Comparison between in vivo and theoretical bite performance: Using multi-body modelling to predict muscle and bite forces in a reptile skull

In biomechanical investigations, geometrically accurate computer models of anatomical structures can be created readily using computed-tomography scan images. However, representation of soft tissue structures is more challenging, relying on approximations to predict the muscle loading conditions that are essential in detailed functional analyses. Here, using a sophisticated multi-body computer model of a reptile skull (the rhynchocephalian Sphenodon), we assess the accuracy of muscle force predictions by comparing predicted bite forces against in vivo data. The model predicts a bite force almost three times lower than that measured experimentally. Peak muscle force estimates are highly sensitive to fibre length, muscle stress, and pennation where the angle is large, and variation in these parameters can generate substantial differences in predicted bite forces. A review of theoretical bite predictions amongst lizards reveals that bite forces are consistently underestimated, possibly because of high levels of muscle pennation in these animals. To generate realistic bites during theoretical analyses in Sphenodon, lizards, and related groups we suggest that standard muscle force calculations should be multiplied by a factor of up to three. We show that bite forces increase and joint forces decrease as the bite point shifts posteriorly within the jaw, with the most posterior bite location generating a bite force almost double that of the most anterior bite. Unilateral and bilateral bites produced similar total bite forces; however, the pressure exerted by the teeth is double during unilateral biting as the tooth contact area is reduced by half.     

The growth of the skull and jaw muscles and its functional consequences in the New Zealand rabbit (Oryctolagus cuniculus)

Between weaning and adulthood, the length and height of the facial skull of the New Zealand rabbit (Oryctolagus cuniculus) double, whereas much less growth occurs in the width of the face and in the neurocranium. There is a five-fold increase in mass of the masticatory muscles, caused mainly by growth in cross-sectional area. The share of the superficial masseter in the total mass increases at the cost of the jaw openers. There are changes in the direction of the working lines of a few muscles. A 3-dimensional mechanical model was used to predict bite forces at different mandibular positions. It shows that young rabbits are able to generate large bite forces at a wider range of mandibular positions than adults and that the forces are directed more vertically. In young and adult animals, the masticatory muscles differ from each other with respect to the degree of gape at which optimum sarcomere length is reached. Consequently, bite force can be maintained over a range of gapes, larger than predicted on basis of individual length-tension curves. Despite the considerable changes in skull shape and concurrent changes in the jaw muscles, the direction of the resultant force of the closing muscles and its mechanical advantage remain stable during growth. Observed phenomena suggest that during development the possibilities for generation of large bite forces are increased at the cost of a restriction of the range of jaw excursion.     

Comparative functional analysis of skull morphology of tree-gouging primates

Many primates habitually feed on tree exudates such as gums and saps. Among these exudate feeders, Cebuella pygmaea, Callithrix spp., Phaner furcifer, and most likely Euoticus elegantulus elicit exudate flow by biting into trees with their anterior dentition. We define this behavior as gouging. Beyond the recent publication by Dumont ([1997] Am J Phys Anthropol 102:187-202), there have been few attempts to address whether any aspect of skull form in gouging primates relates to this specialized feeding behavior. However, many researchers have proposed that tree gouging results in larger bite force, larger internal skull loads, and larger jaw gapes in comparison to other chewing and biting behaviors. If true, then we might expect primate gougers to exhibit skull modifications that provide increased abilities to produce bite forces at the incisors, withstand loads in the skull, and/or generate large gapes for gouging.We develop 13 morphological predictions based on the expectation that gouging involves relatively large jaw forces and/or jaw gapes. We compare skull shapes for P. furcifer to five cheirogaleid taxa, E. elegantulus to six galagid species, and C. jacchus to two tamarin species, so as to assess whether gouging primates exhibit these predicted morphological shapes. Our results show little morphological evidence for increased force-production or load-resistance abilities in the skulls of these gouging primates. Conversely, these gougers tend to have skull shapes that are advantageous for creating large gapes. For example, all three gouging species have significantly lower condylar heights relative to the toothrow at a given mandibular length in comparison with closely related, nongouging taxa. Lowering the height of the condyle relative to the mandibular toothrow should reduce the stretching of the masseters and medial pterygoids during jaw opening, as well as position the mandibular incisors more anteriorly at wide jaw gapes. In other words, the lower incisors will follow a more vertical trajectory during both jaw opening and closing.We predict, based on these findings, that tree-gouging primates do not generate unusually large forces, but that they do use relatively large gapes during gouging. Of course, in vivo data on jaw forces and jaw gapes are required to reliably assess skull functions during gouging.     

Dry versus wet and gross: Comparisons between the dry skull method and gross dissection in estimations of jaw muscle cross-sectional area and bite forces in sea otters

Bite force is a measure of feeding performance used to elucidate links between animal morphology, ecology, and fitness. Obtaining live individuals for in vivo bite-force measurements or freshly deceased specimens for bite force modeling is challenging for many species. Thomason's dry skull method for mammals relies solely on osteological specimens and, therefore, presents an advantageous approach that enables researchers to estimate and compare bite forces across extant and even extinct species. However, how accurately the dry skull method estimates physiological cross-sectional area (PCSA) of the jaw adductor muscles and theoretical bite force has rarely been tested. Here, we use an ontogenetic series of southern sea otters (Enhydra lutris nereis) to test the hypothesis that skeletomuscular traits estimated from the dry skull method accurately predicts test traits derived from dissection-based biomechanical modeling. Although variables from these two methods exhibited strong positive relationships across ontogeny, we found that the dry skull method overestimates PCSA of the masseter and underestimates PCSA of the temporalis. Jaw adductor in-levers for both jaw muscles and overall bite force are overestimated. Surprisingly, we reveal that sexual dimorphism in craniomandibular shape affects temporalis PCSA estimations; the dry skull method predicted female temporalis PCSA well but underestimates male temporalis PCSA across ontogeny. These results highlight the importance of accounting for sexual dimorphism and other intraspecific variation when using the dry skull method. Together, we found the dry skull method provides an underestimation of bite force over ontogeny and that the underlying anatomical components driving bite force may be misrepresented.     

Function-dependent shape characteristics of the human skull

Using the FEM-program ANSYS 5.4, we have shaped a model of the human skull in which the flow of forces and the relative location and magnitudes of stresses are investigated. Forces are applied from below through the tooth row of the upper jaw. An ample volume is provided for the transmission of these bite forces upward to the roof of the braincase, where bearings counteract the forces from below. Within this volume, no other morphological features are considered than two cone-shaped orbits and a nasal channel which has a rounded, triangular cross section, extending upward between the orbits. Under loads (= bite forces) acting simultaneously in the directions and relative sizes of realistic bite- and chewing forces, there occurred stress concentrations inside the model which resemble closely the morphological characteristics of the human skull. The most remarkable pathways of stresses correspond to Toldt's and Benninghoff's nasal, zygomatic and pterygoid pillars. Aside from these stress concentrations, stress-free regions become visible at places, where the skull shows excavations: the vaulted palate with canalis incisivus, the canine fossa, superior and inferior orbital fissure, or cavities like the maxillary sinuses and cavum cranii. Behind the posterior molars and the pterygoid, the stresses disappear abruptly, and in the side wall of the nasal cavity a maxillary hiatus remains without stresses. A flow of forces comparable to, but not at the exact position of the zygomatic arch extends from the highly stressed zygomatic bone rearward and upward. In a later step of simulation, somewhat deeper, at the place of the really existing zygomatic arch, a series of small forces was applied, which correspond to the resultant force that is created by the redirection of the pull of the m. masseter into the temporal fascia. This--biologically reasonable--manipulation of the model leads to a reduction of the forces in the zygomatic bone, and to a downward shift of the zygomatic arch and its isolation from the skull's side wall by a deep, stress-free temporal fossa. The similarity between the stress flow in the model and the shape of the skull seems to indicate that the skull, like the bones of the postcranial skeleton, develops its shape in dependence from the mechanic stressing through the process of causal histogenesis. In view of experimental results, the possibility cannot be ruled out, that the safety factors in the skull deviate from those in the postcranial skeleton.     

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.     

A new psittacosaur from Inner Mongolia and the parrot-like structure and function of the psittacosaur skull

We describe a new species of psittacosaur, Psittacosaurus gobiensis, from the Lower Cretaceous of Inner Mongolia and outline a hypothesis of chewing function in psittacosaurs that in many respects parallels that in psittaciform birds. Cranial features that accommodate increased bite force in psittacosaurs include an akinetic skull (both cranium and lower jaws) and differentiation of adductor muscle attachments comparable to that in psittaciform birds. These and other features, along with the presence of numerous large gastroliths, suggest that psittacosaurs may have had a high-fibre, nucivorous (nut-eating) diet.Psittacosaurs, alone among ornithischians, generate oblique wear facets from tooth-to-tooth occlusion without kinesis in either the upper or lower jaws. This is accomplished with a novel isognathous jaw mechanism that combines aspects of arcilineal (vertical) and propalinal (horizontal) jaw movement. Here termed clinolineal (inclined) jaw movement, the mechanism uses posteriorly divergent tooth rows, rather than kinesis, to gain the added width for oblique occlusion. As the lower tooth rows are drawn posterodorsally into occlusion, the increasing width between the upper tooth rows accommodates oblique shear. With this jaw mechanism, psittacosaurs were able to maintain oblique shearing occlusion in an akinetic skull designed to resist high bite forces.     

Effects of gape and tooth position on bite force and skull stress in the dingo (Canis lupus dingo) using a 3-dimensional finite element approach

Models of the mammalian jaw have predicted that bite force is intimately linked to jaw gape and to tooth position. Despite widespread use, few empirical studies have provided evidence to validate these models in non-human mammals and none have considered the influence of gape angle on the distribution of stress. Here using a multi-property finite element (FE) model of Canis lupus dingo, we examined the influence of gape angle and bite point on both bite force and cranial stress. Bite force data in relation to jaw gape and along the tooth row, are in broad agreement with previously reported results. However stress data showed that the skull of C. l. dingo is mechanically suited to withstand stresses at wide gapes; a result that agreed well with previously held views regarding carnivoran evolution. Stress data, combined with bite force information, suggested that there is an optimal bite angle of between 25 degrees and 35 degrees in C. l. dingo. The function of these rather small bite angles remains unclear.     

Implications of predatory specialization for cranial form and function in canids

The shape of the cranium varies widely among members of the order Carnivora, but the factors that drive the evolution of differences in shape remain unclear. Selection for increased bite force, bite speed or skull strength may all affect cranial morphology. We investigated the relationship between cranial form and function in the trophically diverse dog family, Canidae, using linear morphometrics and finite element (FE) analyses that simulated the internal and external forces that act on the skull during the act of prey capture and killing. In contrast to previous FE-based studies, we compared models using a newly developed method that removes the effects of size and highlights the relationship between shape and performance. Cranial shape varies among canids based on diet, and different selective forces presumably drove evolution of these phenotypes. The long, narrow jaws of small prey specialists appear to reflect selection for fast jaw closure at the expense of bite force. Generalists have intermediate jaw dimensions and produce moderate bite forces, but their crania are comparable in strength to those of small prey specialists. Canids that take large prey have short, broad jaws, produce the largest bite forces and possess very strong crania. Our FE simulations suggest that the remarkable strength of skulls of large prey specialists reflect the additional ability to resist extrinsic loads that may be encountered while struggling with large prey items.     

Functional structure of the skull in hominoidea

Finite elements stress analysis (FESA) was used to investigate the flow of compressive forces which occur if a homogenous, three-dimensional body representing the skull is loaded by simulated bite forces against the tooth row. Model 1 represents the snout alone. Bite forces are applied simultaneously, but increase rearward. Stresses in the model concentrate along the anterior contour and the lower surface of the model, leaving unstressed a nasal opening and a wide naso-oral connection. Model 2 represents the facial region, as far as the temporomandibular joint. The orbits and the nasal cavity are assumed to be present a priori. Model 3 applies reactions to the bite forces in the temporal fossa, corresponding to the origins of the masticatory muscles. Regions of the model under compressive stress correspond closely to the arrangement of bony material in a hominoid skull. If only the stress-bearing finite elements on each section are combined, and the stress-free parts neglected, the resulting three-dimensional shape is surprisingly similar to a hominoid skull. If bite forces are applied to parts of the tooth row only, the stress patterns are lower, asymmetrical and do not spread into all regions that are stress-bearing in simultaneous biting on all teeth. In model 2, the highest stresses occur at the tooth roots and along the forehead on top of the nasal roof. There are no marked stress concentrations on top of the orbits. The resulting shape resembles that of an orang-utan. In model 3, the highest stresses also occur at the tooth roots, but the circles of force mostly close below the brain case, so that the stress concentration in the forehead region remains much less marked. In this model, however, the stress concentrations are very similar to hollow brow ridges. The entire resulting shape resembles that of gorilla or chimpanzee skulls. A typical gracile australopithecine skull (STS-5) also shows clear similarities to the patterns of stress flow in our models. Compared to our earlier study of the modern human skull, differences relate to: the relative length and width of the dental arcade, the relative size of the brain case and the position of the arcade relative to the brain case. It seems that these traits are the points of attack of selective pressures, while all other morphological details are simply consequences of stress flow.     

Feeding mechanics and bite force modelling of the skull of Dunkleosteus terrelli, an ancient apex predator

Placoderms are a diverse group of armoured fishes that dominated the aquatic ecosystems of the Devonian Period, 415-360 million years ago. The bladed jaws of predators such as Dunkleosteus suggest that these animals were the first vertebrates to use rapid mouth opening and a powerful bite to capture and fragment evasive prey items prior to ingestion. Here, we develop a biomechanical model of force and motion during feeding in Dunkleosteus terrelli that reveals a highly kinetic skull driven by a unique four-bar linkage mechanism. The linkage system has a high-speed transmission for jaw opening, producing a rapid expansion phase similar to modern fishes that use suction during prey capture. Jaw closing muscles power an extraordinarily strong bite, with an estimated maximal bite force of over 4400 N at the jaw tip and more than 5300 N at the rear dental plates, for a large individual (6 m in total length). This bite force capability is the greatest of all living or fossil fishes and is among the most powerful bites in animals.     

Predicted pattern of human muscle activity during clenching derived from a computer assisted model: symmetric vertical bite forces

A computer assisted three-dimensional model of the jaw, based on linear programming, is presented. The upper and lower attachments of the muscles of mastication have been measured on a single human skull and divided into thirteen independent units on each side--a total of 26 muscle elements. The direction (in three dimensions) and maximum forces that could be developed by each muscle element, the bite reaction and two joint reactions are included in the model. It is shown for symmetrical biting that a model which minimizes the sum of the muscle forces used to produce a given bite force activates muscles in a way which corresponds well with previous observations on human subjects. A model which minimizes the joint reactions behaves differently and is rejected. An analysis of the way the chosen model operates suggests that there are two types of jaw muscles, power muscles and control muscles. Power muscles (superficial masseter, medial pterygoid and some of temporalis) produce the bite force but tend to displace the condyle up or down the articular eminence. This displacement is prevented by control muscles (oblique temporalis and lateral pterygoid) which have very poor moment arms for generating usual bite forces, but are efficient for preventing condylar slide. The model incorporates the concept that muscles consist of elements which can contract independently. It predicts that those muscle elements with longer moment arms relative to the joint are the first to be activated and, as the bite force increases, a ripple of activity spreads into elements with shorter moment arms. In general, the model can be used to study the three-dimensional activity in any system of joints and muscles.     

The shrew tamed by Wolff's law: Do functional constraints shape the skull through muscle and bone covariation?

Bone is a highly plastic tissue that reflects the many potential sources of variation in shape. Here, we focus on the functional aspects of bone remodeling. We choose the skull for our analyses because it is a highly integrated system that plays a fundamental role in feeding and is thus, likely under strong natural selection. Its principal mechanical components are the bones and muscles that jointly produce bite force and jaw motion. Understanding the covariations among these three components is of interest to understand the processes driving the evolution of the feeding apparatus. In this study, we quantitatively and qualitatively compare interactions between these three components in shrews from populations known to differ in shape and bite force. Bite force was measured in the field using a force transducer and skull shape was quantified using surface geometric morphometric approaches based on µCT‐scans of the skulls of same individuals. The masseter, temporalis, pterygoideus, and digastricus muscles of these individuals were dissected and their cross sectional areas determined. Our results show strong correlations between bite force and muscle cross sectional areas as well as between bite force and skull shape. Moreover, bite force explains an important amount of skull shape variation. We conclude that interactions between bone shape and muscle characteristics can produce different morpho‐functional patterns that may differ between populations and may provide a suitable target for selection to act upon. J. Morphol. 276:301–309, 2015. © 2014 Wiley Periodicals, Inc.     

Comparative bite forces and canine bending strength in feline and sabretooth felids: implications for predatory ecology

The sabretooth felids were widespread across much of the world in the Late Tertiary, and appear to have been an important group of large predators. Owing to the substantially different skull morphology of derived sabretooths compared with extant felids, there has been considerable debate over the killing mode, bite forces, and bending strength of the large upper canines, and over the implications of these characteristics on feeding ecology. Debates have, however, usually been based on indirect comparisons of force vectors. In this paper, I provide assessments of the estimated force output from the jaw adductor muscles, based on estimates of muscle cross-sectional areas and force vectors, along with canine bending strengths, in a variety of sabretooth felids, in comparison with extant felids. In general, sabretoothed felids had moderately powerful bites, albeit with less jaw adductor power for their body sizes compared with extant felids, sometimes markedly so. Less derived sabrecats appear to have had proportionally higher bite forces than derived forms. The length of the upper canines seemingly compromised their bending strength at any given body size, and again this was most marked in derived forms. However, compared with estimated jaw adductor forces, the canines of sabrecats appear, if anything, to have been stronger than those of extant conical-toothed felids. It has previously been suggested that large sabretoothed felids hunted large prey with a canine shearing bite, powered in part by the jaw adductors and in part by the muscles of the upper neck–occipital region. The present results of canine bending strengths versus the predicted bite force from the jaw adductors supports this suggestion.  © 2007 The Linnean Society of London, Zoological Journal of the Linnean Society , 2007, 151 , 423–437.     

Functional basis for sexual differences in bite force in the lizard Anolis carolinensis

In many species of lizards, males attain greater body size and have larger heads than female lizards of the same size. Often, the dimorphism in head size is paralleled by a dimorphism in bite force. However, the underlying functional morphological basis for the dimorphism in bite force remains unclear. Here, we test whether males are larger, and have larger heads and bite forces than females for a given body size in a large sample of Anolis carolinensis . Next, we test if overall head shape differs between the sexes, or if instead specific aspects of skull shape can explain differences in bite force. Our results show that A. carolinensis is indeed dimorphic in body and head size and that males bite harder than females. Geometric morphometric analyses show distinct differences in skull shape between males and females, principally reflecting an enlargement of the jaw adductor muscle chamber. Jaw adductor muscle mass data confirm this result and show that males have larger jaw adductors (but not jaw openers) for a given body and head size. Thus, the observed dimorphism in bite force in A. carolinensis is not merely the result of an increase in head size, but involves distinct morphological changes in skull structure and the associated jaw adductor musculature.  © 2007 The Linnean Society of London, Biological Journal of the Linnean Society , 2007, 91 , 111–119.     

Feedback control from the jaw joints during biting: An investigation of the reptile Sphenodon using multibody modelling

Sphenodon, a lizard-like reptile, is the only living representative of a group that was once widespread at the time of the dinosaurs. Unique jaw mechanics incorporate crushing and shearing motions to breakdown food, but during this process excessive loading could cause damage to the jaw joints and teeth. In mammals like ourselves, feedback from mechanoreceptors within the periodontal ligament surrounding the teeth is thought to modulate muscle activity and thereby minimise such damage. However, Sphenodon and many other tetrapods lack the periodontal ligament and must rely on alternative control mechanisms during biting. Here we assess whether mechanoreceptors in the jaw joints could provide feedback to control muscle activity levels during biting. We investigate the relationship between joint, bite, and muscle forces using a multibody computer model of the skull and neck of Sphenodon. When feedback from the jaw joints is included in the model, predictions agree well with experimental studies, where the activity of the balancing side muscles reduces to maintain equal and minimal joint forces. When necessary, higher, but asymmetric, joint forces associated with higher bite forces were achievable, but these are likely to occur infrequently during normal food processing. Under maximum bite forces associated with symmetric maximal muscle activation, peak balancing side joint forces were more than double those of the working side. These findings are consistent with the hypothesis that feedback similar to that used in the simulation is present in Sphenodon.     

Basicranial axis length v. skull length in analysis of carnivore skull shape

Skull length is the measurement most commonly used as a standard against which other aspects of cranial morphology are compared to derive an index of relative size or proportions. However, skull length is composed of two different functional components, facial skull and cerebral skull, which vary independently and have different scaling relationships with body size. An analysis of carnivore skull shape with measurements standardized against basicranium length produced very different results than an analysis using skull length as the standard. For example, expressions of relative size of cranial measurements were reduced by 13% in mustelids and increased by 20% in canids, reflecting removal of jaw length (short in mustelids and long in canids) from the comparative standard (basicranial axis length). Cranial measurements scale with higher allometric exponents against basicranial axis length than against skull length.     

The evolution of development: two portraits of skull ossification in pipoid frogs

Abstract.— Development creates morphology, and the study of developmental processes has repeatedly shed light on patterns of morphological evolution. However, development itself evolves as well, often concomitantly with changes in life history or in morphology. In this paper, two approaches are used to examine the evolution of skull development in pipoid frogs. Pipoids have highly unusual morphologies and life histories compared to other frogs, and their development also proves to be remarkable. First, a phylogenetic examination of skull bone ossification sequences reveals that jaw ossification occurs significantly earlier in pipoids than in other frogs; this represents a reversal to the primitive vertebrate condition. Early jaw ossification in pipoids is hypothesized to result from the absence of certain larval specializations possessed by other frogs, combined with unusual larval feeding behaviors. Second, thin-plate spline morphometric studies of ontogenetic shape change reveal important differences between pipoid skull development and that of other frogs. In the course of frog evolution, there has been a shift away from salamander-like patterns of ontogenetic shape change. The pipoids represent the culmination of this trend, and their morphologies are highly derived in numerous respects. This study represents the first detailed examination of the evolution of skull development in a diverse vertebrate clade within a phylogenetic framework. It is also the first study to examine ossification sequences across vertebrates, and the first to use thin-plate spline morphometrics to quantitatively describe ontogenetic trajectories.     

Dietary hardness, loading behavior, and the evolution of skull form in bats

The morphology and biomechanics of the vertebrate skull reflect the physical properties of diet and behaviors used in food acquisition and processing. We use phyllostomid bats, the most diverse mammalian dietary radiation, to investigate if and how changes in dietary hardness and loading behaviors during feeding shaped the evolution of skull morphology and biomechanics. When selective regimes of food hardness are modeled, we found that species consuming harder foods have evolved skull shapes that allow for more efficient bite force production. These species have shorter skulls and a greater reliance on the temporalis muscle, both of which contribute to a higher mechanical advantage at an intermediate gape angle. The evolution of cranial morphology and biomechanics also appears to be related to loading behaviors. Evolutionary changes in skull shape and the relative role of the temporalis and masseter in generating bite force are correlated with changes in the use of torsional and bending loading behaviors. Functional equivalence appears to have evolved independently among three lineages of species that feed on liquids and are not obviously morphologically similar. These trends in cranial morphology and biomechanics provide insights into behavioral and ecological factors shaping the skull of a trophically diverse clade of mammals.