark coordinates and thin-plate spline interpolations to warp preexisting turtle shell models. Each actual turtle specimen was loaded to failure, and the load at failure and mode of fracture were then compared with the behavior predicted by the models. Overall, the models performed very well, despite the fact that many simplifying assumptions were made for analysis. Regressions of observed on predicted loads were significant for the dataset as a whole, as well as in separate analyses within two turtle species, and the direction of fracture was generally consistent with the patterns of stresses observed in the models. This was true even when size (an important factor in determining strength) was removed from analyses - the models were also able to predict which shells would be relatively stronger or weaker. Although some residual variation remains unexplained, this study supports the idea that warped FE models run with simplifying assumptions at least can provide useful information for comparative biomechanical studies.

Inferring locomotor behaviours in Miocene New World monkeys using finite element analysis, geometric morphometrics and machine-learning classification techniques applied to talar morphology

The talus is one of the most commonly preserved post-cranial elements in the platyrrhine fossil record. Talar morphology can provide information about postural adaptations because it is the anatomical structure responsible for transmitting body mass forces from the leg to the foot. The aim of this study is to test whether the locomotor behaviour of fossil Miocene platyrrhines could be inferred from their talus morphology. The extant sample was classified into three different locomotor categories and then talar strength was compared using finite-element analysis. Geometric morphometrics were used to quantify talar shape and to assess its association with biomechanical strength. Finally, several machine-learning (ML) algorithms were trained using both the biomechanical and morphometric data from the extant taxa to infer the possible locomotor behaviour of the Miocene fossil sample. The obtained results show that the different locomotor categories are distinguishable using either biomechanical or morphometric data. The ML algorithms categorized most of the fossil sample as arboreal quadrupeds. This study has shown that a combined approach can contribute to the understanding of platyrrhine talar morphology and its relationship with locomotion. This approach is likely to be beneficial for determining the locomotor habits in other fossil taxa.

The biomechanical role of the chondrocranium and sutures in a lizard cranium

The role of soft tissues in skull biomechanics remains poorly understood. Not least, the chondrocranium, the portion of the braincase which persists as cartilage with varying degrees of mineralization. It also remains commonplace to overlook the biomechanical role of sutures despite evidence that they alter strain distribution. Here, we examine the role of both the sutures and the chondrocranium in the South American tegu lizard Salvator merianae We use multi-body dynamics analysis (MDA) to provide realistic loading conditions for anterior and posterior unilateral biting and a detailed finite element model to examine strain magnitude and distribution. We find that strains within the chondrocranium are greatest during anterior biting and are primarily tensile; also that strain within the cranium is not greatly reduced by the presence of the chondrocranium unless it is given the same material properties as bone. This result contradicts previous suggestions that the anterior portion (the nasal septum) acts as a supporting structure. Inclusion of sutures to the cranium model not only increases overall strain magnitudes but also leads to a more complex distribution of tension and compression rather than that of a beam under sagittal bending.

Computational biomechanics changes our view on insect head evolution

Despite large-scale molecular attempts, the relationships of the basal winged insect lineages dragonflies, mayflies and neopterans, are still unresolved. Other data sources, such as morphology, suffer from unclear functional dependencies of the structures considered, which might mislead phylogenetic inference. Here, we assess this problem by combining for the first time biomechanics with phylogenetics using two advanced engineering techniques, multibody dynamics analysis and finite-element analysis, to objectively identify functional linkages in insect head structures which have been used traditionally to argue basal winged insect relationships. With a biomechanical model of unprecedented detail, we are able to investigate the mechanics of morphological characters under biologically realistic load, i.e. biting. We show that a range of head characters, mainly ridges, endoskeletal elements and joints, are indeed mechanically linked to each other. An analysis of character state correlation in a morphological data matrix focused on head characters shows highly significant correlation of these mechanically linked structures. Phylogenetic tree reconstruction under different data exclusion schemes based on the correlation analysis unambiguously supports a sistergroup relationship of dragonflies and mayflies. The combination of biomechanics and phylogenetics as it is proposed here could be a promising approach to assess functional dependencies in many organisms to increase our understanding of phenotypic evolution.

Reacquisition of the lower temporal bar in sexually dimorphic fossil lizards provides a rare case of convergent evolution

Temporal fenestration has long been considered a key character to understand relationships amongst reptiles. In particular, the absence of the lower temporal bar (LTB) is considered one of the defining features of squamates (lizards and snakes). In a re-assessment of the borioteiioid lizard Polyglyphanodon sternbergi (Cretaceous, North America), we detected a heretofore unrecognized ontogenetic series, sexual dimorphism (a rare instance for Mesozoic reptiles), and a complete LTB, a feature only recently recognized for another borioteiioid, Tianyusaurus zhengi (Cretaceous, China). A new phylogenetic analysis (with updates on a quarter of the scorings for P. sternbergi) indicates not only that the LTB was reacquired in squamates, but it happened independently at least twice. An analysis of the functional significance of the LTB using proxies indicates that, unlike for T. zhengi, this structure had no apparent functional advantage in P. sternbergi, and it is better explained as the result of structural constraint release. The observed canalization against a LTB in squamates was broken at some point in the evolution of borioteiioids, whereas never re-occuring in other squamate lineages. This case of convergent evolution involves a mix of both adaptationist and structuralist causes, which is unusual for both living and extinct vertebrates.

Estimating cranial musculoskeletal constraints in theropod dinosaurs

Many inferences on the biology, behaviour and ecology of extinct vertebrates are based on the reconstruction of the musculature and rely considerably on its accuracy. Although the advent of digital reconstruction techniques has facilitated the creation and testing of musculoskeletal hypotheses in recent years, muscle strain capabilities have rarely been considered. Here, a digital modelling approach using the freely available visualization and animation software Blender is applied to estimate cranial muscle length changes and optimal and maximal possible gape in different theropod dinosaurs. Models of living archosaur taxa (Alligator mississippiensis, Buteo buteo) were used in an extant phylogenetically bracketed framework to validate the method. Results of this study demonstrate that Tyrannosaurus rex, Allosaurus fragilis and Erlikosaurus andrewsi show distinct differences in the recruitment of the jaw adductor musculature and resulting gape, confirming previous dietary and ecological assumptions. While the carnivorous taxa T. rex and Allo. fragilis were capable of a wide gape and sustained muscle force, the herbivorous therizinosaurian E. andrewsi was constrained to small gape angles.

Masticatory biomechanics in the rabbit: a multi-body dynamics analysis

Multi-body dynamics is a powerful engineering tool which is becoming increasingly popular for the simulation and analysis of skull biomechanics. This paper presents the first application of multi-body dynamics to analyse the biomechanics of the rabbit skull. A model has been constructed through the combination of manual dissection and three-dimensional imaging techniques (magnetic resonance imaging and micro-computed tomography). Individual muscles are represented with multiple layers, thus more accurately modelling muscle fibres with complex lines of action. Model validity was sought through comparing experimentally measured maximum incisor bite forces with those predicted by the model. Simulations of molar biting highlighted the ability of the masticatory system to alter recruitment of two muscle groups, in order to generate shearing or crushing movements. Molar shearing is capable of processing a food bolus in all three orthogonal directions, whereas molar crushing and incisor biting are predominately directed vertically. Simulations also show that the masticatory system is adapted to process foods through several cycles with low muscle activations, presumably in order to prevent rapidly fatiguing fast fibres during repeated chewing cycles. Our study demonstrates the usefulness of a validated multi-body dynamics model for investigating feeding biomechanics in the rabbit, and shows the potential for complementing and eventually reducing in vivo experiments.

In Vivo Measurement of Mesokinesis in Gekko gecko: The Role of Cranial Kinesis during Gape Display, Feeding and Biting

Cranial kinesis refers to movements of skeletal sub-units relative to one another at mobile sutures within the skull. The presence and functional significance of cranial kinesis has been investigated in various vertebrates, with much of our understanding coming from comparative studies and manipulation of ligamentous specimens. Drawing on these studies, cranial kinesis in lizards has been modeled as a four-bar linkage system involving streptostyly (rotation of the quadrate), hypokinesis (dorsoventral flexion and extension of the palato-maxillary sub-unit), mesokinesis (dorsoventral flexion and extension of the snout at the fronto-parietal suture) and metakinesis (sliding movements between parietal and supraocciptal bones). In vivo studies, although limited, suggest that cranial kinesis serves an important role during routine behaviors such as feeding. Here, we use X-ray Reconstruction Of Moving Morphology to further quantify mesokinesis in vivo in Gekko gecko during three routine behaviors: gape display, biting and post-ingestion feeding. During gape display, the snout rotates dorsally above rest position, with mesokinesis accounting for a 10% increase in maximum gape over that achieved solely by the depression of the lower jaw. During defensive biting, the snout rotates ventrally below rest position to participate in gape closure. Finally, ventroflexion of the snout also occurs during post-ingestion feeding, accounting for 42% of gape closure during intra-oral transport, 86% during puncture-crushing, and 61% during pharyngeal packing. Mesokinesis thus appears to facilitate prey puncturing by allowing the snout to rotate ventrally so that the upper teeth pierce the prey item, thus limiting the need for large movements of the lower jaw. This is suggested to maintain a firm grip on the prey and reduce the possibility of prey escape. More generally, this study demonstrates that mesokinesis is a key component of defensive biting and gape display behaviors, as well as post-ingestion feeding, all of which are linked to organismal fitness.

Virtual reconstruction and prey size preference in the mid Cenozoic thylacinid, Nimbacinus dicksoni (Thylacinidae, Marsupialia)

Thylacinidae is an extinct family of Australian and New Guinean marsupial carnivores, comprizing 12 known species, the oldest of which are late Oligocene (∼24 Ma) in age. Except for the recently extinct thylacine (Thylacinus cynocephalus), most are known from fragmentary craniodental material only, limiting the scope of biomechanical and ecological studies. However, a particularly well-preserved skull of the fossil species Nimbacinus dicksoni, has been recovered from middle Miocene (∼16-11.6 Ma) deposits in the Riversleigh World Heritage Area, northwestern Queensland. Here, we ask whether N. dicksoni was more similar to its recently extinct relative or to several large living marsupials in a key aspect of feeding ecology, i.e., was N. dicksoni a relatively small or large prey specialist. To address this question we have digitally reconstructed its skull and applied three-dimensional Finite Element Analysis to compare its mechanical performance with that of three extant marsupial carnivores and T. cynocephalus. Under loadings adjusted for differences in size that simulated forces generated by both jaw closing musculature and struggling prey, we found that stress distributions and magnitudes in the skull of N. dicksoni were more similar to those of the living spotted-tailed quoll (Dasyurus maculatus) than to its recently extinct relative. Considering the Finite Element Analysis results and dental morphology, we predict that N. dicksoni likely occupied a broadly similar ecological niche to that of D. maculatus, and was likely capable of hunting vertebrate prey that may have exceeded its own body mass.

In vivo cranial bone strain and bite force in the agamid lizard Uromastyx geyri

In vivo bone strain data are the most direct evidence of deformation and strain regimes in the vertebrate cranium during feeding and can provide important insights into skull morphology. Strain data have been collected during feeding across a wide range of mammals; in contrast, in vivo cranial bone strain data have been collected from few sauropsid taxa. Here we present bone strain data recorded from the jugal of the herbivorous agamid lizard Uromastyx geyri along with simultaneously recorded bite force. Principal and shear strain magnitudes in Uromastyx geyri were lower than cranial bone strains recorded in Alligator mississippiensis, but higher than those reported from herbivorous mammals. Our results suggest that variations in principal strain orientations in the facial skeleton are largely due to differences in feeding behavior and bite location, whereas food type has little impact on strain orientations. Furthermore, mean principal strain orientations differ between male and female Uromastyx during feeding, potentially because of sexual dimorphism in skull morphology.

The morphology of the mouse masticatory musculature

The mouse has been the dominant model organism in studies on the development, genetics and evolution of the mammalian skull and associated soft-tissue for decades. There is the potential to take advantage of this well studied model and the range of mutant, knockin and knockout organisms with diverse craniofacial phenotypes to investigate the functional significance of variation and the role of mechanical forces on the development of the integrated craniofacial skeleton and musculature by using computational mechanical modelling methods (e.g. finite element and multibody dynamic modelling). Currently, there are no detailed published data of the mouse masticatory musculature available. Here, using a combination of micro-dissection and non-invasive segmentation of iodine-enhanced micro-computed tomography, we document the anatomy, architecture and proportions of the mouse masticatory muscles. We report on the superficial masseter (muscle, tendon and pars reflecta), deep masseter, zygomaticomandibularis (anterior, posterior, infraorbital and tendinous parts), temporalis (lateral and medial parts), external and internal pterygoid muscles. Additionally, we report a lateral expansion of the attachment of the temporalis onto the zygomatic arch, which may play a role in stabilising this bone during downwards loading. The data presented in this paper now provide a detailed reference for phenotypic comparison in mouse models and allow the mouse to be used as a model organism in biomechanical and functional modelling and simulation studies of the craniofacial skeleton and particularly the masticatory system.

The role of the sutures in biomechanical dynamic simulation of a macaque cranial finite element model: implications for the evolution of craniofacial form

The global biomechanical impact of cranial sutures on the face and cranium during dynamic conditions is not well understood. It is hypothesized that sutures act as energy absorbers protecting skulls subjected to dynamic loads. This hypothesis predicts that sutures have a significant impact on global patterns of strain and cranial structural stiffness when analyzed using dynamic simulations; and that this global impact is influenced by suture material properties. In a finite element model developed from a juvenile Rhesus macaque cranium, five different sets of suture material properties for the zygomaticotemporal sutures were tested. The static and dynamic analyses produced similar results in terms of strain patterns and reaction forces, indicating that the zygomaticotemporal sutures have limited impact on global skull mechanics regardless of loading design. Contrary to the functional hypothesis tested in this study, the zygomaticotemporal sutures did not absorb significant amounts of energy during dynamic simulations regardless of loading speed. It is alternatively hypothesized that sutures are mechanically significant only insofar as they are weak points on the cranium that must be shielded from unduly high stresses so as not to disrupt vitally important growth processes. Thus, sutural and overall cranial form in some vertebrates may be optimized to minimize or otherwise modulate sutural stress and strain.

Sensitivity and ex vivo validation of finite element models of the domestic pig cranium

A finite element (FE) validation and sensitivity study was undertaken on a modern domestic pig cranium. Bone strain data were collected ex vivo from strain gauges, and compared with results from specimen-specific FE models. An isotropic, homogeneous model was created, then input parameters were altered to investigate model sensitivity. Heterogeneous, isotropic models investigated the effects of a constant-thickness, stiffer outer layer (representing cortical bone) atop a more compliant interior (representing cancellous bone). Loading direction and placement of strain gauges were also varied, and the use of 2D membrane elements at strain gauge locations as a method of projecting 3D model strains into the plane of the gauge was investigated. The models correctly estimate the loading conditions of the experiment, yet at some locations fail to reproduce correct principal strain magnitudes, and hence strain ratios. Principal strain orientations are predicted well. The initial model was too stiff by approximately an order of magnitude. Introducing a compliant interior reported strain magnitudes more similar to the ex vivo results without notably affecting strain orientations, ratios or contour patterns, suggesting that this simple heterogeneity was the equivalent of reducing the overall stiffness of the model. Models were generally insensitive to moderate changes in loading direction or strain gauge placement, except in the squamosal portion of the zygomatic arch. The use of membrane elements made negligible differences to the reported strains. The models therefore seem most sensitive to changes in material properties, and suggest that failure to model local heterogeneity in material properties and structure of the bone may be responsible for discrepancies between the experimental and model results. This is partially attributable to a lack of resolution in the CT scans from which the model was built, and partially due to an absence of detailed material properties data for pig cranial bone. Thus, caution is advised when using FE models to estimate absolute numerical values of breaking stress and bite force unless detailed input parameters are available. However, if the objective is to compare relative differences between models, the fact that the strain environment is replicated well means that such investigations can be robust.

Model sensitivity and use of the comparative finite element method in mammalian jaw mechanics: mandible performance in the gray wolf

Finite Element Analysis (FEA) is a powerful tool gaining use in studies of biological form and function. This method is particularly conducive to studies of extinct and fossilized organisms, as models can be assigned properties that approximate living tissues. In disciplines where model validation is difficult or impossible, the choice of model parameters and their effects on the results become increasingly important, especially in comparing outputs to infer function. To evaluate the extent to which performance measures are affected by initial model input, we tested the sensitivity of bite force, strain energy, and stress to changes in seven parameters that are required in testing craniodental function with FEA. Simulations were performed on FE models of a Gray Wolf (Canis lupus) mandible. Results showed that unilateral bite force outputs are least affected by the relative ratios of the balancing and working muscles, but only ratios above 0.5 provided balancing-working side joint reaction force relationships that are consistent with experimental data. The constraints modeled at the bite point had the greatest effect on bite force output, but the most appropriate constraint may depend on the study question. Strain energy is least affected by variation in bite point constraint, but larger variations in strain energy values are observed in models with different number of tetrahedral elements, masticatory muscle ratios and muscle subgroups present, and number of material properties. These findings indicate that performance measures are differentially affected by variation in initial model parameters. In the absence of validated input values, FE models can nevertheless provide robust comparisons if these parameters are standardized within a given study to minimize variation that arise during the model-building process. Sensitivity tests incorporated into the study design not only aid in the interpretation of simulation results, but can also provide additional insights on form and function.

An efficient method of modeling material properties using a thermal diffusion analogy: an example based on craniofacial bone

The ability to incorporate detailed geometry into finite element models has allowed researchers to investigate the influence of morphology on performance aspects of skeletal components. This advance has also allowed researchers to explore the effect of different material models, ranging from simple (e.g., isotropic) to complex (e.g., orthotropic), on the response of bone. However, bone's complicated geometry makes it difficult to incorporate complex material models into finite element models of bone. This difficulty is due to variation in the spatial orientation of material properties throughout bone. Our analysis addresses this problem by taking full advantage of a finite element program's ability to solve thermal-structural problems. Using a linear relationship between temperature and modulus, we seeded specific nodes of the finite element model with temperatures. We then used thermal diffusion to propagate the modulus throughout the finite element model. Finally, we solved for the mechanical response of the finite element model to the applied loads and constraints. We found that using the thermal diffusion analogy to control the modulus of bone throughout its structure provides a simple and effective method of spatially varying modulus. Results compare favorably against both experimental data and results from an FE model that incorporated a complex (orthotropic) material model. This method presented will allow researchers the ability to easily incorporate more material property data into their finite element models in an effort to improve the model's accuracy.

In vivo bone strain and finite-element modeling of the craniofacial haft in catarrhine primates

Hypotheses regarding patterns of stress, strain and deformation in the craniofacial skeleton are central to adaptive explanations for the evolution of primate craniofacial form. The complexity of craniofacial skeletal morphology makes it difficult to evaluate these hypotheses with in vivo bone strain data. In this paper, new in vivo bone strain data from the intraorbital surfaces of the supraorbital torus, postorbital bar and postorbital septum, the anterior surface of the postorbital bar, and the anterior root of the zygoma are combined with published data from the supraorbital region and zygomatic arch to evaluate the validity of a finite-element model (FEM) of a macaque cranium during mastication. The behavior of this model is then used to test hypotheses regarding the overall deformation regime in the craniofacial haft of macaques. This FEM constitutes a hypothesis regarding deformation of the facial skeleton during mastication. A simplified verbal description of the deformation regime in the macaque FEM is as follows. Inferior bending and twisting of the zygomatic arches about a rostrocaudal axis exerts inferolaterally directed tensile forces on the lateral orbital wall, bending the wall and the supraorbital torus in frontal planes and bending and shearing the infraorbital region and anterior zygoma root in frontal planes. Similar deformation regimes also characterize the crania of Homo and Gorilla under in vitro loading conditions and may be shared among extant catarrhines. Relatively high strain magnitudes in the anterior root of the zygoma suggest that the morphology of this region may be important for resisting forces generated during feeding.

Combining geometric morphometrics and functional simulation: an emerging toolkit for virtual functional analyses

The development of virtual methods for anatomical reconstruction and functional simulation of skeletal structures offers great promise in evolutionary and ontogenetic investigations of form-function relationships. Key developments reviewed here include geometric morphometric methods for the analysis and visualization of variations in form (size and shape), finite element methods for the prediction of mechanical performance of skeletal structures under load and multibody dynamics methods for the simulation and prediction of musculoskeletal function. These techniques are all used in studies of form and function in biology, but only recently have they been combined in novel ways to facilitate biomechanical modelling that takes account of variations in form, can statistically compare performance, and relate performance to form and its covariates. Here we provide several examples that illustrate how these approaches can be combined and we highlight areas that require further investigation and development before we can claim a mature theory and toolkit for a statistical biomechanical framework that unites these methods.

Strain in the ostrich mandible during simulated pecking and validation of specimen-specific finite element models

Finite element (FE) analysis is becoming a frequently used tool for exploring the craniofacial biomechanics of extant and extinct vertebrates. Crucial to the application of the FE analysis is the knowledge of how well FE results replicate reality. Here I present a study investigating how accurately FE models can predict experimentally derived strain in the mandible of the ostrich Struthio camelus, when both the model and the jaw are subject to identical conditions in an in-vitro loading environment. Three isolated ostrich mandibles were loaded hydraulically at the beak tip with forces similar to those measured during force transducer pecking experiments. Strains were recorded at four gauge sites at the dorsal and ventral dentary, and medial and lateral surangular. Specimen-specific FE models were created from computed tomography scans of each ostrich and loaded in an identical fashion as in the in-vitro test. The results show that the strain magnitudes, orientation, patterns and maximum : minimum principal strain ratios are predicted very closely at the dentary gauge sites, even though the FE models have isotropic and homogeneous material properties and solid internal geometry. Although the strain magnitudes are predicted at the postdentary sites, the strain orientations and ratios are inaccurate. This mismatch between the dentary and postdentary predictions may be due to the presence of intramandibular sutures or the greater amount of cancellous bone present in the postdentary region of the mandible and requires further study. This study highlights the predictive potential of even simple FE models for studies in extant and extinct vertebrates, but also emphasizes the importance of geometry and sutures. It raises the question of whether different parameters are of lesser or greater importance to FE validation for different taxonomic groups.

Biomechanical assessment of evolutionary changes in the lepidosaurian skull

The lepidosaurian skull has long been of interest to functional morphologists and evolutionary biologists. Patterns of bone loss and gain, particularly in relation to bars and fenestrae, have led to a variety of hypotheses concerning skull use and kinesis. Of these, one of the most enduring relates to the absence of the lower temporal bar in squamates and the acquisition of streptostyly. We performed a series of computer modeling studies on the skull of Uromastyx hardwickii, an akinetic herbivorous lizard. Multibody dynamic analysis (MDA) was conducted to predict the forces acting on the skull, and the results were transferred to a finite element analysis (FEA) to estimate the pattern of stress distribution. In the FEA, we applied the MDA result to a series of models based on the Uromastyx skull to represent different skull configurations within past and present members of the Lepidosauria. In this comparative study, we found that streptostyly can reduce the joint forces acting on the skull, but loss of the bony attachment between the quadrate and pterygoid decreases skull robusticity. Development of a lower temporal bar apparently provided additional support for an immobile quadrate that could become highly stressed during forceful biting.

Assessment of the role of sutures in a lizard skull: a computer modelling study

Sutures form an integral part of the functioning skull, but their role has long been debated among vertebrate morphologists and palaeontologists. Furthermore, the relationship between typical skull sutures, and those involved in cranial kinesis, is poorly understood. In a series of computational modelling studies, complex loading conditions obtained through multibody dynamics analysis were imposed on a finite element model of the skull of Uromastyx hardwickii, an akinetic herbivorous lizard. A finite element analysis (FEA) of a skull with no sutures revealed higher patterns of strain in regions where cranial sutures are located in the skull. From these findings, FEAs were performed on skulls with sutures (individual and groups of sutures) to investigate their role and function more thoroughly. Our results showed that individual sutures relieved strain locally, but only at the expense of elevated strain in other regions of the skull. These findings provide an insight into the behaviour of sutures and show how they are adapted to work together to distribute strain around the skull. Premature fusion of one suture could therefore lead to increased abnormal loading on other regions of the skull causing irregular bone growth and deformities. This detailed investigation also revealed that the frontal-parietal suture of the Uromastyx skull played a substantial role in relieving strain compared with the other sutures. This raises questions about the original role of mesokinesis in squamate evolution.