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

Dynamic finite element modelling of the macaque mandible during a complete mastication gape cycle

Three-dimensional finite element models (FEMs) are powerful tools for studying the mechanical behaviour of the feeding system. Using validated, static FEMs we have previously shown that in rhesus macaques the largest food-related differences in strain magnitudes during unilateral postcanine chewing extend from the lingual symphysis to the endocondylar ridge of the balancing-side ramus. However, static FEMs only model a single time point during the gape cycle and probably do not fully capture the mechanical behaviour of the jaw during mastication. Bone strain patterns and moments applied to the mandible are known to vary during the gape cycle owing to variation in the activation peaks of the jaw-elevator muscles, suggesting that dynamic models are superior to static ones in studying feeding biomechanics. To test this hypothesis, we built dynamic FEMs of a complete gape cycle using muscle force data from in vivo experiments to elucidate the impact of relative timing of muscle force on mandible biomechanics. Results show that loading and strain regimes vary across the chewing cycle in subtly different ways for different foods, something which was not apparent in static FEMs. These results indicate that dynamic three-dimensional FEMs are more informative than static three-dimensional FEMs in capturing the mechanical behaviour of the jaw during feeding by reflecting the asymmetry in jaw-adductor muscle activations during a gape cycle. This article is part of the theme issue 'Food processing and nutritional assimilation in animals'.

Divergent strategies in cranial biomechanics and feeding ecology of the ankylosaurian dinosaurs

Ankylosaurs were important megaherbivores of Jurassic and Cretaceous ecosystems. Their distinctive craniodental anatomy and mechanics differentiated them from coexisting hadrosaurs and ceratopsians, and morphological evidence suggests dietary niche partitioning between sympatric ankylosaurids and nodosaurids. Here, we investigate the skull biomechanics of ankylosaurs relative to feeding function. First, we compare feeding functional performance between nodosaurids and ankylosaurids applying finite element analysis and lever mechanics to the skulls of Panoplosaurus mirus (Nodosauridae) and Euoplocephalus tutus (Ankylosauridae). We also compare jaw performance across a wider sample of ankylosaurs through lever mechanics and phylogenetic comparative methods. Mandibular stress levels are higher in Euoplocephalus, supporting the view that Panoplosaurus consumed tougher foodstuffs. Bite force and mechanical advantage (MA) estimates indicate that Panoplosaurus had a relatively more forceful and efficient bite than Euoplocephalus. There is little support for a role of the secondary palate in resisting feeding loads in the two ankylosaur clades. Several ankylosaurs converged on similar jaw mechanics, while some nodosaurids specialised towards high MA and some ankylosaurids evolved low MA jaws. Our study supports the hypothesis that ankylosaurs partitioned dietary niches in Late Cretaceous ecosystems and reveals that the two main ankylosaur clades evolved divergent evolutionary pathways in skull biomechanics and feeding habits.

Bridging Performance and Adaptive Landscapes to Understand Long-Term Functional Evolution

AbstractUnderstanding functional adaptation demands an integrative framework that captures the complex interactions between form, function, ecology, and evolutionary processes. In this review, we discuss how to integrate the following two distinct approaches to better understand functional evolution: (1) the adaptive landscape approach (ALA), aimed at finding adaptive peaks for different ecologies, and (2) the performance landscape approach (PLA), aimed at finding performance peaks for different ecologies. We focus on the Ornstein-Uhlenbeck process as the evolutionary model for the ALA and on biomechanical modeling to estimate performance for the PLA. Whereas both the ALA and the PLA have each given insight into functional adaptation, separately they cannot address how much performance contributes to fitness or whether evolutionary constraints have played a role in form-function evolution. We show that merging these approaches leads to a deeper understanding of these issues. By comparing the locations of performance and adaptive peaks, we can infer how much performance contributes to fitness in species' current environments. By testing for the relevance of history on phenotypic variation, we can infer the influence of past selection and constraints on functional adaptation. We apply this merged framework in a case study of turtle shell evolution and explain how to interpret different possible outcomes. Even though such outcomes can be quite complex, they represent the multifaceted relations among function, fitness, and constraints.

A toolbox for the retrodeformation and muscle reconstruction of fossil specimens in Blender

Accurate muscle reconstructions can offer new information on the anatomy of fossil organisms and are also important for biomechanical analysis (multibody dynamics and finite-element analysis (FEA)). For the sake of simplicity, muscles are often modelled as point-to-point strands or frustra (cut-off cones) in biomechanical models. However, there are cases in which it is useful to model the muscle morphology in three dimensions, to better examine the effects of muscle shape and size. This is especially important for fossil analyses, where muscle force is estimated from the reconstructed muscle morphology (rather than based on data collected in vivo). The two main aims of this paper are as follows. First, we created a new interactive tool in the free open access software Blender to enable interactive three-dimensional modelling of muscles. This approach can be applied to both palaeontological and human biomechanics research to generate muscle force magnitudes and lines of action for FEA. Second, we provide a guide on how to use existing Blender tools to reconstruct distorted or incomplete specimens. This guide is aimed at palaeontologists but can also be used by anatomists working with damaged specimens or to test functional implication of hypothetical morphologies.

A toolbox for the retrodeformation and muscle reconstruction of fossil specimens in Blender

Accurate muscle reconstructions can offer new information on the anatomy of fossil organisms and are also important for biomechanical analysis (multibody dynamics and finite-element analysis (FEA)). For the sake of simplicity, muscles are often modelled as point-to-point strands or frustra (cut-off cones) in biomechanical models. However, there are cases in which it is useful to model the muscle morphology in three dimensions, to better examine the effects of muscle shape and size. This is especially important for fossil analyses, where muscle force is estimated from the reconstructed muscle morphology (rather than based on data collected in vivo). The two main aims of this paper are as follows. First, we created a new interactive tool in the free open access software Blender to enable interactive three-dimensional modelling of muscles. This approach can be applied to both palaeontological and human biomechanics research to generate muscle force magnitudes and lines of action for FEA. Second, we provide a guide on how to use existing Blender tools to reconstruct distorted or incomplete specimens. This guide is aimed at palaeontologists but can also be used by anatomists working with damaged specimens or to test functional implication of hypothetical morphologies.

A toolbox for the retrodeformation and muscle reconstruction of fossil specimens in Blender

Accurate muscle reconstructions can offer new information on the anatomy of fossil organisms and are also important for biomechanical analysis (multibody dynamics and finite-element analysis (FEA)). For the sake of simplicity, muscles are often modelled as point-to-point strands or frustra (cut-off cones) in biomechanical models. However, there are cases in which it is useful to model the muscle morphology in three dimensions, to better examine the effects of muscle shape and size. This is especially important for fossil analyses, where muscle force is estimated from the reconstructed muscle morphology (rather than based on data collected in vivo). The two main aims of this paper are as follows. First, we created a new interactive tool in the free open access software Blender to enable interactive three-dimensional modelling of muscles. This approach can be applied to both palaeontological and human biomechanics research to generate muscle force magnitudes and lines of action for FEA. Second, we provide a guide on how to use existing Blender tools to reconstruct distorted or incomplete specimens. This guide is aimed at palaeontologists but can also be used by anatomists working with damaged specimens or to test functional implication of hypothetical morphologies.

The diet of early birds based on modern and fossil evidence and a new framework for its reconstruction

Birds are some of the most diverse organisms on Earth, with species inhabiting a wide variety of niches across every major biome. As such, birds are vital to our understanding of modern ecosystems. Unfortunately, our understanding of the evolutionary history of modern ecosystems is hampered by knowledge gaps in the origin of modern bird diversity and ecosystem ecology. A crucial part of addressing these shortcomings is improving our understanding of the earliest birds, the non-avian avialans (i.e. non-crown birds), particularly of their diet. The diet of non-avian avialans has been a matter of debate, in large part because of the ambiguous qualitative approaches that have been used to reconstruct it. Here we review methods for determining diet in modern and fossil avians (i.e. crown birds) as well as non-avian theropods, and comment on their usefulness when applied to non-avian avialans. We use this to propose a set of comparable, quantitative approaches to ascertain fossil bird diet and on this basis provide a consensus of what we currently know about fossil bird diet. While no single approach can precisely predict diet in birds, each can exclude some diets and narrow the dietary possibilities. We recommend combining (i) dental microwear, (ii) landmark-based muscular reconstruction, (iii) stable isotope geochemistry, (iv) body mass estimations, (v) traditional and/or geometric morphometric analysis, (vi) lever modelling, and (vii) finite element analysis to reconstruct fossil bird diet accurately. Our review provides specific methodologies to implement each approach and discusses complications future researchers should keep in mind. We note that current forms of assessment of dental mesowear, skull traditional morphometrics, geometric morphometrics, and certain stable isotope systems have yet to be proven effective at discerning fossil bird diet. On this basis we report the current state of knowledge of non-avian avialan diet which remains very incomplete. The ancestral dietary condition in non-avian avialans remains unclear due to scarce data and contradictory evidence in Archaeopteryx. Among early non-avian pygostylians, Confuciusornis has finite element analysis and mechanical advantage evidence pointing to herbivory, whilst Sapeornis only has mechanical advantage evidence indicating granivory, agreeing with fossilised ingested material known for this taxon. The enantiornithine ornithothoracine Shenqiornis has mechanical advantage and pedal morphometric evidence pointing to carnivory. In the hongshanornithid ornithuromorph Hongshanornis only mechanical advantage evidence indicates granivory, but this agrees with evidence of gastrolith ingestion in this taxon. Mechanical advantage and ingested fish support carnivory in the songlingornithid ornithuromorph Yanornis. Due to the sparsity of robust dietary assignments, no clear trends in non-avian avialan dietary evolution have yet emerged. Dietary diversity seems to increase through time, but this is a preservational bias associated with a predominance of data from the Early Cretaceous Jehol Lagerstätte. With this new framework and our synthesis of the current knowledge of non-avian avialan diet, we expect dietary knowledge and evolutionary trends to become much clearer in the coming years, especially as fossils from other locations and climates are found. This will allow for a deeper and more robust understanding of the role birds played in Mesozoic ecosystems and how this developed into their pivotal role in modern ecosystems.

Rethinking the use of finite element simulations in comparative biomechanics research

In the past 15 years, the finite element (FE) method has become a ubiquitous tool in the repertoire of evolutionary biologists. The method is used to estimate and compare biomechanical performance implicated as selective factors in the evolution of morphological structures. A feature common to many comparative studies using 3D FE simulations is small taxonomic sample sizes. The time-consuming nature of FE model construction is considered a main limiting factor in taxonomic breadth of comparative FE analyses. Using a composite FE model dataset, I show that the combination of small taxonomic sample sizes and comparative FE data in analyses of evolutionary associations of biomechanical performance to feeding ecology generates artificially elevated correlations. Such biases introduce false positives into interpretations of clade-level trends. Considering this potential pitfall, recommendations are provided to consider the ways FE analyses are best used to address both taxon-specific and clade-level evolutionary questions.

Bone remodeling analysis for a swine skull at continuous scale based on the smoothed finite element method

In order to study bone response during chewing, bone remodeling analysis at a continuous scale is performed to a swine skull obtained using μCT. The smoothed finite element method (S-FEM) is utilized to replace the finite element method (FEM) in bone remodeling as it is solving the "overly-stiff" problem in FEM by introducing strain smoothing technology to soften the stiffness matrix. Three S-FEM models with different levels of softening effects are developed, including node-based, edge-based, and face-based, which leads to various bone remodeling results for a better understanding of the remodeling process. During the remodeling process, the strain energy density is used as the mechanical stimulus, and the surface elements or smoothing domains are regarded as cortical bone. Under the action of mechanical stimuli, cortical bone and cancellous bone have been remodeled. In remodeling progress, ES-FEM shows close results as compared with the experimental μCT in nodal bone density distribution, FEM and FS-FEM are close to the μCT experimental model in average nodal density. In summary, the combined use of several methods provides more angles for the description of bone remodeling.

Primary stability analysis of stemless shoulder implants

Although the primary stability of joint implants is fundamental for successful osseointegration, little is know about this issue in the context of stemless shoulder implants. Considering 3D finite element models, the purpose of this study was to evaluate the primary stability of five stemless designs, based on the Sidus, SMR, Simpliciti, Eclipse, and Global Icon stemless systems. Three alternative bone quality conditions were considered for cancellous bone. For the Sidus, SMR, and Simpliciti designs, which do not possess a collar that sits on the cortical rim of the humeral resected surface, contact and no contact conditions were considered between the bone surface and the humeral head components. Micromotions at bone-implant interfaces promoting osseointegration were computed as a measure of primary stability for eight load cases consisting of peak in vivo joint loads measured during selected upper limb activities. Under good bone quality conditions, all stemless designs presented micromotions below 150 μm. The Eclipse-based and Global-Icon based designs were the least sensitive to bone quality. Stemless designs presenting a solid collar or contact between the humeral head component and bone provided more stability. Overall, the Eclipse-based and Global Icon-based designs presented the best performance from the primary stability point of view. However, if bone adaptation data available in the literature are considered along with the primary stability data computed here, the Global Icon-based design, as well as other designs, might be considered superior long-term options due to their better compromise between primary stability and impact on bone adaptation.

The use of extruded finite-element models as a novel alternative to tomography-based models: a case study using early mammal jaws

Finite-element (FE) analysis has been used in palaeobiology to assess the mechanical performance of the jaw. It uses two types of models: tomography-based three-dimensional (3D) models (very accurate, not always accessible) and two-dimensional (2D) models (quick and easy to build, good for broad-scale studies, cannot obtain absolute stress and strain values). Here, we introduce extruded FE models, which provide fairly accurate mechanical performance results, while remaining low-cost, quick and easy to build. These are simplified 3D models built from lateral outlines of a relatively flat jaw and extruded to its average width. There are two types: extruded (flat mediolaterally) and enhanced extruded (accounts for width differences in the ascending ramus). Here, we compare mechanical performance values resulting from four types of FE models (i.e. tomography-based 3D, extruded, enhanced extruded and 2D) in Morganucodon and Kuehneotherium. In terms of absolute values, both types of extruded model perform well in comparison to the tomography-based 3D models, but enhanced extruded models perform better. In terms of overall patterns, all models produce similar results. Extruded FE models constitute a viable alternative to the use of tomography-based 3D models, particularly in relatively flat bones.

Finite element and deformation analyses predict pattern of bone failure in loaded zebrafish spines

The spine is the central skeletal support structure in vertebrates consisting of repeated units of bone, the vertebrae, separated by intervertebral discs (IVDs) that enable the movement of the spine. Spinal pathologies such as idiopathic back pain, vertebral compression fractures and IVD failure affect millions of people worldwide. Animal models can help us to understand the disease process, and zebrafish are increasingly used as they are highly genetically tractable, their spines are axially loaded like humans, and they show similar pathologies to humans during ageing. However, biomechanical models for the zebrafish are largely lacking. Here, we describe the results of loading intact zebrafish spinal motion segments on a material testing stage within a micro-computed tomography machine. We show that vertebrae and their arches show predictable patterns of deformation prior to their ultimate failure, in a pattern dependent on their position within the segment. We further show using geometric morphometrics which regions of the vertebra deform the most during loading, and that finite-element models of the trunk subjected reflect the real patterns of deformation and strain seen during loading and can therefore be used as a predictive model for biomechanical performance.

The Mechanical Effect of the Periodontal Ligament on Bone Strain Regimes in a Validated Finite Element Model of a Macaque Mandible

The primary anatomical function of the periodontal ligament (PDL) is to attach teeth to their sockets. However, theoretical and constitutive mechanical models have proposed that during mastication the PDL redistributes local occlusal loads and reduces the jaw's resistance to torsional deformations. These hypotheses imply that accurately modeling the PDL's material properties and geometry in finite element analysis (FEA) is a prerequisite to obtaining precise strain and deformation data. Yet, many finite element studies of the human and non-human primate masticatory apparatus exclude the PDL or model it with simplicity, in part due to limitations in μCT/CT scan resolution and material property assignment. Previous studies testing the sensitivity of finite element models (FEMs) to the PDL have yielded contradictory results, however a major limitation of these studies is that FEMs were not validated against in vivo bone strain data. Hence, this study uses a validated and subject specific FEM to assess the effect of the PDL on strain and deformation regimes in the lower jaw of a rhesus macaque (Macaca mulatta) during simulated unilateral post-canine chewing. Our findings demonstrate that the presence of the PDL does influence local and global surface strain magnitudes (principal and shear) in the jaw. However, the PDL's effect is limited (diff. ~200-300 με) in areas away from the alveoli. Our results also show that varying the PDL's Young's Modulus within the range of published values (0.07-1750 MPa) has very little effect on global surface strains. These findings suggest that the mechanical importance of the PDL in FEMs of the mandible during chewing is dependent on the scope of the hypotheses being tested. If researchers are comparing strain gradients across species/taxa, the PDL may be excluded with minimal effect on results, but, if researchers are concerned with absolute strain values, sensitivity analysis is required.

Cranial suture biomechanics in Metoposaurus krasiejowensis (Temnospondyli, Stereospondyli) from the upper Triassic of Poland

Cranial sutures connect adjacent bones of the skull and play an important role in the absorption of stresses that may occur during different activities. The Late Triassic temnospondyl amphibian Metoposaurus krasiejowensis has been extensively studied over the years in terms of skull biomechanics, but without a detailed description of the function of cranial sutures. In the present study, 34 thin sections of cranial sutures were examined in order to determine their histovariability and interpret their biomechanical role in the skull. The histological model was compared with three-dimensional-finite element analysis (FEA) simulations of the skull under bilateral and lateral biting as well as skull-raising loads for maximum and minimum principal stress. Histologically, only two sutural morphologies were recognised in the skull of Metoposaurus: interdigitated sutures (commonly associated with compressive stresses) are dominant along the entire length of the skull roof and palate; tongue-and-groove sutures (commonly associated with tensile stresses) are present across the maxilla. FEA shows a much more complex picture of stress type and distribution than predicted by sutures. Common to both methods is a predominance of compressive stresses which act on the skull during biting. The methods predict different stress regimes during biting in the posterior part of the skull: where histological analysis suggests compression, FEA predicts tension. For lateral biting and skull raising, histological and digital reconstructions show similar general patterns but with some variations.

Feeding Biomechanics in Billfishes: Investigating the Role of the Rostrum through Finite Element Analysis

Billfishes are large pelagic fishes that have an extreme elongation of the upper jaw bones forming the rostrum. Recent kinematic and biomechanical studies show the rostrum to be associated to feeding, however, it is less clear how the wide range of morphologies present among billfish may affect their striking behavior. In this study, we aim to assess the mechanical performance of different rostrum morphologies under loads that simulate feeding and to test existing hypotheses of species-specific feeding behaviors. We use finite element analysis (FEA)-a physics-based method that predicts patterns of stress and strain in morphologically complex structures under specified boundary conditions-to test hypotheses on the form and mechanical performance of billfish rostra. Patterns of von Mises stress and total strain energy suggest that distinct rostral morphologies may be functionally segregated. The rounder blue marlin rostrum may be better suited for a wide range of slashing motions to disable prey, whereas the more flattened swordfish rostrum appears to be more specialized for lateral swiping during prey capture. The almost homogenous stress distribution along each rostrum implies their possible use as a predatory weapon regardless of morphological differences between species. The mechanical implications of other less commonly reported behaviors such as spearing are discussed, as well as the potential impact of hydrodynamics in shaping the evolution of the rostrum in this lineage. Anat Rec, 2019. © 2019 American Association for Anatomy.

Pterosaur dietary hypotheses: a review of ideas and approaches

Pterosaurs are an extinct group of Mesozoic flying reptiles, whose fossil record extends from approximately 210 to 66 million years ago. They were integral components of continental and marginal marine ecosystems, yet their diets remain poorly constrained. Numerous dietary hypotheses have been proposed for different pterosaur groups, including insectivory, piscivory, carnivory, durophagy, herbivory/frugivory, filter-feeding and generalism. These hypotheses, and subsequent interpretations of pterosaur diet, are supported by qualitative (content fossils, associations, ichnology, comparative anatomy) and/or quantitative (functional morphology, stable isotope analysis) evidence. Pterosaur dietary interpretations are scattered throughout the literature with little attention paid to the supporting evidence. Reaching a robustly supported consensus on pterosaur diets is important for understanding their dietary evolution, and their roles in Mesozoic ecosystems. A comprehensive examination of the pterosaur literature identified 314 dietary interpretations (dietary statement plus supporting evidence) from 126 published studies. Multiple alternative diets have been hypothesised for most principal taxonomic pterosaur groups. Some groups exhibit a high degree of consensus, supported by multiple lines of evidence, while others exhibit less consensus. Qualitative evidence supports 87.3% of dietary interpretations, with comparative anatomy most common (62.1% of total). More speciose groups of pterosaur tend to have a greater range of hypothesised diets. Consideration of dietary interpretations within alternative phylogenetic contexts reveals high levels of consensus between equivalent monofenestratan groups, and lower levels of consensus between equivalent non-monofenestratan groups. Evaluating the possible non-biological controls on apparent patterns of dietary diversity reveals that numbers of dietary interpretations through time exhibit no correlation with patterns of publication (number of peer-reviewed publications through time). 73.8% of dietary interpretations were published in the 21st century. Overall, consensus interpretations of pterosaur diets are better accounted for by non-biological signals, such as the impact of the respective quality of the fossil record of different pterosaur groups on research levels. That many interpretations are based on qualitative, often untestable lines of evidence adds significant noise to the data. More experiment-led pterosaur dietary research, with greater consideration of pterosaurs as organisms with independent evolutionary histories, will lead to more robust conclusions drawn from repeatable results. This will allow greater understanding of pterosaur dietary diversity, disparity and evolution and facilitate reconstructions of Mesozoic ecosystems.

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.

Computational biomechanical analyses demonstrate similar shell-crushing abilities in modern and ancient arthropods

The biology of the American horseshoe crab, Limulus polyphemus, is well documented-including its dietary habits, particularly the ability to crush shell with gnathobasic walking appendages-but virtually nothing is known about the feeding biomechanics of this iconic arthropod. Limulus polyphemus is also considered the archetypal functional analogue of various extinct groups with serial gnathobasic appendages, including eurypterids, trilobites and other early arthropods, especially Sidneyia inexpectans from the mid-Cambrian (508 Myr) Burgess Shale of Canada. Exceptionally preserved specimens of S. inexpectans show evidence suggestive of durophagous (shell-crushing) tendencies-including thick gnathobasic spine cuticle and shelly gut contents-but the masticatory capabilities of this fossil species have yet to be compared with modern durophagous arthropods. Here, we use advanced computational techniques, specifically a unique application of 3D finite-element analysis (FEA), to model the feeding mechanics of L. polyphemus and S. inexpectans: the first such analyses of a modern horseshoe crab and a fossil arthropod. Results show that mechanical performance of the feeding appendages in both arthropods is remarkably similar, suggesting that S. inexpectans had similar shell-crushing capabilities to L. polyphemus This biomechanical solution to processing shelly food therefore has a history extending over 500 Myr, arising soon after the first shell-bearing animals. Arrival of durophagous predators during the early phase of animal evolution undoubtedly fuelled the Cambrian 'arms race' that involved a rapid increase in diversity, disparity and abundance of biomineralized prey species.

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.

Structure-function covariation with nonfeeding ecological variables influences evolution of feeding specialization in Carnivora

Skull shape convergence is pervasive among vertebrates. Although this is frequently inferred to indicate similar functional underpinnings, neither the specific structure-function linkages nor the selective environments in which the supposed functional adaptations arose are commonly identified and tested. We demonstrate that nonfeeding factors relating to sexual maturity and precipitation-related arboreality also can generate structure-function relationships in the skulls of carnivorans (dogs, cats, seals, and relatives) through covariation with masticatory performance. We estimated measures of masticatory performance related to ecological variables that covary with cranial shape in the mammalian order Carnivora, integrating geometric morphometrics and finite element analyses. Even after accounting for phylogenetic autocorrelation, cranial shapes are significantly correlated to both feeding and nonfeeding ecological variables, and covariation with both variable types generated significant masticatory performance gradients. This suggests that mechanisms of obligate shape covariation with nonfeeding variables can produce performance changes resembling those arising from feeding adaptations in Carnivora.

A three-dimensional strain measurement method in elastic transparent materials using tomographic particle image velocimetry

Background

The mechanical interaction between blood vessels and medical devices can induce strains in these vessels. Measuring and understanding these strains is necessary to identify the causes of vascular complications. This study develops a method to measure the three-dimensional (3D) distribution of strain using tomographic particle image velocimetry (Tomo-PIV) and compares the measurement accuracy with the gauge strain in tensile tests.

Methods and findings

The test system for measuring 3D strain distribution consists of two cameras, a laser, a universal testing machine, an acrylic chamber with a glycerol water solution for adjusting the refractive index with the silicone, and dumbbell-shaped specimens mixed with fluorescent tracer particles. 3D images of the particles were reconstructed from 2D images using a multiplicative algebraic reconstruction technique (MART) and motion tracking enhancement. Distributions of the 3D displacements were calculated using a digital volume correlation. To evaluate the accuracy of the measurement method in terms of particle density and interrogation voxel size, the gauge strain and one of the two cameras for Tomo-PIV were used as a video-extensometer in the tensile test. The results show that the optimal particle density and interrogation voxel size are 0.014 particles per pixel and 40 × 40 × 40 voxels with a 75% overlap. The maximum measurement error was maintained at less than 2.5% in the 4-mm-wide region of the specimen.

Conclusions

We successfully developed a method to experimentally measure 3D strain distribution in an elastic silicone material using Tomo-PIV and fluorescent particles. To the best of our knowledge, this is the first report that applies Tomo-PIV to investigate 3D strain measurements in elastic materials with large deformation and validates the measurement accuracy.

The impact of gape on the performance of the skull in chisel-tooth digging and scratch digging mole-rats (Rodentia: Bathyergidae)

The African mole-rats (Bathyergidae) are a family of rodents highly adapted for life underground. Previous research has shown that chisel-tooth digging mole-rats (which use their incisors to dig burrows) are clearly distinguishable from scratch diggers (which only use the forelimbs to tunnel) on the basis of morphology of the skull, and that the differences are linked to the production of high bite forces and wide gapes. We hypothesized that the skull of a chisel-tooth digging mole-rat would perform better at wider gapes than that of a scratch digging mole-rat during incisor biting. To test this hypothesis, we created finite-element models of the cranium of the scratch digging Bathyergus suillus and the chisel-tooth digging Fukomys mechowii, and loaded them to simulate incisor bites at different gapes. Muscle loads were scaled such that the ratio of force to surface area was the same in both models. We measured three performance variables: overall stress across the cranium, mechanical efficiency of biting and degree of deformation across the skull. The Fukomys model had a more efficient incisor bite at all gapes, despite having greater average stress across the skull. In addition, the Fukomys model deformed less at wider gapes, whereas the Bathyergus model deformed less at narrower gapes. These properties of the cranial morphology of Fukomys and Bathyergus are congruent with their respective chisel-tooth and scratch digging behaviours and, all other factors being equal, would enable the more efficient production of bite force at wider gapes in Fukomys. However, in vivo measurements of muscle forces and activation patterns are needed to fully understand the complex biomechanics of tooth digging.

Reconstructing the past: methods and techniques for the digital restoration of fossils

During fossilization, the remains of extinct organisms are subjected to taphonomic and diagenetic processes. As a result, fossils show a variety of preservational artefacts, which can range from small breaks and cracks, disarticulation and fragmentation, to the loss and deformation of skeletal structures and other hard parts. Such artefacts can present a considerable problem, as the preserved morphology of fossils often forms the basis for palaeontological research. Phylogenetic and taxonomic studies, inferences on appearance, ecology and behaviour and functional analyses of fossil organisms strongly rely on morphological information. As a consequence, the restoration of fossil morphology is often a necessary prerequisite for further analyses. Facilitated by recent computational advances, virtual reconstruction and restoration techniques offer versatile tools to restore the original morphology of fossils. Different methodological steps and approaches, as well as software are outlined and reviewed here, and advantages and disadvantages are discussed. Although the complexity of the restorative processes can introduce a degree of interpretation, digitally restored fossils can provide useful morphological information and can be used to obtain functional estimates. Additionally, the digital nature of the restored models can open up possibilities for education and outreach and further research.

Comparative cephalopod shell strength and the role of septum morphology on stress distribution

The evolution of complexly folded septa in ammonoids has long been a controversial topic. Explanations of the function of these folded septa can be divided into physiological and mechanical hypotheses with the mechanical functions tending to find widespread support. The complexity of the cephalopod shell has made it difficult to directly test the mechanical properties of these structures without oversimplification of the septal morphology or extraction of a small sub-domain. However, the power of modern finite element analysis now permits direct testing of mechanical hypothesis on complete, empirical models of the shells taken from computed tomographic data. Here we compare, for the first time using empirical models, the capability of the shells of extant Nautilus pompilius, Spirula spirula, and the extinct ammonite Cadoceras sp. to withstand hydrostatic pressure and point loads. Results show hydrostatic pressure imparts highest stress on the final septum with the rest of the shell showing minimal compression. S. spirula shows the lowest stress under hydrostatic pressure while N. pompilius shows the highest stress. Cadoceras sp. shows the development of high stress along the attachment of the septal saddles with the shell wall. Stress due to point loads decreases when the point force is directed along the suture as opposed to the unsupported chamber wall. Cadoceras sp. shows the greatest decrease in stress between the point loads compared to all other models. Greater amplitude of septal flutes corresponds with greater stress due to hydrostatic pressure; however, greater amplitude decreases the stress magnitude of point loads directed along the suture. In our models, sutural complexity does not predict greater resistance to hydrostatic pressure but it does seem to increase resistance to point loads, such as would be from predators. This result permits discussion of palaeoecological reconstructions on the basis of septal morphology. We further suggest that the ratio used to characterize septal morphology in the septal strength index and in calculations of tensile strength of nacre are likely insufficient. A better understanding of the material properties of cephalopod nacre may allow the estimation of maximum depth limits of shelled cephalopods through finite element analysis.

Decoupled form and function in disparate herbivorous dinosaur clades

Convergent evolution, the acquisition of morphologically similar traits in unrelated taxa due to similar functional demands or environmental factors, is a common phenomenon in the animal kingdom. Consequently, the occurrence of similar form is used routinely to address fundamental questions in morphofunctional research and to infer function in fossils. However, such qualitative assessments can be misleading and it is essential to test form/function relationships quantitatively. The parallel occurrence of a suite of morphologically convergent craniodental characteristics in three herbivorous, phylogenetically disparate dinosaur clades (Sauropodomorpha, Ornithischia, Theropoda) provides an ideal test case. A combination of computational biomechanical models (Finite Element Analysis, Multibody Dynamics Analysis) demonstrate that despite a high degree of morphological similarity between representative taxa (Plateosaurus engelhardti, Stegosaurus stenops, Erlikosaurus andrewsi) from these clades, their biomechanical behaviours are notably different and difficult to predict on the basis of form alone. These functional differences likely reflect dietary specialisations, demonstrating the value of quantitative biomechanical approaches when evaluating form/function relationships in extinct taxa.

The Tarsometatarsus of the Ostrich Struthio camelus: Anatomy, Bone Densities, and Structural Mechanics

Background

The ostrich Struthio camelus reaches the highest speeds of any extant biped, and has been an extraordinary subject for studies of soft-tissue anatomy and dynamics of locomotion. An elongate tarsometatarsus in adult ostriches contributes to their speed. The internal osteology of the tarsometatarsus, and its mechanical response to forces of running, are potentially revealing about ostrich foot function.

Methods/Principal Findings

Computed tomography (CT) reveals anatomy and bone densities in tarsometatarsi of an adult and a young juvenile ostrich. A finite element (FE) model for the adult was constructed with properties of compact and cancellous bone where these respective tissues predominate in the original specimen. The model was subjected to a quasi-static analysis under the midstance ground reaction and muscular forces of a fast run. Anatomy–Metatarsals are divided proximally and distally and unify around a single internal cavity in most adult tarsometatarsus shafts, but the juvenile retains an internal three-part division of metatarsals throughout the element. The juvenile has a sparsely ossified hypotarsus for insertion of the m. fibularis longus, as part of a proximally separate third metatarsal. Bone is denser in all regions of the adult tarsometatarsus, with cancellous bone concentrated at proximal and distal articulations, and highly dense compact bone throughout the shaft. Biomechanics–FE simulations show stress and strain are much greater at midshaft than at force applications, suggesting that shaft bending is the most important stressor of the tarsometatarsus. Contraction of digital flexors, inducing a posterior force at the TMT distal condyles, likely reduces buildup of tensile stresses in the bone by inducing compression at these locations, and counteracts bending loads. Safety factors are high for von Mises stress, consistent with faster running speeds known for ostriches.

Conclusions/Significance

High safety factors suggest that bone densities and anatomy of the ostrich tarsometatarsus confer strength for selectively critical activities, such as fleeing and kicking predators. Anatomical results and FE modeling of the ostrich tarsometatarsus are a useful baseline for testing the structure’s capabilities and constraints for locomotion, through ontogeny and the full step cycle. With this foundation, future analyses can incorporate behaviorally realistic strain rates and distal joint forces, experimental validation, and proximal elements of the ostrich hind limb.

An integrative method for testing form-function linkages and reconstructed evolutionary pathways of masticatory specialization

Morphology serves as a ubiquitous proxy in macroevolutionary studies to identify potential adaptive processes and patterns. Inferences of functional significance of phenotypes or their evolution are overwhelmingly based on data from living taxa. Yet, correspondence between form and function has been tested in only a few model species, and those linkages are highly complex. The lack of explicit methodologies to integrate form and function analyses within a deep-time and phylogenetic context weakens inferences of adaptive morphological evolution, by invoking but not testing form-function linkages. Here, we provide a novel approach to test mechanical properties at reconstructed ancestral nodes/taxa and the strength and direction of evolutionary pathways in feeding biomechanics, in a case study of carnivorous mammals. Using biomechanical profile comparisons that provide functional signals for the separation of feeding morphologies, we demonstrate, using experimental optimization criteria on estimation of strength and direction of functional changes on a phylogeny, that convergence in mechanical properties and degree of evolutionary optimization can be decoupled. This integrative approach is broadly applicable to other clades, by using quantitative data and model-based tests to evaluate interpretations of function from morphology and functional explanations for observed macroevolutionary pathways.

Cranial biomechanics underpins high sauropod diversity in resource-poor environments

High megaherbivore species richness is documented in both fossil and contemporary ecosystems despite their high individual energy requirements. An extreme example of this is the Late Jurassic Morrison Formation, which was dominated by sauropod dinosaurs, the largest known terrestrial vertebrates. High sauropod diversity within the resource-limited Morrison is paradoxical, but might be explicable through sophisticated resource partitioning. This hypothesis was tested through finite-element analysis of the crania of the Morrison taxa Camarasaurus and Diplodocus. Results demonstrate divergent specialization, with Camarasaurus capable of exerting and accommodating greater bite forces than Diplodocus, permitting consumption of harder food items. Analysis of craniodental biomechanical characters taken from 35 sauropod taxa demonstrates a functional dichotomy in terms of bite force, cranial robustness and occlusal relationships yielding two polyphyletic functional ‘grades’. Morrison taxa are widely distributed within and between these two morphotypes, reflecting distinctive foraging specializations that formed a biomechanical basis for niche partitioning between them. This partitioning, coupled with benefits associated with large body size, would have enabled the high sauropod diversities present in the Morrison Formation. Further, this provides insight into the mechanisms responsible for supporting the high diversities of large megaherbivores observed in other Mesozoic and Cenozoic communities, particularly those occurring in resource-limited environments.

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.

Comparative finite element analysis of the cranial performance of four herbivorous marsupials

Marsupial herbivores exhibit a wide variety of skull shapes and sizes to exploit different ecological niches. Several studies on teeth, dentaries, and jaw adductor muscles indicate that marsupial herbivores exhibit different specializations for grazing and browsing. No studies, however, have examined the skulls of marsupial herbivores to determine the relationship between stress and strain, and the evolution of skull shape. The relationship between skull morphology, biomechanical performance, and diet was tested by applying the finite element method to the skulls of four marsupial herbivores: the common wombat (Vombatus ursinus), koala (Phascolarctos cinereus), swamp wallaby (Wallabia bicolor), and red kangaroo (Macropus rufus). It was hypothesized that grazers, requiring stronger skulls to process tougher food, would have higher biomechanical performance than browsers. This was true when comparing the koala and wallaby (browsers) to the wombat (a grazer). The cranial model of the wombat resulted in low stress and high mechanical efficiency in relation to a robust skull capable of generating high bite forces. However, the kangaroo, also a grazer, has evolved a very different strategy to process tough food. The cranium is much more gracile and has higher stress and lower mechanical efficiency, but they adopt a different method of processing food by having a curved tooth row to concentrate force in a smaller area and molar progression to remove worn teeth from the tooth row. Therefore, the position of the bite is crucial for the structural performance of the kangaroo skull, while it is not for the wombat which process food along the entire tooth row. In accordance with previous studies, the results from this study show the mammalian skull is optimized to resist forces generated during feeding. However, other factors, including the lifestyle of the animal and its environment, also affect selection for skull morphology to meet multiple functional demands.

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.

Bone-breaking bite force of Basilosaurus isis (Mammalia, Cetacea) from the late Eocene of Egypt estimated by finite element analysis

Bite marks suggest that the late Eocence archaeocete whale Basilosaurus isis (Birket Qarun Formation, Egypt) fed upon juveniles of the contemporary basilosaurid Dorudon atrox. Finite element analysis (FEA) of a nearly complete adult cranium of B. isis enables estimates of its bite force and tests the animal's capabilities for crushing bone. Two loadcases reflect different biting scenarios: 1) an intitial closing phase, with all adductors active and a full condylar reaction force; and 2) a shearing phase, with the posterior temporalis active and minimized condylar force. The latter is considered probable when the jaws were nearly closed because the preserved jaws do not articulate as the molariform teeth come into occulusion. Reaction forces with all muscles active indicate that B. isis maintained relatively greater bite force anteriorly than seen in large crocodilians, and exerted a maximum bite force of at least 16,400 N at its upper P3. Under the shearing scenario with minimized condylar forces, tooth reaction forces could exceed 20,000 N despite lower magnitudes of muscle force. These bite forces at the teeth are consistent with bone indentations on Dorudon crania, reatract-and-shear hypotheses of Basilosaurus bite function, and seizure of prey by anterior teeth as proposed for other archaeocetes. The whale's bite forces match those estimated for pliosaurus when skull lengths are equalized, suggesting similar tradeoffs of bite function and hydrodynamics. Reaction forces in B. isis were lower than maxima estimated for large crocodylians and carnivorous dinosaurs. However, comparison of force estimates from FEA and regression data indicate that B. isis exerted the largest bite forces yet estimated for any mammal, and greater force than expected from its skull width. Cephalic feeding biomechanics of Basilosaurus isis are thus consistent with habitual predation.

A virtual world of paleontology

Computer-aided visualization and analysis of fossils has revolutionized the study of extinct organisms. Novel techniques allow fossils to be characterized in three dimensions and in unprecedented detail. This has enabled paleontologists to gain important insights into their anatomy, development, and preservation. New protocols allow more objective reconstructions of fossil organisms, including soft tissues, from incomplete remains. The resulting digital reconstructions can be used in functional analyses, rigorously testing long-standing hypotheses regarding the paleobiology of extinct organisms. These approaches are transforming our understanding of long-studied fossil groups, and of the narratives of organismal and ecological evolution that have been built upon them.

Morphological and functional diversity in therizinosaur claws and the implications for theropod claw evolution

Therizinosaurs are a group of herbivorous theropod dinosaurs from the Cretaceous of North America and Asia, best known for their iconically large and elongate manual claws. However, among Therizinosauria, ungual morphology is highly variable, reflecting a general trend found in derived theropod dinosaurs (Maniraptoriformes). A combined approach of shape analysis to characterize changes in manual ungual morphology across theropods and finite-element analysis to assess the biomechanical properties of different ungual shapes in therizinosaurs reveals a functional diversity related to ungual morphology. While some therizinosaur taxa used their claws in a generalist fashion, other taxa were functionally adapted to use the claws as grasping hooks during foraging. Results further indicate that maniraptoriform dinosaurs deviated from the plesiomorphic theropod ungual morphology resulting in increased functional diversity. This trend parallels modifications of the cranial skeleton in derived theropods in response to dietary adaptation, suggesting that dietary diversification was a major driver for morphological and functional disparity in theropod evolution.

Comparative finite-element analysis: a single computational modelling method can estimate the mechanical properties of porcine and human vertebrae

Significant advances in the functional analysis of musculoskeletal systems require the development of modelling techniques with improved focus, accuracy and validity. This need is particularly visible in the fields, such as palaeontology, where unobservable parameters may lie at the heart of the most interesting research questions, and where models and simulations may provide some of the most innovative solutions. Here, we report on the development of a computational modelling method to generate estimates of the mechanical properties of vertebral bone across two living species, using elderly human and juvenile porcine specimens as cases with very different levels of bone volume fraction and mineralization. This study is presented in two parts; part I presents the computational model development and validation, and part II the virtual loading regime and results. This work paves the way for the future estimation of mechanical properties in fossil mammalian bone.

Feeding biomechanics in Acanthostega and across the fish-tetrapod transition

Acanthostega is one of the earliest and most primitive limbed vertebrates. Its numerous fish-like features indicate a primarily aquatic lifestyle, yet cranial suture morphology suggests that its skull is more similar to those of terrestrial taxa. Here, we apply geometric morphometrics and two-dimensional finite-element analysis to the lower jaws of Acanthostega and 22 other tetrapodomorph taxa in order to quantify morphological and functional changes across the fish-tetrapod transition. The jaw of Acanthostega is similar to that of certain tetrapodomorph fish and transitional Devonian taxa both morphologically (as indicated by its proximity to those taxa in morphospace) and functionally (as indicated by the distribution of stress values and relative magnitude of bite force). Our results suggest a slow tempo of morphological and biomechanical changes in the transition from Devonian tetrapod jaws to aquatic/semi-aquatic Carboniferous tetrapod jaws. We conclude that Acanthostega retained a primitively aquatic lifestyle and did not possess cranial adaptations for terrestrial feeding.

Edentulism, beaks, and biomechanical innovations in the evolution of theropod dinosaurs

Maniraptoriformes, the speciose group of derived theropod dinosaurs that ultimately gave rise to modern birds, display a diverse and remarkable suite of skeletal adaptations. Apart from the evolution of flight, a large-scale change in dietary behavior appears to have been one of the main triggers for specializations in the bauplan of these derived theropods. Among the different skeletal specializations, partial or even complete edentulism and the development of keratinous beaks form a recurring and persistent trend in from the evolution of derived nonavian dinosaurs. Therizinosauria is an enigmatic maniraptoriform clade, whose members display these and other osteological characters thought to be correlated with the shift from carnivory to herbivory. This makes therizinosaurians prime candidates to assess the functional significance of these morphological characters. Based on a highly detailed biomechanical model of Erlikosaurus andrewsi, a therizinosaurid from the Upper Cretaceous of Mongolia, different morphological configurations incorporating soft-tissue structures, such as a keratinous rhamphotheca, are evaluated for their biomechanical performance. Our results indicate that the development of beaks and the presence of a keratinous rhamphotheca would have helped to dissipate stress and strain, making the rostral part of the skull less susceptible to bending and displacement, and this benefit may extend to other vertebrate clades that possess rhamphothecae. Keratinous beaks, paralleled by edentulism, thus represent an evolutionary innovation developed early in derived theropods to enhance cranial stability, distinct to postulated mass-saving benefits associated with the origin of flight.

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.

Masticatory biomechanics of the Laotian rock rat, Laonastes aenigmamus, and the function of the zygomaticomandibularis muscle

The Laotian rock rat, Laonastes aenigmamus, is one of the most recently discovered species of rodent, and displays a cranial morphology that is highly specialised. The rostrum of L. aenigmamus is exceptionally elongate and bears a large attachment site for the infraorbital portion of the zygomaticomandibularis muscle (IOZM), which is particularly well-developed in this species. In this study, we used finite element analysis to investigate the biomechanical performance of the Laotian rock rat cranium and to elucidate the function of the IOZM. A finite element model of the skull of L. aenigmamus was constructed and solved for biting on each of the teeth (incisors, premolar and molars). Further load cases were created and solved in which the origin of the IOZM had been moved anteriorly and posteriorly along the rostrum. Finally, a set of load cases were produced in which the IOZM was removed entirely, and its force was redistributed between the remaining masticatory muscles. The analysis showed that, during biting, the most stressed areas of the skull were the zygomatic and orbital regions. Compared to other rodents, L. aenigmamus is highly efficient at incisor gnawing, but less efficient at molar chewing. However, a relatively constant bite force across the molar tooth row may be an adaptation to folivory. Movement of the origin of the IOZM had little on the patterns of von Mises stresses, or the overall stress experienced by the cranium. However, removal of the IOZM had a substantial effect on the total deformation experienced by the skull. In addition, the positioning and presence of the IOZM had large impact on bite force. Moving the IOZM origin to the anterior tip of the rostrum led to a substantially reduced bite force at all teeth. This was hypothesised to be a result of the increasing horizontal component to the pull of this muscle as it is moved anteriorly along the rostrum. Removal of the IOZM also resulted in reduced bite force, even when the total input muscle force was maintained at the same level. It was thus concluded that the function of the IOZM in L. aenigmamus is to increase bite force whilst reducing cranial deformation. If the IOZM can be shown to have this function in other rodent groups, this may help explain the evolution of this muscle, and may also provide an understanding of why it has evolved independently several times within rodents.

In vivo bone strain and finite element modeling of the mandible of Alligator mississippiensis

Forces experienced during feeding are thought to strongly influence the morphology of the vertebrate mandible; in vivo strain data are the most direct evidence for deformation of the mandible induced by these loading regimes. Although many studies have documented bone strains in the mammalian mandible, no information is available on strain magnitudes, orientations or patterns in the sauropsid lower jaw during feeding. Furthermore, strain gage experiments record the mechanical response of bone at a few locations, not across the entire mandible. In this paper, we present bone strain data recorded at various sites on the lower jaw of Alligator mississippiensis during in vivo feeding experiments. These data are used to understand how changes in loading regime associated with changes in bite location are related to changes in strain regime on the working and balancing sides of the mandible. Our results suggest that the working side mandible is bent dorsoventrally and twisted about its long-axis during biting, and the balancing side experiences primarily dorsoventral bending. Strain orientations are more variable on the working side than on the balancing side with changes in bite point and between experiments; the balancing side exhibits higher strain magnitudes. In the second part of this paper, we use principal strain orientations and magnitudes recorded in vivo to evaluate a finite element model of the alligator mandible. Our comparison demonstrates that strain orientations and mandibular deformation predicted by the model closely match in vivo results; however, absolute strain magnitudes are lower in the finite element model.

Finite element analysis of a micromechanical model of bone and a new 3D approach to validation

Finite Element Analysis (FEA) is now widely used to analyse the mechanical behaviour of bone structures. Ideally, simulations are validated against experimental data. To date, validation of Finite Element Models (FEMs) has been 2 Dimensional (2D) only, being based on comparison with surface-mounted strain gauge readings. In this study we present a novel 3-Dimensional (3D) approach to validation that allows comparison of modelled with experimental results between any two points in 3D space throughout the structure, providing magnitude and direction data for comparison, internally and externally. Specifically, we validate a FEM of a rat tibia, including trabecular network geometry, using a material testing stage housed within a microCT scanner. We further apply novel landmark based morphometric approaches to more effectively compare modelled and experimental results. 542 landmark points on the cortical and trabecular bone surfaces of the model were selected and validated in 3D against experimental data. This approach may hold considerable potential in fields wherein a better understanding of the mechanical behaviour of trabecular networks is important, e.g., the studies of osteoporosis and trabecular loss after orthopaedic implant insertion.

Functional evolution of the feeding system in rodents

The masticatory musculature of rodents has evolved to enable both gnawing at the incisors and chewing at the molars. In particular, the masseter muscle is highly specialised, having extended anteriorly to originate from the rostrum. All living rodents have achieved this masseteric expansion in one of three ways, known as the sciuromorph, hystricomorph and myomorph conditions. Here, we used finite element analysis (FEA) to investigate the biomechanical implications of these three morphologies, in a squirrel, guinea pig and rat. In particular, we wished to determine whether each of the three morphologies is better adapted for either gnawing or chewing. Results show that squirrels are more efficient at muscle-bite force transmission during incisor gnawing than guinea pigs, and that guinea pigs are more efficient at molar chewing than squirrels. This matches the known diet of nuts and seeds that squirrels gnaw, and of grasses that guinea pigs grind down with their molars. Surprisingly, results also indicate that rats are more efficient as well as more versatile feeders than both the squirrel and guinea pig. There seems to be no compromise in biting efficiency to accommodate the wider range of foodstuffs and the more general feeding behaviour adopted by rats. Our results show that the morphology of the skull and masticatory muscles have allowed squirrels to specialise as gnawers and guinea pigs as chewers, but that rats are high-performance generalists, which helps explain their overwhelming success as a group.

Modeling the human mandible under masticatory loads: which input variables are important?

Finite element analyses (FEA) that have simulated masticatory loadings of the human mandible differ significantly with regard to their basic input variables such as material properties, constraints, and applied forces. With sensitivity analyses it is possible to assess how the choice of different input values and the degree of model simplification affect FEA results. However, published FEA studies are rarely accompanied by sensitivity analyses so that the robusticity of their results is impossible to assess. Here, we conduct a sensitivity analysis with an FE model of a human mandible to quantify the relative importance of several modeling decisions: (1) the material properties assigned to the cancellous bone tissue; (2) the inclusion or not of the periodontal ligament; (3) the constraints at the joints and bite point; and (4) the orientation of applied muscle forces. We study the effects of varying these properties by analysing the strain magnitudes and directions across the model surface. In addition, we perform a geometric morphometric analysis of the deformation resulting from the loading of each model. The results show that the effects of altering the different model properties can be significant and that most effects are potentially large enough to cause problems for the biological interpretation of FEA results. We therefore recommend that researchers conduct more sensitivity analyses than at present to assess the robusticity of their FEA results and their biological conclusions.

Virtual experiments, physical validation: dental morphology at the intersection of experiment and theory

Computational models such as finite-element analysis offer biologists a means of exploring the structural mechanics of biological systems that cannot be directly observed. Validated against experimental data, a model can be manipulated to perform virtual experiments, testing variables that are hard to control in physical experiments. The relationship between tooth form and the ability to break down prey is key to understanding the evolution of dentition. Recent experimental work has quantified how tooth shape promotes fracture in biological materials. We present a validated finite-element model derived from physical compression experiments. The model shows close agreement with strain patterns observed in photoelastic test materials and reaction forces measured during these experiments. We use the model to measure strain energy within the test material when different tooth shapes are used. Results show that notched blades deform materials for less strain energy cost than straight blades, giving insights into the energetic relationship between tooth form and prey materials. We identify a hypothetical 'optimal' blade angle that minimizes strain energy costs and test alternative prey materials via virtual experiments. Using experimental data and computational models offers an integrative approach to understand the mechanics of tooth morphology.

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.

Finite element modelling of squirrel, guinea pig and rat skulls: using geometric morphometrics to assess sensitivity

Rodents are defined by a uniquely specialized dentition and a highly complex arrangement of jaw-closing muscles. Finite element analysis (FEA) is an ideal technique to investigate the biomechanical implications of these specializations, but it is essential to understand fully the degree of influence of the different input parameters of the FE model to have confidence in the model's predictions. This study evaluates the sensitivity of FE models of rodent crania to elastic properties of the materials, loading direction, and the location and orientation of the models' constraints. Three FE models were constructed of squirrel, guinea pig and rat skulls. Each was loaded to simulate biting on the incisors, and the first and the third molars, with the angle of the incisal bite varied over a range of 45°. The Young's moduli of the bone and teeth components were varied between limits defined by findings from our own and previously published tests of material properties. Geometric morphometrics (GMM) was used to analyse the resulting skull deformations. Bone stiffness was found to have the strongest influence on the results in all three rodents, followed by bite position, and then bite angle and muscle orientation. Tooth material properties were shown to have little effect on the deformation of the skull. The effect of bite position varied between species, with the mesiodistal position of the biting tooth being most important in squirrels and guinea pigs, whereas bilateral vs. unilateral biting had the greatest influence in rats. A GMM analysis of isolated incisor deformations showed that, for all rodents, bite angle is the most important parameter, followed by elastic properties of the tooth. The results here elucidate which input parameters are most important when defining the FE models, but also provide interesting glimpses of the biomechanical differences between the three skulls, which will be fully explored in future publications.