The global impact of sutures assessed in a finite element model of a macaque cranium

Sagittal suture strain in capuchin monkeys (Sapajus and Cebus) during feeding

OBJECTIVES

Morphological variation in cranial sutures is used to infer aspects of primate feeding behavior, including diet, but strain regimes across sutures are not well documented. Our aim is to test hypotheses about sagittal suture morphology, strain regime, feeding behavior, and muscle activity relationships in robust Sapajus and gracile Cebus capuchin primates.

MATERIALS AND METHODS

Morphometrics of sinuosity in three regions of the sagittal suture were compared among museum specimens of Sapajus and Cebus, as well as in robust and gracile lab specimens. In vivo strains and bilateral electromyographic (EMG) activity were recorded from these regions in the temporalis muscles of capuchin primates while they fed on mechanically-varying foods.

RESULTS

Sapajus and the anterior suture region exhibited greater sinuosity than Cebus and posterior regions. In vivo data reveal minor differences in strain regime between robust and gracile phenotypes but show higher strain magnitudes in the middle suture region and higher tensile strains anteriorly. After gage location, feeding behavior has the most consistent and strongest impact on strain regime in the sagittal suture. Strain in the anterior suture has a high tension to compression ratio compared to the posterior region, especially during forceful biting in the robust Sapajus-like individual.

DISCUSSION

Sagittal suture complexity in robust capuchins likely reflects feeding behaviors associated with mechanically challenging foods. Sutural strain regimes in other anthropoid primates may also be affected by activity in feeding muscles.

Assessment of the mechanical role of cranial sutures in the mammalian skull: Computational biomechanical modelling of the rat skull

Cranial sutures are fibrocellular joints between the skull bones that are progressively replaced with bone throughout ontogeny, facilitating growth and cranial shape change. This transition from soft tissue to bone is reflected in the biomechanical properties of the craniofacial complex. However, the mechanical significance of cranial sutures has only been explored at a few localised areas within the mammalian skull, and as such our understanding of suture function in overall skull biomechanics is still limited. Here, we sought to determine how the overall strain environment is affected by the complex network of cranial sutures in the mammal skull. We combined two computational biomechanical methods, multibody dynamics analysis and finite element analysis, to simulate biting in a rat skull and compared models with and without cranial sutures. Our results show that including complex sutures in the rat model does not substantially change overall strain gradients across the cranium, particularly strain magnitudes in the bones overlying the brain. However, local variations in strain magnitudes and patterns can be observed in areas close to the sutures. These results show that, during feeding, sutures may be more important in some regions than others. Sutures should therefore be included in models that require accurate local strain magnitudes and patterns of cranial strain, particularly if models are developed for analysis of specific regions, such as the temporomandibular joint or zygomatic arch. Our results suggest that, for mammalian skulls, cranial sutures might be more important for allowing brain expansion during growth than redistributing biting loads across the cranium in adults.

How suture networks improve the protective function of natural structures: A multiscale investigation

Myriad natural protective structures consist of bone plates joined by convoluted unmineralized (soft) collagenous sutures. Examples of such protective structures include: shells of turtles, craniums of almost all animals (including humans), alligator armour, armadillo armour, and others. The function of sutures has been well researched. However, whether, and if so how, sutures improve protective performance during a predator attack has received limited attention. Sutures are ubiquitous in protective structures, and this motivates the question as to whether sutures optimize the protective function of the structure. Hence, in this work the behaviour of structures that contain sutures during predator attacks is investigated. We show that sutures decrease the maximum strain energy density that turtle shells experience during predator attacks by more than an order of magnitude. Hence, sutures make turtle shells far more resilient to material failure, such as, fracture, damage, and plastic deformations. Additionally, sutures increase the viscous behaviour of the shell causing increased dissipation of energy during predator attacks. Further investigations into the influence of sutures on behaviour during locomotion and breathing are also presented. The results presented in this work motivate the inclusion of sutures in biomimetically designed protective structures, such as helmets and protective clothing. STATEMENT OF SIGNIFICANCE: Myriad bony protective structures contain networks of sutures, that is con- voluted soft collagenous tissue. Their ubiquity motivates the question, whether, and if so how, sutures improve protective performance. Hence, this work inves- tigates how sutures affect protective performance using computational experi- ments. Due to the length scale of sutures being far smaller than the structures in which they reside, classical modelling approaches are prohibitively expensive. Hence, in this work, a multiscale approach is taken. To our knowledge, this is the first multiscale investigation of structures that contain sutures. Among other insights, we show that sutures decrease the maximum strain energy density in structures during predator attacks by over an order of mag- nitude. Hence, sutures make structures far more resilient to failure.

Modeling tooth enamel in FEA comparisons of skulls: Comparing common simplifications with biologically realistic models

Palaeontologists often use finite element analyses, in which forces propagate through objects with specific material properties, to investigate feeding biomechanics. Teeth are usually modeled with uniform properties (all bone or all enamel). In reality, most teeth are composed of pulp, dentine, and enamel. We tested how simplified teeth compare to more realistic models using mandible models of three reptiles. For each, we created models representing enamel thicknesses found in extant taxa, as well as simplified models (bone, dentine or enamel). Our results suggest that general comparisons of stress distribution among distantly related taxa do not require representation of dental tissues, as there was no noticeable effect on heatmap representations of stress. However, we find that representation of dental tissues impacts bite force estimates, although magnitude of these effects may differ depending on constraints. Thus, as others have shown, the detail necessary in a biomechanical model relates to the questions being examined.

Divided zygoma in Holocene human populations from Northern China

Objectives

Divided zygoma (DZ) occurs in contemporaneous human populations, with the highest incidences in people from East Asia and Southern Africa. The present study examines the prevalence and variation of this condition in the Holocene populations of Northern China for the first time.

Methods

In this study, 1145 skulls from various human populations living in Northern China from the Neolithic Age to recent dynasties (5000‐300 years BP) were examined. Specifically, cranial measurements and a CT scan were conducted to quantify craniofacial morphology.

Results

Fifteen skulls were identified with DZ, revealing an overall prevalence of 1.3% in the collection, while it was determined to be higher in North Asian and Northeast Asian regional groups. In skulls with unilateral DZ, the superior division of the zygoma was generally slender, while the inferior division of the zygoma was more robust. In skulls with bilateral DZ, the maxillae were generally more laterally extended. Moreover, unilateral DZ skulls displayed differences in cortical bone thickness between two sides of the facial skeleton.

Discussion

In context, the distribution pattern within these data points toward a greater prevalence of the DZ phenotype in North and Northeast Asian regional groups, suggesting a hypothesis that the DZ trait is more frequent in populations characterized by flat and broad faces. Accordingly, further studies into the DZ condition will deepen our understanding of developments in plasticity, variation, and recent evolution of the human cranium.

Merging cranial histology and 3D-computational biomechanics: a review of the feeding ecology of a Late Triassic temnospondyl amphibian

Finite Element Analysis (FEA) is a useful method for understanding form and function. However, modelling of fossil taxa invariably involves assumptions as a result of preservation-induced loss of information in the fossil record. To test the validity of predictions from FEA, given such assumptions, these results could be compared to independent lines of evidence for cranial mechanics. In the present study a new concept of using bone microstructure to predict stress distribution in the skull during feeding is put forward and a correlation between bone microstructure and results of computational biomechanics (FEA) is carried out. The bony framework is a product of biological optimisation; bone structure is created to meet local mechanical conditions. To test how well results from FEA correlate to cranial mechanics predicted from bone structure, the well-known temnospondyl Metoposaurus krasiejowensis was used as a model. A crucial issue to Temnospondyli is their feeding mode: did they suction feed or employ direct biting, or both? Metoposaurids have previously been characterised either as active hunters or passive bottom dwellers. In order to test the correlation between results from FEA and bone microstructure, two skulls of Metoposaurus were used, one modelled under FE analyses, while for the second one 17 dermal bone microstructure were analysed. Thus, for the first time, results predicting cranial mechanical behaviour using both methods are merged to understand the feeding strategy of Metoposaurus. Metoposaurus appears to have been an aquatic animal that exhibited a generalist feeding behaviour. This taxon may have used two foraging techniques in hunting; mainly bilateral biting and, to a lesser extent, lateral strikes. However, bone microstructure suggests that lateral biting was more frequent than suggested by Finite Element Analysis (FEA). One of the potential factors that determined its mode of life may have been water levels. During optimum water conditions, metoposaurids may have been more active ambush predators that were capable of lateral strikes of the head. The dry season required a less active mode of life when bilateral biting is particularly efficient. This, combined with their characteristically anteriorly positioned orbits, was optimal for ambush strategy. This ability to use alternative modes of food acquisition, independent of environmental conditions, might hold the key in explaining the very common occurrence of metoposaurids during the Late Triassic.

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.

Cell Mechanics of Craniosynostosis

Craniosynostosis is the premature fusion of the calvarial sutures that is associated with a number of physical and intellectual disabilities spanning from pediatric to adult years. Over the past two decades, techniques in molecular genetics and more recently, advances in high-throughput DNA sequencing have been used to examine the underlying pathogenesis of this disease. To date, mutations in 57 genes have been identified as causing craniosynostosis and the number of newly discovered genes is growing rapidly as a result of the advances in genomic technologies. While contributions from both genetic and environmental factors in this disease are increasingly apparent, there remains a gap in knowledge that bridges the clinical characteristics and genetic markers of craniosynostosis with their signaling pathways and mechanotransduction processes. By linking genotype to phenotype, outlining the role of cell mechanics may further uncover the specific mechanotransduction pathways underlying craniosynostosis. Here, we present a brief overview of the recent findings in craniofacial genetics and cell mechanics, discussing how this information together with animal models is advancing our understanding of craniofacial development.

The Biomechanics of Zygomatic Arch Shape

Mammalian zygomatic arch shape is remarkably variable, ranging from nearly cylindrical to blade-like in cross section. Based on geometry, the arch can be hypothesized to be a sub-structural beam whose ability to resist deformation is related to cross sectional shape. We expect zygomatic arches with different cross sectional shapes to vary in the degree to which they resist local bending and torsion due to the contraction of the masseter muscle. A stiffer arch may lead to an increase in the relative proportion of applied muscle load being transmitted through the arch to other cranial regions, resulting in elevated cranial stress (and thus, strain). Here, we examine the mechanics of the zygomatic arch using a series of finite element modeling experiments in which the cross section of the arch of Pan troglodytes has been modified to conform to idealized shapes (cylindrical, elliptical, blade-like). We find that the shape of the zygomatic arch has local effects on stain that do not conform to beam theory. One exception is that possessing a blade-like arch leads to elevated strains at the postorbital zygomatic junction and just below the orbits. Furthermore, although modeling the arch as solid cortical bone did not have the effect of elevating strains in other parts of the face, as had been expected, it does have a small effect on stress associated with masseter contraction. These results are counterintuitive. Even though the arch has simple beam-like geometry, we fail to find a simple mechanical explanation for the diversity of arch shape. Anat Rec, 299:1734-1752, 2016. © 2016 Wiley Periodicals, Inc.

Validation experiments on finite element models of an ostrich (Struthio camelus) cranium

The first finite element (FE) validation of a complete avian cranium was performed on an extant palaeognath, the ostrich (Struthio camelus). Ex-vivo strains were collected from the cranial bone and rhamphotheca. These experimental strains were then compared to convergence tested, specimen-specific finite element (FE) models. The FE models contained segmented cortical and trabecular bone, sutures and the keratinous rhamphotheca as identified from micro-CT scan data. Each of these individual materials was assigned isotropic material properties either from the literature or from nanoindentation, and the FE models compared to the ex-vivo results. The FE models generally replicate the location of peak strains and reflect the correct mode of deformation in the rostral region. The models are too stiff in regions of experimentally recorded high strain and too elastic in regions of low experimentally recorded low strain. The mode of deformation in the low strain neurocranial region is not replicated by the FE models, and although the models replicate strain orientations to within 10° in some regions, in most regions the correlation is not strong. Cranial sutures, as has previously been found in other taxa, are important for modifying both strain magnitude and strain patterns across the entire skull, but especially between opposing the sutural junctions. Experimentally, we find that the strains on the surface of the rhamphotheca are much lower than those found on nearby bone. The FE models produce much higher principal strains despite similar strain ratios across the entirety of the rhamphotheca. This study emphasises the importance of attempting to validate FE models, modelling sutures and rhamphothecae in birds, and shows that whilst location of peak strain and patterns of deformation can be modelled, replicating experimental data in digital models of avian crania remains problematic.

The impact of simplifications on the performance of a finite element model of a Macaca fascicularis cranium

In recent years finite element analysis (FEA) has emerged as a useful tool for the analysis of skeletal form-function relationships. While this approach has obvious appeal for the study of fossil specimens, such material is often fragmentary with disrupted internal architecture and can contain matrix that leads to errors in accurate segmentation. Here we examine the effects of varying the detail of segmentation and material properties of teeth on the performance of a finite element model of a Macaca fascicularis cranium within a comparative functional framework. Cranial deformations were compared using strain maps to assess differences in strain contours and Procrustes size and shape analyses, from geometric morphometrics, were employed to compare large scale deformations. We show that a macaque model subjected to biting can be made solid, and teeth altered in material properties, with minimal impact on large scale modes of deformation. The models clustered tightly by bite point rather than by modeling simplification approach, and fell out as being distinct from another species. However localized fluctuations in predicted strain magnitudes were recorded with different modeling approaches, particularly over the alveolar region. This study indicates that, while any model simplification should be undertaken with care and attention to its effects, future applications of FEA to fossils with unknown internal architecture may produce reliable results with regard to general modes of deformation, even when detail of internal bone architecture cannot be reliably modeled.

The relationship between cranial structure, biomechanical performance and ecological diversity in varanoid lizards

Skull structure is intimately associated with feeding ability in vertebrates, both in terms of specific performance measures and general ecological characteristics. This study quantitatively assessed variation in the shape of the cranium and mandible in varanoid lizards, and its relationship to structural performance (von Mises strain) and interspecific differences in feeding ecology. Geometric morphometric and linear morphometric analyses were used to evaluate morphological differences, and finite element analysis was used to quantify variation in structural performance (strain during simulated biting, shaking and pulling). This data was then integrated with ecological classes compiled from relevant scientific literature on each species in order to establish structure-function relationships. Finite element modelling results showed that variation in cranial morphology resulted in large differences in the magnitudes and locations of strain in biting, shaking and pulling load cases. Gracile species such as Varanus salvadorii displayed high strain levels during shaking, especially in the areas between the orbits. All models exhibit less strain during pull back loading compared to shake loading, even though a larger force was applied (pull =30N, shake = 20N). Relationships were identified between the morphology, performance, and ecology. Species that did not feed on hard prey clustered in the gracile region of cranial morphospace and exhibited significantly higher levels of strain during biting (P = 0.0106). Species that fed on large prey clustered in the elongate area of mandible morphospace. This relationship differs from those that have been identified in other taxonomic groups such as crocodiles and mammals. This difference may be due to a combination of the open 'space-frame' structure of the varanoid lizard skull, and the 'pull back' behaviour that some species use for processing large prey.

The sensitivity of biological finite element models to the resolution of surface geometry: a case study of crocodilian crania

The reliability of finite element analysis (FEA) in biomechanical investigations depends upon understanding the influence of model assumptions. In producing finite element models, surface mesh resolution is influenced by the resolution of input geometry, and influences the resolution of the ensuing solid mesh used for numerical analysis. Despite a large number of studies incorporating sensitivity studies of the effects of solid mesh resolution there has not yet been any investigation into the effect of surface mesh resolution upon results in a comparative context. Here we use a dataset of crocodile crania to examine the effects of surface resolution on FEA results in a comparative context. Seven high-resolution surface meshes were each down-sampled to varying degrees while keeping the resulting number of solid elements constant. These models were then subjected to bite and shake load cases using finite element analysis. The results show that incremental decreases in surface resolution can result in fluctuations in strain magnitudes, but that it is possible to obtain stable results using lower resolution surface in a comparative FEA study. As surface mesh resolution links input geometry with the resulting solid mesh, the implication of these results is that low resolution input geometry and solid meshes may provide valid results in a comparative context.

Descriptive anatomy and three-dimensional reconstruction of the skull of the early tetrapod Acanthostega gunnari Jarvik, 1952

The early tetrapod Acanthostega gunnari is an iconic fossil taxon exhibiting skeletal morphology reflecting the transition of vertebrates from water onto land. Computed tomography data of two Acanthostega skulls was segmented using visualization software to digitally separate bone from matrix and individual bones of the skull from each other. A revised description of cranial and lower jaw anatomy in this taxon based on CT data includes new details of sutural morphology, the previously undescribed quadrate and articular bones, and the mandibular symphysis. Sutural morphology is used to infer loading regime in the skull during feeding, and suggests Acanthostega used its anterior jaws to initially seize prey while smaller posterior teeth were used to restrain struggling prey during ingestion. Novel methods were used to repair and retrodeform the skull, resulting in a three-dimensional digital reconstruction that features a longer postorbital region and more strongly hooked anterior lower jaw than previous attempts while supporting the presence of a midline gap between the nasals and median rostrals.

Biomechanical implications of intraspecific shape variation in chimpanzee crania: moving toward an integration of geometric morphometrics and finite element analysis

In a broad range of evolutionary studies, an understanding of intraspecific variation is needed in order to contextualize and interpret the meaning of variation between species. However, mechanical analyses of primate crania using experimental or modeling methods typically encounter logistical constraints that force them to rely on data gathered from only one or a few individuals. This results in a lack of knowledge concerning the mechanical significance of intraspecific shape variation that limits our ability to infer the significance of interspecific differences. This study uses geometric morphometric methods (GM) and finite element analysis (FEA) to examine the biomechanical implications of shape variation in chimpanzee crania, thereby providing a comparative context in which to interpret shape-related mechanical variation between hominin species. Six finite element models (FEMs) of chimpanzee crania were constructed from CT scans following shape-space Principal Component Analysis (PCA) of a matrix of 709 Procrustes coordinates (digitized onto 21 specimens) to identify the individuals at the extremes of the first three principal components. The FEMs were assigned the material properties of bone and were loaded and constrained to simulate maximal bites on the P(3) and M(2) . Resulting strains indicate that intraspecific cranial variation in morphology is associated with quantitatively high levels of variation in strain magnitudes, but qualitatively little variation in the distribution of strain concentrations. Thus, interspecific comparisons should include considerations of the spatial patterning of strains rather than focus only on their magnitudes.

Mechanical properties of cranial bones and sutures in 1-2-year-old infants

BACKGROUND

The mechanical properties of 1-2-year-old pediatric cranial bones and sutures and their influential factors were studied to better understand how the pediatric calvarium reacts to loading.

MATERIAL AND METHODS

Cranial bone and suture specimens were extracted from seven fresh-frozen human infant cadavers (1.5±0.5 years old). Eight specimens were obtained from each subject: two frontal bones, two parietal bones, two sagittal suture samples, and two coronal suture samples. The specimens were tested in a three-point bend setup at 1.5 mm/s. The mechanical properties, such as ultimate stress, elastic modulus, and ultimate strain, were calculated for each specimen.

RESULTS

The ultimate stress and elastic modulus of the frontal bone were higher than those of the parietal bone (P<0.05). No differences were found between the coronal and sagittal sutures in ultimate stress, elastic modulus, or ultimate strain (P>0.05). The ultimate stress and elastic modulus of the frontal and parietal bones were higher than those of the sagittal and coronal sutures (P<0.05), whereas the opposite ultimate strain findings were revealed (P<0.05).

CONCLUSIONS

There was no significant difference in ultimate stress, elastic modulus, or ultimate strain between the sagittal and coronal sutures. However, there were significant differences in ultimate stress, elastic modulus, and ultimate strain between the frontal and parietal bones as well as between the cranial bones and sutures.

Beware the black box: investigating the sensitivity of FEA simulations to modelling factors in comparative biomechanics

Finite element analysis (FEA) is a computational technique of growing popularity in the field of comparative biomechanics, and is an easily accessible platform for form-function analyses of biological structures. However, its rapid evolution in recent years from a novel approach to common practice demands some scrutiny in regards to the validity of results and the appropriateness of assumptions inherent in setting up simulations. Both validation and sensitivity analyses remain unexplored in many comparative analyses, and assumptions considered to be ‘reasonable’ are often assumed to have little influence on the results and their interpretation.

Here we report an extensive sensitivity analysis where high resolution finite element (FE) models of mandibles from seven species of crocodile were analysed under loads typical for comparative analysis: biting, shaking, and twisting. Simulations explored the effect on both the absolute response and the interspecies pattern of results to variations in commonly used input parameters. Our sensitivity analysis focuses on assumptions relating to the selection of material properties (heterogeneous or homogeneous), scaling (standardising volume, surface area, or length), tooth position (front, mid, or back tooth engagement), and linear load case (type of loading for each feeding type).

Our findings show that in a comparative context, FE models are far less sensitive to the selection of material property values and scaling to either volume or surface area than they are to those assumptions relating to the functional aspects of the simulation, such as tooth position and linear load case. Results show a complex interaction between simulation assumptions, depending on the combination of assumptions and the overall shape of each specimen. Keeping assumptions consistent between models in an analysis does not ensure that results can be generalised beyond the specific set of assumptions used. Logically, different comparative datasets would also be sensitive to identical simulation assumptions; hence, modelling assumptions should undergo rigorous selection. The accuracy of input data is paramount, and simulations should focus on taking biological context into account. Ideally, validation of simulations should be addressed; however, where validation is impossible or unfeasible, sensitivity analyses should be performed to identify which assumptions have the greatest influence upon the results.

Cranial sutures work collectively to distribute strain throughout the reptile skull

The skull is composed of many bones that come together at sutures. These sutures are important sites of growth, and as growth ceases some become fused while others remain patent. Their mechanical behaviour and how they interact with changing form and loadings to ensure balanced craniofacial development is still poorly understood. Early suture fusion often leads to disfiguring syndromes, thus is it imperative that we understand the function of sutures more clearly. By applying advanced engineering modelling techniques, we reveal for the first time that patent sutures generate a more widely distributed, high level of strain throughout the reptile skull. Without patent sutures, large regions of the skull are only subjected to infrequent low-level strains that could weaken the bone and result in abnormal development. Sutures are therefore not only sites of bone growth, but could also be essential for the modulation of strains necessary for normal growth and development in reptiles.

Patterns and implications of extensive heterochrony in carnivoran cranial suture closure

Heterochronic changes in the rate or timing of development underpin many evolutionary transformations. In particular, the onset and rate of bone development have been the focus of many studies across large clades. In contrast, the termination of bone growth, as estimated by suture closure, has been studied far less frequently, although a few recent studies have shown this to represent a variable, although poorly understood, aspect of developmental evolution. Here, we examine suture closure patterns across 25 species of carnivoran mammals, ranging from social-insectivores to hypercarnivores, to assess variation in suture closure across taxa, identify heterochronic shifts in a phylogenetic framework and elucidate the relationship between suture closure timing and ecology. Our results show that heterochronic shifts in suture closure are widespread across Carnivora, with several shifts identified for most major clades. Carnivorans differ from patterns identified for other mammalian clades in showing high variability of palatal suture closure, no correlation between size and level of suture closure, and little phylogenetic signal outside of musteloids. Results further suggest a strong influence of feeding ecology on suture closure pattern. Most of the species with high numbers of heterochronic shifts, such as the walrus and the aardwolf, feed on invertebrates, and these taxa also showed high frequency of closure of the mandibular symphysis, a state that is relatively rare among mammals. Overall, caniforms displayed more heterochronic shifts than feliforms, suggesting that evolutionary changes in suture closure may reflect the lower diversity of cranial morphology in feliforms.

A sensitivity analysis to the role of the fronto-parietal suture in Lacerta bilineata: a preliminary finite element study

Cranial sutures are sites of bone growth and development but micromovements at these sites may distribute the load across the skull more evenly. Computational studies have incorporated sutures into finite element (FE) models to assess various hypotheses related to their function. However, less attention has been paid to the sensitivity of the FE results to the shape, size, and stiffness of the modeled sutures. Here, we assessed the sensitivity of the strain predictions to the aforementioned parameters in several models of fronto-parietal (FP) suture in Lacerta bilineata. For the purpose of this study, simplifications were made in relation to modeling the bone properties and the skull loading. Results highlighted that modeling the FP as either an interdigitated suture or a simplified butt suture, did not reduce the strain distribution in the FP region. Sensitivity tests showed that similar patterns of strain distribution can be obtained regardless of the size of the suture, or assigned stiffness, yet the exact magnitudes of strains are highly sensitive to these parameters. This study raises the question whether the morphogenesis of epidermic scales in the FP region in the Lacertidae is related to high strain fields in this region, because of micromovement in the FP suture.

Masticatory loadings and cranial deformation in Macaca fascicularis: a finite element analysis sensitivity study

Biomechanical analyses are commonly conducted to investigate how craniofacial form relates to function, particularly in relation to dietary adaptations. However, in the absence of corresponding muscle activation patterns, incomplete muscle data recorded experimentally for different individuals during different feeding tasks are frequently substituted. This study uses finite element analysis (FEA) to examine the sensitivity of the mechanical response of a Macaca fascicularis cranium to varying muscle activation patterns predicted via multibody dynamic analysis. Relative to the effects of varying bite location, the consequences of simulated variations in muscle activation patterns and of the inclusion/exclusion of whole muscle groups were investigated. The resulting cranial deformations were compared using two approaches; strain maps and geometric morphometric analyses. The results indicate that, with bite force magnitude controlled, the variations among the mechanical responses of the cranium to bite location far outweigh those observed as a consequence of varying muscle activations. However, zygomatic deformation was an exception, with the activation levels of superficial masseter being most influential in this regard. The anterior portion of temporalis deforms the cranial vault, but the remaining muscles have less profound effects. This study for the first time systematically quantifies the sensitivity of an FEA model of a primate skull to widely varying masticatory muscle activations and finds that, with the exception of the zygomatic arch, reasonable variants of muscle loading for a second molar bite have considerably less effect on cranial deformation and the resulting strain map than does varying molar bite point. The implication is that FEA models of biting crania will generally produce acceptable estimates of deformation under load as long as muscle activations and forces are reasonably approximated. In any one FEA study, the biological significance of the error in applied muscle forces is best judged against the magnitude of the effect that is being investigated.

Mechanics of cranial sutures during simulated cyclic loading

Previous computational and experimental analyses revealed that cranial sutures, fibrous joints between the bones, can reduce the strain experienced by the surrounding skull bones during mastication. This damping effect reflects the importance of including sutures in finite element (FE) analyses of the skull. Using the FE method, the behaviour of three suture morphologies of increasing complexity (butt-ended, moderate interdigitated, and complex interdigitated) during static loading was recently investigated, and the sutures were assumed to have linear elastic properties. In the current study, viscoelastic properties, derived from published experimental results of the nasofrontal suture of young pigs (Sus scrofa), are applied to the three idealised bone-suture models. The effects of suture viscoelasticity on the stress, strain, and strain energy in the models were computed for three different frequencies (corresponding to periods of 1, 10, and 100s) and compared to the results of a static, linear elastic analysis. The range of applied frequencies broadly represents different physiological activities, with the highest frequency simulating mastication and the lowest frequency simulating growth and pressure of the surrounding tissues. Comparing across all three suture morphologies, strain energy and strain in the suture decreased with the increase in suture complexity. For each suture model, the magnitude of strain decreased with an increase in frequency, and the magnitudes were similar for both the elastic and 1s frequency analyses. In addition, a viscous response is less apparent in the higher frequency analyses, indicating that viscous properties are less important to the behaviour of the suture during those analyses. The FE results suggest that implementation of viscoelastic properties may not be necessary for computational studies of skull behaviour during masticatory loading but instead might be more relevant for studies examining lower frequency physiological activities.

Changes in biomechanical strain and morphology of rat calvarial sutures and bone after Tgf-β3 inhibition of posterior interfrontal suture fusion

Craniofacial sutures are bone growth fronts that respond and adapt to biomechanical environments. Little is known of the role sutures play in regulating the skull biomechanical environment during patency and fusion conditions, especially how delayed or premature suture fusion will impact skull biomechanics. Tgf-β3 has been shown to prevent or delay suture fusion over the short term in rat skulls, yet the long-term patency or its consequences in treated sutures is not known. It was therefore hypothesized that Tgf-β3 had a long-term impact to prevent suture fusion and thus alter the skull biomechanics. In this study, collagen gels containing 3 ng Tgf-β3 were surgically placed superficial to the posterior interfrontal suture (IFS) and deep to the periosteum in postnatal day 9 (P9) rats. At P9, P24, and P70, biting forces and strains over left parietal bone, posterior IFS, and sagittal suture were measured with masticatory muscles bilaterally stimulated, after which the rats were sacrificed and suture patency analyzed histologically. Results demonstrated that Tgf-β3 treated sutures showed less fusion over time than control groups, and strain patterns in the skulls of the Tgf-β3-treated group were different from that of the control group. Although bite force increased with age, no alterations in bite force were attributable to Tgf-β3 treatment. These findings suggest that the continued presence of patent sutures can affect strain patterns, perhaps when higher bite forces are present as in adult animals.

The importance of craniofacial sutures in biomechanical finite element models of the domestic pig

Craniofacial sutures are a ubiquitous feature of the vertebrate skull. Previous experimental work has shown that bone strain magnitudes and orientations often vary when moving from one bone to another, across a craniofacial suture. This has led to the hypothesis that craniofacial sutures act to modify the strain environment of the skull, possibly as a mode of dissipating high stresses generated during feeding or impact. This study tests the hypothesis that the introduction of craniofacial sutures into finite element (FE) models of a modern domestic pig skull would improve model accuracy compared to a model without sutures. This allowed the mechanical effects of sutures to be assessed in isolation from other confounding variables. These models were also validated against strain gauge data collected from the same specimen ex vivo. The experimental strain data showed notable strain differences between adjacent bones, but this effect was generally not observed in either model. It was found that the inclusion of sutures in finite element models affected strain magnitudes, ratios, orientations and contour patterns, yet contrary to expectations, this did not improve the fit of the model to the experimental data, but resulted in a model that was less accurate. It is demonstrated that the presence or absence of sutures alone is not responsible for the inaccuracies in model strain, and is suggested that variations in local bone material properties, which were not accounted for by the FE models, could instead be responsible for the pattern of results.

Probabilistic finite element analysis of a craniofacial finite element model

We employed a probabilistic finite element analysis (FEA) method to determine how variability in material property values affects stress and strain values in a finite model of a Macaca fascicularis cranium. The material behavior of cortical bone varied in three ways: isotropic homogeneous, isotropic non-homogeneous, and orthotropic non-homogeneous. The material behavior of the trabecular bone and teeth was always treated as isotropic and homogeneous. All material property values for the cranium were randomized with a Gaussian distribution with either coefficients of variation (CVs) of 0.2 or with CVs calculated from empirical data. Latin hypercube sampling was used to determine the values of the material properties used in the finite element models. In total, four hundred and twenty six separate deterministic FE simulations were executed. We tested four hypotheses in this study: (1) uncertainty in material property values will have an insignificant effect on high stresses and a significant effect on high strains for homogeneous isotropic models; (2) the effect of variability in material property values on the stress state will increase as non-homogeneity and anisotropy increase; (3) variation in the in vivo shear strain values reported by Strait et al. (2005) and Ross et al. (2011) is not only due to variations in muscle forces and cranial morphology, but also due to variation in material property values; (4) the assumption of a uniform coefficient of variation for the material property values will result in the same trend in how moderate-to-high stresses and moderate-to-high strains vary with respect to the degree of non-homogeneity and anisotropy as the trend found when the coefficients of variation for material property values are calculated from empirical data. Our results supported the first three hypotheses and falsified the fourth. When material properties were varied with a constant CV, as non-homogeneity and anisotropy increased the level of variability in the moderate-to-high strains decreased while the level of variability in the moderate-to-high stresses increased. However, this is not the pattern observed when CVs calculated from empirical data were applied to the material properties where the lowest level of variability in both stresses and strains occurred when the cranium was modeled with a low level of non-homogeneity and anisotropy. Therefore, when constant material property variability is assumed, inaccurate trends in the level of variability present in modest-to-high magnitude stresses and strains are produced. When the cranium is modeled with the highest level of accuracy (high non-homogeneity and anisotropy) and when randomness in the material properties is calculated from empirical data, there is a large level of variability in the significant strains (CV=0.369) and a low level of variability in the modest-to-high magnitude stresses (CV=0.150). This result may have important implications with regard to the mechanical signals driving bone remodeling and adaptation through natural selection.

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.

Strain accommodation in the zygomatic arch of the pig: a validation study using digital speckle pattern interferometry and finite element analysis

It has been repeatedly suggested that mammalian cranial sutures act not only to allow growth but also to reduce the levels of strain experienced by the skull during feeding. However, because of the added complexity they introduce, sutures are rarely included in finite element (FE) models, despite their potential to influence strain results. Because sutures present different morphologies and with differing degrees of internal fusion, many different methods of modeling may be necessary to accurately measure strain environments. Alternatively, these variables may exert very little influence on the scale of a whole-skull model. To validate suture modeling methods, four alternative ways of including a suture in 3D FE models of the pig zygomatic arch were considered and compared with ex vivo experimental data from digital speckle pattern interferometry (DSPI). The use of DSPI rather than traditional strain gauge techniques allows strain gradients around the suture as well as the motions of the two bones to be observed. Results show that the introduction of 3D elements assigned more compliant material properties than the surrounding bone, is the most effective way of modeling both morphologies of suture, both in tension and compression. However, models containing no suture are almost indistinguishable from these compliant suture models, beyond the high strain gradient immediately adjacent to the suture. Conversely, modeling the suture as an open break in the mesh, or with spring elements assigned suture properties, fails to reproduce the experiment. Thus, although a solid but flexible model of sutures is preferred, the similarity between these models and those without sutures tentatively suggests that such extra detail may be unnecessary in pigs if the behavior of the whole skull is of interest.

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.

A bidirectional interface growth model for cranial interosseous suture morphogenesis

Interosseous sutures exhibit highly variable patterns of interdigitation and corrugation. Recent research has identified fundamental molecular mechanisms of suture formation, and computer models have been used to simulate suture morphogenesis. However, the role of bone strain in the development of complex sutures is largely unknown, and measuring suture morphologies beyond the evaluation of fractal dimensions remains a challenge. Here we propose a morphogenetic model of suture formation, which is based on the paradigm of Laplacian interface growth. Computer simulations of suture morphogenesis under various boundary conditions generate a wide variety of synthetic sutural forms. Their morphologies are quantified with a combination of Fourier analysis and principal components analysis, and compared with natural morphological variation in an ontogenetic sample of human interparietal suture lines. Morphometric analyses indicate that natural sutural shapes exhibit a complex distribution in morphospace. The distribution of synthetic sutures closely matches the natural distribution. In both natural and synthetic systems, sutural complexity increases during morphogenesis. Exploration of the parameter space of the simulation system indicates that variation in strain and/or morphogen sensitivity and viscosity of sutural tissue may be key factors in generating the large variability of natural suture complexity.

A finite element analysis of masticatory stress hypotheses

Understanding how the skull transmits and dissipates forces during feeding provides insights into the selective pressures that may have driven the evolution of primate skull morphology. Traditionally, researchers have interpreted masticatory biomechanics in terms of simple global loading regimes applied to simple shapes (i.e., bending in sagittal and frontal planes, dorsoventral shear, and torsion of beams and cylinders). This study uses finite element analysis to examine the extent to which these geometric models provide accurate strain predictions in the face and evaluate whether simple global loading regimes predict strains that approximate the craniofacial deformation pattern observed during mastication. Loading regimes, including those simulating peak loads during molar chewing and those approximating the global loading regimes, were applied to a previously validated finite element model (FEM) of a macaque (Macaca fascicularis) skull, and the resulting strain patterns were compared. When simple global loading regimes are applied to the FEM, the resulting strains do not match those predicted by simple geometric models, suggesting that these models fail to generate accurate predictions of facial strain. Of the four loading regimes tested, bending in the frontal plane most closely approximates strain patterns in the circumorbital region and lateral face, apparently due to masseter muscle forces acting on the zygomatic arches. However, these results indicate that no single simple global loading regime satisfactorily accounts for the strain pattern found in the validated FEM. Instead, we propose that FE models replace simple cranial models when interpreting bone strain data and formulating hypotheses about craniofacial biomechanics.